Mass Transfer and Chemical Reaction in Gas-Liquid-Liquid Systems

MASS TRANSFER AND CHEMICAL REACTION IN GAS-LIQUID-LIQUID SYSTEMS

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Universiteit Twente, op gezag van de rector magnificus, Prof.dr. F.A. van Vught, volgens besluit van het College voor Promoties in het openbaar te verdedigen op vrijdag 4 december 1998 te 16.45 uur

door

Derk Willem Frederik Brilman geboren op 19 februari 1968 te Meppel Dit proefschrift is goedgekeurd door de promotoren

Prof. dr. ir. G.F. Versteeg

Prof. dr. ir. W.P.M. van Swaaij aan Sandra, aan mijn ouders Referent: dr.ir. L. Petrus

The research in this thesis was financially supported by the Shell Research and Technology Centre in Amsterdam, The Netherlands.

No part of this book may be reproduced in any form by any means, nor transmitted, nor translated into a machine language without written permission from the author

Brilman, D.W.F.

Mass Transfer and Chemical Reaction in Gas-Liquid-Liquid Systems

Thesis University of Twente, The Netherlands

ISBN 90-36512212

Printing and binding: Print Partners Ipskamp, Enschede, The Netherlands Summary

Gas-liquid-liquid reaction systems may be encountered in several important fields of application as e.g. hydroformylation, alkylation, carboxylation, polymerisation, hydrometallurgy, biochemical processes and fine chemicals manufacturing. However, the reaction engineering aspects of these systems have only been considered occasionally. For systems with very slow reaction kinetics this is not surprising, as the three phases will be at physical equilibrium. In reaction systems with fast parallel and consecutive reactions the effects of mass transfer and mixing on the product yield can be significant. A fascinating example of such a reaction system is the Koch synthesis of Pivalic Acid. In this work this reaction system was chosen as model system to study these effects.

In the Koch reaction system the reactants isobutene (or equivalent carbocation precursor), carbon monoxide and water originate each from different phases. They react in the presence of an acidic catalyst in the aqueous sulfuric acid catalyst phase to form Pivalic Acid. Additional to this main reaction isomerisation, oligomerisation and disproportionation can take place, which can lead to a spectacular diversity of byproducts.

For analysing the effects of mass transfer and mixing in this complex reaction system the reaction kinetics need to be known and were therefore studied. The first step in the Koch reaction mechanism is the formation of a carbocation. For isobutene (and trans-2-butene) the protonation kinetics were determined by gas absorption experiments using a stirred cell. The sulfuric acid concentration was found to have a pronounced influence on the reaction kinetics (and on the solubility of the hydrocarbons), which could be described with an activity based reaction rate equation using the Hammett Acidity Function for the protonating activity of the catalyst solution.

For isobutanol as reactant the Koch synthesis of Pivalic Acid could be followed through the carbon monoxide consumption rate. Using this, the effect of the presence of Pivalic Acid in the catalyst solution has been studied. It is shown that the addition of Pivalic Acid to the sulfuric acid catalyst solution drastically reduces the catalyst solution acidity. This implies for the industrially frequently applied completely backmixed reactors that they operate at a considerable lower acid strength than may be expected by the initial catalyst composition. Further, the apparent reaction kinetics at different temperature, pressure and acid strength were determined. A simple equilibrium model for the four basic reaction steps in the Koch reaction mechanism was able to

I Summary describe the sharp increase in the Pivalic Acid solubility in the sulfuric acid catalyst solution without using fit parameters . It has been reported frequently that the addition of an immiscible organic liquid phase to a gas - aqueous liquid phase system may significantly increase the gas absorption rate. The effects reported in literature on the mass transfer parameters, like the gas-liquid interfacial area and gas holdup, are discussed short. No general trends can be derived from the reported results in literature. Additional research in this area is therefore desired. However, these effects are insufficient to account for the observed enhancement of the gas absorption rate. Direct contact of the gas phase and the dispersed organic phase may offer one explanation for the gas absorption enhancement. Scouting experiments have shown the existence of ‘complexes’ of gas bubbles and organic phase drops, irrespective of the initial spreading coefficient for this system. A criterion for the possible formation of these complexes based on a surface energy consideration is proposed.

Alternatively, analogous to gas-liquid-solid systems, the presence of small droplets in the mass transfer zone at the gas-liquid interface may increase the gas absorption rate through the ‘grazing’ or ‘shuttle mechanism’. In this work instationary, heterogeneous, multiparticle mass transfer models (1, 2 and 3-Dimensional) have been developed, which were not available in literature. For the instationary heterogeneous multiparticle models developed in this work the effect of different process parameters was studied. Special attention is given to the translation of modeling results into the prediction of gas absorption fluxes, which is required due to the infinite number of particle configurations possible in a multiparticle system. A straightforward strategy is proposed to obtain gas absorption fluxes from single particle simulations. The modeling results obtained by this strategy and mass transfer models are compared to experimental data reported in literature.

Turbulence modification by the presence of dispersed phase particles has been reported frequently in literature, especially for gas-solid systems. The extent of these effects in a stirred gas-liquid- liquid multiphase reactor was, however, not clear. Using the well known mixing sensitive diazo- coupling reaction, the influences of the addition of solid particles, gas bubbles and organic liquid drops on the product distribution was investigated. For this reaction system it was found that the experimental results could be described by the Engulfment model, when implementing effective dispersion density and -viscosity. For the liquid-liquid experiments it was found that mass transfer effects caused a de-localisation of the reaction zone. The Engulfment micromixing model

II Summary extended with liquid-liquid mass transfer for the bulk liquid phases described reasonably well the experimental results.

For tert-butanol and isobutene the Koch synthesis of Pivalic Acid proceeded too fast to follow via the CO consumption rate and a strong influence of the hydrocarbon reactant feed rate on the product yield was observed. This feed rate effect could be attributed to the gas-liquid mass transfer rate. Moreover, saturating the reactant feed (before injection) with carbon monoxide has a beneficial effect on the product yield. Transport of CO to the reaction zone, located near the feed inlet, is therefore the main parameter in determining the product yield. At the same time, it is concluded for the reaction conditions studied (a 96 wt% H2SO4 catalyst solution, 293 K, 40 bar CO pressure) that both the carbonylation reaction and the undesired oligomerisation reactions are fast reactions with respect to gas-liquid mass transfer and mixing.

The effect of an immiscible, inert, organic liquid phase on the product distribution was studied for tert-butanol as reactant. A considerable improvement of the product yield was observed, especially at lower stirring rates. This can, at least partially, be explained from an enlarged CO absorption capacity at increasing dispersed phase fraction. Nevertheless, even at conditions in which the initial CO absorption capacity of the liquid-liquid in the semi-batch system is sufficient for complete conversion of the tert-butanol reactant injected dispersion, the conversion to acids remains limited. Insufficient local mixing near the feed inlet and chemical reaction equilibria will play a role in these cases. Additional experimental work and modeling is, however, required to test if the combination of a (micro-)mixing model with the kinetic rate expressions and the equilibrium model obtained in this study successfully describes the reaction products obtained for the Koch synthesis of Pivalic Acid from isobutene at various conditions in an agitated multiphase reactor.

III Summary

IV Samenvatting

Gas-vloeistof-vloeistof meerfasen-systemen worden in diverse toepassingsvelden binnen de procestechnologie aangetroffen, zoals bijvoorbeeld in processen gebaseerd op hydroformylerings-, alkylerings-, carboxylering- en polymerisatie reakties, hydrometallurgische en biochemische processen en in de fabricage van enkele fijnchemicaliën. De specifieke reactorkundige aspecten van dit type reaktiesystemen zijn echter slechts nauwlijks bestudeerd. Wanneer de optredende chemische reacties langzaam verlopen in vergelijking met de stofoverdracht tussen de verschillende fasen, kunnen de fasen op fysisch evenwicht worden verondersteld en vereist de aanwezigheid van drie verschillende fasen geen nadere bestudering. Echter, in het geval van een complex netwerk van snelle, deels irreversibele, chemische reacties zullen aspecten als stofoverdracht tussen de fasen en menging in de fasen in meer of mindere mate de uiteindelijke productverdeling bepalen. Een fascinerend voorbeeld van een dergelijk reaktiesysteem is de Koch synthese van Pivalinezuur. In dit werk is daarom dit reaktiesysteem gekozen om de interactie tussen stofoverdracht, menging en snelle chemische reacties in een gas-vloeistof-vloeistof reaktiesysteem nader te bestuderen.

Voor het analyseren van de optredende effecten van stofoverdracht en menging op de produktverdeling voor een complex reaktienetwerk in een gas-vloeistof-vloeistof meerfasen systeem, is het gewenst de reaktiekinetiek van de belangrijkste deelstappen uit het reaktiemechanisme te kennen.

De eerste stap in het reactiemechanisme is de vorming van een carbokation. Voor isobuteen en trans-2-buteen is deze protoneringskinetiek bepaald door middel van gasabsorptie experimenten. Hierbij is gebruik gemaakt van een goed gedefinieerde modelreactor, te weten een geroerde cel met een glad gas-vloeistof oppervlak van bekende afmeting. Uit de absorptie-experimenten bleek dat de zwavelzuurconcentratie veruit de belangrijkste parameter was voor de absorptiesnelheid. De voor de interpretatie van de absorptiefluxen benodigde oplosbaarheidsgegevens en diffusie- coëfficiënten in de reactieve zwavelzuurfase zijn deels experimenteel bepaald, deels afgeschat met behulp van een schattingsmethode gebaseerd op een analogie voor de (meetbare) oplosbaarheid van inerte componenten zoals isobutaan. Voor de beschrijving van de reactiekinetiek bleek het gebruik van een reactiesnelheids-vergelijking gebaseerd op de protoneringsactiviteit van de katalysator noodzakelijk.

V Samenvatting

Doordat de andere deelstappen niet afzonderlijk bestudeerd konden worden, is vervolgens de totale synthese van Pivalinezuur bestudeerd. Door de totale koolmonoxide consumptie en consumptiesnelheid te registreren, is naast de invloeden van druk, temperatuur en zuursterkte, met name het effect van de aanwezigheid van Pivalinezuur in de katalysator-oplossing onderzocht. Hieruit bleek dat de toevoeging van Pivalinezuur een drastische verlaging van de katalysator- activiteit teweeg bracht, welke kon worden gerelateerd aan een sterk afgenomen zuurgraad van de katalysator-oplossing. Deze afname is zelfs sterker dan die ten gevolge van een equimolaire toevoeging van water. Dit resultaat impliceert dat voor industriële toepassingen de katalysator- activiteit in de reactor significant lager zal zijn, dan mogelijk op basis van de initiële katalysator compositie zou worden verwacht. Een eenvoudige evenwichtsbeschrijving voor de vier basisstappen in het Koch reaktiemechanisme bleek in staat de sterk toenemende oplosbaarheid van Pivalinezuur in de katalysatoroplossing bij hogere zwavelzuur concentraties te beschrijven.

In de literatuur is veelvuldig opgemerkt dat de gas absorptiesnelheid in een gas-vloeistof systeem significant kan worden vergroot door de toevoeging van een onmengbare, tweede, vloeistoffase met een grotere oplosbaarheid voor de over te dragen gasfase component. De in de literatuur beschreven effecten op de verschillende stofoverdrachtsparameters, zoals het specifiek stofuitwisselend oppervlak en de gasfractie zijn kort samengevat, maar blijken elk afzonderlijk onvoldoende is om de waargenomen versnelling van het gas-vloeistof stofoverdrachtsproces te kunnen verklaren. Derhalve is nader onderzoek naar de optredende stofoverdrachtsprocessen gewenst. Eén van de mogelijke verklaringen voor deze versnelling is het optreden van direkt contact tussen de gasfase en de disperse vloeistoffase. Uit verkennende experimenten is gebleken dat zogeheten ‘complexen’ van gasbellen en disperse (organische) fase vloeistofdruppels kunnen bestaan in een waterige, continue, fase, onafhankelijk van de (initiële) spreidingscoëfficiënt van het systeem. Op basis van een grensvlakenergie-beschouwing is een kriterium voor het bestaan van deze complexen afgeleid.

Een alternatieve verklaring voor de versnelling van de gas-vloeistof stofoverdracht is de aanwezigheid van kleine disperse fase vloeistofdruppels in de stofoverdrachtszone nabij het gas- vloeistof grensvlak. Dit fenomeen, dat voor het eerst in gas-vloeistof-vast systemen werd waargenomen, wordt het ‘grazing-’ of ook wel ‘shuttle-mechanisme’ genoemd. In dit proefschrift is dit absorptiemechanisme beschreven met behulp van instationaire, heterogene (één-, twee en

VI Samenvatting drie-dimensionale) stofoverdrachtsmodellen voor één of meerdere deeltjes in de stofoverdrachtsfilm nabij het gas-vloeistof grensvlak. Met deze modellen is de invloed van diverse procesparameters, zoals de karakteristieke contacttijd en geometrische positie van het deeltje (of van de deeltjes) ten opzichte van het grensvlak onderzocht. Aangezien er in principe een oneindig aantal geometrische configuraties van druppels in de stofoverdrachtsfilm mogelijk is, is er met name ook aandacht besteed aan de vertaling van de modelresultaten in een voorspelling van de daadwerkelijke gasabsorptieflux. Een direkte methodiek, uitgaande van één-deeltje simulaties en van numeriek bepaalde deeltje-deeltje interactie-algorithmes, is in dit proefschrift geïntroduceerd. De op deze wijze verkregen modelresultaten zijn vervolgens vergeleken met experimentele data uit de literatuur.

In een meerfasen systeem kan de (lokale) turbulentie intensiteit, en daarmee de snelheid van inmenging van een toegevoerde reaktant, worden beïnvloed door de aanwezigheid van deeltjes van een disperse fase. Hoewel het effect van vaste stof deeltjes op de turbulentie-intensiteit in een gasstroom reeds vaker is onderzocht, is het uit de literatuur niet duidelijk in hoeverre deze effecten optreden in een geroerde gas-vloeistof-vloeistof meerfasen reactor en op een schaal die relevant is voor meervoudige, snelle chemische reakties. Met behulp van een goed gedefinieerd reactiesysteem, waarvan de produktverdeling gevoelig is voor de locale turbulentie-intensiteit op het punt waar de reaktant in de geroerde tankreactor wordt geïnjecteerd, is dit effect onderzocht voor de aanwezigheid van gasbellen, vloeistofdruppels en glasparels van diverse grootte. Het Engulfment micromengmodel, dat voor één-fase systemen de productverdeling voor dit reaktiesysteem goed kan beschrijven bij wisselende procescondities, bleek in staat ook voor de meerfasen systemen de verandering in de produktverdeling te kunnen voorspellen, mits de effectieve dispersie dichtheid en -viscositeit als invoerparameters in het model worden gebruikt. Voor de experimenten met vloeistof-vloeistof dispersies moet bovendien met de verdeling van de reaktanten over beide vloeistoffasen rekening worden gehouden. In deze studie zorgde dit voor een de-localisering van de reactiezone; de reaktie vond nu verspreid over de gehele tankinhoud plaats, in plaats van in de nabijheid van het voedingspunt. Verdiscontering van het stoftransport tussen beide vloeistoffasen in het Engulfment model leverde een goede beschrijving van de experimentele resultaten op.

VII Samenvatting

Tot slot is de Koch synthese van Pivalinezuur met tert-butanol (en daarnaast ook met isobuteen) als reaktant onderzocht. Onder de gekozen condities verliep deze reaktie te snel om met behulp van de koolmonoxide consumptiesnelheid (via gas absorptie) te kunnen volgen in de semi-batch bedreven geroerde tank reactor. De injectiesnelheid van tert-butanol en isobuteen blijkt een sterke invloed op de uiteindelijke opbrenst aan Koch zuren te hebben, waaruit is geconcludeerd dat de aanvoer van koolmonoxide vanuit de gasfase naar de reactiezone een sterk selectiviteits bepalende factor is. Tegelijkertijd kan worden geconcludeerd dat onder de gebruikte procescondities zowel de carbonyleringsstap als de ongewenste oligomerisatie reaktie zeer snel zijn, in vergelijking tot de koolmonoxide aanvoer en macromenging in de gebruikte reactor.Het meevoeren van koolmonoxide met de tert-butanol voeding blijkt dan ook een positief effect op totale opbrenst aan Koch zuren te hebben.

Het toevoegen van een inerte, onmengbare, organische vloeistoffase (heptaan) aan het reaktiesysteem geeft een significante verhoging van de produkt opbrengst, met name in het geval van experimenten bij lage toerentallen. Dit kan, op zijn minst ten dele, worden verklaard door een toenemende initiële koolmonoxide capaciteit per volume vloeistofdispersie bij toenemende heptaanfractie. Echter, zelfs onder condities waarbij de initiële capaciteit voldoende groot is voor volledige conversie van tert-butanol naar Pivalinezuur blijft de conversie beperkt. Mengeffecten en chemische evenwichten lijken hier nog een rol te spelen. Een integratie van de elementen aangereikt in dit werk, en enig additioneel experimenteel en theoretisch werk, is noodzakelijk om te testen of een reactormodel kan worden opgesteld dat de productopbrengst en -verdeling kan beschrijven onder verschillende procescondities.

VIII Contents

General Introduction 1 Introduction 1 The Koch synthesis 3 Present work 6

1. On the estimation of the diffusion coefficient and solubility of isobutene and trans-2-butene in aqueous sulfuric acid solutions 9

1. Introduction 11 2. Measurement of diffusion coefficients with a diaphragm cell 13 3. Estimation of solubility of gas phase components in electrolyte solutions 14 4. Experimental 18 5. Results 21 6. Conclusion 25 Notation 26 References 27

2. On the absorption of isobutene and trans-2-butene in sulfuric acid solutions 29

1. Introduction 31 2. Reaction mechanism and -kinetics 33 3. Theory 36 4. Experimental work 44 5. Physico-chemical parameters 46 6. Absorption experiments 48 7. Conclusions 55 Notation 56 References 57

3. The Koch synthesis of Pivalic Acid from isobutanol using sulfuric acid as catalyst 59

1. Introduction 61 2. Literature overview 63 3. Experimental 71 4. Results 74 5. Discussion 82 6. Conclusions 84 Notation 85 References 86

IX Contents

Appendix A The Effect of the addition of Pivalic Acid to aqueous sulfuric acid solutions on the Hammett Acidity Function 89

Appendix B On the product composition in the catalyst solution 95

4. Gas absorption in liquid-liquid dispersions 101

1. Introduction 103 2. Literature overview 105 3. Gas-dispersed phase contact in an agitated G-L-L contactor 111 4. Enhancement of gas absorption in liquid-liquid dispersions by complexes 114 5. Discussion and conclusions 117 Notation 118 References 119

5. A one-dimensional instationary heterogeneous mass transfer model for gas absorption in multiphase systems 121

1. Introduction 123 2. Previous work 126 3. Development of a heterogeneous, 1-D, instationary, multiparticle model 130 4. Simulation results 134 5. Comparison with experimental results and with a homogeneous model 144 6. Discussion 149 7. Conclusions 152 Notation 153 References 154

6. Heterogeneous mass transfer models for gas absorption in multiphase systems 157

1. Introduction 159 2. Heterogeneous mass transfer models 167 3. Results of simulations with one dispersed phase particle 177 4. Particle-particle interaction 183 5. On the prediction of absorption fluxes 189 6. Discussion and conclusions 195 Notation 196 References 197

X Contents

7. Experimental study of the effect of bubbles, drops and particles on the product distribution for a mixing sensitive, parallel-consecutive reaction system 201

1. Introduction 203 2. Theory 205 3. Experimental 211 4. Results 215 5. Discussion and conclusions 223 Notation 225 References 226

8. On the Koch synthesis of Pivalic Acid from tert-butanol and isobutene using sulfuric acid as catalyst 229

1. Introduction 231 2. Reaction mechanism and reaction kinetics 232 3. Experimental 235 4. Experimental results 239 5. Discussion 245 6. Concluding remarks 251 Notation 252 References 253

XI Contents

XII General Introduction

Introduction

Multiphase reaction systems are frequently encountered in chemical reaction engineering practice. Among them, the class of gas-liquid-liquid (G-L-L) systems received relatively little attention, although some important applications are involved with this type of operation. Examples of important gas-liquid-liquid reaction systems are e.g. hydroformylation (Kuntz, 1987), carboxylation (Falbe, 1980), polymerisation reactions (as in the SHOP process, see e.g. Freitas and Gum, 1979), alkylation, biochemical processes and fine chemicals manufacturing (Mills and Chaudhari, 1997).

An elegant and important industrial application is found in the hydroformylation of propene to butyraldehyde. In this process all reactants (propene, carbon monoxide and hydrogen) are initially present in the gas phase. The reaction is facilitated by a homogeneous catalyst dissolved in the aqueous phase and the reaction products constitute an immiscible organic liquid phase. This enables an easy separation of the product from the catalyst solution and the catalyst solution can be re-used. The SHOP oligomerisation process is another example of a process using the same concept.

Especially this recycling of the catalyst solution is an important issue. Gas-liquid-liquid systems may become more frequently applied due to recent developments in the field of homogeneous catalysis (Herrmann and Kohlpaintner, 1993; Chaudhari et al., 1995). Homogeneous catalysts can be very stereoselective, they generally do not suffer from internal mass transfer limitations as encountered with catalysts fixed on solid carrier materials (single active sites in solution), but usually they are more expensive. Total recycling of the homogeneous catalyst is therefore required. Locating a homogeneous catalyst in a separate liquid phase introduces an additional mass transfer step, but enables the desired recycling via simple phase separation.

In some cases it may be beneficial to add deliberately a second liquid phase to a gas-liquid (reaction) system. For instance, in fermentation processes sometimes an immiscible liquid phase is added to the fermentation broth to improve on gas-liquid mass transfer (Yoshida et al., 1970).

1 General Introduction

Other objectives can e.g. be found in shifting the position of chemical reaction equilibria by selective product removal or to allow an easy separation (and recycle) of reactants or products via phase separation. However, the benefits by adding an immiscible liquid phase should overcompensate the additional costs for the extra separation step required. The importance of studying the reaction engineering aspects of gas-liquid-liquid systems has been stressed several times (see e.g. Yoshida et al., 1970; Gaunand, 1986; Mills and Chaudhari, 1997). However, no complete study on the relevant aspects has been performed.

From a reaction engineering point of view, the co-existence of the three phases requires no special attention in case of very slow reaction rates, as the mass transfer rates will be relatively unimportant and the phases are at physical equilibrium. At higher reaction rates, however, the effects of mass transfer and mixing will become more and more important. Especially when the reaction selectivity is sensitive to local reactant concentrations. An example of such a reaction system is found in the synthesis of carboxylic acids via the Koch reaction.

In the production of tertiary carboxylic acids via the Koch synthesis the reactants carbon monoxide, alkenes and water originate from the gas phase, an organic liquid phase and the aqueous liquid phase respectively. The reactants, originating from all three different phases, react in the presence of an acid catalyst in the aqueous liquid phase. For the reaction to take place, gas- liquid and liquid-liquid mass transfer must be accomplished. In literature it is reported that operating parameters like the carbon monoxide pressure, agitation and catalyst composition have a pronounced effect on the selectivity obtained. The Koch synthesis, therefore, appears to be a challenging reaction system to study the effects of mass transfer and mixing in a gas-liquid-liquid reaction system.

2 General Introduction

The Koch Synthesis

In 1955 Herbert Koch (1955) published a pioneering study on the synthesis of quaternary carboxylic acids (Figure 1) from olefins, carbon monoxide and water, see Figures 1 and 2.

R= R + RCOOH R + CO H R" C R' + + RCOOH 2 RCO COOH H O 2 Figure 1 Koch Acids Figure 2 Reaction mechanism according _ to Koch (1955)

Using a strong acidic catalyst solution, the sterically hindered carboxylic acids could be produced at relatively mild conditions (10-100 bar CO partial pressure, 273 - 373 K). Up till then, this was only achieved at rather extreme conditions (400-600 K, 500 - 1000 bar CO partial pressure), see Falbe (1980). The process according to Koch was soon after 1955 commercialized by companies as e.g. SHELL ('Versatic Acids') and EXXON ('Neo Acids'). A considerable amount of patent literature has appeared since then, indicating the economical significance of the products made by these processes. The sterically hindered carboxylic acids produced are used as (specialty) intermediates for the production of resins and lacquers and (to a lesser extent) for the production of agrochemicals, cosmetics and medical applications (Falbe, 1980; Ullmann, 1986).

Orginally, a two step process was proposed for the Koch synthesis. In the first reaction step olefins (or alcohols) were added to a strong acid solutions under a medium pressure (50-100 bar) carbon monoxide atmosphere. The carbocations formed in the acid solution are trapped by carbon monoxide to form acylcarbocations. In a second process step water is added, hydration of the acylium ions occurs and carboxylic acids are obtained. Though several strong acids were proposed as catalyst, generally a mixture of a Lewis acid (esp. BF3) and a Brønstedt acid (e.g.

H3PO4, H2SO4 or H2O) is preferred for the easy catalyst separation and recycle by phase separation.

3 General Introduction

A simplified flowsheet of the production process of SHELL is given in Figure 3, according to Falbe (1980).

G-L-L Reactor

CO Distillation alkene

catalyst wash train recycle

water

Figure 3 Simplified Process Flow Diagram

As can be seen from Figure 3 the concept of two reactor stages was abandoned and replaced by a single high-pressure reaction step. Global process conditions are presented in Table I. The conditions may vary significantly with the catalyst and reactant used.

Table I Reported Process Conditions for the Koch synthesis

CO Pressure 20 - 100 bar Temperature 290 - 380 K mean residence 0.5 - 5 hours time

catalyst systems HF, H2SO4, H3PO4,

BF3⋅H2O, BF3⋅H2SO4,

BF3.H3PO4 ...

In this study sulfuric acid is chosen as catalyst system since the properties of this catalyst system are more established and the sulfuric acid catalyst system offers the possibility to study the reaction system in both the gas-liquid and gas-liquid-liquid mode respectively. In this way the effect of an immiscible liquid phase can be studied separately. The required dilution and

4 General Introduction reconcentration of the catalyst system hampers large scale application of this catalyst system, however, solutions for this have been claimed (Komatsu et al., 1974; Kawasaki, 1987).

The Koch reaction system is rather complex to operate, due to the gas-liquid-liquid three phase system and the complex reaction scheme with fast parallel/consecutive reactions. Additional to the desired reaction steps of the Koch carbonylation reaction undesired oligomerisation, isomerisation and cracking occurs. Carbon monoxide partial pressure, agitation (liquid mixing), gas-liquid mass transfer and composition of the catalyst solution (acid mixture ratios, water content etc.) are considered the main operating parameters determining selectivity and yield (Koch, 1955; Falbe, 1980). The product quality is not only determined by the number of carbon atoms in the product. Especially for high carbon number carboxylic acids the isomeric form is important for the properties of final product applications obtained. In this study, attention is focussed on the smallest Koch Acid, Pivalic Acid.

5 General Introduction

Present work

As the general scope is to improve on insight in the processes of mass transfer accompanied by chemical reaction and mixing in gas-liquid-liquid systems, thereby using the Koch synthesis as demonstration system, several phenomena of this reaction system are studied separately.

In the Chapters I, II, III and VIII an analysis of the reaction kinetics involved in the Koch synthesis of Pivalic Acid from isobutanol, tertiairy butanol and isobutene is reported. The first reaction step in the Koch reaction of pivalic acid, the protonation reaction, is studied separately in a gas-liquid stirred cell contactor using gas absorption experiments for isobutene and trans-2- butene. For deriving the reaction kinetics from these gas absorption fluxes, the solubility and diffusion coefficient for these components in the sulfuric acid catalyst solution are required. Measurements (where possible) and an estimation technique to obtain these physico-chemical properties are presented in Chapter 1.

The pronounced effect of catalyst concentration on the rate of protonation found (Chapter 2) indicates that activities instead of concentrations should be used in the kinetic rate expressions. Through modeling of the absorption process the operating window for performing gas absorption experiments in an absorption regime where reaction kinetics can be determined, is investigated for the activity based reaction rate equation.

In Chapter 3 experimental work on the Koch synthesis of Pivalic Acid using isobutanol as reactant is discussed. The reaction rate is in this study determined by recording the CO consumption rate. Effects of CO pressure, temperature and catalyst composition are studied. Special attention is given to the effect of the presence of the reaction product, Pivalic Acid, on the reaction rate.

In the Koch synthesis of Pivalic Acid it is shown (Chapters 3 and 8) that mass transfer from the gas phase to the reaction zone can be essential for the selectivity and product yield obtained. Gas absorption in liquid-liquid dispersions is therefore given considerable attention in the chapters 4 to 6. The presence of an immiscible (organic) liquid phase may enhance or retard the gas-liquid mass transfer rate, when compared to the gas-aqueous liquid phase system (Yoshida et al., 1970). A short literature overview on the relevant mass transfer parameters in gas-liquid-liquid systems will be presented in Chapter 4.

6 General Introduction

The enhancement of gas-liquid mass transfer in these multiphase systems is often explained by the ‘shuttle- or grazing mechanism’, originally proposed for gas-liquid-solid processes (Kars et al., 1979). An additional mechanism for the enhancement of gas-liquid mass transfer could be caused by direct contact of the gas phase with the dispersed (organic) phase. This is discussed in relation to qualitative experiments on the existence of direct gas-dispersed organic phase contact.

In the chapters 5 and 6 heterogeneous mass transfer models are developed, which describe mass transfer (with or without chemical reaction) for the situation in which small droplets are present within the mass transfer zone near the gas-liquid interface. In Chapter 5 an one-dimensional heterogeneous mass transfer model is presented, which is used to investigate the relevance of several system parameters. In Chapter 6 an overview of reported experimental and modeling studies on this mass transfer enhancement effect is presented, as well as the newly developed 2-D and 3-D instationary, multi-droplet, heterogeneous mass transfer models. The prediction of gas absorption fluxes from these 3-D models deserves special consideration and a complete modeling strategy is proposed. The results obtained from the models and strategy are compared with experimental data by Littel et al. (1994)

The effect of the presence of a dispersed phase on (micro-)mixing in multiphase systems was studied experimentally in Chapter 7. In this study the parallel/consecutive diazo coupling reaction system of Bourne et al. (1981) was used as test-reaction. Gas bubbles, glass beads and liquid droplets were applied as dispersed phase.

Finally, in Chapter 8 the effects of gas-liquid mass transfer and liquid phase mixing on the product yield in the Koch synthesis of Pivalic Acid from isobutene and tert-butanol are investigated. Especially the effect of an immiscible (inert) liquid phase on the final product distribution through its effect on gas-liquid mass transfer and liquid phase mixing is discussed. Although the analysis of the Koch reaction is not completed with this work, some pieces of the puzzle are completed and can be used in the construction of a more complete picture of this fascinating reaction system.

7 General Introduction

References

Bourne J.R., Kozicki F., Rys P., 1981, Mixing and fast chemical reaction - I : Test reactions to determine segregation, Chem.Engng.Sci., 36, 1643-1648

Chaudhari R.V., Bhattacharya A., Bhanage B.M., 1995, Catalysis with soluble complexes in gas- liquid-liquid systems, Catalysis Today, 24, 123-133

Falbe J., 1980, ’New synthesis with carbon monoxide; Ch. V.: Koch Reactions (H. Bahrmann)’ , Springer-Verlag, Berlin

Freitas E.R., Gum C.R., 1979, Shell’s Higher Olefin Process, CEP, (1), 73-76.

Gaunand A., 1986, Oxidation of Cu(I) by oxygen in concentrated NaCl solutions-III. Kinetics in a stirred two-phase and three-phase reactor, Chem.Engng.Sci., 41, 1-9

Herrmann W.A., Kohlpaintner C.W., 1993, Water soluble ligands, metal complexes and catalysts: synergism of homogeneous and heterogeneous catalysis, Angew.Chem. (Int.Ed.Engl), 32, 1524- 1544

Kars R.L., Best R.J., Drinkenburg A.A.H., 1979, The sorption of propane in slurries of active carbon in water, Chem. Engng. J., 17, 201-210

Kawasaki H. (Idemitsu Petrochemical Co., Ltd.), 1988, Process for producing carboxylic acid, Eur.Pat.Appl., EP 298 431

Koch H., 1955, Carbonsäure-Synthese aus Olefinen, Kohlenoxyd und Wasser, Brennstoff- Chemie, 36, 21/22, 321-328

Komatsu Y., Tamura T., Asano K., Tsuji H., Fujii K., 1974, ‘Study on the production of branched chain carboxylic acid - Method of hydrogen fluoride and sulphuric acid catalyst recovery in the Koch reaction’, Bull.Jap.Petr.Inst., 16 (2), 124-131

Kuntz E.G., 1987, Homogeneous catalysis ... in water, ChemTech, 9, 570-575

Littel R.J., Versteeg G.F. and Van Swaaij W.P.M., 1994, Physical absorption of CO2 and propene into toluene/water emulsions, A.I.Ch.E. J., 40, 1629-1638

Mills P.L., Chaudhari R.V., 1997, Multiphase catalytic reactor engineering and design for pharmaceuticals and fine chemicals, Catal.Today, 37, 367-404

Ullmann’s Encyclopedia of Industrial Chemistry, 1986, 5th ed., vol. A-6, 235-248, VCH Verlagsgesellschaft, Weinheim

Yoshida F., Yamane T., Miyamoto Y., 1970, Oxygen absorption into oil-in-water emulsions. A study on hydrocarbon fermentors, Ind.Eng.Chem.Proc.Des.Dev., 9, 570-577

8 Chapter 1

On the estimation of the diffusion coefficient and solubility of isobutene and trans-2-butene in aqueous sulfuric acid solutions

Abstract

The diffusion coefficient and, especially, the physical solubility of isobutene in strong sulfuric acid solutions can not be determined experimentally due to the occurrence of fast chemical reactions. In the present contribution these physico-chemical parameters are estimated. For the solubility an isobutane-isobutene analogy is applied, using the estimation technique by Rudakov et al. (1987).Diffusion coefficients for inert gases in electrolyte solutions were measured using a modified diaphragm cell. It was found for CO2 and N2O in KCl solutions that the diffusion coefficient is not a function of the ionic strength of the electrolyte solution.

9 Chapter 1

10 Chapter 1

1. Introduction

The absorption of butenes in sulfuric acid solutions is found in large scale processes of considerable industrial importance. Especially the removal of isobutene from C4-streams produced by a naphtha cracker via selective hydration and the production of sec-butanol from linear butenes are important industrial applications. Therefore considerable attention has been paid to the mechanism and kinetics of the protonation reactions of olefins in (strong) acid solutions. However, the reaction kinetics found in literature are not consistent and no data are available for sulfuric acid solutions of 80 wt% and higher. The latter regime is of interest for e.g. the Koch reaction of isobutene to pivalic acid.

In addition to the reaction kinetics, physico-chemical properties like the solubility and diffusion coefficient of the butenes in the sulfuric acid solution are required to enable mass transfer calculations in designing the processes mentioned. Also for the experimental determination of the reaction kinetics for the protonation reaction of isobutene from gas absorption experiments these data must be known (Brilman et al., 1997).

Since the protonation of, especially, isobutene in moderately to strong acidic solutions is fast to extremely fast, these physico-chemical properties cannot be measured directly. In order to come to a reasonable estimation of these it is proposed to use an analogy; e.g. an isobutane-isobutene analogy (see also Zhang and Hayduk, 1984). The usefulness of this type of analogies is probably best demonstrated by the frequently used CO2-N2O analogy in the research and design studies for amine treating processes (Laddha et al., 1981) (Versteeg et al., 1996).

For the selection of an inert component (in aqueous acid solutions) which resembles isobutene best, the physico-chemical properties of a number of compounds were compared. Isobutane seems to resemble isobutene quite well, judging by the properties of isobutane and isobutene listed in Table I

11 Chapter 1

Table I Properties of Isobutene and Isobutane (Reid et al., 1987; Yaws, 1995)

Isobutene Isobutane

molar mass [g/mole] 56.107 58.123 melting point [K] 132.81 113.54 boiling point [K] 266.25 261.4 3

Tcritical [K] 417.90 408.14

Pcritical [MPa] 3.999 3.648 acentric factor [-] 0.1893 0.177 dipole moment [Debye] 0.5 0.1 3 Vm (298 K, 1 bar) [m /mol] 24.1 24.2 2nd virial coefficient (298 K) [m3/mol] - 6.5⋅10-4 - 6.5⋅10-4 solubility in water (298 K, 1 bar) [m3/mol] 6.0 0.8 diffusion coefficient in water [m2/s] 10.4⋅10-10 9.9⋅10-10 solubility parameter [J/m3]1/2 1.4954⋅104 1.4027⋅104

The major difference between these components is found in the dipole moment, which is directly reflected in the difference in solubility in polar solvents as water. Another, more polar, inert gaseous component which resembles isobutene equally well as isobutane does, was however not found.

Essentially, two specific properties are required for interpreting isobutene absorption fluxes in terms of mass transfer rates and reaction kinetics. The first one is the solubility of isobutene in the sulfuric acid solutions, the second one is the diffusion coefficient of isobutene in the same solutions. Both properties will be estimated by comparing with experimentally determined data for isobutane and other gases, determined in this work and taken from literature.

12 Chapter 1

2. Measurement of diffusion coefficients with a diaphragm cell

A diaphragm cell has been used frequently to determine diffusion coefficients. In this technique two well mixed phases are separated by a porous, non-permselective membrane, which is filled by the phase in which the diffusion coefficient is to be determined. In this case, where diffusion coefficients of gas phase components in a liquid phase will be determined, the membrane is filled with liquid. The liquid inside the membrane will be stagnant at not too high stirring rates in the liquid bulk. By determining (in this case) the gas absorption flux the diffusion coefficient of the absorbed gas phase component in the liquid phase can be calculated, when the bulk phase compositions are known, using the well known film theory. The gas-liquid diaphragm cells used in literature often require relatively long measurement times (1-2 days, see e.g. Gubbins et al., 1966) before a pressure drop in the gas phase could be determined accurately. This problem has been overcome in the present study by using two gas phase chambres connected via a differential pressure indicator. One chambre is kept at a fixed reference pressure and the gas is absorbed from the other one. From mass balances for both the gas phase and the liquid phase (and applying the ideal gas law) the diffusion coefficient can be evaluated from pressure vs. time data, see Eqs. (1)- (5)

Pio, Pt() Overall balance : V +=VC V i +VC() t (1) g RT LLo, g RT LL

Vg dP P Gas phase : i =−kAm()i −C (2) RT dt L RT L

Initial conditions : t = 0 : P = Po , CL = CL,o = 0 (2-a)

For isobutane and isobutylene the Redlich-Kwong-Soave equation of state was used instead of the ideal gas law for evaluating the diffusion coefficients. In Equation (2) the kL value represents the mass transfer coefficient according to the film theory : D = i k L δ (3) The characteristic effective film thickness, δ, is now determined by the dimensions of the membrane dm, its porosity and the tortuosity of the pores respectively. Since these values are constant, but not known on beforehand, a (configuration depending) membrane calibration factor, f , can be defined and can be determined experimentally : D ε k A = i A = D f (4) L τ i d m

13 Chapter 1

The membrane parameter f can be measured by calibration experiments with known systems. In this work the absorption of CO2 and N2O in water was used for this purpose. From Equations (1) and (2) the apparent kLA value can be determined from experiments using Equation (5), and with this the calibration factor f is calculated according to Equation (4). When the membrane is calibrated (and the value of f is known) the diffusion coefficient can be determined for other gas phase components.

 P  i,t ()+ −  * Vg mVL Vg   P   1 m   i,o  = −  +  ln k LA  t (5)  mVL   VL Vg     

3. Estimation of solubility of gas phase components in electrolyte solutions

The solubility of a gas phase component i in aqueous solutions generally decreases on addition of electrolytes (‘salting out’). This decrease, corresponding with an increase in the activity coefficient of component i in the liquid phase according to classical thermodynamics, can often be described for aqueous solutions using the classical Sechenow equation (see Equation 6-a) and summing the contribution of the different ions present (as in the Debije-Hückel Limiting Law).

   He  = (based on ionic strength) log   ∑ KiIi (6-a)  Heo  i  He  (based on salt concentration) log  = ∑K c (6-b)  o  i  He  i

Weisenberger and Schumpe (1996) proposed an alternative estimation method (see Equation 6- b), based on the salt concentrations. At slightly more concentrated solutions (roughly above 0.5 M) more sophisticated activity models for electrolyte solutions are to be preferred (see e.g. Pitzer et al. (1996) for a model, claimed to be valid for 0-6 M H2SO4 solutions). At even higher (sulfuric acid) electrolyte concentrations, these models are no longer valid and even ‘salting in’ may occur. Since there are no activity models available for the regime of interest for the Koch synthesis (> 70 wt% H2SO4), a more empirical approach has to be used.

14 Chapter 1

For concentrated sulfuric acid solutions the gas phase solubility of a small number of components has been reviewed by Rudakov et al. (1987). From this overview it became clear that the solubility curve at increasing acid content is non-linear and shows a minimum. The position of the minimum depends on the gas used; a fair correlation of the position of the minimum and of the ratio of the solubilities in 100% H2O and 100% H2SO4 with the molar volume of the solute was observed.

The method proposed by Rudakov et al. (1987) is in fact a Sechenow technique, describing a

‘salting out’ effect in an ‘ideal’ (or ‘regular’) solution of H2SO4 and H2O. For the solubility of a gaseous solute j in an (homogeneous) mixture of N solvents the following addition rule can be applied : ( )= ( ) lnHemix,j ∑ xi ln Hei,j (7) i=1..N in which xi represents the mole fraction of solvent i in the solution.

According to the method by Rudakov et al. (1987), the deviation of the actual solubility parameter α from the solubility in a ‘regular solution’, αRS, of H2O and H2SO4 is related to the total ionic concentration c, according to Equation (8).

∆ log(ααα )=− log( ) log( ) =− log( α )xxxBc log( α ) − log( ) =⋅ (8) RS HO2 HO 2 HSO 24 HSO 24

The total ionic concentration c required, is unfortunately not well known for the concentrated solutions considered. An alternative relationship, and more convenient approach, was presented by Rudakov et al. (1987) using the result of McDevit and Long (1952) that ionic salting out is proportional with the Excess Molar Volume (VE) of the medium,   VE ∆ log(ααα )=− log( ) log( ) =⋅L   (9) RS  V  with the Excess Molar Volume VE being defined by :

VE = V − x V − x V (10) H 2O H 2O H 2SO 4 H 2SO 4 and L is a parameter depending on the non-electrolyte. The parameter L can be calculated according to Equation (11).

15 Chapter 1

V L = n with β the compressibility factor of the solution (11) 2.3 RTM β

β = x β + x β (12) H2O H2O H2SO4 H2SO4 and M is a, solute dependent, parameter. For β and β the values proposed by Rudakov H2O H2SO4 et al. (1987) were taken. The M value can be determined by data fitting for inert components (which was done for isobutane, isopentane, cyclopentane, methane, hydrogen and helium), but in case of reactive gases its value needs to be estimated. A fair correlation of M with the molar volume of the inert gaseous solutes in solution was obtained for the above mentioned set of gases, see Figure 1.

6 10

M α α αH2O / H2SO4/ α H2SO4 H2O 5 1

4 0.1

0.01 2 Mcorr.fact. Mfit-corr.fact (trend line calibration set) 0.001 1 α α aH2SO4/aH2O (H2O) / (H2SO4) α( α( aH2SO4/aH2OH2O) / H2SO (fit)4) (trend line calibration

0 0.0001 20 40 60 80 100 120 3 Vn [cm /mol]

Figure 1 Correlation of M and α / α with V (data taken from Rudakov et al.,1987) H2SO4 H2O n

The method describes the set of data reasonably well, as is illustrated by Figure 2. In this figure the experimental data by Rudakov et al. (1987) and additional datapoints measured are presented, as well as the solubility estimated by the above mentioned method. It can be seen, however, that within the range 50-80 wt% H2SO4 the deviations between model prediction and experimental determined datapoints are relatively large, but still within 30%. The general trend is, however,

16 Chapter 1 reasonably well described. This technique will be used for estimating the isobutene and trans-2- butene solubility in aqueous sulfuric acid solutions.

m (H2O) / m

0.1

m(H2O)/mRudakov et (Rudakov al. (1987) et al., 1987) experimental (this work) (estimated) 0.01 0 20406080100

wt% H2SO4

Figure 2 Relative solubility of isobutane in aqueous sulfuric acid solutions at 298 K

17 Chapter 1

4. Experimental

4.1 Diffusion coefficients Diffusion coefficients of isobutane, isobutene and carbon dioxide in water and aqueous sulfuric acid solutions were determined using a diaphragm diffusion cell. The cell is depicted in Figure 3.

data atmosphere acquisition

vacuum P

Gas Supply Reference chambre ∆P Gas chambre

degassing vessel

Liquid phase

atmosphere

Diaphragm cell

Figure 3 Diaphragm cell for measurement of liquid phase diffusion coefficients of gas phase components

The cell contains two gas phase chambers, separated by a glass wall. The diaphragm cell is completely thermostated. The pressure indicator of the upper gas chamber operates within the range 0-1000 mbar, having an accuracy of 1 mbar. This pressure is the reference pressure during the measurements. The lower gas phase chamber is separated from the liquid phase by a non- permselective, liquid filled membrane, made of sintered glass. Various differential pressure indicators (Druck, 600DP series) were used. A typical example is a differential pressure indicator operating within the range 0-12 mbar (± 1% of full scale).

18 Chapter 1

Table 1I Characteristics of the diaphragm cell

Liquid phase volume 282.5 ml Gas phase lower chamber 187.5 ml upper chamber 170.5 ml Diaphragm material sintered glass spheres pore size (type P2) 10-20 µm porosity 45 % thickness 4.0 mm diameter 60 mm Operating range pressure upper chamber ≤ 1000 mbar differential pressure (various; 0-1 mbar to 0-1000 mbar) Temperature 280 - 313 K stirrer speed (aq. soln.) 20-60 rpm

Calibration of the diaphragms used

With carbon dioxide and nitrous oxide diffusion coefficient measurements were performed at 298 K to calibrate the diaphragm. The diaphragm was characterized by determining experimentally the ratio f = A⋅ε/(τ⋅dm) for different stirrer speeds. It was found that this ratio f was independent of stirrer speed within the range of 20 - 60 rpm. Moreover, the same value (0.47 ± 0.01 m) was found for the CO2-water and the N2O-water experiments respectively.

Owing to the use of differential pressure indicators a major disadvantage of the diaphragm cell technique, the relatively long measurement times, could be substantially reduced. Typically, one single experiment took one hour. This could be optimized by choosing differential pressure indicators with various operating windows. Some experimental restrictions were found when operating with isobutane absorption in sulfuric acid solutions. The extremely low solubility (< 1 mol/m3 at the operating conditions), especially at moderately high acid concentrations, resulted in scatter in the estimated diffusion coefficients and no accurate determination was possible. These deviations could be caused by the absorption of isobutane in the vacuum grease between the upper and lower half of the cell, diffusion of isobutane through the short (10 mm) Viton tubes to the differential pressure indicator and/or small fluctuations in the thermostat bath temperature. It was found for this particular setup that the gas-liquid distribution coefficient m should exceed

19 Chapter 1

0.05 [-] for reliable operation (and standard deviations in the diffusion coefficients determined within 5%) of this diaphragm cell.

4.2 Solubility measurements

vacuum supply bottle

Figure 4 Experimental setup solubility measurement

Solubilities of the gas phase components were determined by gas absorption experiments in a thermostated glass reactor of, in total, 1130 ml. The cell is equipped with a Hastelloy C-22 gas- inducing Medimex stirrer. Physical equilibrium between gas and liquid phase was usually reached in 20-30 seconds. This rapid equilibration enables the use of the solubility determination method for trans-2-butene up to 60 wt% H2SO4 solutions. The temperature was controlled using a Tamson T1000 thermostat bath (accuracy: ± 0.1 K). The liquid phase volumes used were in general 500-600 ml. The pressure drop was registrated used a pressure indicator (Druck PTX- 620, range 0 -1500 mbar (± 1 mbar)). The cell was operated batch wise with respect to both the liquid phase and the gas phase. Prior to filling the gas space with the gas to be absorbed, the liquid was degassed by applying vacuum while stirring. Gases were purchased from Hoek Loos and were not further purified; isobutane (99.95 %), isobutene (99.7 %) and CO2 (99.9%) were absorbed in aqueous sulfuric acid solutions prepared from 95-97 wt% pro analyses grade H2SO4, (purchased from Merck). Acid concentration was determined by titration.

20 Chapter 1

Accuracy of the solubilities was generally good (less than 1% deviation) for m values of 0.01 and higher. In case of lower gas phase solubilities the inaccuracy increased to 5-10%, which was e.g. encountered for isobutane in moderately strong sulfuric acid solutions (40-60 wt%).

5. Results

5.1 Diffusion coefficients In order to check whether ionic strength of the liquid phase influences the apparent diffusion coefficients experiments with potassium chloride solutions were performed. Aqueous potassium chloride solutions were selected for this, since the addition of KCl to water does not change the viscosity of the solution significantly (less than 2% increase, up to 3 M KCl; Weast, 1986). With this, the effects of ionic strength and solution viscosity could be separated.

Table III Diffusion coefficients of CO2 and N2O in 0-3 M. KCl solutions at 293 K.

KCl D (CO2) D (N2O)

[M] [10-9 m2/s] [10-9 m2/s]

0.00 1.73 1.63

0.10 1.76 -

0.80 1.75 -

1.00 1.66 1.63

2.00 1.68 1.64

3.00 1.76 1.63

Table IV Solubility and Diffusion coefficients of CO2 in H2SO4 solutions at 298 K

H2SO4 η (cP) mCO2 No. exp. s.d. DCO2 No. s.d. exp. (wt%) (10-9 m2/s)

0 0.893 0.84 3 0.003 1.93 2 0.005 54 5 0.71 2 0.002 0.71 1 0 70 12 0.67 2 0.003 0.42 2 0 80 19 0.63 2 0.003 0.34 2 0.04 85 1 0.15 1 90 1 0.10 1 96 20 0.94 2 0.02 0.19 1

21 Chapter 1

For CO2 and N2O in aqueous KCl solutions it was found that the diffusion coefficient did not change within the range 0 - 3 M (within experimental accuracy of ± 5%). Ionic strength and/or the activity coefficient of the diffusing gas phase component, therefore, do not seem to have any influence on the apparent Fick diffusion coefficient.

Due to the extremely low solubility isobutane could not successfully be used at all conditions to determine its diffusion coefficient in sulfuric acid solutions. Therefore, carbon dioxide was used for this purpose. The experimental results are given in Table IV. The diffusion coefficient of isobutene in aqueous sulfuric acid solutions can, according to Gubbins et al. (1966) be estimated by measuring the diffusion coefficient of other inert gases. Gubbins et al. (1966) suggested that the ratio of the diffusion coefficient in the aqueous solution to the diffusion coefficient in water would be the same for both gases, considering the low (mole) fraction of the gas phase component in a saturated liquid phase. This would justify the use of an other inert gas as CO2 for the diffusion coefficient estimation for isobutene and trans-2-butene.

For various gas phase components available diffusion coefficient data for aqueous electrolyte solutions were summarized in Figure 5. From this figure it is clear that the data are reasonably well correlated by (D⋅η)0.6 = constant (deviations generally less than 10%).

0.5

ln(D/Do) CO2 NaCl 0 CO2 [NaNO3] CO2 Na2SO4 CO2 MgCl2 -0.5 CO2 Mg(NO3)2 CO2 MgSO4 -1 N2O K2CO3 + 10 % H2 MgCL2 -1.5 CO2 H2SO4

- 10 % H2 MgSO4 -2 CH4 MgCl2 CH4 MgSO4 96 wt% FIT ln(D/Do) -2.5 85 wt% FIT 10% 90 wt% FIT -10% -3 0 0.5 1 1.5 2 2.5 3 ln (η/ηo)

Figure 5 Correlation of literature data on gas diffusion in aqueous electrolyte solutions and

CO2/H2SO4 data (this work) at 298K. [ Data were taken from Gubbins et al. (1966), Ratcliff and Holdcroft (1963) and Joosten and Danckwerts (1972) ]

22 Chapter 1

It can be seen from this figure that aqueous sulfuric acid solutions behave like other (less viscous) aqueous electrolyte solutions. The proposed correlation apparently even holds for aqueous sulfuric acid solutions up to 80 wt% and having a relative viscosity of nearly 20. The experimental values at 85, 90 and 96 wt% deviate from the correlation, probably due to the fact that water is no longer in excess in sulfuric acid solutions exceeding 84.5 wt%. The relationship (D⋅η)0.6 = constant was also found for the diffusion coefficient of several amines in aqueous amine solutions (Snijder et al., 1993).

5.2 Solubility The solubility of isobutene and trans-2-butene in aqueous sulfuric acid solutions was estimated with the method described before. Using Figure 1, the parameter M for isobutene and trans-2- butene was estimated to be 3.4 for both gases. For estimating α (H2SO4) again Figure 1 (and α

(H2O) which can be measured or found in literature) was used. With these, the relative solubilities at different acid strength as presented in Figure 4 have been calculated.

m(H2O) / m ( )

Exp. data trans-2-butene

H2SO4 m

0.1 wt% [-] Sankholkarm(H2O)/m &(Sankholkar, Sharma (1973 1973) ) trans-2-butene m(H20)/m (experimental, this work) 0 0.152 (experimental, this work) 30 0.067 (mestimated(H20)/m) (estimated) 44 0.060 GehlawatGehlawat && SharmaSharma ((19681968)) 54 0.046 isobutene 60 0.042 (mestimated(H2O)/m) (estimated)

0.01 0 20406080100 wt% H2SO4

Figure 6 Relative solubility of isobutene and trans-2-butene in aqueous sulfuric acid solutions at 298 K Due to the estimation method based on partial molar volume in aqeous solutions the relative solubilities of trans-2-butene and isobutene in aqueous sulfuric acid solutions differ only slightly.

23 Chapter 1

In the low acid regime the protonation reaction is slow, and the physical solubility can be estimated from gas absorption experiments if the liquid phase is saturated relatively fast. From Figure 6 it may be concluded that the estimation method works reasonably well for, at least, trans-2-butene up to 60 wt% sulfuric acid solutions. For the datapoint from Sankholkar and Sharma (1973) at 50wt% it is believed that the solubility measurement is disturbed by consumption due to chemical reaction.

Extrapolation of the method to gas phase components differing drastically in properties from those of the calibration set is not recommended. For carbon dioxide, which is used in the diffusion coefficient estimation, the solubilities were determined experimentally and by the estimation method mentioned above. The results, presented in Figure 7, clearly show that the estimation method used is an oversimplification. The data by Markham and Kobe (1941) and the data of Shchenikova et al. (1957) were retrieved from the IUPAC Solubility Data Series (62). The local minimum in the curve, which can also be seen in Figure 2, at approximately 60 wt% H2SO4 is not predicted by the model; this would require e.g. the introduction of a third component to the regular solution. Nevertheless, the order of magnitude of the solubility remains predicted fairly well. By adapting the M value a slightly better overall description of the experimental data can be obtained, as is shown in Figure 7.

3 Markham, Kobe (1941) m(H2O) / m Shchenikova et al. (1957) 2.5 experimental (this work) model (model fitted to experimental data) 2

1.5

0.5

0 0 20406080100

wt% H2SO4

Figure 7 Relative solubility of CO2 in aqueous sulfuric acid solutions at 298 K

24 Chapter 1

6. Conclusion

The diaphragm cell with the differential pressure concept was found to be convenient for a quick determination of diffusion coefficient, while maintaining a reasonable (engineering) accuracy of 1-3%. Since it was found that the diffusion of gases in inert electrolyte solutions is not influenced by the ionic strength of the solution, but apparently only by solution viscosity, a fairly good estimation of the diffusion coefficient in aqueous electrolyte solutions is obtained by using Eq. 13:

(D⋅η)0.6 = constant (for a particular gas, at constant temperature) (13)

The (order of magnitude of the) physical solubility of isobutene and trans-2-butene in aqueous sulfuric acid solutions at different acid strenghts is most likely to be estimated fairly well by using a method, proposed by Rudakov et al. (1987), although deviations up to 50% can not be excluded (especially within the range 60-80 wt%).

Acknowledgements The author wishes to thank C.J.D. Zwart for his valuable contribution to the experimental work and G.J. Mollenhorst and B. Knaken for constructing the diaphragma cell and -setup respectively.

25 Chapter 1

Notation

A surface area [m2] a specific surface area [m2/m3] B fit parameter (Equation 8) [-] C concentration [mole/m3] D Diffusion coefficient [m2/s] dm membrane thickness [m] f membrane calibration factor [m] He Henry coefficient [Pa] I ionic strength [mol/m3] kL mass transfer coefficient [m/s] L parameter defined in Equation (11) [-] M fit parameter in Equation (11) [-] m distribution coefficient (=Cliquid / Cgas) [-] P Pressure [Pa] R gas constant ( = 8.314 ) [J/mole K] t time [s] T temperature [K] V (molar) volume [m3 (/mole)] Vn molar volume of gas phase solute in water [m3/mole] x mole fraction [-]

Greek symbols

α distribution coefficient ( =1/m = Cgas / Cliquid) [-] β compressibility [1/Pa] δ film thickness (film model) [m] ε porosity of the membrane [-] η viscosity [kg/ms] τ tortuosity of the membrane pores [-] super- and subscripts E excess g gas phase i,j component i resp. j L liquid phase mix mixture RS regular solution o initial value

26 Chapter 1

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Gubbins K.E., Bhatia K.K., Walker R.D., 1966, Diffusion of gases in electrolytic solutions, AIChE J., 12, 548-552.

Scharlin P., Cargill R.W., 1996, Carbon dioxide in water and aqueous electrolyte solutions (IUPAC Solubility Data Series), vol. 62, 142-144

Joosten G.E.H., Danckwerts P.V., 1972, Solubility and diffusivity of nitrous oxide in equimolar potassium carbonate-potassium bicarbonate solutions at 25°C and 1 Atm., J.Chem.Eng.Data, 17, 452-454

Laddha S.S., Diaz J.M., Danckwerts P.V., 1981, The N2O analogy: the solubilities of CO2 and N2O in aqueous solutions of organic compounds, Chem.Engng.Sci., 36, 228-229

McDevit W.F., Long F.A., 1952, The activity coefficient of benzene in aqueous salt solutions, J.Am.Chem.Soc.., 74, 1773-1777

Ratcliff G.A., Holdcroft J.G., 1963, Diffusivities of gases in aqueous electrolyte solutions, Trans.Inst.Chem.Eng., 41, 315-319

Reid R.C., Prausnitz J.M., Poling B.E., 1987, The properties of gases and liquids, 4th edition, McGraw Hill, New York.

Rudakov E.S., Lutsyk A.I., Suikov S.Y., 1987, Extremal Change in solubility of non-electrolytes in the water-sulfuric acid system (0-100% H2SO4). Modification of the Sechenow equation, Russ.J.Phys.Chem., 61, 601-607

Snijder E.D., te Riele M.J.M., Versteeg G.F., van Swaaij W.P.M., 1993, Diffusion coefficients of several aqueous alkanolamine solutions, J.Chem.Eng.Data, 38, 475-480

Versteeg G.F., van Dijck L.A.J., van Swaaij W.P.M., 1996, On the kinetics between CO2 and alkanolamines both in aqueous and non-aqueous solutions. An overview, Chem.Eng.Comm., 144, 113-158

Weisenberger S., Schumpe A., 1996, Estimation of gas solubilities in salt solutions at temperatures from 273 K to 363 K, AIChE Journal, 42, 298-300

Weast R.C., 1986, CRC Handbook of Chemistry and Physics, 66th ed., CRC Press, Florida

Yaws C.L., 1995, Handbook of Transport Property data, Gulf Publishing Company

Zhang G., Hayduk W., 1984, The solubility of isobutane and isobutylene in associated solvents, Can.J.Chem.Eng., 62, 713-718

27 Chapter 1

28 CHAPTER 2

On the absorption of isobutene and trans-2-butene in sulfuric acid solutions

Abstract

In reactions in which alkenes react in the presence of homogeneous Brønstedt acid catalysts the protonation step is rate determining. Existing reaction rate correlations for protonation of butenes in sulfuric acid solutions are not consistent and limited to sulfuric acid concentrations below 80 wt%. The absorption of isobutene and trans-2-butene in sulfuric acid solutions was studied in the range 30-98 wt%. Re-evaluation of literature data, completed with new data from this study revealed a set of kinetic rate data which coincide satisfactorily. Experiments and modeling of the absorption experiments showed a strong dependence of the reaction rate on local mixture composition through the activity coefficient of the protonating agent. This strong dependence prevents the occurrence of a diffusion limited absorption regime. Application of the usually used criteria for operating in the kinetic regime can lead to erroneous results.

29 Chapter 2

30 Chapter 2

1. Introduction

The absorption of alkenes, e.g. butenes, in sulfuric acid solutions is frequently found in large scale commercial applications. Especially the removal of isobutene from C4-streams produced by a naphtha cracker via selective hydration and the production of sec-butanol from linear butenes are important industrial applications. In these processes the first reaction step is the formation of a highly reactive intermediate species; the carbocation. In a second step water is added directly to react to the corresponding alcohol or, alternatively, in a second step a hydrogensulfate ion may be added to form a butylhydrogensulfate ester, which can be hydrolyzed to give the corresponding alcohol in an indirect route. For both the direct and indirect hydration path the protonation step is assumed to be rate determining.

Proton transfer reactions can be extremely fast, e.g. the second order forward reaction rate constant for the reaction of a proton and a hydroxide ion to form water was found to be 1.4⋅1011 [l/mole s] (Eigen, 1963), which is probably the fastest reaction known in aqueous solution.

Comparable rates are e.g. found in case of dissolving acid gases as HCN and H2S in water. For ‘diffusion-controlled’ reactions of non-ionic species the ‘rate constant’ for bimolecular reactions is estimated to be 8⋅109 mole/l s for reactions in water. In other solvents this value will decrease with increasing solvent viscosity. However, for the protonation of unsaturated hydrocarbons the experimentally found reaction rates are much lower than for the cases mentioned above.

Since the 1940s considerable attention has been paid to the mechanism and kinetics of the protonation reaction of olefins in (strong) acid solutions. However, summarizing the literature results on the reaction kinetics it can be concluded that, especially for 2-butenes, no consistency exists for the observed dependency of the kinetic rate constants on acid strength for the protonation of butenes in sulfuric acid solutions (see Figure 1). Moreover, no data are available for experiments in sulfuric acid solutions of 80 wt% and more, which are typical concentrations used for e.g., the Koch reaction and alkylation reactions.

This chapter deals with a study of the protonation kinetics for isobutene and trans-2-butene in highly concentrated sulfuric acid solutions. Because of the observed discrepancy between the data presented in literature and because of the lack of information for highly concentrated acid solutions an experimental study of the absorption kinetics over the range of 30-96 wt% sulfuric acid

31 Chapter 2 solutions was carried out to study these reaction kinetics of the protonation step. Since concentrated acid solutions are thermodynamically highly non-ideal, it seems appropriate to base the reaction rate expression on activities instead of concentrations of the reactants. Among others, Pohorecki and Moniuk (1988) have shown that the reaction rate for the reaction of a hydroxide ion with dissolved carbon dioxide is strongly influenced by the ionic strength of the solution. Moreover, Engel et al. (1995) have demonstrated that a very good correlation of experimental data for the hydrogenation of bicarbonate to formic acid and vice versa is obtained by using a kinetic relation based on activities.

10 10 log(k1,app) 8

6 Sankholkar, Sharma (1973) isobutene 4 Gehlawat, Sharma (1968) 2-butene Chwang (1978) 2 Lucas, Eberz (1934)

isobutene Knittel, Tidwell (1977) 0 isobutene 1-butene Knittel, Tidwell (1977) 2-butene -2 Knittel, Tidwell (1977) Taft (1952) 2-butene -4 Mehra (1988) Mehra (1988) -6 1-butene Deckwer/Popovic (1975) cis, trans Deckwer/Puxbaumer (1975) -8 2-butene Deckwer/Puxbaumer (1975) -10 -2024681012 -Ho

Figure 1 Apparent kinetic rate constants for the absorption of butenes in sulfuric acid solutions as reported in literature

As the major part of the literature data were obtained by absorption experiments and since it is shown that the absorption is substantially affected by the acid strength, the reactive absorption process is also studied theoretically in order to exclude possible disturbing influences of mass transfer limitations.

32 Chapter 2

2. Reaction mechanism and - kinetics

During the absorption of butenes in sulfuric acid solutions several reaction products can be formed; including alcohols, esters with sulfuric acid, ethers, sulphonic acids, oligomerisation and cracking products (Robey, 1941). The variety of reaction products formed depends severely on the butene used, acid strength, local mixing conditions and temperature. From the literature it can be concluded that these reactions proceed via the initial formation of a carbocation. This initial reaction step is generally assumed to be rate determining. Irrespective of the reactions following this initial step the protonation kinetics can, under certain conditions, be determined from butene absorption kinetics.

2.1 Reaction mechanism The mechanism of protonation reactions in homogeneous Brønstedt acid solutions has been discussed several times in literature. It can be concluded that no agreement exists on the exact mechanism. So far, the mechanism is claimed to proceed either via an A-1 or via an A-SE-2 mechanism. The A-1 mechanism was proposed for the protonation of isobutene by Taft (1952). In this mechanism no water is included in the transition state of the rate determining step, which was supported by a low entropy of activation for the hydration of isobutene.

Among others, Kresge et al. (1971) suggest that the protonation mechanism for simple olefins is the A-SE-2 mechanism. This suggestion is supported by experiments in which general acid catalysis was observed for the protonation of 2,3 dimethyl 2-butene and trans-cyclo octene. For both the A-

1 and the A-SE-2 mechanism it can be derived that, assuming elementary reaction steps, the reaction rate will be first order for the butene used and the proton(ating species) respectively. In literature the protonation reaction rate was found to be first order in the butene concentration in all cases.

2.2 Reaction Kinetics As concluded in section 2.1, the rate determining step for the hydration of olefins is the formation of an intermediate carbocation from the olefin and a proton or a proton donating compound. In describing reaction kinetics usually power-law reaction rate expressions are applied, based on the concentrations of the reactants involved. Considering the very pronounced dependency of the kinetics of protonation reactions on acid strength, the thermodynamic non-ideality of the acid

33 Chapter 2 solutions is probably the most important factor affecting the reaction kinetics. Several studies (e.g. Pohorecki and Moniuk, 1988; Engel et al., 1995) have shown that the conversion of concentration based reaction rate equations to activity based reaction rate equations reduced the scatter in correlating experimental data considerably for the thermodynamically non-ideal gas absorption processes.

This was also already recognized by Taft (1952), who found that describing the hydration kinetics for isobutene in aqueous nitric acid solutions with rate expressions using the concentrations of the reacting species (butene concentration, c B, and acid concentration, c A, respectively) only leads to acceptable results for very dilute acid solutions. Taft correlated his kinetic rate data successfully to the Hammett acidity function Ho for the acid solutions. Since the Hammett acidity function is an indicator for the protonating activity of the acid solution, this can be considered a first approximation to correct for the thermodynamic non-ideality of the solution.

Since the early work of Hammett et al. (1948) proton activities are generally indicated using an proton activity scale, determined experimentally by measuring the extent of ionization of inert, weak indicator bases with a well-known ionization constant. The originally proposed Hammett cancellation assumption was shown to be invalid, and more than one hundred different acidity scales have been developed and tabulated, of which the original Hammett Acidity function (Ho), based on nitroaniline indicators is most commonly used. Attempts to derive a more general acidity function, e.g. the Excess Acidity Function and the Bunnett-Olson method (Cox, 1983), supported by the observation that the different acidity scales approximately show a mutual linear dependency, have been developed, but this has not lead to a generally accepted result yet.

In this work an elementary bimolecular reaction is assumed between the butene and an acid compound (a proton or a proton donor). It is proposed that the reaction kinetics can be described using a reaction rate expression based on the activities of the reactants in the reaction mentioned above. In this case (which corresponds with an A-SE-2 mechanism) the rate expression becomes : * −=Rkaak++++ =γγ cckackc = = (1) B T BH T BH BH h HB 1,app B

In this expression kT represents the intrinsic kinetic rate constant, which no longer depends on acid concentration. The apparent first order reaction rate constant k1,app = kT⋅ aH+ ⋅ γB thus depends linearly on the proton activity and the activity coefficient of butene in the solution. Note that assuming an A-1 mechanism would lead to the same overall equations.

34 Chapter 2

The apparent first order rate constant k1,app is often found to be proportional to the Hammett acidity function 10 ∝− Ho (see Table I): logkHo1,app (2)

10 This result is consistent with the derivation given above, since −∝Holog() a + . H

In Table I the reaction rate expressions found in literature are summarized. From Table I and Figure 1 respectively, it can be concluded that the kinetic rate data reported in literature do not yield a consistent set of data for the observed dependency of the kinetic rate constants for the protonation of butenes in sulfuric acid solutions on acid strength. At high and low acid strength the protonation of trans-2-butene seems to become faster than the protonation of isobutene, which is rather unrealistic since a secondary instead of the more stable tertiary carbocation must be formed.

Table I Rate expressions for hydration of simple olefins in aqueous acid solutions

10 a alkene wt% H2SO4 T [K] log k1,app Method References ethylene 78 - 88 298 -1.54 ⋅ Ho - 14.8 1 Chwang et al., 1977 propylene 48 - 60 298 -1.39 ⋅ Ho - 8.62 1 Chwang et al, 1977 1-butene 30 - 50 303 -0.55 ⋅ Ho - 4.5 2 Deckwer,Puxbaumer, 1975 2-butenes 25 - 60 303 -0.55 ⋅ Ho - 3.5 2 Deckwer,Puxbaumer, 1975 cis-2-butene 48 - 58 298 -1.49 ⋅ Ho - 8.34 1 Chwang, Tidwell, 1978 trans-2-butene 48 - 58 298 -1.40 ⋅ Ho - 8.35 1 Chwang, Tidwell., 1978 2-butenes 70 - 80 301 -2.05 ⋅ Ho - 10.8 3 Sankholkar, Sharma, 1973 isobutene 49 - 70 303 -1.60 ⋅ Ho - 3.6 4 Gehlawat, Sharma, 1968 isobutene 10 - 50 303 -1.50 ⋅ Ho - 3.0 5 Deckwer et al., 1975 isobutene 0.1 - 1.5 M HNO3 soln. 298 -1.10 ⋅ Ho - 1.55 6 Taft, 1952 2-methyl-2-butene 61 - 75 301 -1.49 ⋅ Ho - 1.31 3 Sankholkar, Sharma, 1973 3-hexene (E) 48 - 58 298 -1.39 ⋅ Ho - 7.96 1 Chwang, Tidwell., 1978 3-hexene (Z) 48 - 58 298 -1.35 ⋅ Ho - 7.89 1 Chwang, Tidwell, 1978 cyclohexene 45 - 57 298 -1.28 ⋅ Ho - 7.35 1 Chwang et al., 1977 a Methods used are as follows: 1, slow reaction regimes (homogeneous liquid phase reaction), UV detection method; 2, reaction in the transition regime: homogeneous liquid phase reaction to ... (method 3); 3, pseudo first order reaction regime (E = Ha) using a stirred cell apparatus; 4, pseudo first order reaction regime (E = Ha) using a laminar jet apparatus; 5, reaction in the slow - and transition reaction regime, using a bubble column; 6, slow reaction regimes (homogeneous reaction), pressure decrease is measured 3. Theory

In gas absorption in which gas-liquid mass transfer is accompanied by a chemical reaction in the liquid phase the gas absorption rate may be enhanced significantly. Generally, for describing this effect the enhancement factor concept is applied, in which the enhancement factor, E, is defined as

35 Chapter 2 the ratio of the specific rate of gas absorption in a reactive liquid to the specific rate of absorption under identical conditions in a non-reactive liquid (physical mass transfer). Due to the importance of this enhancement factor for design purposes, several theoretical models have been developed to calculate this effect. Well known and frequently used one-parameter models are the film model, the Higbie penetration model and the Danckwerts surface renewal model. For several (asymptotic) cases analytical expressions have been derived for irreversible reaction kinetics, based on concentration based power law reaction kinetics (van Krevelen and Hoftijzer, 1948; Hikita and Asai, 1963; DeCoursey, 1974). A review of the approximate analytical solutions and numerical models for reversible reactions is given by van Swaaij and Versteeg (1992). The model equations derived for the description of absorption of olefins in acid solutions were solved numerically, using numerical techniques identical to those applied by Versteeg et al. (1989).

The absorption of butenes in sulfuric acid solutions, accompanied by the protonation reaction can + ⇔⇔+ be represented as follows: C48 H (G) + H (L) C49 H() L products () L In this theoretical part the experimental conditions of the absorption experiments are analyzed to assure that mass transfer limitations do not occur. In the experiments ambient temperature and moderately to highly concentrated fresh acid solutions are applied and the product loading of the solution at the end of the experiments is low (< 0.01 M). Considering that under these conditions isobutene nor tert-butanol can be extracted from the acid solution with inert solvents, it seems justified that a proton is bonded to the reaction products. The reaction can then be considered irreversible. Thus, the concentration based equilibrium constant for the protonation reaction was 9 chosen rather high (Keq,c = 10 [l/mol]). Schematically, the reaction system, as it was implemented → in the absorption model, is simplified to : B(G) + A(L) ← C(L )

In section 2.2 it was concluded that the reaction rate expression should be based on activities, in accordance with existing kinetic correlations for the isobutene-sulfuric acid reaction system.

3.1 Model equations In this study the processes of mass transfer accompanied by chemical reaction during gas absorption are modelled for the penetration theory of Higbie for the chemical system of the present work. The mass balance for each species is given by equation (3).

∂cxt(,) ∂c2 i =+i Di Ri with i = A, B, C (3) ∂t ∂x2

36 Chapter 2

Initially, the liquid phase only contains liquid phase reactant A (Acid) and contains no dissolved gasphase reactant B (Butene) nor product C.

I.C. t = 0 ∀xci (x,t) = 0 (i = B, C) bulk cA (x,t) = cA

The boundary conditions at the gas-liquid interface were obtained by assuming that A and C are non-volatile and by implementing continuity of mass flux for component B at the gas-liquid interface. ∂ct(,)00 He c (,) t  B.C. x = 0 t > 0 −=−D B kc BB  B ∂x gB,, Bg RT  ∂ct(,)0 −=D i 0 (i = non volatile components A,C) i ∂x Since the loading of the liquid phase is negligible during the absorption experiments, no significant variations of the liquid bulk phase composition occurs. Therefore, no material balance over the liquid bulk phase is required.

x = ∞ t > 0 ci (x,t) = ci,bulk = 0 (i = B, C) bulk cA (x,t) = cA

The reaction rate terms RA(x,t) = RB(x,t) = - RC(x,t) are assumed to be first order towards the butene activity (aB) and first order towards proton activity (aA) respectively, as given in equation (1*):

−= =γγ =* =⋅ RxtkaaBTBA(,) [] kTBABA [ cc ][] kachAB [] k1,app c B (1*) (,)xt (,)xt (,)xt (,)xt

10 From previous studies it was often found that log k1,app = a ⋅ (-Ho) + b , as can be seen in Table I. With (1*) the reaction rate expression becomes : {}−+ −=Rxtk(,)[]γγ cc =10aHoxtb(,) cxt (,) (4) B T ABAB(,)xt B With this, an expression for the product of the concentration based activity coefficients can be derived: −+ 10aHoxtb((,)) ()γγ = (5) AB(,)xt kcT A (,) xt Since the sparingly soluble gas phase component is assumed to have no influence on the local acidity, -Ho and (γA γB) will be an unique function of the local acid concentration cA. At infinite dilution (cA → 0) the acid concentration will be determined by the water dissociation equilibrium.

37 Chapter 2

# Writing equation (1*) as -RB(x,t) = kT [γB γA cB cA](x, t) = k (x, t) [cB cA ] (x, t) yields an expression which is very similar to the one for the well known situation of gas absorption followed by a bimolecular irreversible chemical reaction -RB(x,t) = k1,1 [cB cA ] (x, t) . The major difference is the apparent kinetic rate constant, k# (x, t), which now strongly depends on local liquid phase composition.

In this theoretical study the diffusion process is described using Ficks Law and in most of the calculations all diffusion coefficients are taken equal and constant. Considering the non-ideality of the liquid phase it would be appropriate to incorporate the effect of an activity gradient on the diffusion process. For binary systems the effect of an activity gradient can be described using a thermodynamic correction factor ΓI : Di = Di,o⋅ Γi = Di,o (1 + xi ⋅ d {lnγi} / d xi ).

Since no reliable activity models are available for the concentrated sulfuric acid solutions, the effect was approximated by treating sulfuric acid solutions as a binary mixture of water and the protonating agent sulfuric acid. The acid activity coefficient γΑ is now defined according to Eq. (5*). −+ 10 aHob() γ = (5*) A * kxhA

Using this approximation, the thermodynamic correction factor ΓA = (1+xA⋅d{lnγA}/dxA) is found to be approximately constant (10-15) for molfractions of H2SO4 > 0.15 (> 50 wt%). For a few cases this thermodynamic correction factor for the diffusion coefficient of the liquid phase reactant was implemented to study its effect.

The impact of the activity based reaction rate equation on the reactive absorption process has been studied by performing two types of simulations at identical bulk phase composition. One for the activity based rate equation, using the reaction rate expression given in equation (6-a) and one for the concentration based rate, given in equation (6-b). In the first case the apparent second order rate coefficient kT γA γB varies strongly with local liquid phase compositions, whereas in the latter case this rate coefficient is constant

−=γγ =aHob()−+ case I: RkBTABAB cc10 cB (6-a)

38 Chapter 2

()−+ 10 aHoc()A b γγ = with AB o (varies with local cA) kch A

−+ 10aHob() −=# # = case II: RkccBBA with k = constant (6-b) ()c A bulk

In absence of mass transfer limitations both rate expressions will yield the same result.

3.2 Results In the simulations where the effect of the activity based reaction rate equation is studied, in fact 10 only the value of the a-parameter in the (-Ho) vs. log (k1,app) correlation is relevant. This parameter solely represents the dependency of the local activity coefficients product on the local acid concentration. From Table I it is clear that this parameter varies in a rather narrow range. A value of 1.4 was selected for the simulations. In the simulations presented here the diffusion coefficients of the components A and B were taken equal, unless stated otherwise. The Hatta number, as defined in Table II for bulk liquid phase conditions, was varied in this study via the # reaction rate constants kT (Eq.6-a) and k (Eq.6-b).

In Figure 2 the enhancement factors, EB, for the absorption flux of gas phase component B calculated are plotted versus the Hatta number for reactant B. The Hatta numbers are calculated using liquid bulk phase conditions for the acid concentration cA. For case II, the open symbols in Figure 2, it is clear that at higher Hatta numbers the enhancement factor is no longer determined by reaction kinetics, but by diffusional mass transfer. This is the so-called instantaneous reaction regime, which is characterized by the infinite enhancement factor for irreversible reactions (Westerterp et al., 1984) :

  D Dc =+B  A A, bulk  (7) E B,∞ 1 i DA  DcBB 

39 Chapter 2

1000 EB = HaB EB, 00 =461

100

10 EB,oo = 5.6

1 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06

HaB

Figure 2 Enhancement factor vs. Ha-number for gas phase component B

open symbols, solid lines : concentration based reaction rate equation (case II) closed symbols, dashed lines : activity based reaction rate equation (case I )

For case II the EB - HaB curves can be predicted by the approximate solution methods for irreversible bimolecular reactions mentioned before. For the activity based reaction rate equation (case I) the calculated enhancement factors differ significantly from the curves obtained for case II. In bimolecular reaction systems for which an activity based reaction rate expression applies, the enhancement factors can therefore not be predicted from approximate or analytical solutions for irreversible bimolecular reactions. Two important effects can be distinguished from Figure 2.

First, it is clear that at high values for HaB the infinite enhancement factor calculated according to equation (7) is not reached (yet), not even for cases in which the kinetic rate constant is increased to values which are in order of magnitude of rate constants for diffusion controlled reactions in this system (109 [l/mole s] and higher). It can, therefore, be concluded that for this reaction system the infinite enhancement factor cannot be reached.

A second conclusion is of direct practical importance for interpreting experimentally determined absorption fluxes in order to obtain kinetic rate constants. In standard chemical engineering

40 Chapter 2 textbooks it can be found that kinetic absorption experiments for fast, bimolecular gas-liquid reactions should be carried out in the fast, pseudo first order regime (Westerterp et al., 1984). For this regime the experimentally determined enhancement EB equals the Hatta number. This line, EB =

HaB, is plotted in Figure 2. It can be seen from Figure 2 that the experimental operating window for kinetic experiments is significantly smaller for the system with the activity based rate equation; the dashed lines deviate at significantly lower HaB values from the EB=HaB line ( HaB/EB,∞ < 0.01 ).

Parts a-d of Figure 3 clearly show the difference in concentration profiles found for the components A and B in case I and II near the gas-liquid interface at the end of the contact time. Whereas for case II the instantaneous regime is reached for HaB/EB,∞ > 20, depletion of B near the gas-liquid hardly occurs in case of the activity based rate expression at identical bulk phase conditions. One may expect from these concentration profiles that the enhancement factor for case I may exceed the enhancement factor for case II, since there is less depletion of component A. However, this is not true !

From Figure 2 it is found that the enhancement factor for case I is significantly lower than the enhancement factor for case II. This can be explained by considering the activity profiles instead of the concentration profiles of component A near the gas liquid interface.

41 Chapter 2

HaB ≈ 0.3EB,inf

1.00 Case I 1.00 i Case I CB/CB A 0.80 0.80 A CA/CA,bulk Case II 0.60 0.60 Case II

0.40 0.40

0.20 0.20 B 0.00 0.00 0.0E+00 5.0E-05 1.0E-04 1.5E-04 0E+00 5E-06 1E-05 x (µm) x (µm)

(a) (b)

HaB ≈ 50 EB,inf

1.00 1.00 C /C i Case I B B A Case I 0.80 0.80 CA/CA,bulk A 0.60 0.60 Case I 0.40 0.40

0.20 0.20 B Case II Case II Case II A 0.00 0.00 0.0E+00 5.0E-05 1.0E-04 1.5E-04 0E+00 2E-06 4E-06 µ x (µm) x ( m) (c) (d)

Figure 3 Concentration profiles components B (gas phase) and A (liquid phase) in the mass transfer zone near the gas-liquid interface. In Figures b and d the region at the gas-

liquid interface is presented in more detail. EB,∞ is calculated according to Equation (7)

Case I: activity based reaction rate equation Case II: concentration based reaction rate equation

In the Figures 4-a and 4-b generalized curves are created for both the irreversible bimolecular (1,1) reaction (case II) and for reaction rate equation based on activities (case I). In these plots the Hatta number and the enhancement factors are scaled to the infinite enhancement factor as calculated by equation (7) for bulk liquid phase conditions. These generalized curve seems valid (within a few

percent accuracy) for not too low values of the infinite enhancement factor (EB,∞ > 10). This result is not surprising for case II, considering the approximate analytical solutions mentioned. For case I, however, it also seems possible to create such a generalized curve for the reaction system considered.

42 Chapter 2

1 (E -1) / (E -1) 0.9 B B,oo

0.8

0.7

0.6 EB,oo 5.63 0.5 47.204 0.4 463 4621 0.3 46211

0.2

0.1

0 0.001 0.01 0.1 1 10 100 1000 HaB / EB,oo

Figure 4-a A generalized curve for (1,1) reactions with a concentration based reaction rate expression

In constructing Figure 4-b, EB,∞ was calculated using equation (7) and varied by changing the i concentration of B at the gas-liquid interface, cB . Again it is clear that even for large ratios of

5 HaB/EB,∞ (> 10 ) the infinite enhancement factor will not be reached.

1 (EB-1/(EB,oo-1) 0.9

0.8

0.7

0.6

0.5

0.4 EB,oo 0.3 461 0.2 47 5.7 0.1

0 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000

HaB / EB,oo

Figure 4-b A generalized curve for reactions with an activity based reaction rate expression

E B,∞ is calculated according to equation (7)

43 Chapter 2

In a few simulations the diffusion coefficient of the acid was increased by a factor 10 and 100 to account for the effect of the non-ideality of the acid solution on the diffusion process, as explained in Section 3.1. As expected the operating regime is enlarged since DA directly influences the infinite enhancement factor according to equation (7). Calculated enhancements did follow the generalized curve presented in Figure 4-b.

4. Experimental work

The absorption experiments in the slow reaction regime were carried out using an intensely stirred gas-liquid reactor, equipped with a gas-inducing stirrer. The reactor used was operated batch wise for the gas phase and the liquid phase (full batch experiment).

The experiments in the fast pseudo first order regime (EB = HaB ; HaB > 3 and HaB/EB,∞< 0.01, see Section 3) were carried out in a stirred cell contactor with a flat interface. The stirred cell set-up (Figure 5) was operated using the liquid phase loaded batchwise in all experiments.

PI PI gas out, to vacuum liquid in gas phase storage

liquid out

Figure 5 Setup with stirred cell apparatus (total volume 1050 ml, S = 71.0 cm2 )

44 Chapter 2

The gas phase was used batch wise (at low fluxes) and semi batchwise at high absorption rates. In the full batch experiments the absorption rate was registrated from pressure drop versus time in the stirred cell using a personal computer for data acquisition. In the (gas phase) semi-batch mode the reactor pressure was kept constant at an operating pressure in the range of 5 - 1000 mbar (± 0.3 mbar), using a PID controller reading the actual reactor pressure from a sensitive pressure indicator and regulating the gas phase mass flow to the stirred cell through a mass flow controller. Temperature of the (bulk) liquid phase was kept constant at 293.15 K (± 0.1 K). Absorption rates were determined by registrating the pressure drop versus time in the gas phase storage vessel.

For the gas phase the assumption of ideal gas phase behavior is valid for the semi-batch experiments at partial pressures below 5.104 Pa. For batch experiments in the slow reaction regime (at approximately 0.9 bar) the non-ideal behavior of the gas phase was taken into account. The change of the compressibility factor z in PV = z⋅RT could safely be neglected over the pressure drop during the experiment.

From mass balances for the gas and liquid phase the absorption flux can be related to the intrinsic reaction kinetics. The equations used for PB - t data interpretation are listed in Table II. The experimental procedures were tested successfully and the setups were characterised by physical absorption experiments of carbon dioxide and butenes in water and measuring reaction kinetics for carbon dioxide absorption in alkanol amine solutions. From these experiments was concluded that kinetic absorption experiments could be carried out.

Chemicals Acid solutions of different strengths were composed from 96 wt% pro analyses sulfuric acid (Merck) and demineralized water. Acid strength was determined accurately using a standard NaOH titration method with a Mettler DL25 Titrator. For the experiments freshly prepared (unloaded) acid solutions were used, since the presence of butanol will influence both the solution acidity as well as the butene solubility (Friedrich, 1981,1984). Trans-2-butene (quality 1.5) and isobutene (quality 2.3) were purchased from Praxair. Impurities in trans-2-butene consist merely of isobutene (2.5%) and butanes (2.0%). Since the absorption of isobutene is much faster (about a factor 1000) than that of trans-2-butene, only full-batch experiments were performed with trans-2-butene. The initial rapid decrease of the reactor pressure was attributed to the presence of isobutene and was

45 Chapter 2 quantitatively in line with the initial amount of the isobutene in the gas phase and experimentally determined specific absorption rates for isobutene under the reaction conditions involved.

Table II Time-pressure correlations for interpretation of absorption fluxes

Reaction regime Criteria Mode of operation / time-pressure correlation

≤ slow bulk liquid Ha B 0.2 gas- and liquid phase filled batch wise   2 PtB() 1 VL phase reaction ()AL −1 Ha << 1 ln  =−m t B = B 11  PtB()0  + VG kaLapp k1,

liquid phase in batch, gas phase :

 Pt()  S ≤ ≤  B  =− fast pseudo first 2 Ha B E A,∞ - batch wise ln = mkBappB1, D t  PtB()0  Vg V dP P sv Bsv, =− rB, order regime - Semi batch: mkBappB1, D St RTsv dt RT

k D =>1,app B with HaB 1 (Hatta number) kLB,

Vbulk AL = (Hinterland ratio) Vfilm

5. Physico-chemical parameters

Since sulfuric acid solutions are highly non-ideal and the protonation of butenes is relatively fast, physico-chemical parameters as the diffusion coefficient and the solubility of butenes in sulfuric acid solutions are difficult to obtain experimentally. An (iso-)butane-(iso)butene analogy is therefore proposed, similar to the well known N2O - CO2 analogy applied for estimating CO2 solubility and diffusivity in aqueous alkanolamine solutions (Laddha et al., 1981).

46 Chapter 2

Solubility The solubility of gaseous butenes in sulfuric acid solutions can be determined directly from experiments in case of absorption experiments in the slow reaction regime (Ha < 0.2) from the initial pressure decrease in the batch reactor or by the bromide-bromate method (Lucas and Eberz, 1934). At higher acid concentrations direct measurement of butene solubility is no longer possible. At low acid concentrations a common salting-out behavior is found for most substances in aqueous sulfuric acid solutions. At higher acid concentrations (from 30 wt%) the Setchenow equation does not hold any longer and salting-out is overestimated by a Setchenow equation (Friedrich et al., 1981). Moreover, at higher acid concentrations (> 50wt%) even salting-in will occur. This effect was recognized by several authors (Friedrich et al., 1981; Sanders, 1985).

Rudakov et al. (1989) proposed a correlation for estimating the solubility of gaseous components in aqueous sulfuric acid solutions of 0-100 wt%. This correlation, based on experimental data for 9 inert components including isobutane, isopentane, cyclopentane and methane was used to estimate the isobutene and trans-2-butene solubility in sulfuric acid solutions of different strength. For additional, more detailed information the reader is referred to Chapter I of this thesis.

Diffusion coefficient The liquid phase diffusion coefficient of gaseous solutes in electrolyte solutions strongly depends on the liquid phase viscosity. For a large number of electrolyte solutions the experimentally determined Fick diffusion coefficients of several gases can be reasonably correlated (at constant temperature) to viscosity by a modified Stokes-Einstein equation:

D⋅η0.6 = constant (8)

This correlation was tested for CO2 in sulfuric acid solutions (Brilman, 1998). Up to 84 wt% Equation (8) seems to hold. At higher acid strengths (86, 90 and 96 wt%) the diffusion coefficient -9 2 of CO2 was approximately constant at 0.2 10 m /s. For the butenes the same ratio D/DH2O = 0.1 was assumed in this range.

47 Chapter 2

6. Absorption experiments

6.1 Absorption of isobutene The absorption of isobutene in sulfuric acid solutions was studied in the range 30-98 wt% sulfuric acid, using the stirred cell set-up. The absorption fluxes were independent of the stirrer speed, which was varied over the range 30 - 66 rev/min (kL increases approximately with 40%). The standard deviation for the absorption fluxes was usually within 5%, except for the experiments at 96 wt% where the standard deviation was 20%. The reaction is apparently first order in isobutene, since the specific rate of absorption was found to be proportional to the partial pressure of isobutene. This result is in accordance with previous studies of Taft (1952) and Gehlawat and Sharma (1968).

Derivation of the kinetic rate constants from absorption fluxes introduces some uncertainties with respect towards the physico-chemical data used (solubility, diffusivity) used. For comparison with literature data it is therefore more appropriate to compare directly the absorption fluxes. The obtained absorption fluxes coincide with the existing data of Gehlawat and Sharma (1968) (see Figure 6). The experimentally determined specific absorption fluxes are reported in Table III.

1.0E+01 J [mol/m2 bar s] 1.0E+00

1.0E-01

1.0E-02

1.0E-03 laminar jet, T = 303 K, (Gehlawat, Sharma, 1968)

extrapolated values to T = 293 K; (Gehlawat,Sharma, 1968) 1.0E-04 batch experiments, initial rate at P =1 atm. (this work)

semi-batch experiments, P = constant < 1 bar (this work) 1.0E-05 23456789101112 - Ho

Figure 6 Comparison of absorption flux data for isobutene in sulfuric acid solutions at 293 - 303 K

48 Chapter 2

Table III Absorption fluxes for isobutene in sulfuric acid solutions at 293.1 K

2) 2) 3) wt% reaction regime PB mk1,app D m D k1,app 2 1) 9 2 H2SO4 [10 Pa] [m/s] [-] [10 m /s] [1/s]

40.5 fast pseudo 1 order 500 1.16⋅10-6 0.056 0.49 9.10⋅10-1 45.2 fast pseudo 1 order 400 3.42⋅10-6 0.053 0.45 3.00⋅10 0 48.9 fast pseudo 1 order 1000 4.25⋅10-6 0.055 0.41 1.53⋅10 1 54.0 fast pseudo 1 order 1000 6.26⋅10-6 0.051 0.37 4.10⋅10 1 56.5 fast pseudo 1 order 140 1.06⋅10-5 0.051 0.35 1.30⋅10 2 61.9 fast pseudo 1 order 1000 1.68⋅10-5 0.051 0.30 3.66⋅10 2 62.5 fast pseudo 1 order 1000 2.59⋅10-5 0.051 0.30 8.81⋅10 2 64.1 fast pseudo 1 order 90 4.40⋅10-5 0.048 0.28 2.93⋅10 3 67.1 fast pseudo 1 order 90 5.91⋅10-5 0.049 0.27 5.46⋅10 3 71.6 fast pseudo 1 order 14 2.18⋅10-4 0.055 0.21 7.37⋅10 4 75.5 fast pseudo 1 order 70 2.64⋅10-4 0.063 0.18 9.70⋅10 4 76.0 fast pseudo 1 order 30 3.25⋅10-4 0.064 0.18 1.70⋅10 5 80.2 fast pseudo 1 order 40 1.66⋅10-3 0.081 0.15 2.00⋅10 6 86.0 fast pseudo 1 order 18 4.5 ⋅10-3 0.13 0.10 1.50⋅10 7 88.3 fast pseudo 1 order ? 20 7.7 ⋅10-3 0.16 0.10 2.30⋅10 7 96.0 fast pseudo 1 order ? 4 - 32 3.5 ⋅10-2 0.59 0.10 3.50⋅10 7 98 fast pseudo 1 order ? 10 6 ⋅10-2 0.98 0.10 3.60⋅10 7 Notes

1) Reported fluxes are taken from semi-batch experiments at given partial pressures, except for the experiments at “1000 mbar” where initial absorption fluxes are taken from batch experiments 2 3 Reported flux: the specific molar absorption rate in [mol/m s] at 1 mol/m gas phase concentration 2) Estimated using an isobutene-isobutane analogy (Brilman, 1998) 3) Assuming that the conditions for the fast pseudo first order reaction regime are fulfilled

In the estimation of the physico-chemical parameters the possible errors made, though probably up to 100% for solubility and diffusivity, are small with respect to the variation of the calculated kinetic rate constants with changing acid strength (k1,app varies over more than 10 decades ! ). Using the isobutane-isobutene analogy for the interpretation of the flux data of Gehlawat and Sharma (1968) together with additional flux data determined in this study and incorporating data of other authors for the homogeneous reaction regime a fairly good correlation of kinetic rate constants with the Hammett acidity function is obtained, as can be seen in Figure 7, using the

10 following correlation: log k1,app = a ⋅ (-Ho) + b The kinetic rate constants thus determined in the enhanced mass transfer regime are found to be consistent with data, available from literature, for the slow reaction regime (homogeneous liquid phase reaction). The best overall correlation for k1,app at 293 K is given by equation (9).

10 log k1,app = -1.35 ⋅ Ho - 3.3 (9)

49 Chapter 2

10.0 10 log(k1,app) recalculated, see Table V 8.0 ( )( ) assuming E = Ha 6.0

4.0

2.0 Gehlawat, Sharma (1968)

(E = Ha) (this work) 0.0 Lucas, Eberz (1934)

Knittel, Tidwell (1977) -2.0 Taft (1952)

-4.0 Mehra (1988) Deckwer/Popovic (1975) -6.0 -2024681012 -Ho

Figure 7 Correlation of kinetic rate constants for the protonation of isobutene in sulfuric acid solutions at 293 K.

6.2 Absorption of trans-2-butene

The protonation of trans-2-butene was studied in the slow reaction regime (HaB < 0.2) and in the fast pseudo-first order reaction regime (HaB > 2). The intensely stirred tank reactor could be operated in the slow reaction regime for acid concentrations up to 60% sulfuric acid. The rate of trans-2-butene absorption was found to depend linearly on the butene partial pressure. From the initial pressure drop in each experiment the solubility of trans-2-butene under the reaction conditions was determined with an accuracy of 5%. The experiments in the stirred cell setup at acid concentrations of more than 70 wt% sulfuric acid showed that the specific rate of absorption was independent of the stirring speed which was varied within the range 30 - 80 rev/min. Experimentally determined absorption fluxes for the fast reaction regime and estimated kinetic rate constants for the slow reaction regime are listed in Table IV. The standard deviation for the absorption fluxes is less than 5%.

50 Chapter 2

Table IV Absorption fluxes for trans-2-butene in sulfuric acid solutions at 293.1 K

1) 2) 2) wt% reaction regime PB mk1,app D m D k1,app 2 3) 9 2 H2SO4 [10 Pa] [m/s] [-] [10 m /s] [1/s]

30.0 slow reaction 0.070 5.43⋅10 -7 45.0 slow reaction 0.057 2.17⋅10 -5 50.0 slow reaction 0.055 5.89⋅10 -5 54.0 slow reaction 0.054 4.18⋅10 -4 61.4 slow reaction 0.053 2.22⋅10 -2 71.4 fast pseudo 1 order < 150 9.72⋅10-7 0.054 0.22 1.50 78.9 fast pseudo 1 order < 90 7.52⋅10-6 0.066 0.16 8.12⋅10 1 86.0 fast pseudo 1 order < 65 8.67⋅10-5 0.11 0.1 6.46⋅10 3 90.0 fast pseudo 1 order < 30 4.00⋅10-4 0.18 0.1 4.90⋅10 4 96.0 fast pseudo 1 order < 10 2.71⋅10-3 0.56 0.1 2.51⋅10 5

Notes

1) Absorption experiments performed in a stirred cell contactor with flat interface (fast pseudo first order regime) and an intensely stirred tank reactor (slow reaction regime). 2) Italic printed values are obtained by estimation using an 2-butene-isobutane analogy 3) 2 3 The specific molar absorption rate in [mol/m s] at 1 mol/m gasphase concentration

The absorption fluxes of Sankholkar and Sharma (1973) are not completely consistent with the present data. Possibly due to the fact that Sankholkar and Sharma produced their own butenes, in which some isobutene may have been present which is much faster reacting, by dehydration of sec- butylalcohol. A few percent of isobutene (2-3%) can already account for the observed difference.

Experimental data from this work for the homogeneous regime as well as for the fast pseudo first order regime (EA=HaA) could be correlated fairly good with the Hammett acidity function, see Figure 8. These data are in accordance with data of Knittel and Tidwell (1977), Chwang et al. (1978) and Mehra (1988). The data do not confirm the measurements by Deckwer and Puxbaumer (1975). Considering the relatively short measurement times applied by Deckwer and Puxbaumer, the deviating results are probably caused by the presence of a minor amount of isobutylene in the 1- and 2-butenes used. Their data set seems in conflict with most other data available in literature

(Figure 1) and was therefore left out of Figure 8. The overall correlation for k1,app (at 293 K) is found to be :

10 log k1,app = -1.5 ⋅ Ho - 9.0 (10)

51 Chapter 2

8 trans-2-butene (homogeneous) (this work) 6 10 trans-2-butene (E=Ha) (this work) logk1,app Sankholkar, Sharma (1973) 4 Chwang (1978)

2 Knittel, Tidwell (1977)

Knittel, Tidwell (1977) 0 Mehra (1988) -2

-4

-6

-8

-10 012345678910 -Ho

Figure 8 Correlation of kinetic rate constants for the protonation of trans-2-butene in sulfuric acid solutions at 293 K.

6.3 Analyzing the absorption experiments From the modeling study it is now clear that the conditions for operation in the fast, pseudo first order absorption regime are more stringent than on beforehand was expected. For the full batch experiments the equations in Table II can be used to obtain an indication of the upper partial pressure of the butene used for which this equation holds. Indications for these pressures are given in Table IV for trans-2-butene. For isobutene it was not possible to conduct reliable full batch experiments for acid concentrations exceeding 86 wt%. For full batch experiments at 76 and 86 wt% the upper partial pressure for the pseudo first order regime, experimentally determined at approximately 115 mbar and 10 mbar were reasonably estimated as 110 and 4 mbar respectively, by using DB⋅ΓB =10⋅DA and the criterion HaB < 0.01⋅EB,∞. For the absorption experiments using the 64 wt% acid solution the experimentally determined upper limit (250 mbar) was more stringent than the one calculated (≈1000 mbar). The isobutene solubility at this acid concentration might be somewhat underestimated. For trans-2-butene it is found that the experimentally determined upper operating pressures for kinetic experiments using 71, 79 and 86 wt% acid solutions (150, 90 and 65 mbar, see Table IV) are significantly lower than the ones determined by the estimation method mentioned (>>1000 mbar

52 Chapter 2

, >> 1000 mbar and 700 mbar respectively). At 90 and 96 wt% acid concentrations these upper partial pressures are reasonably predicted, 74 and 4 mbar, when compared to the experimentally found values of 35 and 15 mbar. Probably the solubility of the butene is somewhat underestimated in the intermediate regime 50-85 wt% and somewhat overestimated in the high acid regime (> 90 wt%).

Using the kinetic rate constant correlations Eq. (9) and Eq. (10) for isobutene and trans-2-butene respectively, the values of HaB/EB,∞ at bulk phase conditions can be estimated. In Table V this criterion is evaluated for the experimental conditions, using a conservative estimation for the diffusion coefficient of the acid component; DA = DB. From the full batch experiments for trans-2- butene absorption in 96 wt% sulfuric acid solution and for isobutene in 86 wt% sulfuric acid solution it is likely that DA >> DB.

Table V Analysis of absorption experiments for trans-2-butene and isobutene absorption in sulfuric acid solutions of different strength

3) Butene wt% HaB Pexp HaB/E∞,B (cA)i / (cA)bulk (-Ho)i H2SO4 [bar] trans-2- butene 71.4 2.2 <150 1) 6.0⋅10-5 78.9 17 < 90 1) 3.9⋅10-4 86.0 1.6⋅102 < 65 1) 4.4⋅10-3 90.0 6.3⋅102 < 30 1) 1.2⋅10-2 96.0 3.7⋅103 < 15 1) 9.8⋅10-2 isobutene 64.1 1.2⋅102 90 2) 2.3⋅10-3 71.6 4.0⋅102 14 2) 1.7⋅10-3 76.0 1.7⋅103 30 2) 1.1⋅10-2 1.0 80.2 4.8⋅103 40 2) 5.0⋅10-2 1.0 86.0 2.8⋅104 18 2) 1.9⋅10-1 0.98 8.1 88.3 5.5⋅104 20 2) 6.0⋅10-1 0.94 7.9 96.0 4.6⋅105 4 2) 1.0⋅10 1 0.86 7.9 98 6.4⋅105 10 2) 2.4⋅10 1 0.82 7.7

Notes: 1) Upper partial pressure of B in the stirred cell for the kinetic regime 2) Partial pressure of B in the semi-batch experiments used. 3) EB,∞ is calculated according to equation (7), assuming DA = DB. This is the maximum HaB/EB,∞ value for the full batch experiments (trans-2-butene)

53 Chapter 2

Using the estimated HaB/EB,∞ values and the generalized curve for this reaction system (Figure 4-b) a value for the ratio (EB - 1)/(EB,∞-1) can be found. Using the van Krevelen-Hoftijzer approach (Westerterp et al., 1984)

()cA EE∞ − i = BB, − (11) ()c EB,∞ 1 A bulk

the acid concentration at the gas liquid interface, (cA)i , can now be estimated. In Table V this is done for isobutene absorption experiments at high acid concentrations. Using these acid concentrations the ‘interface acidity’ (-Ho) i can be calculated. In Figure 7 the calculated rate constants for these acid concentrations are now plotted at their interface acidity (which is the apparent acidity in the reaction zone for the butene component). For the experiments at 96 and 98 wt% H2SO4 the original datapoints at the bulk liquid phase acidity are plotted within brackets.

54 Chapter 2

7. Conclusions

For isobutene and trans-2-butene the protonation kinetics for sulfuric acid solutions up to 98 wt% were studied. Linear correlations of the apparent first order rate constant with Hammett Acidity function Ho were found to be valid up to 90 wt% sulfuric acid solutions. This result supports the idea that reaction kinetics for this type of reaction should be based on the activities of the reacting species.

In modeling the reactive absorption processes an activity based reaction rate expression was used. It is not possible to carry out experiments in the instantaneous reaction regime. Moreover, in the simulations, even for Hatta-numbers which exceed the theoretical infinite enhancement factor from the penetration model by a factor 106, this was not accomplished.

It should be noted that the criteria usually used for the pseudo first order reaction regime are not satisfactory to assure kinetic measurements (see also Versteeg et al. (1989)), since it was shown that the application of the activity based reaction rate equation resulted in a more stringent criterion for the kinetic absorption experiments; HaB < 0.01⋅EB,∞ , which implies a smaller operating window

Using a relatively simple activity model, the experimentally determined mass transfer enhancement factors could be reasonably predicted by the absorption model developed from kinetic experiments conducted under well-known reactions conditions, i.c. experiments in the homogeneous reaction regime or the fast pseudo-first order reaction regime.

Acknowledgments These investigations were supported by the Shell Research & Technology Centre Amsterdam (The Netherlands). The author wishes to thank B. Knaken for constructing the experimental set-ups and F. de Jager, I.M.R. Lemmens, L.H. Oberink and C.J.D. Zwart for their contributions to the experimental work.

55 Chapter 2

Notation ai Activity of component i [mol/l] AL Hinterland ratio [-] ci Concentration of component i [mol/l] 2 Di Diffusion coefficient component i [m /s] 2 Di,o Diffusion coefficient component i at infinite dilution [m /s] EB Enhancement factor for gas-liquid mass transfer of component B [-] EB,∞ Infinite enhancement factor for component B, defined in Eq. (7) [-] HaB Hatta number for component B [-] 3 HeB Henry’s Law constant for component B [mol/m Pa] 10 Ho Hammett Acidity Function (Ho = - log(aH+)) [-] Keq,c Concentration based equilibrium constant, = cC / cA⋅cB [l/mol] st k1,app Apparent 1 order reaction rate constant, defined in Eq. (1) [1/s] kG Gas phase mass transfer coefficient [m/s] * kh Reaction rate constant, = kT⋅γB [l/mol s] kL Liquid-side mass transfer coefficient [m/s] kLa Volumetric, liquid side mass transfer coefficient [1/s] kT Reaction rate constant [1/s] # k Reaction rate constant, = kT⋅γB⋅γA [l/mol s] i mB Distribution coefficient for gas phase component B, mB = (cB,L / cB,G) [-] PB Partial pressure component B [Pa] R Molar gas constant (= 8.314) [J/mol K] 3 Ri Volumetric reaction rate for component i [mol/m s] S Geometric surface area of stirred cell apparatus [m2] t Time [s] T Temperature [K] V Volume [m3] x place coordinate [m]

Greek symbols

γi (concentration based) Activity coefficient of component i [-] Γi Thermodynamic correction factor for the diffusion equation [-] η Viscosity [kg/ms] sub- and superscripts A reactant originating from liquid phase (Acid) B reactant originating from the gas phase (Butene) bulk liquid bulk phase conditions film mass transfer zone at gas-liquid interface G gas phase H+ proton i at the gas-liquid interface L liquid phase r reactor conditions sv conditions in the gasphase storage vessel (for gas in semi-batch experiments)

56 Chapter 2

References

Brilman D.W.F., 1998, On the estimation of the diffusion coefficient and solubility of isobutene and trans-2-butene in aqueous sulfuric acid solutions, University of Twente [Chapter 1 of this thesis]

Chwang, W.K.; Nowlan, V.J.; Tidwell, T.T., 1977, Reactivity of cyclic and acyclic olefinic hydrocarbons in acid-catalyzed hydration, J.Am.Chem.Soc., 99, 7233-7238

Chwang, W.K.; Tidwell, T.T., 1978, Rates of Acid-Catalyzed Hydration of Isomeric Z/E Alkenes. Effects of Steric Crowding on Additions to Alkenes, J.Org.Chem., 43, 1904-1908

Cox, R.A.; Yates, K., 1987, Acidity Functions: an update, Can.J.Chem., 61, 2225-2243

Deckwer, W.-D.; Puxbaumer, H., 1975, Absorptionsdaten für 1- und 2-Buten in Schwefelsäure, Chemie-Ing.-Techn, 47, 163 (MS 194/75)

Deckwer, W.-D; Popovic, M.; Allenbach, U., 1975, Rate constants of the sulfuric acid catalyzed hydration of isobutene from bubble column studies, React.Kin Cat.Lett., 3, 449-454

DeCoursey W.J., 1974, Absorption with chemical reaction: development of a new relation for the Danckwerts model, Chem.Eng.Sci., 29, 1867-1872

Eigen, M., 1963, Protonenübertragung, Säure-Base-Katalyse und enzymatische Hydrolyse. I. Elementarvorgänge, Angew. Chem., 75, 489-508.

Engel, D.C.; Versteeg, G.F.; van Swaaij, W.P.M., 1995, Reaction kinetics of hydrogen and aqueous sodium and potassium bicarbonate catalysed by palladium on activated carbon, Trans.I.Chem.E. 73(A), 701-706

Friedrich, A.; Warnecke, H.; Langemann, H., 1981, Solubility of isobutene in sulfuric acid-tert- butyl alcohol-water mixtures, Ind.Eng.Chem.Process.Des.Dev., 20, 401-403

Friedrich, A.; Warnecke, H.-J.; Langemann, H., 1984, Die Hammettsche Aciditätsfunktion von Schwefelsäure in Wasser-t-Butanol-Lösungen, Z.Phys.Chemie (Leipzig),265, 11-16

Gehlawat, J.K.; Sharma, M.M., 1968, Absorption of isobutene in aqueous solutions of sulfuric acid, Chem.Eng.Sci.,23, 1173-1180,

Hammett L.P., Deyrup A.J., 1932, A series of simple basic indicators. I. The acidity functions of mixtures of sulfuric and perchloric acids with water, J. Am. Chem. Soc.,54, 2721-2739

Hikita, H.; Asai, S., 1963, Gas absorption with (m,n)-th order irreversible chemical reaction, Kagaku, Kogaku, 11, pp.823-830

Knittel, P.; Tidwell, T.T., 1977, Acid-catalyzed hydration of 1,2 disubstituted alkenes, J.Am.Chem.Soc., 99, 3408-3414

57 Chapter 2

Kresge, A.J.; Chiang, Y.; Fitzgerald, P.H.; McDonald, R.S.; Schmid, G.H., 1971, General Acid Catalysis in the Hydration of Simple Olefins. The Mechanism of Olefin Hydration, J.Am.Chem.Soc., 93, 4907-4908 van Krevelen, D.W.; Hoftijzer, P.J., 1948, Kinetics of gas-liquid reactions. Part I: General Theory, Rec.Trav.Chim.,67, 563-586

Laddha, S.S.; Diaz, J.M.; Danckwerts, P.V., 1981, The N2O analogy: the solubilities of CO2 and N2O in aqueous solutions of organic compounds, Chem.Eng.Sci, 36, 226-230

Lucas, H.J.; Eberz, W.F., 1934, The hydration of unsaturated compounds. I. the hydration rate of isobutene in dilute nitric acid, J.Am.Chem.Soc., 56, 460-464

Mehra, A.; Pandit, A.; Sharma, M.M., 1988, Intensification of multiphase reactions through the use of a microphase-II. Experimental, Chem.Eng.Sci.,43, 913-927

Pohorecki, R.; Moniuk, W., 1988, Kinetics of reaction between carbon dioxide and hydroxyl ions in aqueous electrolyte solutions, Chem.Eng.Sci., 43, 1677-1684

Robey, R.F., 1941, Reaction products of olefins with sulfuric acid, Ind.Eng.Chem., 33, 1076-1078

Rudakov, E.S.; Lutsyk, A.I.; Suikov, S.Yu., 1987, Extremal change in solubility of non-electrolytes in the water-sulfuric acid system (0-100% H2SO4). Modification of the Sechenov equation, Russ.J. Phys.Chem., 61, 601-607

Sanders S.J., 1985, Modeling Organics in Aqueous Sulfuric Acid Solutions, Ind.Eng.Chem.Process Des.Dev., 24, 942-948

Sankholkar, D.S.; Sharma, M.M., 1973, Absorption of 2-butene and 2-methyl-2-butene in aqueous solutions of sulfuric acid, Chem.Eng.Sci., 28, 49-54 van Swaaij, W.P.M.; Versteeg, G.F., 1992, Mass transfer accompanied with complex reversible chemical reactions in gas-liquid systems: an overview, Chem.Eng.Sci., 47, 3181-3195

Taft, R.W., 1952, The dependence of the rate of hydration of isobutene on the acidity function Ho and the mechanism for olefin hydration in aqueous acids, J.Am.Chem.Soc., 74, 5372-5376

Versteeg, G.F.; Kuipers, J.A.M; van Beckum, F.P.H.; van Swaaij, W.P.M., 1989, Mass transfer with complex reversible chemical reactions - I. Single reversible chemical reaction, Chem.Eng.Sci., 44, 2295-2310

Westerterp, K.R.; van Swaaij, W.P.M.; Beenackers, A.A.C.M., 1984, Chemical reactor design and operation, Wiley, New York

58 CHAPTER 3

The Koch synthesis of Pivalic Acid from isobutanol using sulfuric acid as catalyst

Abstract

The reaction kinetics for the Koch synthesis of Pivalic Acid from isobutanol in the presence of a sulfuric acid catalyst have been studied. Since the reaction kinetics depend strongly on the acidity of the catalyst solution and were found to be independent of carbon monoxide partial pressure (within the experimental range) it is concluded that the formation of a carbocation (by dehydration or alkylsulfate hydrolysis) is the rate determining step in this reaction. Main byproduct formed is 2-methylbutanoic acid. The selectivity to this product decreases with decreasing acidity.

The presence of Pivalic Acid and isobutanol in the catalyst solution drastically decreases the reaction rate. For Pivalic Acid this effect was shown to be caused by a decrease of the Hammett Acidity for the catalyst solution. For the industrially applied backmixed reactors, this may imply that they operate at a considerable lower acid strength than may be expected by the initial catalyst composition.

59 Chapter 3

60 Chapter 3

1. Introduction

In 1955 Herbert Koch published a pioneering study on the synthesis of tertiary carboxylic acids (having a quaternary C-atom) from olefins, carbon monoxide and water (Koch, 1955).

R" C R'

COOH

Figure 1 General structure of tertiary carboxylic acids

Using a strong homogeneous acidic catalyst solution, the carboxylic acids could be produced at relatively mild conditions (10-100 bar CO partial pressure, 273 - 373 K). Formerly, this was only achieved at more severe conditions (400-600 K, 500 - 1000 bar CO partial pressure).

The vinyl esters of these tertiary carboxylic acids are (specialty) intermediates for the production of resins and lacquers. Owing to the sterical hindrance around the ester bond an excellent thermal stability and resistance to hydrolysis is obtained. Other applications of Koch acids are found in the production of agrochemicals, cosmetics and medical applications (Ullmann, 1986) (Falbe, 1980).

The carboxylic acids are produced from an alkene (or alcohol), carbon monoxide and water, in the presence of a strong acid. Several Brønstedt acids and Lewis acids have been applied as catalyst

(Falbe, 1980). Especially mixtures of BF3 with a Brønstedt acid are attractive for industrial application, since these acid mixtures do not require a re-concentration step and recycling the catalyst solution is straightforward. Concentrated sulfuric acid has been frequently used in lab-scale studies, but its use on industrial scale, however, is restricted because the extraction of the products can only be realised if the acid solution is diluted. Usually, an additional concentration step for the catalyst solution is then required before reuse. However, an economically attractive solution for this was claimed (Kawasaki, 1991). Despite some disadvantages, in this work the relatively well known sulfuric acid system will be used as catalyst system.

61 Chapter 3

Generally, the reaction is operated as gas-liquid-liquid reaction system since the reactants originate from different phases; carbon monoxide as gas phase reactant, the alkene is introduced as organic liquid phase and water and the catalyst are present within the aqueous catalyst phase. Depending on the process operating conditions, the Koch acids produced will be transferred to the organic phase. Due to parallel-consecutive reaction routes with fast, chemical reactions in combination with mass transfer phenomena the reaction product distribution is very sensitive to the process operating conditions, resulting in a substantial potential for selectivity improvements of the overall process.

In order to allow a more detailed analysis of the effects of mass transfer and mixing on the product distribution for this reaction system, first the reaction kinetics for the production of the smallest Koch acid, Pivalic Acid, will be studied. By choosing Pivalic Acid as the model compound the number of possible isomers is minimized and the effect of different reactants, as isobutene, butanols and diisobutylene, leading to the same Pivalic Acid product can be studied.

Initially, isobutanol was chosen as reactant instead of isobutene since isobutanol is expected to be less reactive and the characteristics of the Pivalic Acid reaction system can be studied more easily. For the synthesis of Koch acids, and more specifically Pivalic Acid, first a literature overview focusing on the main reaction steps and the effect of the main process conditions on the reaction kinetics and product distribution will be presented.

62 Chapter 3

2. Literature overview

2.1 Reaction mechanism The generally accepted mechanism for the Koch reaction (see Figure 2) includes four reversible reaction steps (Koch, 1955, Falbe, 1980). In Figure 1 the initiating component is an alkene, but alcohols can be used as well, as was done in this chapter. However, then a dehydration step is preceding the Koch mechanism as presented in Figure 2.

= R + RCOOH R + CO H

+ + RCOOH 2 RCO

H O 2 Figure 2 General reaction mechanism (Falbe, 1980)

For isobutanol as starting material the following main reactions will occur :

+ + C4H10O+ H ⇔ C4H9 + H2O (1)

+ + C4H9 (primary carbocation) ⇔ C4H9 (tertiary carbocation) (1-a)

+ + C4H9 + CO ⇔ C4H9CO (2)

+ + C4H9CO +H2O ⇔ C4H9COOH (3)

+ + C4H9COOH ⇔ C5H10O2 +H (4)

In this reaction system the acidic catalyst is indispensable and the acid strength of the catalyst solution is an important factor. The well known Hammett Acidity scale, as defined in Eq. (5) for the protonation of base I, will be used to characterize the acid strength of the catalyst solution.

+ + γ []IH a H I =−+ =− (5) Ho pK IH log log γ + []I IH

63 Chapter 3

The Hammett Acidity Function Ho is, in fact, a measure of the tendency of the medium to protonate a base I. The Ho-value for sulfuric acid solutions can be found in several tabulations (Paul and Long, 1957; Jorgenson and Hartter, 1963), see also Appendix A of this chapter. Although never a complete study on the detailed reaction kinetics of the complete Koch reaction system was published in literature, some of the reaction steps were used in studies on stabilized carbocations in superacidic media, see e.g. the work by Hogeveen (1967a,b,c). Results found in literature for the individual reaction steps are discussed below.

2.1.1 Dehydration of isobutanol; formation of a carbocation The formation of a carbocation from isobutanol is in fact a two-step reaction involving the protonation of the alcohol, followed by the release of a water molecule. Unfortunately, for the protonation and dehydration kinetics of isobutanol in (strong) sulfuric acid solutions no (experimental) data were found in literature. The formation of carbocations from olefins, which may lead to the same C4 carbocations, has been studied more frequently in literature. For isobutene and trans-2-butene the literature data were recently reviewed and extended by Brilman et al. (1997, see Chapter 2). In these cases the protonation kinetics depend strongly on the acid strength (or Ho) of the catalyst solution and a log-linear relationship between the apparent first order (in the alcohol or alkene concentration) reaction rate constant for the protonation reaction and the Hammett Acidity function Ho is found. From literature data it can be concluded that a similar dependency on Ho is also valid for the dehydration kinetics of alcohols. An overview of a few of these data is presented in Figure 3.

Since the dehydration of isobutanol initially produces a primary carbocation, it is expected that the dehydration rate of isobutanol will be somewhat slower or at maximum equal to the protonation rate of trans-2-butene. However, as isobutanol can also react directly with the sulfuric acid catalyst to an ester compound, a concerted dehydration mechanism may occur, possibly resulting in unexpected high dehydration rates, as e.g. is observed in the case of formic acid decomposition (Hogeveen, 1967b)

64 Chapter 3

10 2-phenyl-2-propanol (Deno et al., 1965) t-pentylalcohol (in HNO3) (Boyd, Taft, 1960) (tertiary carbocat ion) 8 trans-2-butene (Brilman et al., 1997) 10Log k 1 isobutene (Brilman et al., 1997) 6 ethylene (Chwang et al., 1977) (secundary carbocat ion) 4 propylene (Chwang et al., 1977)

(primary carbocat ion) -2

-4

-6

-8

-10 -2024681012 -Ho

Figure 3 Hydration rates of olefins and dehydration rates of alcohols in sulfuric acid solutions at ambient temperatures.

2.1.2 Isomerization of the carbon skeleton After the dehydration of isobutanol initially a primary carbocation is formed which will rapidly rearrange to a tertiary carbocation (most stable) or a secondary carbocation.

CH3 C H C CCH 3 + 2 CC+ C C C - H2O H + C C C + H CC CC (I) C C C H + + + OH OH H C C CH 2 3 2 C CC C CH 2 H+ (II) Hogeveen and Roobeek (1970) studied the interconversion between the tert-butyl and the sec-butyl

+ acylcations (RCO ) in HF/SBF5 (1:1 wt/wt) at T ≥ 353 K. For this reaction, occurring via a decarbonylation-isomerisation-carbonylation mechanism, the rearrangement of the carbon skeleton of the carbocation was rate determining. For C5 carbocations, however, the carbonylation reaction was found to be slow reaction step in the overall mechanism.

65 Chapter 3

A free enthalpy diagram for this interconversion has been presented by Hogeveen and Roobeek (1970), showing that the relative stability of the carbocations decreases with approximately 40 kJ/mole per step in the order tertiary > secondary > primary. When assuming that the isomerisation reaction in sulfuric acid will be not faster than in the superacidic media used by Hogeveen, a maximum overall reaction rate for the conversion of methylbutyric to the trimethyl carbocations respectively can be estimated to be 10-8 [1/s]. Secondary carboxylic acids (as methylbutanoic acids) would then be almost kinetically stable in this study, once they are formed.

2.1.3 The carbonylation / decarbonylation equilibrium The decarbonylation reaction of the t-butyl acylcation has been studied by Hogeveen et al. (1970) for HF/SbF5 and FHSO3/SbF5 superacidic media. Since the acidic solvent seems not directly involved in the reaction mechanism the results (relative reaction rates and equilibrium position) obtained for the superacidic media may be similar to those for the sulfuric acid solutions used in this study. The results from work by Hogeveen et al. (1970) and Hogeveen and Roobeek (1970) can be summarized to : ⋅ the carbonylation reaction is first-order with respect to the cation concentration and the carbon monoxide concentration in the acid solution ⋅ the second order rate constant for the carbonylation reaction was found to be 104 [L/mole s] for tertiary carbocations. For secondary and primary carbocations this rate is approximately 7 10 10 and 10 [l/mole s] respectively (at 293K in HF/SbF5 (1:1 wt/wt)). ⋅ the rate of decarbonylation was found to be independent of the (superacidic) solvent system. and independent of the structure of R (the alkyl group of the acyl carbocation RCO+), as long as R is an acyclic tertiary alkyl carbocation ⋅ the carbonylation equilibrium constant was found to be on the order of 102-103 L/mole at 293 K.

It is stressed again, however, that the results mentioned above hold explicitly for the conditions used by Hogeveen and coworkers, and it is uncertain if these results also hold for the sulfuric acid catalyst system.

2.1.4 Hydration of the acylcarbocation / hydrolysis of protonated carboxylic acids The hydration/dehydration of acylcarbocations has been studied very scarcely. Kinetic rate data have not been reported for sulfuric acid solutions. Extrapolation from measurements in other

66 Chapter 3 solvents may yield erroneous results, as is illustrated by the relatively slow decomposition of formic acid and acetic acid in HF-BF3 whereas the reaction is fast in (less acidic) concentrated sulfuric acid solutions (Hogeveen, 1967b, 1967c).

The hydration equilibrium in sulfuric acid solutions has been studied by Deno (1964c) for acetic acid, propionic acid and isobutyric acid. For these compounds the acidity of the sulfuric acid + + solutions at which the acyl carbocation is half-hydrated ( [RCO ] = [RCOOH2 ] ) was determined and found to be within the range 15-25% SO3 in H2SO4. For Pivalic Acid this would imply that (most likely) the equilibrium position of reaction (3) is at the right hand side for the conditions applied in this work (70 - 96 wt% H2SO4).

2.1.5 Deprotonation / protonation of carboxylic acids The protonation / deprotonation reaction for carboxylic acids in strong acid solutions can usually be considered at equilibrium. Deno et al. (1964c) estimated the sulfuric acid concentrations for acetic acid, propionic acid and isobutyric acid at which these components are half-protonated ( [RCOOH] + = [RCOOH2 ]) at equilibrium by NMR techniques to be 77 - 82 wt%. This aspect will be discussed in Appendix B on the reaction equilibria in the catalyst solution.

2.2 Other reaction mechanisms For the sulfuric acid catalyst system a few alternative intermediate reaction components have been proposed. Koch (1955) mentioned that in case alkenes are used as reactant initially alkylsulfuric acid (R-OSO3H) may be formed. In the reaction mechanism according to Eidus et al. (1962) acyl sulfuric acid (R-CO-OSO3H) intermediate products are proposed, but no direct evidence for their existence was presented.

Esterification of isobutanol with sulfuric acid may also be important. This reaction, however, is usually carried out in the presence of excess isobutanol (Goto et al., 1989). Experimental work of Tian (1950) has shown that in excess sulfuric acid esters can be formed and hydrolyzed quickly. The ester content after only a few minutes may be negligible. Deno and Newman (1950) studied the mechanism and kinetics of the sulfation of various alcohols, among them isobutanol. The equilibrium conversion was always less than 60% (usually 10-30%) and the esters formed disappeared rapidly (within a few minutes) in excess sulfuric acid (100 wt%). Due to the excess sulfuric acid used, esterification is likely to be of minor importance.

67 Chapter 3

In this work the carbocation mechanism is adopted at this point for describing the mechanism (as long as the carbocation mechanism is able to describe the results obtained).

2.3 Oligomerisation and other side reactions Due to the reversibility of the reactions a minor amount of olefinic components may be present in the acid solution, leading to polymerisation reactions. For the addition of butanols or isobutene to sulfuric acid solutions it is well known that oligomeric products (dimers, trimers and tetramers of isobutene) will be formed in 75-85 wt% sulfuric acid solutions. The first step in the oligomerisation is the reversible formation of C8 carbocations from a tert-butyl cation and isobutene :

C C C C CCC + C CC CCC C C (dimerization) + + C

Thermodynamically, the equilibrium is at the side of the oligomers under the process conditions considered. Nevertheless, depending on the protonation equilibrium for isobutene in the solvent + concerned, almost all C8 cations may be cleaved. This protonation equilibrium, determining the t- + C4H9 / C4H8 ratio, was discussed by Hogeveen (1969c) for a HF catalyst solution. Hogeveen estimated the pK value of the protonation reaction for isobutene in the range [-5, 7] for the HF + -2.5 solution, whereas Deno (1964b) estimated the t-C4H9 / C4H8 ratio in 96% H2SO4 to be 10 (the original estimation by Deno was 10-3.5 using Ho = -9 (instead of ≈ -10) at 96 wt% sulfuric acid). The dimers and higher oligomers formed may lead to higher carboxylic acids via the basic reaction steps discussed above. It will be clear that C9 and C13 isomeric acids are the primary products in

+ this case. Isobutylene trimer cations and higher (≥ C12 ) can undergo additionally β-scission and other disproportionation reactions, leading to fragments other than C4 components. Under certain conditions (poor mixing, low CO pressure etc.) an impressive diversity of products can be obtained.

Deno et al. (1964a) identified the products formed by the t-butyl cation in 96 wt% sulfuric acid solutions in the absence of carbon monoxide. Under these conditions 50% of the reactant was converted to stable polyalkylcyclopentyl cations (PACP) and 50% to an immiscible alkane fraction. The reaction rate of the formation of the stable PACP cations was found to be second order in the tert-butyl cation concentration, and thus favored by high local concentration of the tert-butyl cations.

68 Chapter 3

+ + tert-C H i-C4H8 + H 4 9 R R R + + tert-C H + x C4H8 + alkanes 4 9 R R

Formation of polyalkylcyclopentyl cations in strong sulfuric acid solutions

The reaction products found for isobutene, trimethylpentenes and 1- and 2-butanol in 96 wt% acid solutions were identical to those for tert-butanol.

Other side reaction which may occur include alkyl sulfate formation, sulfonation (at higher temperatures and acidities) and carbonization of the hydrocarbons used. These side reactions will be more pronounced at higher acid concentrations and higher temperatures.

2.4 Influence of process conditions The studies of the Koch synthesis presented in literature usually deal with the description of trends in yield and selectivity via changes of the carbon monoxide pressure, temperature or catalyst solution composition. Generally, it is found that the carboxylic acid yield increases with CO pressure and with the olefin carbon number. Increasing the CO pressure also results in more acids having a tertiary (instead of quaternary) carbon atom bearing the carboxylic acid group and a reduction of the yield on acids, derived from oligomerization products (Koch, 1955; Falbe, 1980).

Sulfuric acid was the first catalyst system used in the Koch synthesis. According to several (patent) publications the catalyst solution should contain over 80 wt% sulfuric acid and an excess of catalyst should be applied; catalyst-olefin ratios mentioned in patent literature vary from 5 to 10 [wt/wt]. The process conditions usually applied include temperatures of 273 - 350 K and carbon monoxide partial pressures of 10 to 150 bar [Falbe, 1980].

The use of isobutanol in the Koch synthesis, using 96 wt% sulfuric acid as catalyst was studied by Eidus et al. (1962) and Eidus and Kaal (1963). The acid yield, based on isobutanol, increased from 41 to 51% with the CO pressure from 5 to 75 bar. The acid product consisted

69 Chapter 3

of Pivalic Acid (about 80%), 2-methylbutyric acid (5-15%) and C9-acids. Higher acids (> C9) were not found. The 2-methylbutyric acid content increased also with the CO pressure. According to Eidus and co-workers the product had a ‘dark-brown color’ (which may indicate that significant carbonization or oxidation had occurred during reaction or analysis /sampling).

100 100 Acids Yield [%] Isobutanol Yield [%] Esters Isobutene 80 80 Diiso, tri-isobutene

60 60

40 40

20 20

0 0 0 20406080 70 80 90 100

P (CO) [bar] wt% H3PO4

Figure 4 Effect of pressure of acid yield Figure 5 Product composition vs. acid concentration H2SO4:isobutanol = 10 mole/mole, T=298 K H3PO4 : isobutanol = 5 mole/mole, T = 298 K [data from Eidus and Kaal, 1963] [data from Eidus et al., 1968]

Isobutanol and isobutene have also been used by Eidus et al. (1968) using phosphoric acid as catalyst. In their study the products mentioned above were identified, as well as their isobutyl esters. With increasing catalyst concentration an increasing yield of carboxylic acids was obtained. The amount of isobutene oligomers and esters formed went through a maximum (see Figure 5).

The Ho value of 100% H3PO4 solution (≈ -5) is approximately equal to that of a 65wt% H2SO4 solution. It is not clear why in this latter study isobutanol-esters of the tertiary carboxylic acids were formed, and not in the preceding study with sulfuric acid as catalyst. Other differences between these studies are the higher temperatures applied (398 K vs. 298 K), the CO partial pressures (125 bar vs. 5-75 bar), the stirring rates (2800 rpm vs. 800 rpm) and the copper coating applied for the stirrer and vessel. As known from other studies, see e.g. Souma and Sano (1973), copper carbonyls, Cu(CO)x, may be formed and catalyse the reaction.

2.5 Reaction kinetics for the isobutanol / sulfuric acid system From the literature overview presented above, it can be concluded that the reaction kinetics for the isobutanol / H2SO4 system are not uniquely determined, not even the rate determining step. In this work, the overall reaction kinetics will be determined by following the CO consumption rate. By varying process parameters as CO partial pressure, temperature and catalyst composition the reaction system will be analysed. 3. Experimental

70 Chapter 3

3.1 Equipment The experiments were carried out using a high pressure autoclave. The experimental set-up is shown schematically in Figure 6. The high pressure autoclave was usually operated semi-batch wise. The Büchi reactor (0.5 liter Hastelloy C-22 stainless steel) could be pressurized up to 60 bar and was equipped with a gas-inducing, 6 blade Rushton type stirrer and a baffle mounted on the deckle. To minimize mass transfer limitations and inhomogeneities the stirrer speed was chosen relatively high at 1800 rpm.

N2 MFC

CO Injection vessel T

P dump vessel

CO Storage vessel vacuum atmosphere T P

reactor

sample point Figure 6 Experimental set up

3.2 Experimental procedure kinetic experiments Prior to an experiment, the thermostated reactor was filled with ± 210 ml sulfuric acid catalyst solution. The solution was degassed by applying vacuum while stirring. The injection vessel was filled with the liquid phase reactant isobutanol. The reactor was pressurized via a pressure reducer at the desired reaction pressure via the bypass line. The bypass line is closed (the reactor is now operated fully batch wise) and the gas inducing stirrer is started. From these physical absorption experiments the CO solubility as well as the volumetric gas-liquid mass transfer parameter, kLa, can be determined from the pressure and temperature vs. time data recorded by the PC data acquisition system. After this, the reactor pressure was reduced by 1.5 bar to create a pressure drop over the injection vessel. Data acquisition and stirring (default at 1800 rpm) is started again. Both valves of

71 Chapter 3 the injection vessel were opened and the carbon monoxide flow is used to inject the reactant. Injection of the reactant is usually accomplished within 4 seconds (for 8 g isobutanol). Pressure is now maintained at the desired reactor pressure (± 0.01 bar) by a pressure regulating system, consisting of a PC + PID controller system using a Mass Flow Controller (MFC) to control the reactor pressure. The data acquisition program records continuously the temperature and pressure of both the reactor and the CO supply vessel. If the CO consumption ends, data acquisition is stopped. From the pressurized reactor a sample of about 100 grams from the reaction mixture is directly quenched on 200 grams of ice-water under vigorous stirring. After this, the reactor pressure is relieved, the reactor is emptied and cleaned several times with water, once with acetone, dried and closed under a nitrogen atmosphere.

3.3 Analysis of reaction products The sample (≈ 100 g) of the reactor contents, quenched on icewater (≈ 200 g.), was extracted in four steps with about 60 g. heptane (99.9+ %, Merck, pro analyses). The organic layer was analyzed by gas chromatography using a Varian 3400 GC (FID detector, 250°C injection temperature and 300°C detection temperature, DB-FFAP column 30 m × 0.258 mm, 0.25 µm film, split injection

(1:100), He or N2 carrier gas). Column temperature was kept for 1 min. at 120°C and then increased with 10°C/min to 240°C, where it was maintained for about 20 minutes. The organic layer was titrated with a 0.01 M NaOH solution to determine the total concentration of weak acids.

No sulfuric acid was found in this layer for the experiments using the 96 wt% H2SO4 catalyst, but some H2SO4 was found in an experiment at 85 wt%. Further, a sample of the quenched product (before extraction) was titrated on total weak acids. The consumption of carbon monoxide during the reaction was recorded and used for the reaction kinetics as well as calculation of the total amount of CO containing products (acids) formed. The acid yield, YA, reported in this work refers to the molar ratio of the total amount of acids formed to the total amount of isobutanol injected.

72 Chapter 3

3.4 Evaluation of mass transfer coefficients and reaction kinetics The mass transfer coefficient and the chemical reaction kinetics were evaluated from the recorded pressure and temperature curves. For the determination of the volumetric gas-liquid mass transfer coefficient, the following equations can be derived from a simple mole balance for the gas and liquid phase, in case of batch wise operation (Eq. (6-a)) and for semi-batch operation respectively (reactor pressure is kept constant and the liquid phase is operated batch-wise, see Eq. (6-b) ).

 nn−  n batch experiments : ln gt,, geq  =−ka go, t (6-a)  −  L  nngo,, geq n geq,

 nn−  semi-batch experiments: ln sv,, t sv eq  =−kat (6-b)  −  L  nnsv,, o sv eq 

Both types of experiments have been conducted and identical results were found. Considering the moderately high carbon monoxide pressures and temperatures applied, the application of ideal gas phase behavior does not cause significant errors (≤ 1%).

It will be assumed initially that the reaction is first order in isobutanol, in accordance with the overall reaction stoechiometry and corresponding to results found for the carbonylation reaction (see Hogeveen, 1970) and dehydration of other alcohols as rate determining step. For a first order reaction in isobutanol the apparent reaction rate constant can be determined from P-t data in absence of gas-liquid mass transfer limitations using Eq. (7-a) or Eq. (7-b) .

 nn−  n batch experiments : ln gt,, geq =−k go, t (7-a)  −  ov  nngo,, geq n geq,

 nn−  semi-batch experiments : ln sv,, t sv eq  =−kt (7-b)  −  ov  nnsv,, o sv eq 

73 Chapter 3

4. Results

4.1 Reaction Kinetics Reaction kinetics were evaluated from the pressure-time (P-t) recordings as the CO-consumption rate could be followed conveniently. For example, an experiment at 293 K, using a 96 wt%

H2SO4 catalyst solution took about 45 minutes. From the gas-liquid mass transfer experiments an apparent volumetric mass transfer coefficient of 0.2 [1/s] was derived, indicating that gas-liquid mass transfer is not limiting. However, in the minute just after injection of the isobutanol some depletion of the CO-concentration in the liquid phase may occur. By using the overall, first order reaction rate constant for the CO consumption rate, as determined from the kinetic experiments, it can be calculated that in this short period less than 10% of the isobutanol will be converted. The amount of CO dissolved physically in the catalyst solution (thus already present in the catalyst solution before isobutanol injection) is sufficient for approximately 10% conversion of the injected reactant at the standard set of conditions (8.3 g. isobutanol in 210 ml catalyst solution).

On injection of the isobutanol a (temporal) temperature rise of about 5 K was observed. From the results of reactant injection experiments under N2, this temperature rise should (most likely) be attributed to the dissolution of isobutanol in the catalyst solution (∆Hs ≈ 35 KJ/mole). The effects of CO partial pressure, temperature and acid strength concentration will now be considered respectively.

4.1.1 Effect of carbon monoxide pressure and temperature In studying the effect of the carbon monoxide partial pressure and the reaction temperature the initial catalyst composition and amount of isobutanol injected was kept constant. The kinetic rate experiments were conducted at 278-320 K and at 5-60 bar carbon monoxide partial pressure. On analysis of the P-t data excellent linear correlations of the experimental data were obtained using Eq. (7-a) and (7-b), indicating that the reaction is indeed first order in the isobutanol concentration and thus confirming the previously made assumption. The influence of pressure on the apparent first order reaction rate constant is shown in Figure 7. From the results presented in Figure 7, kov seems to be independent of the carbon monoxide partial pressure, suggesting that CO is not involved in the rate determining step.

74 Chapter 3

1.0E-02

kov [1/s]

1.0E-03 294 K

279 K

1.0E-04 0 1020304050607080

PCO [bar]

Figure 7 Influence of PCO on the overall first order reaction rate constant for CO consumption

Conditions: 294 K, 400 g of 96 wt% H2SO4, 10 g of isobutanol, tinj < 3 s. 279 K, 370 g of 96 wt% H2SO4, 8.5 g of isobutanol, tinj < 3 s.

-3 PCO : ln (kov) 70 bar -4 35 bar Fit (10 g. i-BOH) 40 bar (8 g. i-BOH) -5

-6

-7

-8

-9 0.0031 0.0032 0.0033 0.0034 0.0035 0.0036 0.0037 1/T [1/K]

Figure 8 Arrhenius plot for the overall first order reaction rate constant for CO consumption

Conditions 70, 35 bar series, 278

In the experiment series of Figure 8 the reaction temperature was varied and an apparent activation energy of 85 (±5) KJ/mole was found from the Arrhenius plot.

75 Chapter 3

4.1.2 Effect of catalyst solution acidity

In Figure 9 the effect of the initial acid strength on the apparent first order reaction rate constant kov is presented for a set of experiments at constant temperature and CO pressure, but with varying acid concentration. As ordinate, the initial acid strength (Ho value) of the unloaded sulfuric acid solution is used, as calculated using the fit-correlation of literature data presented in Appendix A of this chapter. In the experiments presented in Figure 9 it was chosen keep to the volumetric amount of catalyst solution constant, in order to use almost constant isobutanol concentrations within the series. Unavoidably, however, the catalyst-to-isobutanol ratio now decreases simultaneously with the decreasing acid concentration.

The Ho value of the catalyst solution is rather sensitive to the water content of the solution. When the reaction of isobutanol to Pivalic Acid is completed no net consumption or production of water occurs. However, also the reactant isobutanol and the product Pivalic Acid may influence the acidity of the catalyst solution.

1.0E-02

kov [1/s]

1.0E-03

1.0E-04

1.0E-05

1.0E-06 67891011

(-Ho)o

Figure 9 Influence of (initial) acid strength on the overall carbonylation kinetics Conditions: T = 286 K, PCO = 40 bar, 220 ml H2SO4 solution, 8.3 g of isobutanol, tinj < 3 s.

Therefore, experiments in which the amount of isobutanol was varied and experiments in which Pivalic Acid was initially present in the catalyst solution have been been conducted. In Figure 10

76 Chapter 3 the results of experiments with different amounts of Pivalic Acid present in an initially 96 wt% sulfuric acid solution are presented.

Considering the strong influence of the Hammett Acidity Function (Figure 9) and of the presence of Pivalic Acid on the CO consumption rate (Figure 10), it was speculated that the addition of Pivalic Acid may cause a significant drop in the acidity of the catalyst solution. This was confirmed by the experimental results of determining the Hammett Acidity function for aqueous sulfuric acid solutions with and without the addition of Pivalic Acid. These experiments are discussed in more detail in Appendix A. From these measurements it was shown that the addition of Pivalic Acid reduced the Hammett Acidity of the catalyst solution more strongly than an equimolar amount of water. For the range of acid strengths investigated [70-90 wt%] the change in Hammett Acidity could be related to the Pivalic Acid content using Eq. (8) (see also Figure 11).

∆Ho ≈ 0.08 ⋅ (wt%pivalic acid) {}≈ 0.095 ⋅ (mol% pivalic acid) (8)

1.0E-02

kov [1/s]

1.0E-03

1.0E-04

1.0E-05

1.0E-06 0 20 40 60 80 100 120 140 160 initial Pivalic Acid [g]

Figure 10 Influence of Pivalic Acid initially present in the catalyst solution on CO consumption rate

Conditions: 400 g of 96 wt% H2SO4, 293 K, 40 bar CO, 8.3 g of isobutanol

A further validation of this was obtained by performing a set of kinetic experiments with (a fixed amount of) isobutanol at different initial acid concentrations and with different amounts of Pivalic Acid initially present.

77 Chapter 3

0.0 70.5 ∆ (-Ho) 72 75.2 76.8 78.4 -0.4 79.2 82 84 88 89 (trend line) -0.8

-1.2 0 0.04 0.08 0.12 0.16 wt. fraction pivalic acid Figure 11 Influence of initially present Pivalic Acid on the Hammett Acidity Function for the catalyst solution (at 293 K - 298 K)

For the catalyst solutions loaded with initially present Pivalic Acid the Ho value of these solutions was calculated according to Eq. (8), leading to the results presented in Figure 12.

1.0E-02 Series296 wt% Series196 wt%, loaded kov [1/s] Series594 wt% Series692 wt% 1.0E-03 Series1190 wt%, Series389 wt% Series489 wt%, loaded Series787 wt% Series884 wt% 1.0E-04 Series982 wt%

Series1089 wt%, + C6

1.0E-05

1.0E-06 67891011 -Ho

Figure 12 Influence of initially present Pivalic Acid on kov. The Ho-values for loaded solutions are calculated using Eq. (8) for T = 293 K. All experiments: 8.3 g of isobutanol, 40 bar CO

and H2SO4 : isobutanol ≈ 33 (mole/mole)

78 Chapter 3

Although Eq. (8) was derived from Ho measurements with catalyst solutions of initially 70-89 wt% sulfuric acid, the experiments with loaded solutions of initially 96 wt% H2SO4 are described equally well. In Figure 12 a single data point is included in which another tertiary carboxylic acid, 2,2 dimethyl butanoic acid (C6 acid), is used instead of Pivalic Acid, showing that the effect observed seems not to be restricted to Pivalic Acid only.

The effect of isobutanol on the (apparent) Ho value was studied by performing experiments with different amounts of catalyst solution and isobutanol. As example, the results for an initially 91 wt% H2SO4 solution and different amounts of isobutanol are presented in Figure 13.

1.0E-03

kov [1/s]

1.0E-04

H2SO4 isobutanol kov molar ratio -5 91 wt%, [g] [g] (10 1/s) H2SO4 / isobutanol 373 24.7 8.60 10.4 1.0E-05 374 3.7 31.0 69.5 380 8.3 25.0 31.5 368 14.6 15.0 17.4 697 14.6 28.5 32.9 270 14.6 12.5 12.7

1.0E-06 0 10203040506070

H2SO4 / isobutanol ratio [mole/mole]

Figure 13 Dependency of kinetic rate constant on the molar ratio H2SO4- isobutanol (catalyst-to-reactant ratio)

In Figure 13 the importance of the ratio H2SO4/isobutanol can be recognized. In the experiment series presented in the Figures 7-10 and 12 this ratio was usually approximately 30. The decrease of the overall CO consumption kinetics at lower ratios of H2SO4/isobutanol can be described as a decrease in the solution acidity with increasing isobutanol content, analogous to the effect of Pivalic

79 Chapter 3

Acid. With this, an overall fit of all available data for the isobutanol / H2SO4 / Pivalic Acid system is presented in Figure 14.

1.0E-02 10 log(kov) = 0.75 * (-Ho) - 10.3

kov [1/s] -Ho = (-Ho)o + 0.095 * (mole% pivalic acid) + 0.17 * (mole% isobutanol)

1.0E-03

1.0E-04

1.0E-05

1.0E-06 567891011 -Ho

Figure 14 Overall fit of kov (293 K) for the Pivalic Acid synthesis from isobutanol, H2SO4 as catalyst.

PCO <70 bar, 278 < T < 315 K,(Ho)o < -6.5, isobutanol < 12 wt %, Pivalic Acid < 28 wt %

Apparently, the acidity of the catalyst solution is the main parameter determining the overall reaction kinetics for the Koch synthesis of Pivalic Acid. The acidity is, however, rather sensitive to the catalyst solution composition.

4.2 Reaction products

For the experiments with isobutanol a relatively clean reaction product was obtained, consisting of, primarily, Pivalic Acid and 2-methylbutanoic acid, see Table I.

In general, the selectivity to Pivalic Acid increases with decreasing acidity, increasing CO pressure and lower temperatures. Therefore, it is concluded that 2-methylbutanoic - and higher acids are formed if local CO depletion can occur. This, probably, is best demonstrated by the last experiment presented in Table I, in which the stirrer was started 25 s after isobutanol injection.

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Table I Some reaction product distributions

Process conditions Yield Product distribution by GC analysis

P T H2SO4 iso-C4H10O on isobutanol Pivalic 2-methyl C6 C9 > C9 acids Acid butanoic acids acids [bar] [K] [wt%] [g] YA [%] acid [%] [%] [%] [%] [%] 701) 294 96.0 9.5 84 86 14 - - - 251) 294 96.0 9.9 85 84 12 - 4 - 81) 294 96.0 9.9 76 80 9 - 11 - 40 279 96.0 8.2 89 84 16 - - - 40 295 96.0 8.3 84 78 21 - 1 - 40 315 96.0 8.4 89 79 18.5 - 2.5 - 40 287 92.5 8.3 65 84 13 - 3.0 - 40 287 87.1 8.3 71 90 3.3 - 5.3 - 40 286 82.8 8.9 34 2) 94 0.2 0.3 5.6 - 40 317 96.0 8.6 42 3) 66 16.7 4.2 9.1 4.0

1) other reactor set-up was used 2) reaction not completed 3) stirrer was started approximately 25 s after injection of isobutanol

The total yield on acids was calculated by CO consumption, GC analysis and titration. Deviations between these methods were usually less than 10%, indicating that all acids are extracted by the extraction solvent after quenching the reactor sample. Therefore, the remaining isobutanol which was not retrieved as acid, most likely did not react with CO. Analysis of the quenched reactor sample after extraction on total organic compounds (TOC-analysis) and GC-analysis after neutralizing completely this acid layer indicated the presence of isobutanol, which may have been present as alkylsulfuric acid in the catalyst solution. The formation of these components may also account for the substantial influence of isobutanol on the apparent solution acidity. Esters of Pivalic Acid with isobutanol were detected in small amounts (1-2 %). For one of the experiments samples were taken during the reaction after 1500, 3000, 5000 and 8500 s, see Table II.

The results of Table II show that initially more higher acids are formed and further that the production of 2-methylbutanoic acid is relatively slow or, alternatively, a consecutive reaction. One explanation may be that the 2-methylbutanoic acids are formed from a relatively slow decomposition of alkylsulfuric acids. The isomerisation of the carbon chain may occur during the

81 Chapter 3 hydrolysis of the alkylsulfuric acid or it may already have occured prior to the alkylsulfate formation.

Table II Analysis of products formed during an experiment (40 bar, 286 K, 452 g of 96 wt% H2SO4, 10 g of isobutanol)

Yield Product distribution by GC analysis

Sample sample % Pivalic 2-methyl isobutanol C9 acids ID time of acid butanoic acid [s] final yield [%] [%] [%] [%] no. 1 1500 40 85 8 3.6 3.3 no. 2 3000 70 82 14 1.0 2.8 no. 3 5000 90 81 17 0.3 1.7 no. 4 8500 100 79 19 0.1 1.2

Two blank runs were performed in which Pivalic Acid was injected (instead of isobutanol) in 380 g

96 wt% H2SO4 solution (at 5 and 40 bar CO). After one hour samples were taken using the sampling procedure described in section 3. No 2-methylbutanoic acid (only Pivalic Acid) was found in the 'reaction product'. From this, it was concluded that the production of 2-methylbutanoic acid is not a consecutive reaction. As in the kinetic experiments, only approximately 80% of the Pivalic Acid was retrieved, which may indicate that retro-Koch reactions occur. A further analysis of the reaction equilibria in solution is therefore recommended (see also Appendix B of this chapter on the product distribution in the catalyst solution).

5 Discussion

In determining the reaction kinetics it was found that especially the catalyst solution acidity determines the CO consumption rate. The presence of isobutanol and Pivalic Acid influence the solution acidity considerably and it is important in determining the reaction kinetics to recognize these influences on the apparent reaction kinetics.

Since the reaction kinetics depend strongly on the Hammett Acidity Function for the catalyst solution, the effect of temperature on the solution acidity should be considered. Johnson et al. (1969) reported the effect of temperature on the Hammett acidity of sulfuric acid solutions (see Appendix A). Using their results, an apparent activation energy of -36 KJ/mole is obtained, due to

82 Chapter 3 the temperature dependence of -Ho only, thus implying that the activation energy for the intrinsic first order reaction (in isobutanol) is approximately 120 KJ/mole. Since both the reactant (isobutanol) and the main reaction product (Pivalic Acid) affect the (apparent) Hammett Acidity of the catalyst solution, the solution acidity is changed marginally during the course of the reaction in the kinetic experiments. It can be estimated that the net effect on the overall reaction rate constant for CO consumption during an experiment is not more than 20% for experiments with 10 g isobutanol used in this work.

From Figure 7 it appears that CO is not involved in the rate determining step. Dehydration of isobutanol or hydrolysis of alkylsulfuric acids are the main options for the rate determining step in the reaction mechanism. When the results obtained in this study are compared to those presented in 10 Figure 3, it is obvious that the slope of the log kov-Ho line differs from those obtained in the other studies, which may indicate that the reaction occurs via an other reaction mechanism.

10 2-phenyl-2-propanol (Deno et al., 1965) t-pentylalcohol (in HNO3) (Boyd, Taft, 1960) (tertiary carbocat ion) 8 trans-2-butene (Brilman et al., 1997) 10 Log k1 isobutene (Brilman et al., 1997) 6 ethylene (Chwang et al., 1977) propylene (Chwang et al., 1977) (secundary carbocat ion) 4 iso-butanol (this work)

0 (primary carbocat ion) -2

-4

(k ov isobutanol => pivalic acid) -6

-8

-10 -2024681012 -Ho

Figure 15 Comparison of kov with dehydration and protonation results for olefins and tertiary alcohols

10 The slope of the log(kov) - Ho plot (≈ 0.75) agrees with the results of Deno and Newman (1950) for the rate of sulfation of 1- and 2-butanol, where a corresponding value of 0.8 is found. It is, however, uncertain if the same slope should be expected for the hydrolysis of alkylsulfates. Since the esterification of isobutanol with sulfuric acid may be important, as mentioned in section 2.2

83 Chapter 3 although the maximum conversion of reactant is limited according to Deno and Newman (1950), a few 1HMR and 13C NMR experiments were performed to study the extent of ester formation in 96 wt% sulfuric acid solution. Isobutanol (and 1- and 2-butanol) formed esters to a minor extent (less than 10%), whereas for tert-butanol and Pivalic Acid no esters with sulfuric acid were detected.

6. Conclusions Pivalic Acid can be produced from isobutanol using sulfuric acid as a catalyst solution without many byproducts. The major byproduct is 2-methylbutanoic acid, if gas-liquid mass transfer limitations are excluded. The selectivity towards 2-methylbutanoic acid is generally less than 20% and decreases strongly with decreasing acidity.

The reaction is first order in isobutanol and the overall reaction rate can be monitored through the CO consumption. Since the overall reaction rate depends strongly on the acidity of the catalyst solution and does not depend on CO partial pressure, dehydration of isobutanol is most likely to be rate determining. The presence of Pivalic Acid and isobutanol strongly reduces the apparent reaction rate constant. For Pivalic Acid this was shown experimentally to be caused by a decrease in solution acidity. For the industrially applied backmixed reactors in the Koch synthesis, this may imply that these operate at much lower values for Ho and, consequently, even for faster reacting components as isobutene the protonation step may then become rate determining.

In one of the experiments in which the stirrer was started after 25 s. it was found that in the Koch synthesis of Pivalic Acid the effects of mixing (local acidity) and (extreme) gas-liquid limitations are directly reflected in the product composition, although the overall reaction rate is rather slow. A faster reacting reactant as tert-butanol or isobutene should, however, be preferred for further studying mass transfer and mixing effects in the Koch synthesis of Pivalic Acid.

Acknowledgments The author wishes to acknowledge B. Knaken for constructing the setup, A. Hovestad and W. Lengton for their assistance in the product analysis, W. Verboom (UT) and L Petrus (SHELL) for the useful discussions and especially K. Leer, E.N. Kant, G. Meijer, I.B. Kooijman and N.G. Meesters for their valuable contribution to the experimental work. The Shell Research and Technology Centre Amsterdam is acknowledged for the financial support.

84 Chapter 3

Notation a activity [mole/m3] c concentration [mole/m3] Ho Hammett Acidity Function (defined in Appendix)

∆Hs enthalpy of dissolution (as estimated from the temperature rise) [KJ/mole] kov overall first order reaction rate constant [1/s] kLa volumetric gas-liquid mass transfer coefficient [1/s] ni amount of component i [mole] P Pressure [bar] t time [s] tinj injection time (for the reactant isobutanol) [s] T Temperature [K]

Super- and subscripts

CO carbon monoxide eq equilibrium g gas phase o initial condition sv storage vessel

85 Chapter 3

References

Boyd R.H., Taft R.W., Wolf A.P., Christman D.R., 1960, Studies on the mechanism of olefin- alcohol interconversion. The effect of acidity on the 18O exchange and dehydration rates of t- alcohols, J.Am.Chem.Soc., 82, 4729-4736

Brilman D.W.F., Swaaij W.P.M. van, Versteeg G.F., 1997, On the absorption of isobutene and trans-2-butene in sulfuric acid solutions, Ind. & Eng. Chem. Res., 36, 4638-4650 [Chapter 1 of this thesis]

Brouwer D.M., 1980, 'Reactions of alkylcarbenium ions in relation to isomerization and cracking of hydrocarbons' in Chemistry and Chemical Engineering of Catalytic Processes, ed. R.Prins, G.C.A. Schuit, Sijthoff & Noordhoff, Alphen aan de Rijn, The Netherlands

Chwang W.K., Nowlan V.J., Tidwell T.T., 1977, Reactivity of cyclic anc acyclic olefinic hydrocarbons in acid-catalyzed hydration, J.Am.Chem.Soc., 99, 7233-7238

Deno N.C., Newman M.S., 1950, Mechanism of sulfation of alcohols, J.Am.Chem.Soc., 72, 3852- 3856

Deno N.C., Boyd D.B., Hodge J.D., Pittman C.U., Turner J.O., 1964(a), Carbonium Ions XVI. The Fate of the t-butyl cation in 96% H2SO4, J.Am.Chem.Soc., 86, 1745-1748

Deno N.C., 1964(b), Carbonium Ions, Progr.Phys.Org.Chem., 2, 136-137.

Deno N.C., Pittman C.U., Wisotsky M.J., Carbonium ions. XVIII., 1964(c), The direct observation of saturated and unsaturated acyl cations and their equilibria with protonated acids, J.Am.Chem.Soc., 86, 4370-4372

Eidus Y.T., Puzitkii K.V., Ryabova K.G., 1962, ‘Synthesis of esters and other derivatives of carboxylic acids under acid catalysis conditions form carbon monoxide, olefins and acylating compounds. VIII Synthesis of carboxylic acids and their esters from C3-C5 alcohols and carbon monoxide’, J. Gen.Chem.USSR, 32 (10), 3143-3146

Eidus Y.T., Kaal T.A., 1963, ‘Synthesis of esters and other derivatives of carboxylic acids under acid catalysis conditions form carbon monoxide, olefins and acylating compounds. XI Effect of pressure of carbon monoxide on the course of the methoxycarbonylation of isobutene and of isobutyl alcohol’, J. Gen.Chem.USSR, 33 (10), 3211-3217

Eidus Y.T., Puzitskii K.V., Pirozhkov S.D., 1968 ‘Synthesis of carboxylic acid derivatives under the conditions of acid catalysis from CO, olefins and acylating compounds: XXVI. Carbonylation of isobutylene, diisobutylene and isobutyl alcohol in the presence of orthophosphoric acid’, J. of Org.Chem.USSR, 4 (1), 32-37

Falbe J., 1980, ’New synthesis with carbon monoxide; Ch. V.: Koch Reactions (H. Bahrmann)’ , Springer-Verlag, Berlin

86 Chapter 3

Goto S., Tagawa T., Fukuta Y., 1989, Kinetics of the reaction of sulfuric acid with isobutyl alcohol, Int.J.Chem.Kin., 21 (8), 729-732

Hogeveen H., 1967, Chemistry and spectroscopy in strongly acidic solutions. (a) II. Kinetics of formation and hydration of methyl oxocarbonium ions, Recl.Trav.Chim.Pays-Bas, 86, 289-292 (b) III. Formation of two different entities on protonation of formic acid, Recl.Trav.Chim.Pays-Bas, 86,687-695 (c) IX. Configurational preference in protonated carboxylic acids. Kinetics of reversible alkyl oxocarbonium formation, Recl.Trav.Chim.Pays-Bas, 86, 809-820

Hogeveen H., Gaasbeek C.J., Bickel A.F., 1969, Chemistry and spectroscopy in strongly acidic solutions. XXIII. Reversible reaction between carbonium ions and hydrogen, Recl.Trav.Chim.Pays- Bas, 88, 703-718

Hogeveen H., Baardman F., Roobeek C.F., 1970, Chemistry and spectroscopy in strongly acidic solutions. XXX. Study of the carbonylation of carbonium ions by NMR spectroscopic measurements, Recl.Trav.Chim. Pays-Bas, 89, 227-235

Hogeveen H., Roobeek C.F., 1970, Chemistry and spectroscopy in strongly acidic solutions. XXXIV. Interconversion of secondary and tertiary alkyloxocarbonium ions by decarbonylation- carbonylation. Free-enthalpy diagram, Recl.Trav.Chim. Pays-Bas, 89, 1121-1132

Kawasaki H. (Idemitsu Petrochemical Co., Ltd.), 1991, Process for production of carboxylic acid, Eur.Pat.Appl., EP 467 061

Koch H., 1955, Carbonsäure-Synthese aus Olefinen, Kohlenoxyd und Wasser, Brennstoff-Chemie, 36, 21/22, 321-328

Souma Y., Sano H., 1973, The carbonylation of alcohols catalyzed by Cu(I) carbonyl, Bull.Chem.Soc.Japan, 46, 3237-3240

Tian A., 1950, Sur l’esterification de l’isobutanol, Comptes Rendus, 230, 975-977

87 Chapter 3

88 Chapter 3, Appendix A

APPENDIX A

The effect of the addition of Pivalic Acid to aqueous sulfuric acid solutions on the Hammett Acidity Function

Introduction

The Hammett Acidity Function, Ho, first defined by Hammett and Deyrup in 1932, is a frequently used acidity scale for concentrated acid solutions. The Ho value for a strong acid solution can be determined experimentally by ionisation experiments using an inert, basic, indicator having a well known pKB value.

+ a + γ []IH H I Ho=− pK + log =−log (A-1) IH []I γ + IH

In this equation [I] and [IH+] are the concentrations of the indicator I used in the unprotonated and in the protonated form, IH+, respectively. The ionisation ratio [IH+]/[I] is usually determined experimentally using photospectrometry, see Paul and Long (1957). + λλ− []IH EEI = λλ (A-2) []I EE− + IH

For the sulfuric acid-water system the Ho values at different acid strengths are relatively well known; often the tabulations of Paul and Long (1957) and Jorgenson and Harterr (1963) are used. Since deviations between the Ho values of the various sources are relatively small at lower acid concentrations (up to 70 wt%, see Figure A-1) a single fit of all data in this range for the Ho values vs. acid concentration was made. However, in the range 80-100 wt% the reported Ho values differ significantly, especially the data of Paul and Long (1957). In this work the data of Jorgenson and Hartter (1963), Tickle et al. (1970) and Johnson et al. (1969) were used. The overall fit correlation for Ho at 298 K at different acid concentrations is presented in eq. (A-3), in which w is the weight percentage sulfuric acid.

− Ho(w) = −1.19505 + 0.355722 ⋅ w + 0.045227 ⋅ w 1.5 − 0.14948⋅ w ⋅ Ln(w) + 1⋅10 −45 ⋅ e w (A-3)

For the temperature dependence of the Hammett Acidity function the correlation proposed by Johnson et al. (1969) was adopted, see eq. (A-4) and (A-5).

89 Chapter 3, Appendix A

KT(.29815 − ) −=Ho() T Ho (298 K ) + (A-4) 29815. ⋅T

KYYY=−320255.... ⋅32 − 56 6898 ⋅ + 4 61041 ⋅ − 204 341 , with Y = Ho (298 K) (A-5)

12 Paul, Long (1957) - Ho Jorgenson, Hartter (1963) 10 Johnson et al. (1969) Tickle et al. (1970) Ho-fit 8

-2 0 102030405060708090100

wt% H2SO4

Figure A-1 Correlation of Ho-data for the H2SO4-H2O catalyst system

Tamura et al. (1990) showed that the pressure dependence of the Hammett acidity function at the process conditions is very small. The Ho value increases by approximately 0.3 unit in the range 1- 290 bar. At higher pressures (measurements were done up to 1400 bar) the Ho values remained almost constant. Therefore, at the operating conditions used in commercial and labscale units, the influence of the reactor pressure can be neglected and was therefore not taken into account.

The acidity of the (sulfuric) acid solution is the main parameter determining reaction kinetics in case of acid-catalysed hydration of olefins and - dehydration of alcohols. Also in the Koch synthesis of carboxylic acids the catalyst solution acidity is of major importance. However, as may be seen in Figure A-1, a small change in the solution composition has a significant effect on the Ho value. This is especially true in the range of 80-100 wt% sulfuric acid, which is the operating range for the sulfuric acid catalyst in the Koch reaction system. The presence of weak basic components as the reactants applied and the products obtained may therefore very well affect the

90 Chapter 3, Appendix A solution acidity. Since the Koch reaction is usually operated in a (completely) back-mixed reactor system, the effect of the main reaction product, Pivalic Acid, on the Hammett Acidity Function for the sulfuric acid catalyst solutions was investigated experimentally.

2. Experimental work

Based on the work of Paul and Long (1957) and Jorgenson and Hartter (1963) the indicators 2- bromo-4,6 dinitro aniline (for the range 70-80 wt% H2SO4) and anthraquinone (80-90 wt%) have been selected. The 2-bromo-4,6 dinitro aniline indicator shows absorption maxima at 280 nm (IH+) and 350 nm (I). For the UV measurements indicator concentrations of 0.017 g/l have been used, as Lambert-Beer's Law was found to be valid at indicator concentrations below 0.020 g/l. For evaluation of the ionisation degree [IH+]/[I] according to eq. (A-2) the absorption at 350 nm, as determined with a Philips PU8740 UV/VIS Spectrophotometer, was used. The absorption due the presence of Pivalic Acid was considered negligible, based on the absorption spectrum for a solution of Pivalic Acid in water.

3. Results

First, the method for determining Ho was validated by measuring several aqueous sulfuric acid solutions, see Figure A-2

11 - Ho [-] 10

6 2-bromo 4,6 dinitro aniline

anthraquinone 5 Ho,o correlation (eq. A-3)

4 65 70 75 80 85 90 95 100 wt% H2SO4

Figure A-2 Validation of Ho determination for aqueous sulfuric acid solutions at 293 K with two different indicators

91 Chapter 3, Appendix A

In Figure A-3 the effect of addition of Pivalic Acid is compared to adding water to a 96 wt%, 89 wt% and 80 wt% H2SO4 solution respectively (thus dilution of the sulfuric acid solutions). It appears that on a molar basis, the effect of Pivalic Acid is stronger than the influence of water (Note that on a weight basis the opposite is valid). The reason for this may be found in the protonation and dehydration equilibria of Pivalic Acid. On addition of Pivalic Acid to a strong sulfuric acid solution the Pivalic Acid will be protonated (thereby reducing acidity) and, additionally, dehydration may occur (which is in fact the addition of water).

It should be stressed at this point that these results were obtained for a limited variation of acid strengths in the range of 70-90 wt% H2SO4.

2.00 initial concentration ∆ H2SO4 solution [wt%] Ho 1.80 70.5 1.60 72 1.40 75.2 76.8 1.20 adding 78.4 Pivalic Acid 1.00 79.2 0.80 82 84 0.60 88 0.40 89 0.20 80 wt% soln. adding H O 0.00 89 wt% soln. 2 0 0.1 0.2 0.3 0.4 0.5 96 wt% soln.

mole Pivalic Acid (or mole H2O) added per mole H2SO4

Figure A-3 Influence of addition of water and pivalic acid to H2SO4 solutions of different strength

(Initial Hammett Acidity value (Ho)o is within the range [5.8-8.8])

For the lower acidities (< 75 wt% H2SO4) the solubility of Pivalic Acid is limited, therefore only the results for the addition of small amounts of Pivalic Acid are reported in Figure A-3 for these conditions.

4. Discussion and conclusions

In the range of 70-90 wt% sulfuric acid solutions, and probably also at higher acid strengths, Pivalic Acid has a considerable influence on the apparent acidity of the sulfuric acid solution, as determined by the Ho-measurements using the indicator method described. On a molar basis, the

92 Chapter 3, Appendix A acidity reducing effect of Pivalic Acid on (-Ho) for a sulfuric acid solution significantly exceeds the effect of water addition (dilution). The Ho decrease for sulfuric acid solutions containing Pivalic Acid imply for the Koch synthesis of Pivalic Acid from isobutanol that the overall CO consumption kinetics for the Koch synthesis of Pivalic Acid will decrease correspondingly. This is tested and validated in Chapter III. Since the amount of isobutanol was also found to be important for the CO consumption rate in the Koch synthesis of Pivalic Acid, a similar effect on the Ho value may hold for isobutanol. The effect of isobutanol on the Hammett acidity was, however, not studied further by Ho measurements using the indicator method. For tert-butanol and isobutene the Ho measurements would be disturbed too much by the occurance of chemical reactions (and -products formed) during the measurements.

In Figure A-4 the apparent change in the Ho value, as was recalculated from the measured decrease in the CO consumption kinetics, are presented for different (initial) concentrations of isobutanol in an 91 wt% sulfuric acid solution and of Pivalic Acid present in 70-89 wt% catalyst solutions. Both Pivalic Acid and isobutanol have a strong effect on the reaction kinetics. Analoguous to the effect of the addition of Pivalic Acid, which was shown to be directly related to a decrease in the acidity of the catalyst solution, the influence of the isobutanol content of the catalyst solution on the reaction kinetics will most likely occur via the solution acidity.

4.0 isobutanol ∆ Ho (app.) 3.5 pivalic acid Linear (isobutano 3.0 Linear (pivalic ac 2.5

2.0

1.5

1.0

0.5

0.0 0 0.1 0.2 0.3 0.4 0.5

mole (pivalic acid or isobutanol) / mole H2SO4

Figure A-4 Effect of the presence of reactant (isobutanol) and product (pivalic acid) on the apparent catalyst solution acidity as determined by the CO consumption kinetics for the Koch syntheses of Pivalic Acid

93 Chapter 3, Appendix A

Notation a activity [mole/m3] E extinction H+ protonating species in the catalyst solution Ho Hammett Acidity Function (defined in Appendix) I Indicator K equilibrium constant protonation reaction I + H+ ⇔ IH+ [l/mole] pK - 10log(K) kov overall first order reaction rate constant [1/s] kov,∞ kov, extrapolated to zero reactant concentration [1/s] ni amount of component i [mole] T temperature [K] [..] concentration of .. [mole/m3]

Super- and subscripts I indicator (unprotonated) IH+ protonated indicator o initial condition

Greek symbols

γi activity coefficient component i λ wave length

References

Johnson C.D., Katritzky A.R., Shapiro S.A., 1969, The temperature variation of the Ho Acidity Function in aqueous sulfuric acid solution, J.Am.Chem.Soc., 91, 6654-6662

Jorgenson M.J., Hartter D.R., 1963, A critical re-evaluation of the Hammett Acidity Function at moderate and high acid concentrations of sulfuric acid. New Ho values based solely on a set of primary aniline indicators, J.Am.Chem.Soc., 85, 878-883

Paul M.A., Long F.A., 1957, Ho and related indicator acidity functions, Chem.Rev., 57, 1-45

Tamura K., Dan M., Moriyoshi T., 1990, Pressure dependence of the Hammett Acidity Function (Ho) II. Aqueous sulphuric acid solutions, J.Chem.Res. (M), 849-865

Tickle P., Briggs A.G., Wilson J.M., 1970, The protonation of weak bases. A study of the protonation of some nitroaniline indicators and the determination of the Ho values of aqueous sulphuric acid, J.Chem.Soc. (B), 65-70

94 Chapter 3, Appendix B

APPENDIX B

On the product composition in the catalyst solution

The product composition in the aqueous sulfuric acid solution under reaction conditions may be important for selecting optimum reaction - and quench conditions. In this section an indication for the position of the reaction equilibria (B-1)..(B-4) will be obtained.

a + = + ⇔ + = R R + H R K1 (B-1) aa=+ RH

a + + ⇔ + = RCO R + CO RCO K 2 (B-2) aa+ R CO

a + RCOOH + ⇔ + = 2 RCO + H2O RCOOH2 K 3 (B-3) aa+ RCO HO2

aa+ + ⇔ + = RCOOH H RCOOH2 RCOOH + H K 4 (B-4) a + RCOOH2 Using these equations the product distribution as well as the relative Pivalic Acid solubility may be calculated. The latter is valid only if the physical solubility of Pivalic Acid, [RCOOH], is known under the conditions considered. In this section this value will be assumed to be approximately constant within the range 50-80 wt% and equal to the value at 50 wt% sulfuric acid solution. The Pivalic Acid solubility in a 50 wt% sulfuric acid solution is approximately 50 mole/m3 acid solution. As can be seen from Figure B-1, the Pivalic Acid solubility increases sharply around 70 wt% H2SO4 solutions.

Equation (B-5) now describes the relative solubility S/So (as defined in equation (B-6)), assuming + + + + + that the activity coefficient ratios for RCO /R , RCOOH2 /RCO and RCOOH/RCOOH2 are constant (analoguous to the 'Hammett cancellation assumption')

S a ++a a + 1 =+1 HH + +H + (B-5) S K 'KKa ''KKKa ''' a KKKKa '''' a o 443HO22 432HO CO 4321 HO 2 CO

In this equation So represents the solubility at the reference conditions chosen.

=+ + + S [][][R++ R RCO ][ + RCOOH ][ + RCOOH ] = 2 (B-6) So []RCOOH

95 Chapter 3, Appendix B

For the activities of water and the protonating component H+ a tabulation by Brock Robertson -Ho and Dunford (1964) and the estimation aH+ = 10 were used respectively. Additionally, the equilibrium constants K1'..K4' need to be estimated.

60 (dissolved) wt% Pivalic Acid in est. Solubility saturated solution 50 (not dissolved) Komatsu et al. (1974)

0 55 60 65 70 75 80 85 90

initial wt% H2SO4

Figure B-1 The solubility of Pivalic Acid in H2SO4 solutions at 293 K

Deno et al. (1964) determined the sulfuric acid concentration in which acetic acid and propionic + acid are half-protonated, thus [RCOOH] = [RCOOH2 ], to be 77 and 80 wt% sulfuric acid respectively. Edward and Wang (1962) did similar measurements for propionic acid using UV spectrophotometry. The latter technique was also used in this work for Pivalic Acid. From the experimental results obtained, this value appears to be approximately 69 wt% of sulfuric acid.

According to Eq. (B-4), the value of K4' can now be estimated via Eq. (B-7).

+ + [RCOOH 2 ] a H ' = = ⇒ = + (B-7) ' 1 (69wt%) K 4 a H (69wt%) [RCOOH] K 4

With similar measurements for Pivalic Acid the value of K3' may be obtained via Eq. (B-8), when the water activity is known at these conditions.

[]RCO + 1 ==1 (B-8) []RCOOH+ K' a 23HO2

96 Chapter 3, Appendix B

Deno et al. (1964) determined the conditions at which the concentrations of [RCO+] and + [RCOOH2 ] were equal for propionic acid (23% SO3 in sulfuric acid). Comparable results for the position of this equilibrium. for propionic acid and acetic acid were obtained by Paillous (1977), using an infrared technique. In his experiments with Pivalic Acid the measurement technique failed since decarbonylation was too fast to determine reliable RCO+ concentrations. However, from the tabulation of the water activity by Brock Robertson and Dunford (1964) it seems that the value of 5 K3' will be at least 10 [l/mol].

3 For K2' a value of 10 [l/mol] is taken according to the work by Hogeveen et al. (1970). Deno -2.5 + = (1964b) reported a value of 10 for the ratio [R ]/[R ] in 96 wt% H2SO4 solutions, which would -12.5 imply a K1' value of 10 . Inserting these estimations of K1'..K4' into the equilibrium model, the following results for the solubility of Pivalic Acid (Figure B-2) and for the product composition (Figure B-3 a, b) at different acid strengths are obtained

1000 [set 1] [set 2] relative solubility i log(Ki) log(Ki) S/So [-]

100 1 -12.5 -12.5 2 3.0 6.0 3 5.0 0.0 4 5.6 5.7

Equilibrium Model 1 this work Komatsu et al. (1974) (Best fit of data this work) 0.1 50 60 70 80 90 100

(initial) wt% H2SO4

Figure B-2 Equilibrium model for the solubility of Pivalic Acid in sulfuric acid solutions (293K)

In Figure B-3 c,d) the resulting product composition for set1 and set 2 (which are presented in Figure B-2) is shown. Although the parameter sets describe the solubility curve equally well, the product distribution as well as the sensitivity thereof to the CO pressure differs significantly.

97 Chapter 3, Appendix B

1 1

relative relative concentration concentration

0.75 0.75

RCOOH RCOOH RCOOH2+ RCOOH2+ 0.5 RCO+ 0.5 RCO+ R+ R+ R= R=

0.25 0.25

0 0 50 60 70 80 90 100 50 60 70 80 90 100 wt% H SO 2 4 wt% H2SO4 (a) Product composition at 0.1 bar CO (b) ... and at 40 bar CO -12.5 3 5 5.6 Parameter set : K1' =10 , K2' = 10 , K3' = 10 , K4' = 10

1 1 relative relative concentration concentration

0.75 0.75

RCOOH RCOOH RCOOH2+ RCOOH2+ RCO+ 0.5 RCO+ 0.5 R+ R+ R= R=

0.25 0.25

0 0 50 60 70 80 90 100 50 60 70 80 90 100 wt% H2SO4 wt% H2SO4

(c) Product composition at 1 bar CO (d) ... and at 40 bar -12.5 6 0 5.7 Parameter set : K1' =10 , K2' = 10 , K3' = 10 , K4' = 10

Figure B-3 Product compositions at 0.1 bar and 40 bar CO for two different sets of parameters

Although the equilibrium model presented must be regarded as a simplification of the actual reaction equilibria in the reaction mixture, the observed trend in the Pivalic Acid solubility is reasonably well described using the global parameter set estimated (Figure B-2). The model may prove to be an useful tool in further analysing the influence of e.g. pressure and temperature or quench conditions on the reaction products to be expected.

98 Chapter 3, Appendix B

Notation a activity [mole/m3] H+ protonating species in the catalyst solution K Equilibrium constant, defined in (B-1)..(B-4) R alkyl group R= isobutene R+ tert-butyl cat ion RCO+ tert-butyl acyl cat ion + RCOOH2 protonated Pivalic Acid RCOOH Pivalic Acid S solubility [mole/m3] [..] concentration of ... [mole/m3]

Super- and subscripts

CO carbon monoxide H2O water o initial condition

References

Brock Robertson E., Dunford. H.B., 1964, The state of the proton in aqueous sulphuric acid, J.Am.Chem.Soc., 86, 5080-5089

Deno N.C., Pittman C.U., Wisotsky M.J., Carbonium ions. XVIII., 1964, The direct observation of saturated and unsaturated acyl cations and their equilibria with protonated acids, J.Am.Chem.Soc., 86, 4370-4372

Deno N.C., 1964, Progr.Phys.Org.Chem., 2, 129 ff

Edward J.T., Wang I.J., 1962, Ionization of organic compounds, Can.J.Chem., 40, 966-975

Hogeveen H., Baardman F., Roobeek C.F., 1970, Chemistry and spectroscopy in strongly acidic solutions. Part XXX. Study of the carbonylation of carbonium ions by NMR spectroscopic measurements, Rec.Trav.Chim.Pays Bas, 89, 227-235

Paillous P., 1977, Intermédiares réactionelles en chimie organique: mise en évidence et domaine d'éxistance d'ions acyliums dans des milieux fortements acides, Bull.Soc.Chim.Fr., 415-420

99 Chapter 3, Appendix B

100 CHAPTER 4

Gas absorption in liquid-liquid dispersions

Abstract

In gas-liquid reaction systems the rate of gas absorption is often limiting the production rate due to the low solubility of the gas phase reactants. It has been noticed frequently that the addition of a dispersed liquid phase to a gas-liquid system may increase the gas absorption rate. The effect of the addition of a dispersed liquid phase on the mass transfer parameters like the gas holdup and the interfacial area for a gas-liquid system has been studied occasionally and is reviewed in this work. However, no general results could be derived. Moreover, the observed effects are insufficient to account completely for the enhanced gas absorption rate.

One possible explanation for the observed enhancement of the gas-liquid mass transfer rate is the occurrence of direct gas-dispersed phase contact. Experimental work shows the existence of complexes of a gas bubble and an organic phase droplet under forced and ‘free’ collision conditions. These complexes may be formed on collision of a gas bubble and an organic phase drop if the total amount of surface energy is reduced on the formation of the complex. The contribution of the complex formation mechanism to the overall gas absorption rate is discussed short, but awaiting further study.

101 Chapter 4

102 Chapter 4

1. Introduction

Multi-phase reaction systems are frequently encountered in practical applications. The reaction engineering aspects involved have always been a challenging subject to chemical engineers. Among these systems, gas-liquid-liquid reaction systems received only little attention, although their industrial importance is considerable. Initially, the main applications of gas-liquid-liquid operation were found in bioengineering, carbonylation- and alkylation reactions. In biochemical applications gas absorption in liquid-liquid dispersions is e.g. encountered when hydrocarbons, finely dispersed as droplets in the aqueous phase, are used as substrate in aerobic fermentors (Yoshida et al., 1970).

Recently, the operation of gas-liquid-liquid reaction systems received considerable attention, due to new developments in homogeneous catalysis in aqueous media using noble metal complexes (Herrmann and Kohlpaintner, 1993; Chaudhari et al., 1995). By heterogenizing a homogeneous catalyst in a separate liquid phase the advantages of homogeneous catalysis (as high activity due to the presence of ‘single active sites in solution’ and stereo-selectivity) are combined with an easy catalyst retrieval, which is usually the main disadvantage of homogeneous catalytic processes.

Gas-liquid-liquid reaction systems can nowadays be found in e.g. hydroformylation (Kuntz, 1987), biochemical processes (Junker et al., 1989; Rols et al., 1990), fine chemicals manufacturing (Mills and Chaudhari (1997), hydrogenation, alkylation (e.g. the production of ethylbenzene by alkylation of benzene by ethylene), hydroxycarbonylation (Falbe, 1980), hydrometallurgy (Levy et al., 1981; Gaunand, 1986) and polymerisation reactions, as e.g. found in the SHOP process (Freitas and Gum, 1979) and in gas-liquid emulsion polymerization (Scott et al., 1994).

The class of gas-liquid-liquid reaction systems can be divided into systems which are intrinsic gas- liquid-liquid systems, since the reactants and products form separate phases, and gas-liquid-liquid systems which are deliberately created by adding an immiscible liquid to a gas-liquid reaction system. In the latter case it is aimed for e.g. an increased conversion (and selectivity) for equilibrium reactions by product extraction (Rivalier et al., 1995), to extract reaction inhibiting products (Weilnhammer and Blass, 1994), to enable easy catalyst retrieval by phase settling (as in

103 Chapter 4 the SHOP-process), to increase the gas absorption rate (Junker et al., 1990) or to obtain higher selectivity due to effects on gas-liquid mass transfer and mixing (Schultze et al., 1958) respectively. It will be clear that the benefits of the effects aimed for by adding a dispersed liquid phase, should overcompensate the additional costs involved with an extra separation step required.

The importance of the reaction engineering aspects of gas-liquid-liquid (G-L-L) systems have been stressed several times (Yoshida et al., 1970; Gaunand, 1986; Mills and Chaudhari, 1997), but no extensive, complete study on these aspects has been performed. In G-L-L reaction systems in which the reaction kinetics are slow, the mass transfer phenomena are of minor importance, and frequently the system can be regarded to be at (physical) equilibrium, as in the work of Purwanto and Delmas (1995). However, for higher reaction rates concentration gradients near the interfacial area(s) start to develop and mass transfer influences the observed conversion rates and selectivities.

In accordance with most G-L-L systems encountered in literature, it is assumed in this work that at least one of the reactants originates from the gas phase. The gas absorption rate is thereby often limiting the production capacity in multiphase reactors, since the solubility of the gas phase reactants is usually relatively low (Beenackers and van Swaaij, 1993). This is illustrated, for example, in biochemical engineering applications in which a dispersed organic phase, having a higher solubility for the gas phase component, is deliberately added to the air-aqueous liquid phase system as oxygen transfer agent. In this way, the oxygen transfer rate from the gas phase to the liquid phase can be increased without increasing power input which ultimately may lead to damage for the cell culture (Junker et al., 1990; van Sonsbeek et al., 1992).

In this work attention will, therefore, be focused on gas absorption in (non-emulsified) liquid- liquid dispersions. Phenomena observed in literature will be discussed and an analysis of the mass transfer mechanisms will be presented.

104 Chapter 4

2. Literature overview

In the majority of the work presented in literature on gas absorption in liquid-liquid dispersions an enhanced gas absorption rate compared to the two phase system is reported. In these studies a rather global definition of the enhancement effect is used, by comparing the volumetric mass transfer parameter kLa (at the same driving force) for the two-phase system and three-phase system used, see eq (1).

()kaL = GLL−− E1 (1) ()ka L GL−

The enhanced absorption rate, however, may be caused by changes in the gas-liquid interfacial area a, the gas phase hold-up, the liquid side mass transfer coefficient kL or even by different transport mechanisms for the gas phase component respectively. The studies presented in literature on the gas absorption rates in G-L-L systems as well as studies on the individual mass transfer parameters mentioned above will be discussed.

2.1 Effect of an immersed liquid phase on the mass transfer parameters kLa, kL, a and εG One of the first studies on the effect of the addition of organic substances on gas absorption in an aqueous liquid phase was the one by Eckenfelder and Barnhart (1961). They used gas absorption experiments from rising single bubbles to study the effect of addition of surfactants to an aqueous liquid phase. Since in their experiments the interfacial area a was (assumed to be) known by a photographic method, the effects on kLa and kL could be separated. It was found that especially the kL value initially decreased some 50% with the addition of only small amounts (up to 50 ppm) of surface active organic substances. This may be caused by the surfactant molecules forming a semi-rigid barrier for the transport of the dissolved gas phase components at the interface. After this initial decrease, the apparent kL values as well as the kLa values increased with the amount of organic substance. At concentrations above 2000 ppm a net increase in kLa was observed (E1 = 1.74 at 2 vol% peptone).

Yoshida et al. (1970) found similar effects for the oxygen absorption rate on addition of toluene and oleic acid to water in an agitated, aerated tank reactor. Initially, at low dispersed phase fractions ( < 10 vol%) a value of E1 < 1 was found. However, at increasing dispersed phase hold- up (φv) the value of E1 increased up to about 3 at φv = 25 %, as schematically represented in

105 Chapter 4

Figure 1-a. The same authors also used kerosene and n-alkanes and found a negative effect on the oxygen transfer rate for dispersed phase fractions up to 25 vol% (Fig. 1-b), although the oxygen solubility in these liquids also is significantly higher than in water (Table I). According to Yoshida et al. (1970) the difference in behaviour ‘has something to do’ with the (initial) spreading coefficient Si of the dispersed liquid phases used; liquids having a positive spreading coefficient

(Si > 0) enhance the gas absorption rate whereas liquids with a negative spreading coefficient

(Si<0) retard the gas absorption. The initial spreading coefficient Si determines whether a (organic) liquid droplet will spread initially on the water/gas interface or not, and is defined in equation (2).

Siwgogow=−σσσ///() + (2)

The gas hold-up in these systems has also been determined by Yoshida et al (1970). The results, depicted in Figure 2, demonstrate that the gas hold-up shows similar curves as kLa-φv but this effect is not able to account completely for the observed increase in apparent kLa value. If the bubble size is approximately independent of the hold-up in this range, the apparent relative kL values can be estimated from the variation in kLa and εG, as presented in Figure 3.

5 1

Junker et al. (1990): O2 in FC40 perfluorocarbon (S i >0) E1 E1

Hassan and Robinson (1977): n-dodecane ( S i < 0 ) 4 0.8

Yoshida et al. (1970): O2 in toluene, 0.6 3 oleic acid, Tween 85 (S i >0) Yoshida et al. (1970): kerosene, liquid paraffin ( S i < 0 )

2 0.4

Elibol, Mavituna (1997):

O2 in perfluorodecalin 1 Lekhal et al. (1997): H2 in octene 0.2 (Si>0) Hassan and Robinson (1977):

O2 in n-hexadecane (S i <0) 0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 φ φ v [-] v [-]

Figure 1-a,b Relative volumetric G-L mass transfer coefficients for different organic phases

106 Chapter 4

5 1.4 ε ε toluene Yoshida et al. (1970) G/ G, (G-L) kL / kL, G-L n-alkanes, Linek and Benes (1976) 1.2 oleic acid, Linek and Benes (1976) 4

3 0.8

0.6 2

0.4

toluene (550 rpm) Yoshida et al. (1970) 1 0.2 toluene (1300 rpm) Das et al. (1986) 2-ethyl hexanol (1300 rpm) Das et al. (1986) 0 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.05 0.1 0.15 0.2 0.25 0.3 φ [-] φ v v [-]

Figure 2 Relative gas hold-up Figure 3 Relative kL values

Table I Relative gas phase solubilities for the 1.6 experiments presented in Fig. 1-4 aG-L-L / aG-L 1.4 organic phase mR

1.2 toluene 8.2 1 kerosene 4.3 oleic acid 4.8 0.8 n-dodecane 8.1 0.6 hexadecane 7.5 2-ethyl hexanol 7.5 0.4 toluene (1300 rpm) Das et al. (1986) perfluordecaline 6 0.2 2-ethyl hexanol (1300 rpm) Das et al. (1986) octene 5 2-ethyl hexanol (750 rpm) Mehta, Sharma (1971) FC40 12 0 0 0.05 0.1 0.15 0.2 0.25 0.3 ‘n-alkanes’ 7.5 φ v [-] ‘liq.paraffins’ 4.0

Figure 4 Relative gas-liquid interfacial area

The liquid side mass transfer coefficient kL was the objective of a study by Linek and Benes

(1976) for gas absorption in aqueous dispersions of n-alkans (Si < 0) and oleic acid (Si > 0). For systems with n-alkanes as dispersed phase the kL value remained essentially constant and the hold- up increased to about 18 vol%, which was the phase inversion point as stated by the authors. For oleic acid a sharp initial decrease, followed by a slight increase with φv was observed for the kL value. With the organic phase being the continuous phase, the kL value increased linearly with the volume fraction dispersed phase. Therefore, Linek and Benes (1976) suggested that there is no direct contact between gas and the dispersed liquid phase for o/w (organic in water) dispersions with a negative value for the spreading coefficient. The gas phase transport route is sequential via

107 Chapter 4 g → w → o. For w/o systems a parallel path occurs from the gas phase to both liquid phases according to Linek and Benes (1976), irrespective of the value of the spreading coefficient.

Hassan and Robinson (1977) performed oxygen absorption experiments in a G-L-L system using a sparged, agitated tank reactor. A sharp initial decrease in kLa for n-dodecane and an increase for n-hexadecane with increasing φv was observed, although both components have a negative (initial) spreading coefficient. Further, it was found that the E1 values are independent of the power input ( 103 < P/V < 104 [W/m3] ) and of the gas superficial velocity.

The effect of a dispersed liquid phase on the gas-liquid interfacial area has been studied by Das et al. (1985), using both a physical method (via the bubble size and gas hold-up) and a chemical method (CO2 absorption in NaOH solutions) respectively. As dispersed organic phases toluene, methyl isobutyl keton (MIBK) and 2-ethyl hexanol (EH) were used, together with tricresyl fosfate as anti-foaming agent (which may have influenced the results). A maximum in the interfacial area with increasing volume fraction dispersed phase was found, see Figure 4. As the bubble size in the impeller zone was found to increase linearly with the dispersed phase hold-up for the range of 0 ≤

φv ≤ 0.5, the initial increase was explained by the initial increase in the gas phase hold-up and a slight decrease in bubble size due to coalescence reduction at dispersed phase hold-up φv < 0.2. At higher hold-up's the bubble size starts to increase and the gas hold-up decreases, both effects leading to a decrease in the gas-liquid interfacial area. The initial bubble sizes in the impeller zone were found to be equal for the toluene, MIBK and EH dispersions. The mean bubble size for MIBK and EH is, however, larger, thus it seems that toluene is more effectively hindering bubble coalescence.

Junker et al. (1990a,b) studied oxygen absorption in liquid-liquid dispersions of a typical fermentation broth to which an immiscible perfluorcarbon phase was added. By using fluorophors the oxygen concentration in both phases could be followed and both liquid phases were found to be always at equilibrium. The enhancement factor increased drastically after the inversion point

(55 vol%). Other studies on the apparent kLa values for the oxygen absorption rate on addition of an immiscible liquid phase to fermentation systems include those by e.g. Rols et al. (1990), van de Meer et al. (1992), Liu et al (1994) and Jia et al. (1996). The results of their studies are in agreement with the reported kLa trends mentioned above. Lekhal et al. (1997) studied the

108 Chapter 4

absorption of hydrogen in octene/water dispersions and found a maximum in the kLa-enhancement at 3-4 vol% dispersed phase (see Figure 1-a). The effect was somewhat stronger at higher stirring rates. Chaudhari et al. (1997) found an increasing absorption rate for CO absorption in NaOH solutions on addition of hexane as dispersed phase.

Summarising, the following remarks can be made. Generally, the gas absorption rate is enhanced in the presence of a dispersed organic phase having a higher solubility for the gas phase component. In a few cases, however, a decreased gas absorption rate was observed. The trend of the apparent kLa value with increasing dispersed phase hold-up differs strongly for the systems reported. This may be caused by the physico-chemical properties of the system used or it may be due to the specific hydrodynamic conditions. No conclusive explanation can be presented yet. In most of these experiments not all relevant mass transfer parameters (as gas hold-up, bubble size and drop size) have been considered and effects like an increase in the dispersion viscosity is often disregarded. The effect of an immiscible liquid phase on the individual mass transfer parameters kL, a, εG in gas-liquid-liquid dispersions has been studied in a few cases, but, again, no general results could be derived.

2.2 Gas-liquid mass transfer paths In several publications there is some speculation on the existence of a parallel transport of the gas phase component to the continuous phase and to the dispersed phase via direct gas-dispersed phase contact (see e.g. Yoshida et al., 1970; Linek and Benes, 1976; Hassan and Robinson, 1977; Das et al., 1985; Rols et al., 1990; McMillan and Wang, 1991). According to the literature overview by McMillan and Wang (1991) the g→w→o mass transfer path is the most probable mass transfer path for systems with Si<0, whereas the occurrence of direct gas-dispersed contact for systems with Si>0 remains speculative. The two mass transfer paths are represented schematically in Figure 5.

GAS AQUEOUS PHASE GAS AQUEOUS PHASE

ORGANIC ORGANIC PHASE drops PHASE

Figure 5-a) g→w→o mass transfer path 5-b) g→w, g→o parallel mass transfer paths

109 Chapter 4

Direct gas-dispersed contact was studied experimentally by Roques et al. (1986). In their study gas bubbles and organic phase droplets, both created at the top of small capillaries submerged in water, were brought into forced contact with each other. At contact ‘complexes’ or ‘gas-organic drops’ were formed, see Figure 6, leading to a third transport route; g → o → w, in case these complexes are relatively long-living.

‘gas-organic drops’ or ‘complexes’

Figure 6 ‘Complexes’ formed on coalescence of gas bubbles and organic phase drops

These complexes consist of a gas bubble covered by a skin of organic phase. In their study the drops of organic phase were larger than the gas bubbles. They observed that one drop could incorporate several bubbles. The kinetics of these ‘coalescences’ were found to be influenced significantly by mass transfer. Mass transfer towards the continuous phase (either from the drop or bubble) enhanced the coalescence rate, whereas transfer from the continuous phase to the dispersed phase droplet did hinder coalescence. Typical coalescence times under these forced collision conditions for the ‘pure’ kerosene-air system were found to be 3-4 s. When mass transfer is occurring, the coalescence times were reduced to 0.2 s or increased to ± 10 s respectively. Rols et al. (1990) confirmed the coalescence of bubbles and drops under forced collision conditions for their systems, n-dodecane-water and Furane 66-water.

The gas → organic phase → aqueous phase (g → o → w) mass transfer path may now occur through the formation and break-up of these complexes (as proposed by Rols et al. (1991) for systems with Si > 0), see Figure 7. Depending on size ratios and characteristic timescales this mass transfer route can be considered a parallel route or as a mass transfer resistances-in-series configuration G L

1−φv

φ v

G-L interface

Figure 7 Coalescence of a drop and a bubble and break-up of the complex formed

The existence of these complexes is discussed in the next section.

110 Chapter 4

3. Gas-dispersed phase contact in an agitated G-L-L contactor

From the literature overview it became clear that direct contact through ‘coalescence’ of a dispersed gas phase and a dispersed organic liquid phase is possible when they collide. In the studies presented in the literature overview an organic liquid phase drop and a gas bubble were forced to collide. Whether these collisions and complex formation occur in a multi-phase system where both the drops and bubbles move due to hydrodynamic and gravity forces is uncertain. The relevance of the spreading coefficient as well as the formation of complexes under free-collision have been studied in this work through qualitative, scouting experiments.

First, qualitative experiments for the determination of the spreading coefficient were performed by placing a droplet of an organic liquid phase on a water-air surface. To determine whether or not spreading occurred, the surface was covered with chalk powder. Initial spreading occurred for toluene, dodecane, oleic acid, 1-octanol and heptane, whereas for hexadecane, kerosene, refined petrol and cyclohexane no initial spreading was observed. After mutual saturation of the water and organic phase used, the spreading coefficient S* was negative (no spreading) in all cases. For a completely backmixed G-L-L reaction system the initial spreading coefficient Si is therefore not a relevant parameter and the actual spreading coefficient in mutually saturated systems appears to be negative for all systems.

The forced contact experiments (see Figure 8), similar to those of Roques et al. (1986), were carried out using toluene, dodecane and refined petrol as dispersed phase. In all cases complexes were formed, irrespective of the initial spreading coefficient Si. The organic phases used, were coloured by using Scarlet Red and Tracer Yellow (DAY-GLO Color Comp.) to increase the visibility of the organic-gas drops formed. The effect of the colour compounds on spreading behaviour and on surface tension (as determined by the Wilhelmy plate method using a Krüss K12 Tensiometer) of the organic liquids used was found to be negligible.

111 Chapter 4

‘complex’

organic phase droplet

gas bubble capillary

Figure 8 Forced collision experiments

By video analysis of the experiments, it was observed that coalescence occurred within 0.04 s (being the timescale between two frames) after initiation of the contact. For the coalescence of a second organic phase droplet with the complex a considerable longer contact time, 2-10 seconds, was required.

To study if the complexes will be also formed in a dynamic three phase system, the setup in Figure 9 has been designed and used. water in

organic phase injection waterflow droplets UV light video observation

video bubble

complex

Figure 9 Setup for the 'dynamic' experiments water out

112 Chapter 4

The setup consists of a conical tube, mounted vertically, which is purged with water in downflow. In the conical tube one or more rising bubbles were kept at a stationary position were the buoyancy forces and drag forces balance. To obtain a uniform water velocity it is important to keep the top angle of the contactor as small as possible (3.5 ° in the set up used). The diameters of the gas bubbles and organic phase drops were approximately 3 and 1 mm respectively. Per experiment shots of 1 ml organic phase were injected in the water flow. The organic phases were coloured with Tracer Yellow and could be visualised by UV-light. Approximately once per 5 injections a complex was formed. These results were obtained for all organic phases used, irrespective of the initial spreading coefficient. For oleic acid a complex as represented schemetically below is observed, which is probably due to the relatively high viscosity of the oleic acid. Complex for oleic acid

Both the forced collision experiments (Figure 8) as the dynamic experiments (Figure 9) show that direct gas-dispersed phase contact is very well possible in a G-L-L contactor. The complexes, once formed in the dynamic experiments, remained stable and no break-up or ‘growth of the organic skin’ was observed during additional injection experiments. This implies that the mass transfer path becomes g→o→w in this situation.

The existence of complexes may also be discussed from surface energy considerations. The change in surface energy on complexation can be calculated according to Eq. (3).

∆ =+−−πσ22 σ σ 22 σ ERRRRSgo4 ()[]−−b ow c ow −d gw −b (3)

In this equation Rc represents the radius of the gas-organic complex. If the organic phase drop is significantly smaller than the gas bubble (which is not uncommon), then Rc will be approximately equal to Rb. With this assumption, it can be derived that the formation of a organic-gas drop is favourable (∆ES < 0) if the bubble-to-droplet size ratio satisfies the criterion in Eq (4).

2  R  σ* σ*  b  < ow/ = ow/ (for S* < 0) (4)   σσσ* +−* * − * RSd ow/ og/ wg/

For S* > 0 (if possible), the complexation would be favourable for any size ratio. Note that in these equations the interfacial tensions for a mutually saturated (σ*) system should be used.

113 Chapter 4

Especially the surface tension of water may change drastically on addition of small amounts of an organic phase. According to this criterion it is e.g. impossible to create drop-water complexes in a continuous heptane liquid phase, which can be easily verified by forced contact experiments. Besides the criterion mentioned above, there exists a minimum film thickness, usually 20-100 Å (Davies and Rideal, 1961). Below this minimum film thickness the film breaks up and forms lenses.

4. Enhancement of gas absorption in liquid-liquid dispersions by complexes

From the literature overview it can be concluded that usually the addition of an immiscible organic liquid phase to an aqueous liquid phase leads to an increase of the gas absorption rate. The first requirement for this phenomenon is that the solubility of the gas phase component in the dispersed liquid phase is significantly higher than the solubility in the continuous liquid phase. For the most common gases and organic liquids encountered in the G-L-L systems this condition is satisfied, as can be seen from the solubility ratio mR in Table II (data are taken from Fogg and Gerrard (1991)).

Table II Relative solubilities (mR) of some gases in organic phases at 298 K, 1 bar partial pressure

gas phase Heptane n-Octanol Hexadecafluoroheptane component (alkanes) (alcohols) (perfluorcarbons)

carbon dioxide 2.4 2.4 2.7 hydrogen 6.0 2.7 8.0 carbon monoxide 12.0 4.9 18.1 oxygen 10.9 5.6 19.4 ethene 24.8 12.8

In Table II heptane, octanol and hexadecafluoroheptane were used as typical examples of the compound classes n-alkanes, alcohols and perfluorcarbons respectively. It should be considered that for aqueous electrolyte systems the mR values reported can easily be a factor 2-10 higher than indicated above, due to salting out effects in the aqueous phase. In these situations relative solubility values of 10 - 200 are easily obtained. For specific applications even higher solubility ratios can be found. It is clear that in almost any w/o gas-liquid-liquid system enhancement of gas absorption can be expected.

114 Chapter 4

Two mechanisms may account for the enhanced mass transfer, according to literature. The first one is the so-called shuttle mechanism, which is also encountered in gas-liquid-solid three phase systems. The presence of very fine, gas-absorbing droplets within the mass transfer zone near the gas-liquid interfaces may increase the specific gas absorption rate at unit driving force and unit interfacial area. The shuttle mechanism requires the dispersed phase drops to be very small, about the same order of magnitude of thickness of the mass transfer film (as defined in the well known film model) or smaller. For more details on the mechanism the reader is referred to Beenackers and van Swaaij (1993). More details on experiments and models concerning this mechanism in gas-liquid-liquid systems are presented in the Chapters 5 and 6 (Brilman, 1998).

Another possible mechanism could be the enhancement of gas absorption through direct gas- dispersed phase contact. In the previous section it was shown that this may occur (irrespective of the value of the spreading coefficient) in the form of complexes, if the surface energy criterion

∆ ES < 0 is fulfilled. In the following, attention is focused on this latter mechanism.

Since usually an agitated tank is used for operating G-L-L systems, drop- and bubble size correlations for a sparged, agitated tank may be used to estimate at which conditions the surface energy criterion mentioned is expected to be fulfilled. Taking the correlations by Calderbank (1967) for drops and for gas bubbles in electrolyte solutions Eq (5) is obtained for the bubble-to- drop size ratio.

025. R σ*  µ  ε 04. b ≅⋅10 w ⋅ G  G (5) σ*  µ  φ 05. R d ow/ o v

From Eq(4) and (5) a criterion for a minimum dispersed phase hold-up for the existence of complexes can be derived:

205. ()−S*  σ*   µ  φ >⋅100 ⋅ w  ⋅ G  ⋅ε 08. (6) V σ*  σ*   µ  G ow/ ow o

It should be realised that the correlations of Calderbank (1967) are determined for a certain set of conditions and, even more important, the correlations applied describe the mean bubble and drop diameter in the system. This implies that at a lower hold-up also incidentally complexes can be formed due to the bubble- and drop size distributions.

115 Chapter 4

Application of Eq. (6) is hampered by the availability of, especially σw*, surface tension data in literature. For toluene and kerosene these σw* valued were measured and for benzene the value was presented by Davies and Rideal (1961). With these values, equation (6) was used to estimate the minimum hold-up required at 5 % gas hold-up for toluene/water, kerosene/water and benzene/water systems and the minimum values found are 0.03 (± 0.03) (303 K), 0.3 (± 0.1) (303 K) and 0.15 (±0.05) (293 K) respectively. For the frequently used perfluorcarbon components, the value will be approximately 0.1 (± 0.1).The criterion is, however, rather sensitive to the surface tension values used, especially through S*. For highly viscous organic liquids the criterion in Eq. (6) may not be sufficient. In these cases also the kinetics of spreading may become important.

Before one is able to estimate the contribution of the complex formation to the gas absorption rate, the probability of formation of these complexes in a system is important. To estimate this, the use of a population balance seems appropriate. This has not been done, however, some relevant comments will be made at this stage.

In a three phase agitated system the amount of complexes depends on the number of collisions between gas bubbles and organic phase drops, the ‘coalescence’-probability of these encounters and on the break-up rate. From the dynamic experiments and from energy considerations it seems unlikely that the complexes will break up at other positions than the free surface where the gas bubble escapes to the gas phase. Further, the forced contact experiments showed that the coalescence between a complex and a second organic phase drop requires several seconds of contact time. It is therefore unlikely that this will happen in a dynamic three phase system.

The contribution of the complexes to the gas absorption rate will depend, among other things, on the time scales for saturating the organic phase film in the complexes with the gas phase component and the residence time of the gas bubbles in the system. The calculation of the absorption flux from the gas bubbles and from the complexes requires a gas absorption flux model, in which the organic phase film at the gas-liquid interface can be taken into account. These models have been developed recently (Brilman et al., 1998a, 1998b). An experimental and modeling study investigating the contribution of the complexes formed to the overall gas absorption rate will be initiated in the near future. 5. Discussion and conclusions

116 Chapter 4

The frequently observed apparent increment of the mass transfer parameter kLa for gas absorption in liquid-liquid dispersions with increasing dispersed hold-up is up to date not fully understood.

The hydrodynamic characteristics, as e.g. the gas hold-up and bubble size distribution, may be affected by adding an immiscible organic phase to a gas-aqueous liquid phase system. Also the effect of gas-sparging on critical dispersion stirrer speeds, drop size distribution, phase inversion, optimum stirrer position etc. for liquid-liquid dispersions is also occasionally studied up to now. As a start, a hydrodynamic study may be done in which existing L-L and G-L correlations (for drop- and bubble size, gas hold-up, minimum stirrer speed etc.) are tested for their validity in G- L-L applications.

These hydrodynamic aspects may, at least partly, explain the observed trends in Figures 1-4. For instance, since the surface tension of the continuous aqueous phase will, in most cases, decrease on addition of an organic phase and this effect alone may result in an increase of approximately 10% in the interfacial area. On the other hand, the dispersion viscosity increases with the dispersed phase hold-up and a decrease gas absorption rate with apparent kL value may be expected. The surface tension effect and the effect on gas hold-up are, however, insufficient to explain completely the observed enhancement of the gas absorption rate in all cases. The presence of very small dispersed phase droplets (due to the drop size distribution) in the mass transfer film at the gas-liquid interface enhancing the gas absorption rate is a more plausible explanation.

Direct contact between the gas phase and the dispersed organic phase through the occurrence of complexes offers an alternative explanation for some of the effects encountered. The existence of these complexes under free and forced collision conditions is now established. However, the contribution of the g→o→w transfer pathway to the gas absorption rate is awaiting further study by modeling and unambiguous experimental evidence.

Acknowledgements

The author wishes to acknowledge H. van Dijk for his valuable contribution to the experimental part. A.T.C. Hessels, B.M.A. Wolffenbuttel and T.J.J. van der Sar are acknowledged for their contributions to related work on G-L-L systems. Notation a interfacial area [m2/m3]

117 Chapter 4

E1 enhancement factor, defined in Eq (1) [-] kL liquid side mass transfer coefficient [m/s] kLa volumetric gas-liquid mass transfer coefficient [1/s] 3 3 mR relative solubility or distribution coefficient { [mol/m ]o / [mol/m ]w } [-] P/V power input by agitation [W/m3] R radius [m]

S, Si (initial) spreading coefficient, defined in Eq (2) [mN/m]

Greek symbols

εG gas phase hold-up (based on G-L-L dispersion volume) [-]

φv dispersed phase hold-up (by volume) [-] σ surface- or interfacial tension [mN/m] µ viscosity [kg m/s]

Sub- and superscripts b bubble ddroplet g gas phase G-L two phase gas-liquid system (aqueous liquid phase) G-L-L three phase gas-liquid-liquid system o organic phase w aqueous phase (water) * at saturation conditions

118 Chapter 4

References Beenackers A.A.C.M., van Swaaij W.P.M., 1993, Mass transfer in gas-liquid slurry reactors, Chem.Engng.Sci., 48, 3109-3139

Brilman D.W.F., van Swaaij W.P.M., Versteeg,G.F., 1998, A one-dimensional instationary heterogeneous mass transfer model for gas absorption in multiphase systems, Chem.Eng. & Proc., 37, 471-488

Brilman D.W.F., Goldschmidt M.J.V., van Swaaij W.P.M., Versteeg,G.F., 1998b, Heterogeneous mass transfer models for gas absorption in multiphase systems (Chapter 6)

Calderbank P.H, 1967, Gas absorption from bubbles, Chem.Engr., 209-233

Chaudhari R.V., Bhattacharya A., Bhanage B.M., 1995, Catalysis with soluble complexes in gas- liquid-liquid systems, Catal.Today, 24, 123-133

Chaudhari R.V., Jayasree P., Gupte S.P., Delmas H., 1997, Absorption of CO with reaction in a biphasic medium (aq. NaOH-n-hexane): rate enhancement due to dispersed organic phase and phase-transfer catalysis, Chem.Engng.Sci., 52, 4197-4203

Das T.R., Bandopadhyay A., Parthasarathy R., Kumar R. , 1985, Gas-liquid interfacial area in stirred vessels: the effect of an immiscible liquid phase, Chem.Engng.Sci., 40, 209-214

Davies, Rideal, 1961, Interfacial phenomena, Academic Press Cambridge

Eckenfelder W.W., Barnhart, E.L., 1961, The effect of organic substances on the transfer of oxygen from airbubbles in water, AIChE J., 7, 631-634

Elibol M., Mavituna F., 1997, Characteristics of antibiotic production in a multiphase system, Proc.Biochem., 32, 417-422

Fogg P.G .T., Gerrard W., 1991, Solubility of gases in liquids, J.Wiley & Sons, New York.

Freitas E.R., Gum C.R., 1979, Shell’s Higher Olefin Process, CEP (1), 73-76.

Gaunand A., 1986, Oxidation of Cu(I) by oxygen in concentrated NaCl solutions. III. Kinetics in a stirred two-phase and three-phase reactor, Chem.Engng.Sci., 41, 1-9

Hassan I.T.M., Robinson C.W., 1977, Oxygen transfer in mechanically agitated aqueous systems containing dispersed hydrocarbons, Biotechnol. Bioeng., 19, 661-682

Herrmann W.A., Kohlpaintner C.W., 1993, Water-soluble ligands, metal complexes and catalysts: synergism of homogeneous and heterogeneous catalysis, Angew.Chem.Int.Ed.Engl., 32, 1524- 1544

Jia S., Li P., Park Y.S., Okabe M., 1996, Enhanced oxygen transfer in tower bioreactor on addition of liquid hydrocarbons, J. Ferment.Bioeng., 82, 191-193

Junker B.H., Hatton T.A., Wang D.I.C., 1990, Oxygen transfer enhancement in aqueous / perfluorocarbon fermentation systems: (1990a) I. Experimental Observations, Biotechnol.Bioeng., 35, 578-585

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(1990b) II. Theoretical Analysis, Biotechnol.Bioeng., 35, 586-597 Kuntz E.G., 1987, Homogeneous catalysis ... in water, ChemTech, 570-575 Lekhal A., Chaudhari R.V., Wilhelm A.M., Delmas H., 1997, Gas-liquid mass transfer in gas- liquid-liquid dispersions, Chem.Engng.Sci., 52, 4069-4077 Linek V., Benes P., 1976, A study of the mechanism of gas absorption into oil-water emulsions., Chem.Engng.Sci., 31, 1037-1046

Liu H.-S., Chiung, W.-C., Wang Y.-C., 1994, Effect of lard oil, olive oil and castor oil on oxygen transfer in an agitated fermentor, Biotechn. Techn., 8, 17-20

McMillan J.D., Wang D.I.C., 1990, Mechanisms of oxygen transfer enhancement during submerged cultivation in perfluorochemical-in-water dispersions, Ann.N.Y.Acad.Sci., 289-300

Meer A.B. van der, Beenackers A.A.C.M., Burghard R., Mulder N.H., Fok J.J., 1992, Gas/liquid mass transfer in a four phase stirred fermentor: effects of organic phase hold-up and surfactant concentration, Chem.Engng.Sci., 47, 2369-2374

Mills P.L., Chaudhari R.V., 1997, Multiphase catalytic reactor engineering and design for pharmaceuticals and fine chemicals, Catal.Today, 37, 367-404

Purwanto P., Delmas H., 1995, Gas-liquid-liquid reaction engineering: hydroformylation of 1- octene using a water soluble rhodium complex catalyst, Catal.Today, 24, 135-140

Rivalier P., Duhamet J., Moreau C., Durand R., 1995, Development of a continuous catalytic heterogeneous column reactor with simultaneous extraction of an intermediate product by an organic solvent circulating in countercurrent manner with the aq. phase, Catal.Today, 24,165-171 Rols J.L., Condoret J.S., Fonade C., Goma G., 1990, Mechanism of enhanced oxygen transfer in fermentation using emulsified oxygen vectors, Biotechnol.Bioeng., 35, 427-435

Rols J.L., Condoret J.S., Fonade C., Goma G., 1991, Modeling of oxygen transfer in water through emulsified organic liquids, Chem.Engng.Sci., 46, 1869-1873

Roques H., Aurelle Y., Aoudjehane M., Siem N., Rabat J., 1987, Etude expérimentelle des phénomènes de coalescence dans les systèmes ‘bulles-gouttes’, Rev.de IFP, 42, 163-177

Schneider T., Franz K., Vettermann R., 1990, Agitation of aerated emulsions, Chem.Eng.Technol., 13, 209-213 Schultze G.R., Moos J., Ledwoch K.-D., 1958, Die Umsetzung von gasförmigem Propylen mit Schwefelsäure, Erdöl u. Kohle, 11, 12-13

Scott P.J., Penlidis A., Rempel G.L., 1994, Reactor design considerations for gas-liquid emulsion polymerisations: the ethylene-vinyl acetate example, Chem.Engng.Sci., 49, 1573-1583

Sonsbeek, H.M. van, Blank H. de, Tramper J., 1992, Oxygen transfer in liquid-impelled loop reactors using perfluorocarbon liquids, Biotechnol.Bioeng.., 40, 713-718

Weilnhammer, C., Blass E. , 1994, Continuous fermentation with product recovery by in-situ extraction, Chem.Eng.Technol., 17, 365-373

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Yoshida F., Yamane T., Miyamoto Y., 1970, Oxygen absorption into oil-in-water emulsions. A study on hydrocarbon fermentors, Ind.Eng.Chem.Proc.Des.Dev., 9, 570-577

121 CHAPTER 5

A one-dimensional instationary heterogeneous mass transfer model for gas absorption in multiphase systems

Abstract

For a physically correct analysis (and prediction) of the effect of fine, dispersed phase drops or particles on the mass transfer rate in multiphase systems, it was demonstrated that only three dimensional instationary, heterogeneous mass transfer models should be used. Existing models are either homogeneous, stationary or single particle models. As a first step, a one-dimensional, instationary, heterogeneous multi-particle mass transfer model was developed. With this model the influence of several system parameters was studied and problems and pitfalls in the translation of modeling results for heterogeneous models into a prediction of absorption fluxes are discussed. It was found that only those particles located closely to the gas-liquid interface determine mass transfer. For these particles the distance of the first particle to the gas-liquid interface and the particle capacity turned out to be the most important parameters. Comparisons with a homogeneous model and experimental results are presented. Typical differences in results comparing a homogeneous model with the 1D heterogeneous model developed in this work could be attributed to a change in the near interface geometry. Future work in this field should therefore be directed towards near interface phenomena. Three dimensional mass transfer models, of which a preliminary result is presented, are indispensable for this.

121 Chapter 5

122 Chapter 5

1. Introduction

Three phase reactors, especially slurry reactors, are widely used in the chemical industries for a variety of processes. Frequently the absorption rate of a (sparingly) soluble gas phase reactant to the reaction phase is rate determining (Beenackers and van Swaaij, 1993). Experiments have shown that the gas-liquid mass transfer rate may be significantly enhanced by the presence of a third, dispersed, phase. This phenomenon can be attributed to the diffusing reactant which either absorbs preferentially or is consumed by a chemical reaction, see e.g. Kars et al. (1979) or Mehra et al. (1988). The dispersed phase can be solid (adsorbing or catalyst-) particles or liquid droplets.

Among others Kars et al. (1979) and Alper and Deckwer (1981) have shown experimentally that the addition of fine particles to a gas-liquid system caused an enhancement of the specific gas absorption rate (per unit of driving force and interfacial area), whereas larger particles showed almost no effect. Owing to a particle size distribution also in applications where the mean particle diameter is relatively large, a significant enhancement of the gas absorption rate may be observed. This was confirmed experimentally by Tinge and Drinkenburg (1995), who added very fine particles to a slurry consisting already of larger ones and found that the enhancement of gas absorption to be similar to the enhancement of the gas absorption rate due to the addition of only the same amount of fine particles to a clear liquid.

Such size distributions will certainly occur in case of gas absorption (or solids dissolution) in a liquid-liquid dispersion. Nishikawa et al. (1994) have shown for liquid-liquid systems that the effect of aeration is a broadening of the droplet size distribution, i.e. more fine droplets. This implies that especially for gas - liquid - liquid systems enhancement of gas absorption can be expected when, of course, the solubility of the diffusing component in the dispersed liquid phase exceeds the solubility in the continuous liquid phase.

The presence of these small particles does not only lead to significantly higher absorption rates (up to a factor 10), enabling smaller process equipment, but also selectivity in multistep reaction systems may be affected. In some applications a dispersed phase is added on purpose to a two phase system in order to reduce mass transfer limitations (see e.g. Junker et al., 1990).

123 Chapter 5

Since the effect of the presence of a dispersed phase on mass transfer can be significant, knowledge on the mass transfer mechanism and a model to predict this enhancement effect is desirable. The increase of the specific gas absorption rate, at unit driving force and unit interfacial area, due to the presence of the dispersed phase can be characterized by an enhancement factor, E. This enhancement factor is defined as the ratio of the absorption flux in the presence of the particles to the absorption flux at the same hydrodynamic conditions and driving force for mass transfer without such particles respectively.

Using the definition above, possible effects of the presence of particles on the gas-liquid interfacial area and on local hydrodynamics are taken into account. For a complete and more detailed review the reader is referred to Beenackers and van Swaaij (1993).

The enhancement of the specific absorption flux due to the presence of fine particles has been explained by the so-called ‘grazing’- or ‘shuttle-‘mechanism, see Kars et al. (1979) or Alper et al. (1980). According to this shuttle-mechanism particles pendle frequently between the stagnant mass transfer zone at the gas liquid interface and the liquid bulk. Due to preferential adsorption of the diffusing gas phase component in the dispersed phase particles the concentration of this gas phase reactant in the liquid phase near the interface will be reduced, leading to an increased absorption rate. After a certain contact time, the particle will return to the liquid bulk where the gas phase component is desorbed and the particles regenerated. This shuttle mechanism requires that the dispersed phase particles are smaller than the stagnant mass transfer film thickness, δF according to the film theory. For gas absorption in aqueous media in an intensely agitated contactor a typical value for δF is approximately 10-20 µm, whereas for a stirred cell apparatus this value is typically about a few hundred micron.

In the present study, multiphase systems with a finely dispersed phase will be considered, so that one or more dispersed phase ‘particles’ (which can either be liquid drops or solid particles) may be present within the stagnant film thickness at the gas-liquid interface. This is represented in Figure 1.

124 Chapter 5

G LII

concentration profile diffusing component

0 δp

Figure 1 Fine dispersed phase droplets located within the penetration depth G = gas phase, LI = continuous phase, LII = dispersed phase

A diffusing solute now may or may not encounter one or more droplets when diffusing into the composite medium. From the pioneering modeling work by Holstvoogd et al. (1988), who studied stationary diffusion into a series of liquid cells, each containing one catalyst particle, it became clear that especially those particles which are located most closely to the gas-liquid interface affect mass transfer. This implies that local geometry effects at the gas-liquid interface as e.g. the position of the particles with respect to the interface and with respect to each other (‘particle-particle interaction’) will influence the observed mass transfer enhancement.

The effect of the solubility (or, equivalently, the adsorption capacity) of the dispersed phase for the diffusing solute was investigated by Holstvoogd and van Swaaij (1990) and Mehra (1990), both using an instationary, penetration theory based, homogeneous model for gas-absorption. It was found that particles with a low capacity (i.e. a low relative volumetric solubility mR or adsorption capacity) easily get saturated and do not contribute any longer to the enhancement of gas-liquid mass transfer. For this reason stationary models, like the film model, which neglect the accumulation are inappropriate.

Models reported so far in literature are either homogeneous models (neglecting geometry effects and mass transfer inside the dispersed phase), heterogeneous stationary models (only applicable for very high capacity particles located very close to the gas-liquid interface) or one dimensional, one particle models. These models will be discussed briefly in section 2.

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However, to describe the effect of dispersed phase particles on gas absorption accompanied by chemical reaction it seems more realistically to develop instationary, three dimensional, heterogeneous, multi-particle, mass transfer models.

As a first step in this, an instationary heterogeneous, one dimensional, multi-particle model will be developed, which is the aim of the present contribution. With the present model, first the influence of a single particle to the gas absorption enhancement will be studied. The particle-to-interface distance, particle capacity, diffusion coefficient ratio and chemical reactions are varied. Further, multiparticle simulations will be presented. The coupling of modeling results with absorption rate or flux predictions will be discussed and a comparison with experimental data from literature and with homogeneous models already available in literature will be presented.

2. Previous work

For describing the phenomenon of gas absorption in the presence of dispersed phase particles in the mass transfer zone several approximation models have been developed in the past. The first models developed were the homogeneous models, see the work of Bruining et al. (1986), Mehra (1988), Littel et al. (1994) and van Ede et al. (1995) using the penetration theory or Nagy and Moser (1995) who used the film-penetration theory. Homogeneous models represent the situation of Figure 1 by taking a constant fraction (ε) of the film to be occupied by the dispersed phase. A typical representation of a homogeneous model is given in Figure 2.

GAS mass transfer zone liquid bulk PHASE diffusion L I 1−ε equilibrium / mass transfer

LII ε 0 δ

Figure 2 Typical representation of a homogeneous model

126 Chapter 5

Bruining et al. (1986) and Kars et al. (1979) neglected any mass transfer resistance in or around the dispersed phase droplets and estimated the mass transfer enhancement factor E just by accounting for the increased solubility (capacity) of an effective homogeneous liquid through equation (1-a), in which mR is the volume based solubility ratio of the solute over the dispersed phase and the continuous phase.

= + ε − E 1 (mR 1) (1-a)

The estimation of “a maximum attainable enhancement factor” for absorption in emulsions, based on the penetration theory, was proposed by van Ede et al. (1995), see equation (1b). In this equation DR is the ratio of the diffusion coefficients and represents the effect of complete parallel diffusional transport through the dispersed phase.

= + ε − E 1 (mR DR 1) (1-b)

The latter equation, however, is only valid for liquid-liquid dispersions.

In Figure 2, the dispersed phase is depicted as a separate homogeneous phase, which may offer a parallel transport route to the diffusing solute. The variations between different homogeneous models presented in literature are due to the description of mass transfer towards and inside this dispersed phase. Nagy and Moser (1995) among others accounted for the mass transfer resistance within the dispersed phase, which is neglected in most other models; see e.g. Mehra (1988). Littel et al. (1994) accounted for diffusion through the dispersed phase droplets by introducing an effective diffusion coefficient for the composite medium into the homogeneous model.

Since spherical droplets or particles can for the asymptotic situation only ‘touch’ the gas-liquid interface, the dispersed phase hold-up in this region will vary with the position in the mass transfer zone. Assuming the dispersed phase fraction at the interface to be at overall bulk liquid phase conditions may in this case lead to an overestimation of the enhancement factor by the homogeneous models. This effect was recognized by van Ede et al. (1995), who tried to account for this local geometry effect in this region by varying the dispersed phase hold-up from zero hold-up at the gas-liquid interface to the average bulk liquid phase hold-up at a distance x ≥ dp from the gas-liquid interface. To arrive at a good agreement with the experimental data, parallel diffusion through the dispersed phase was introduced in their model.

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Due to their one-dimensional character all homogeneous models only consider diffusion perpendicular to the gas-liquid interface. However, for particles close to the interface diffusion in other directions than perpendicular to the gas-liquid interface may also be very important. In this case the effect on mass transfer is probably underestimated by the homogeneous models. A homogeneous description of the dispersion is clearly physically not very realistic and may therefore lead to erroneous results for more complex situations.

Pioneering work in developing heterogeneous 3-D, one particle, models was done by Holstvoogd et al. (1988) and Karve and Juvekar (1990). Both developed stationary heterogeneous models for the description of gas absorption in slurry systems with an (infinitely) fast, irreversible chemical reaction at the solid surface. From their results it became clear that the distance of the particles to the gas-liquid interface was a major parameter determining the effect on the mass transfer rate.

These models are, however, not very suitable for absorption in liquid-liquid dispersions because they do not allow for diffusion through the dispersed phase. Furthermore, the model of Karve and Juvekar (1990) assumes an infinite capacity of the particles, thus neglecting the effect of saturation, and the particle position was fixed at the center of the unit cell. Additionally, their model overestimates the effect of neighboring particles, due to the cylindrical geometry of the unit cell applied with a symmetry boundary condition. In the model of Holstvoogd et al. (1988) the particle position was also chosen rather arbitrarily at the center of the unit cell.

Instationary, one dimensional, heterogeneous one particle models were proposed by Junker et al. (1990) and Nagy (1995). In the model by Junker et al. (1990), based on the penetration theory, a droplet can only partially fit within penetration depth for mass transfer, reflecting the rather large droplet sizes dp in their experimental system with respect to the calculated penetration depth δp

(dp > δp). In the model by Junker et al. (1990) the droplets are considered to be cubic, in order to maintain the one-dimensional character, having an equal volume to the spherical droplets

1/3 (d = dp⋅(π/6) ), see Figure 3. In their model each dispersed phase drop in the model (with diameter d) is considered to have a ‘sphere’ of continuous phase surrounding it (total diameter d

+ RD). Using the volume fraction εdis, the thickness of the continuous phase shell can easily be calculated via equation (2-a).

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The gas phase reactant may (or not) encounter such a dispersed phase droplet when diffusing into the liquid dispersion. Both pathways, J1 and J2, are indicated in Figure 3. Clearly, the contribution of both pathways, J1 and J2, should depend on the drop size and dispersed phase hold-up.

According to Junker et al. (1990) the fractional contribution of J2 to the total absorption flux can 2 2 be estimated by d /(RD+d) , based on the projected frontal area. The distance of the dispersed phase to the gas-liquid interface was chosen arbitrarily to be equal to RD (though RD / 2 probably would have been more consistent).

GAS LIQUID

J2 dp J1 d d + R d D

RD d

RD δ

Figure 3 Heterogeneous model by Junker et al.(1990)

The specific absorption flux when the diffusing solute encounters a droplet, J2, is calculated by an analytical expression for instationary diffusion through a ‘plate’ of the continuous phase followed by an semi-infinite medium of the dispersed phase (Crank, 1976), restricting the application of the model to physical mass transfer and zero and first order chemical reactions.

= ⋅ (ε−1/3 − ) R D d 1 (2-a)

 2   2   d   d  J(2-b)= J ⋅ + J ⋅ 1− total 1  2  2  2   (d + R D )   (d + R D ) 

The approach of Nagy (1995) is in many aspects similar to the one of Junker. However, Nagy used the film-penetration model to derive analytical solutions for the situation described in the model of Junker et al. (1990) and for the cases in which the single particle is entirely located within the mass transfer zone. The spacing between drops is the same in each spatial variable and calculated by equation (2-a).

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Since the particle may fit entirely within the mass transfer film two liquid-liquid phase boundaries may be encountered by the diffusing solute. The analytic solutions derived by Nagy for the different cases are therefore significantly more complex, when compared to the model by Junker.

For particles which are located completely within the penetration film thickness δp an averaging technique is required to account for the statistical probability of finding the particle at a certain position. Nagy (1995) assumed equal probability of finding the particle in the range 0 - (δp- dp), see equation (3-b). For the total absorption flux equations (3-a) and (3-b) are used.

= aveε2 /3 + − ε2/ 3 Jhet j J1(1 ) (3-a)

δ −d 1 p p and jav = ∫ J dL , with L the distance to the gas-liquid interface (3-b) δ − 2 p dp 0

3 Development of a heterogeneous 1-D, instationary, multiparticle model

3.1 Model assumptions For the modeling of a gas-liquid absorption process a basic physical mass transfer model must be chosen to describe the absorption process. Well known one parameter models include the film model, the penetration models of Higbie and the Danckwerts surface renewal model (Westerterp et al., 1986). Two parameter models as the film-penetration model may also be used. As mentioned before, due to the finite capacity of the dispersed phase droplets a stationary model, like the film model, is not appropriate. For the homogeneous models Mehra (1988) compared the Higbie penetration model and the Danckwerts surface renewal model and found comparable results. In the present work the Higbie penetration model was used, though the surface renewal model can also be implemented. In the present study it is assumed that the characteristic contact time at the gas-liquid interface for liquid packages also applies for the dispersed phase particles, i.e. emulsion packages at the gas- liquid interface are replaced completely by new emulsion packages from the liquid bulk after a certain contact time τ.

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For comparison of heterogeneous simulation results with experimentally determined absorption rates a proper implementation of the experimental conditions into the model is required.

Especially the representation of the dispersed phase hold-up ε, the particle size (distribution) dp and the choice of a statistical function for the particle position is thereby important. In the present study the following procedure is proposed for this model representation.

gas-liquid interface

(a) δ gas-liquid interface dp p

L δ dslab p (b)

Figure 4 From particles within the penetration depth to a one-dimensional model representation

Consider a ‘cylinder’ of the dispersion, perpendicular to the gas-liquid interface, with a diameter equal to the diameter of the spherical particle (see Figure 4-a). For a correct representation of the volume fraction dispersed phase it can be derived that the number of particles within the mass transfer penetration depth should be equal to 3/2⋅ε⋅δp/dp. Figure 4-a is, however, still not a one- dimensional model since the diffusion path through the dispersed phase particle varies with the radial position. In order to arrive at a one-dimensional representation the spherical particles are replaced by a slab of equal volume (and thus equal absorption capacity). This leads to dslab =

2/3⋅dp, which is represented in Figure 4-b. With this, the number of slabs (particles) in the unit cell is thus equal to N = ε⋅δp/dp. The situation N < 1 may be accounted for by taking the average of the results with cells with no particles and with one particle. For the positions of the particles it is assumed that the probability of finding a particle at a certain position from the interface is equal for every position.

One might have some objections with this representation of the absorption process in the dispersion, since the diffusing solute cannot bypass the dispersed phase particles. It should, however, be realized that due to the instationary character of the process and the statistical distribution of the particles over the penetration depth, still considerable absorption will take

131 Chapter 5 place, even in the case of impermeable solids. This particular situation will be investigated further on.

3.2 Model equations In Figure 5-a a graphical representation of the one dimensional model is given. The gas phase is located on the left hand side, LI represents the continuous liquid phase and LII the dispersed liquid phase droplets.

G LII LI

x = 0 x = δp

Figure 5- a Graphical representation of a multiparticle cell

dC dC D a,c = D a,d C a,c dx a,d dx  C  =  a,d  m R   C  a,c i

continuous dispersed continuous phase phase phase

Figure 5-b Computational grid around one droplet

Figure 5 The one-dimensional, instationary, multi-particle model.

The parameter δp is the penetration depth for mass transfer, as estimated by Higbie’s penetration δπτ= theory for physical absorption in the continuous phase ( pc2D ). The actual penetration depth in the simulation of absorption in a dispersion package will, in general, differ from δp due to a different volumetric absorption capacity of the dispersed phase droplets and the usually different diffusion coefficient within the dispersed phase particles. The model equations, initial conditions (IC) and boundary conditions (BC) for diffusion (with or without chemical reaction in one of the phases) are listed below for the diffusing solute ‘a’:

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  ∂ c ()xt, ∂ 2c ()xt, ac,  ac,  in the continuous phase : = D   + R (4-a) ∂ t ac,  2  ac,  ∂ x 

  ∂ c ()xt, ∂ 2c ()xt, ad,  ad,  in the dispersed phase : = D   + R (4-b) ∂ t ad,  2  ad,  ∂ x 

IC: t = 0 x ≥ 0ca,c = ca,d = 0 (or ca,c = ca,c,bulk and c a,d = ca,d,bulk)(5) * * BC: t > 0 x = 0 ca,c = ca,c (or ca,d = ca,d )

x = 2⋅δp ca,c = 0 (or ca,c = ca,c,bulk)

At the continuous phase - dispersed phase interfaces :

dc dc D ac, = D ad, (6-a) ac, dx ad, dx = cmcad,, R ac (6-b)

At phase boundaries the continuity of mass flux and the distribution of the solute between the phases is accounted for through equation (6). This is indicated in Figure 5-b, where the computational grid around one of the dispersed phase particles is shown.

The terms, Ra,c and Ra,d, in the equations (4-a) and (4-b) which account for possible occurring reactions can be any arbitrary kinetic expression. In case liquid phase reactants are also involved, similar diffusion/ reaction equations have to be added and solved simultaneously. The initial and boundary conditions for non-volatile liquid phase reactants, ‘b’, are then given by equation (7).

IC: t = 0 x ≥ 0cb,c = cb,c,bulk ,cb,d = cb,d,bulk = mR, b ⋅ cb,c,bulk (7) ∂ c ∂c BC: t > 0 x = 0 D bc, = 0,D bd, = 0 bc, ∂x bd, ∂x

x = 2⋅δp cb,c = cb,c,bulk ,cb,d = cb,d,bulk = mR, b ⋅ cb,c,bulk

The above presented model, which was solved numerically using an Euler explicit finite difference method, can be used to explore mass transfer enhancement effects in multiple phase systems. The number of particles as well as their sizes and their positions can be varied arbitrarily. Direct gas- dispersed phase contact can be implemented by placing a particle at the gas-liquid interface; i.e. the distance between the interface and the first dispersed phase particle is equal to zero.

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From the model the specific rate of absorption, which is time dependent, J(t) in [mole/m2 s], and

2 the average specific rate of absorption over the gas-liquid contact time, Jav(τ) in [mole/m s], are obtained. The enhancement factor is defined by the ratio of these fluxes to their equivalent for gas absorption under identical conditions without the presence of a dispersed phase, see Equations (8-a) and (8-b). τ = J(t) τ J av ( ) E(t) , Eav ( ) = (8-a, 8-b) D D c 2 c πt πτ

The enhancement factors E mentioned refer always to the contact time averaged enhancement factor Eav(τ), unless mentioned otherwise. The model was validated against analytical solutions for physical absorption and for absorption accompanied by homogeneous chemical reaction in the continuous phase for situations without particles. After adapting the model to the geometry described by Junker et al. (1990) the results were also validated with the analytical solutions for J2 in their model.

4. Simulation results

4.1 Single particle simulations Simulations are carried out in which the on beforehand identified as most relevant model parameters were varied for the case of only one particle present within the mass transfer penetration depth. Main goal is to investigate the sensitivity of the model calculations for the parameter variations.

The influence of the following parameters were studied: ⋅ particle position.

⋅ ‘particle capacity factors’, including the relative solubility mR and relative diffusivity DR ⋅ first order irreversible reactions in the continuous phase and in the dispersed phase

Bimolecular reactions and special reactions as parallel, consecutive and autocatalytic reactions can easily be implemented in the model, but these situations are not included in the present study.

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Results from this 1-Dimensional heterogeneous model with one particle may be useful for translating simulation results into absorption flux predictions. Therefore, in these simulations the default values for the model parameters involved refer to the conditions taken from the experiments by Littel et al. (1994) and, aditionally, in all simulations an unloaded liquid bulk solution was considered. In next sections the parameter δp is sometimes used as a scaling factor.

This parameter δp refers to the penetration depth at identical conditions for the absorption, but in absence of the particle(s).

4.1.1 Particle position In the work of Holstvoogd et al. (1988) it was clearly demonstrated that the particle position is one of the major parameters. With the present model a few simulations were performed in which the particle size was varied. If the particles were located at the same distance from the gas-liquid interface, the absorption rates calculated were almost identical, but if the position of the centers of the particles was kept constant, the larger particles, being more close to the interface, showed a much higher enhancement factor. It was concluded that especially the distance of the particle to the interface, L, is important in determining the effect on the absorption rate.

Since the relative solubility of the diffusing solute in the particle is also very important, see e.g. equation (1-a), and saturation effects may be important, the influence of the distance of the particle to the gas-liquid interface is studied for finite and infinite capacity particles. For finite capacity particles the enhancement factors as functions of L for different values of the relative solubility parameter mR are shown in Figure 6. In this plot the L value was scaled with respect to

δp, since it was found that by changing Dc, dp and t, identical results were found if L/δp and dp/δp were kept constant. From these results it is clear that the enhancement factor is quite sensitive to the parameter (L/δp). Above values for (L/δp) of 0.3 almost no enhancement is calculated.

th In case of a high relative volumetric solubility mR or an instantaneously fast, irreversible n -order reaction for the diffusing solute (no other components involved) in the dispersed phase droplet or at the surface of a solid catalyst particle the particle capacity may be considered infinite. In these cases the following simple correlation was found to describe the enhancement factor with

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reasonable accuracy (average deviation ≈ 1% in the relevant range 0 - 0.3⋅δp, maximum deviation 2 2 15  δ  (∆E) ± 0.1 unit at L = 0.5⋅δp) : E = +   (9) 16  4L 

For high capacity particles (mR > 1000) located sufficiently close to the gas liquid interface the enhancement factor can be estimated as function of the position L by this equation. Deviations are less than 10% if the degree of saturation of the particles is less than 10%. Note that equation (9) cannot be used for a situation in which there is direct gas-dispersed phase contact (L =0). In these cases mass transfer will be determined by transport within the dispersed phase and in the gas phase.

100 µ dp = 3.0 [ m] mR = D = 1.2410-9 [m2/s] E c infinite DR = 1.85 [ - ] 512 τ = 0.1173 [s] 256 128

64 10 32

1 0.001 0.01 0.1 1 L / dp [-]

Figure 6 Single particle calculations: Variation of position and relative solubility

4.1.2 Particle capacity Next to the distance of the (first) particle to the interface, it is clear from Figure 6 that the ‘capacity’ of the particle plays a significant role in the mass transfer enhancement. Particles having a low relative solubility factor (mR) will be faster ‘saturated’ during the gas-liquid contact time. These particles do not further enhance the mass transfer by acting as a sink for the gas phase component. This effect is demonstrated in Figure 7, where the ‘momentary’ enhancement factor is plotted during the contact time. For saturated particles the relative diffusion coefficient DR of the gas phase component in the dispersed phase then determines whether gas-liquid mass transfer is

136 Chapter 5 enhanced or retarded, when compared to absorption into liquid phase in the absence of particles.

Particle capacity will depend on the relative solubility mR and the particle size dp. For the degree of saturation which will be reached within the contact time also the position of the particle with respect to the interface is important.

50 µ dp = 3.0 [ m] E L = 0.5 [µm] -9 2 40 Dc = 1.24 10 [m /s]

DR = 1.85 [-] τ = 0.1173 [s] 30 mR = 1000 Eav = 20.4

mR = 100 Eav = 13.9 20

10 mR = 30 Eav = 7.6

mR = 10 Eav = 3.1 0 0 0.25 0.5 0.75 1 τ contact time ( t/ ) [-] Figure 7 Momentary enhancement factors during the gas-liquid contact time

For the particles affecting mass transfer, located close to the interface, it can be assumed that a linear concentration profile for diffusion to the first dispersed phase particle will be reached in short time. Neglecting mass transfer resistances within the dispersed phase and mass transfer out of the dispersed phase ‘at the back of the particle’, the following expression for the degree of saturation, which will be reached within the characteristic contact time τ, can be derived.

− 1 τ   d  − Dc π L  p    2 mR     C  m Ld  δ  δ  d = 1− e R p = 1− e (10)  ref   mR Cc 

ref In this equation Cc is the concentration at the same distance from the gas-liquid interface during (physical) absorption in the liquid phase without particles present at further identical conditions. The equation was found to describe this relative degree of saturation of the first particle within 5% deviation.

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4.1.3 Diffusion through the particles In the situation shown in Figure 5-a diffusion occurs alternating in the continuous and dispersed phase (similar to resistances in series). The diffusion coefficient in the dispersed phase will therefore affect the mass transfer process. This effect will only be significant for low capacity particles, when transport through the first particle(s) becomes important. From Figure 8 it can be concluded that for one single, small, particle this effect is limited in practical situations, where 0.1

< DR < 10. Here also, the influence of the particle decreases with increasing distance to the gas- liquid interface. In the legend the limiting value for E in case of impermeable solids is given for a few values of L, under the conditions mentioned.

1.4 E 1.2

1 increasing L increasing L µ 0.8 L = 4 m L [µm] E (limit for DR = 0)

0.25 0.018 0.6 L = 1 µm 0.5 0.037

1.0 0.074 0.4 L = 0.25 µm dp = 3.0 [µm] -9 2 Dc = 1.24 10 [m /s] 2.0 0.147 mR = 1.0 [-] 0.2 τ = 0.1173 [s] 4.0 0.294

0 0.1 1 10 100 DR [-]

Figure 8 Influence of the dispersed phase permeability on the enhancement factor for a single particle

4.1.4 Effect of contact time τ The characteristic average contact time τ was varied over a broad range to investigate its effect on the mass transfer enhancement factor, Eav(τ), due to the presence of a single particle, located at different positions from the gas-liquid interface. This may represent e.g. the effect of an increasing stirring rate in agitated systems. Results are presented in Figure 9. With this, the importance of the effect of the contact time on the enhancement factor is shown. Since the simulations are carried out for particles of given size dp at fixed distances L from the gas-liquid interface the

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characteristic geometrical parameters dp/δp and L/δp vary through δp, which solely depends on τ for a given set of physical properties (mR, DR and Dc). With this, the maximum in these curves can be understood.

25 d = 3.0 [µm] E [-] p m R = 103 [-] 20 -9 2 Dc = 1.24 10 [m /s]

DR = 1.85 [-] τ = 0.1173 [s] 15

10 L = 0.25 [µm] 0.5 1.0 5 2.0 4.0

0 0.0001 0.001 0.01τ [s] 0.1 1 10

Figure 9 Enhancement factors at varying contact times for different positions from the interface

For a given particle position (L) the relative particle position (L/δp) will decrease with increasing contact time, resulting in higher enhancement factors. For very low values of L/δp the particle is saturated relatively fast and does not contribute any longer significantly to the mass transfer enhancement and E decreases again. These curves can further be used to evaluate average absorption fluxes using a surface renewal model. For a few particle positions these data were used to calculate the enhancement factor using the surface renewal model. Differences between the penetration model and surface renewal model results were found to be maximally 10%.

4.1.5 First order, irreversible chemical reactions in the dispersed and continuous phase The effect of a chemical reaction which shows first order reaction kinetics with respect to the gas phase component was investigated separately for the reaction occurring in the dispersed phase and in the continuous phase. Increasing the reaction rate constant for an irreversible first order reaction located in the dispersed phase should increase the absorption flux, until the ‘infinite enhancement factor’ due to the presence of the dispersed phase particle at a certain position is reached. In that case the capacity of the dispersed phase droplet can be considered infinite and the enhancement factor can be approximated by Equation (9). The degree of saturation will be then

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1/2 be low. It was found that this is achieved for mR⋅(1+k1,d ) exceeding approximately the value 1000.

For a first order reaction in the continuous phase the penetration depth will decrease with increasing reaction rate constant (δ’ ≈ δp/Ec,c), thereby reducing the probability to find particles within the mass transfer zone. Therefore, with increasing k1,c value a diminishing effect of the overall mass transfer enhancement due to the presence of particles can be expected. The effect of k1,d and k1,c for a typical application is given in Figure 10. Increasing k1,d at a certain k1,c value again increases the enhancement factor (at constant L/δ’ value) somewhat. The enhancement due to the presence of dispersed phase particles is a function of the ratio of the capacity of the particles to the capacity of the continuous liquid phase which is replaced by the particle

100 one particle infinite capacity µ dp = 3.0 [ m] E mR = 103 [-] k = 100 [1/s] 1,d DR = 1.85 [-] τ = 0.1173 [s] k1,d = 10 [1/s]

k1,d = k1,c = 0 [1/s] k1,c = 10 [1/s] increasing relative particle capacity

k1,c = 100 [1/s]

k1,c = 1000 [1/s]

1 0.001 0.01 0.1 1 L/δ (L/δ')

Figure 10 Variation of the relative particle capacity through the first order reaction rate constant in the continuous phase, k1,c, and in the dispersed phase, k1,d

4.2 Multiparticle calculations For the conditions mentioned in Table I calculations were performed for a multi-particle situation. The position of the particles is shown in the concentration versus x-position graph of Figure 11-a,

140 Chapter 5 where the concentration within the dispersed phase is taken as the relative value with respect to its maximum solubility.

particle position

1.25

c / c* 1

0.75 mR = 1.0

mR = 8.0

0.5

mR = 32

0.25

mR = 0.002

mR = 1024 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x / δp [-]

(a) Concentration profiles

2.5

1.5

0.5

0 0.001 0.01 0.1 1 10 100 1000 10000 mR [-] (b) Enhancement factors vs. relative solubility.

Figure 11 Concentration profiles within the penetration depth (11-a) and enhancement factors (11-b) for the situations represented in Figure 11-a and the conditions reported in Table I

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Table I Conditions applied for the multiparticle calculations of Figure 11.

Parameter Symbol value units

particle diameter dp 0.67 µm hold-up dispersed phase ε 0.10 - distance 1st particle to interface L 5.5 µm number of particles for x = 0 .. δp N 6 - penetration depth without particles δp 42.8 µm relative solubility mR 103 - contact time τ 0.1173 s

-9 2 diffusion coefficient continuous phase Dc 1.24⋅10 m /s

-9 2 diffusion coefficient dispersed phase Dd 2.30⋅10 m /s

From this figure it is clear that with increasing mR the penetration depth decreases and fewer particles are located within the actual penetration depth. Thus only those particles located closely to the gas-liquid interface will cause the gas absorption enhancement. At high mR values (and DR = 1.85) the concentration within the particles is almost uniform; the resistance for mass transfer is located almost exclusively in the continuous liquid phase. For mR values below one, the major resistance for mass transfer is located within the dispersed phase particles. To maintain a certain flux (see also equations (6-a) and (6-b)), through the particles the concentration gradient within the particles will be much steeper in these cases. The calculated enhancement factors for the particle configuration shown in Figure 11-a are plotted versus the relative solubility of solute A in the dispersed phase in Figure 11-b.

For the case of mR =1, also the value of DR was varied between 0.1 and 100. At DR = 0.1 the

‘enhancement’ factor calculated was 0.81, whereas for DR = 100 the enhancement factor was only 1.04. The negligible enhancement effect can be understood using the results presented in Figure 8, considering that in this case the dispersed phase fraction is only 0.10 and the value of L/δp is relatively large (L/δp = 0.13).

The importance of the first few particles near the gas-liquid interface is further stressed by multiparticle calculations in which subsequently one particle was added, until a similar situation as

142 Chapter 5 in Figure 11-a was obtained. The simulation data and obtained mass transfer enhancement factors for these cases are listed in Table II. If the distance of the first particle to the interface is increased the additional enhancement due to the presence of a second particle (slightly) decreases (no data illustrating this are included).

Table II Effect of additional particles on the overall mass transfer enhancement.

Table II-a Conditions applied

Parameter Symbol value units

particle diameter dp 2.0 µm distance 1st particle to interface L 1.0 µm penetration depth without particles δp 42.8 µm distribution coefficient mR 4 - 100 - contact time τ 0.1173 s

-9 2 diffusion coefficient (continuous phase) Dcon 1.24⋅10 m /s

-9 2 diffusion coefficient (dispersed phase) Ddis 2.3⋅10 m /s interparticle distance Lpp 2 µm

Table II-b Simulation results

mR = 100 mR = 10 mR = 4 No. particles E ∆E/(E-1) (%) E ∆E/(E-1) (%) E ∆E/(E-1) (%) 0111 1 7.7072 100 2.2950 100 1.50492 100 2 7.8960 2.7 2.9893 34.9 1.85293 40.8 3 7.8977 0.02 3.1509 7.5 2.01666 16.1 4 ,, 3.1725 1.0 2.06959 4.9 5 3.1744 0.08 2.08250 1.2 6 3.1745 2.08493 0.2 7 ,, 2.08528 0.03

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5. Comparison with experimental results and with a homogeneous model

For a typical homogeneous model (see e.g. Bruining (1986), Mehra (1988) or Littel (1994)) the dispersed phase fraction, as well as the droplet size and relative solubility were varied. The results are presented in Figures 12-a and 12-b. From Figure 12-b e.g. the influence of the particle size on the calculated enhancement factor can be seen, being more important at high mR values.

2.4 10 d = 0.1 µm Limit (Bruining et al. (1986), Eq. 1a ) p 2.2 Limit (Bruining et al. (1986), Eq. 1a ) µ dp = 1.0 m E d = 1.0 µm µ p E dp = 3.0 m 2 µ dp = 6.0 m

1.8 µ dp = 3.0 m 1.6

µ 1.4 dp = 12 m µ dp = 6.0 m

1.2

1 1 0 0.1 0.2 0.3 0.4 0.5 1101001000 m R dispersed phase holdup ε

(a) Variation of dp and hold-up ε (mR =10 ) (b) Influence of dp and mR (ε = 0.10)

Figure 12 Results for a homogeneous model. Conditions applied : mR = 10, ε = 0.10, -5 kGL = 11.6⋅10 [m/s], Sh = 2 is used for the liquid-liquid mass transfer coefficient

For the comparison of homogeneous and heterogeneous models both models respectively were compared with experimental data for the mass transfer enhancement in liquid-liquid systems. In this work the data of Littel et al. (1994) and of Mehra (1988) were used. For the heterogeneous models it is required to average over all possible particle positions within the penetration depth. However, for the conditions used by Littel et al. (1994) and Mehra (1988) a multi-particle simulation showed that in good approximation only the first particle is really determining the gas absorption enhancement, which can also be deduced from the results of Table II. This allows us to use single particle calculations.

Simulations were performed for one single particle present within the penetration depth δp and using the appropriate physico-chemical properties as given with the experimental data. The enhancement factors obtained for different positions of the particle, E (L), were correlated. If N

144 Chapter 5 particles are present within the penetration depth, the distance of the first particle to the gas-liquid interface is likely to be within the range 0 - (δp/N - dp/2) [µm]. In estimating the experimental enhancement factor using the one-dimensional heterogeneous model, the single particle results were averaged over all possible positions within this section of the mass transfer zone:

δ / N −d / 2 1 p p E= ∫ E(L)dL (11) δ d p − p 0 N 2

When more than one particle should be taken into account within the penetration depth (at high volume fractions of very small low capacity particles), the averaging procedure as proposed in equation (11) should be extended to all possible particle configurations. In good approximation, we believe this can be done in a sequential way. The first particle is most likely to be found at a distance 0 - (δp/N-dp/2) from the gas liquid interface. Equation (11) is now used to calculate the average enhancement due the first particle. The first particle is then fixed at a position for which the average enhancement factor is obtained. The next particle is most likely within the range

(δp/N-dp/2) - 2⋅δp/N-dp/2 from the gas liquid interface. Similar to equation (11), the average contribution of this second particle can be calculated. The second particle is then fixed at the position corresponding with that average contribution, and a third particle is considered, and so on. As may be clear from Table II-b seldom more than 4 particles need to be taken into account.

With increasing the dispersed phase hold-up, ε, the number of particles within the penetration depth, N, increases and the first particle will, on the average, be located more closely to the interface. Consequently, the enhancement factor will increase. A comparison of some experimental results from literature with the calculated enhancement factors for the homogeneous and heterogeneous models are given in Table III and in Figure 13.

Figure 13 shows an almost linear increase of the enhancement factor with increasing hold-up for the heterogeneous model, whereas the homogeneous model shows a more ‘logarithmic’ dependency. For absorption in liquid-liquid emulsions this ‘leveling off’ of the enhancement factor with increasing dispersed phase hold-up can be recognized from the experimental data, although the effect is less pronounced than predicted by the homogeneous models (see e.g. the work of van Ede et al. (1995)). For solid catalyst particles (Pd on activated carbon) as dispersed phase,

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Wimmers and Fortuin (1988) found the enhancement to increase linearly with the dispersed phase hold-up for experiments in a stirred tank reactor.

20 experimental (Mehra, 1988) E µ experimental (Littel et al. 1994) heterogeneous model, dp = 2 m 16 µ heterogeneous model, dp = 3 m

12 µ homogeneous model, dp = 3 m

8 µ heterogeneous model, dp = 3 m

4 µ homogeneous model, dp = 3 m

0 0 0.1 0.2 0.3 0.4 dispersed phase hold up ε [-]

Figure 13 Comparison of 1D heterogeneous model and a homogeneous model with experimental results by Littel et al. (1994) and Mehra (1988)

This difference in behaviour of the enhancement factor with increasing dispersed phase hold-up for the homogeneous model and the heterogeneous model can be explained via the position of the dispersed phase with respect to the gas-liquid interface. Varying the dispersed phase hold-up does not change the position of the dispersed phase in case of the homogeneous model (only increases the local fraction). For the heterogeneous model, however, the first particles will be located much closer to the gas-liquid interface with increasing hold-up. This effect causes the enhancement factor to increase almost linearly with the fractional hold-up of the dispersed phase. The importance of the position of the first particle is further illustrated by the data presented in Table

II-b. From this Table it is clear that, when keeping the position of the first particle, Lo, fixed, the addition of more particles within the penetration depth does not contribute significantly to the absorption flux. When the influence of the addition of subsequent particles is simulated as increasing dispersed phase hold-up, the enhancement curves are leveling off (see Figure 14) which, however, is also found for the homogeneous models.

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E [-] Heterogeneous model, mR = 100

Heterogeneous model, mR = 10

Heterogeneous model, mR = 4

Homogeneous model, mR = 10

1 0 0.1 0.2 0.3 0.4 fraction dispersed phase ε [-]

Figure 14 Effect of leveling off of the enhancement factor at constant Lo

The results of the simulations for the heterogeneous model are more sensitive to the particle size than the modeling results for the homogeneous model, which can be recognized from the Figures 12 and 13. This is again explained by the position of the first particle at the gas-liquid interface. At identical dispersed phase hold-up a decrease in particle size implies an increase in the number of particles and, with this, a decrease in the (averaged) distance of the first particle to the gas-liquid interface. For the same reason the average enhancement factor increases with a broadening of the particle size distribution at constant Sauter diameter. This may be essential in modeling the experiments by Mehra (1988), who indicated ‘the droplet size lies in the range of 1-12 µm, with a clustering around 3-4 µm’. The particle size distribution may very well be responsible for the deviations at high or low ε, due to the assumption of a mono-disperse particle size. Unfortunately, none of these experimental studies in literature presented more details on their specific dispersed phase particle size distribution.

In Table III also a comparison between homogeneous and heterogeneous models is made for the situation of inert (impermeable and non-adsorbing) solid microparticles. This was studied experimentally by Geetha and Surender (1994). From their experimental results it is clear that, though undoubtedly significant differences were found for different types of solids, a considerable reduction of the mass transfer coefficient occurs at rather low volume fractions (at which viscosity effects due to the addition of the particles are negligible). From the modeling results it is clear that

147 Chapter 5 this effect is almost not identified in the simulations of the homogeneous models. The extent of this effect seems much better described by the heterogeneous model. It has to be mentioned that at larger volume fractions the mass transfer reduction tends to be overestimated by the heterogeneous model. This may be caused by neglecting lateral diffusion (bypassing of the particles). Simulations with three dimensional heterogeneous models are necessary to support this explanation.

Table III Comparison of homogeneous and heterogeneous simulation results with experimental results

Experimental study mR DR ε dp kL Eexp Ehom Ehet [-] [-] [-] [µm] [m/s] [-] [-] [-]

Littel et al. (1994) 103 1.81 0.034 3.0 11.6⋅10-5 2.22 1.99 1.76 (G-L-L, falling film exp.) 0.187 10.1⋅10-5 4.14 4.34 4.16

Mehra (1988, Table I) 8890 1.7 a) 0.02 3.5 9.8⋅10-6 4.00 2.71 2.6 (S-L-L, stirred cell) 0.05 6.73 5.69 4.4 0.10 9.10 7.94 7.4 0.20 12.00 11.07 12.7

Geetha, Surender (1994) 0 0 0.02 0.33 4⋅10-4 0.55 0.99 0.40 (S-L-S, agitated tank) {SiC} 0.02 ≈ 14⋅10-4 0.68 0.99 0.89 {Kaolin} 0.9 {Iron oxide} 0.63 0.02 ≈ 11⋅10-4 0.99 0.66 a) estimated value

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6. Discussion

From the comparison with experimental data it has become clear that a one-dimensional heterogeneous mass transfer model can reasonably predict absorption fluxes for situations in which the shuttle mechanism determines the mass transfer enhancement. Also the mass transfer retarding effect of inert impermeable solid particles can be accounted for. From the sensitivity analysis it became clear that for a given application, where the parameters mR, dp, ε, τ, DR are usually known, especially the position with respect to the interface remains as important factor. Since the enhancement factor increases almost exponentially with decreasing distance from the gas-liquid interface, it is not sufficient to assume the particles to be at some arbitrary distance from this interface (as e.g. in the models by Junker (1990), Holstvoogd et al. (1988) and Vinke (1992)). Statistical averaging over all positions, using the contribution to the enhancement as weighing factor is required, as in equation (11) where the probability of finding a particle was taken the same for every position within the section of the film under consideration. When more than one particle needs to be taken into account, the sequential approach discussed in section 5 is regarded as a good approximation.

The equal probability of finding a particle at a certain position may be influenced by settling effects, especially relevant for horizontal interfaces as e.g. encountered in a stirred cell (Littel et al., 1994) or by adhesion of particles to the interface (see Wimmers and Fortuin (1988) and Vinke (1992)). This latter effect was found to be very important for slurry systems with activated carbon particles. Brownian motion of the small particles may counteract these settling effects and will result in a more homogeneous distribution. This was studied experimentally for small (silica) particles near gas-liquid interfaces by Al-Naafa and Selim (1993) who found a value of 3⋅10-13

2 m /s for the ‘particle diffusion coefficient Do’ for 1 µm particles, which is in good agreement with the Stokes-Einstein relationship, Do = k T/(3πηdp). With this, the average displacement of a particle due to Brownian motion during gas-liquid contact time τ may be one to several microns. This would imply that in the small zone near the gas liquid interface where the mass transfer enhancement is really determined (≈ 0 - 0.15⋅δp < 10 µm ), the probability for each position is approximately equal.

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From the Figures 12 and 13 from and Table III it is clear that homogeneous and heterogeneous models yield significantly different simulation results, especially concerning the dependency of the enhancement factor on ε and dp. It has been mentioned that the local geometry at the interface changes with increasing ε, causing a more or less linear dependency of E on ε. It should be remembered, however, that at increasing ε the degree of saturation of the first particle does increase. At a certain moment, for finite, not too high, capacity particles, a second or even a third particle needs to be taken into account. This will, undoubtedly, lead to a leveling off of the E-ε curve. Another pitfall is that at increasing hold-up of the dispersed phase the physical limit of a dense packed bed of particles at the interface will be reached. In that case, increasing ε can, physically, not lead to a reduction of the (average) distance of the first layer of particles towards the interface. Geometry of the particle and the packing will become important. For these situations 3 D models are indispensable.

Preliminary results obtained with a (two and )three dimensional model presently being developed are presented in Figure 15 for a single spherical particle with the same physico-chemical properties as reported in Table I, except for the particle diameter being 3.0 µm and the (minimum) particle to interface distance, L, which was 0.64 µm in these simulations.

11 c / c* E 1D 52 % 9 2D 69 %

3D 89 % 7

µ dp = 3 m 1 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0 10.0 radial position [µm]

Figure 15 Enhancement factors at different radial positions from the particle center for a 2-D and 3-D model.

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In this figure the enhancement factors at the gas-liquid interface on different radial positions from the projection of the center of the particle on the interface are presented for the one-dimensional model presented in the present study and for a two-dimensional and a three dimensional model. A few very important aspects can be recognized from this figure. First of all, the particle enhances mass transfer over an area largely exceeding its own projection on the gas-liquid interface. Further, and these effects are related, the enhancement factor at the center position increases in the sequence 1-D > 2-D > 3-D whereas, the degree of saturation of the particle (given percent- wise with respect to the maximum solubility in the legend) increases in the same sequence. The 2- D and 3-D models, in fact equations (4) - (6), were solved using an overlapping grid technique (Chesshire, Henshaw, 1994). More results and details on the computational methods used will presented by Brilman (1998).

This preliminary figure illustrates that although the one-dimensional models give reasonable results, even though the physical situation is not represented completely in accordance with reality in the model, the development of two and, especially, three dimensional models is required to investigate the near interface effects (and particle-particle interaction) more correctly.

New, very accurate experiments in dedicated equipment are however still required, not only to yield reliable data for verifying and comparing the models, but especially information on the specific interface phenomena are required for a more thorough understanding and for the development of the appropriate models. Therefore, in such experiments special attention should be paid to the hold-up of the dispersed phase and possible phase separation or adhesion effects at the interface and to the effect of the particle size distribution. From the analysis above it is clear that for particles located closely to the interface the one dimensional, homogeneous and heterogeneous, models are oversimplified representations of a 3-D reality.

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7. Conclusions

A one dimensional, heterogeneous, instationary mass transfer model was developed to describe diffusion (with or without chemical reaction) in heterogeneous media. At conditions under which significant enhancement of mass transfer occurs, it was shown by multiparticle calculations that only those particles very close to the gas-liquid interface determine the mass transfer enhancement. Effects of among others the particle to interface distance and factors influencing the absorption capacity of the microparticles for the diffusing solute on the mass transfer enhancement were studied, showing the relative importance of the parameters.

A comparison of modeling results with experimental data yields a somewhat different behavior with respect to the dependency of the absorption flux on the dispersed phase hold-up when compared to the homogeneous models due to the changing local geometry near the gas-liquid interface. In some cases heterogeneous models seem to describe the physical situation more correctly. Interpretation of the modeling results is somewhat more complicated since averaging over all possible configurations is required. Especially for multiparticle simulations these averaging techniques, or alternatively, the definition of a representative unit cell, need further consideration.

Considering that only those particles located very near the interface determine mass transfer, attention should be focused on these region. It is therefore believed that the developed one dimensional heterogeneous model as well as the homogeneous models presented in literature remain first-approximation models due to their one-dimensional character. Two and especially three dimensional mass transfer models should therefore be developed to investigate near interface effects and particle interaction. Experimental research investigating the near interface hold-up and the particle distribution within this zone is highly desirable, since it may yield essential information for understanding (and modeling) mass transfer phenomena in the presence of fine particles.

Acknowledgments The authors wish to thank M.J.V. Goldschmidt for his contribution to the modeling part and the SHELL Research and Technology Center in Amsterdam (The Netherlands) for the financial support.

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Notation c concentration [mol/m3] D diffusion coefficient [m2/s] DR relative diffusion coefficient { Dd / Dc } [-] d characteristic particle diameter [m] dp particle diameter [m] E enhancement factor [-] Ec,c enhancement factor due to chemical reaction in the continuous phase [-] J mass transfer flux [mol/m2 s] jav average mass transfer flux for the heterogeneous cell, equation (3) [mol/m2 s] k1 first order reaction rate constant [1/s] kL liquid side mass transfer coefficient [m/s] L distance to the gas-liquid interface [m] Lo distance of first particle to the gas-liquid interface (multi-particle calc.) [m] 3 3 mR relative solubility or distribution coefficient { [mol/m ]LII / [mol/m ]LI } [-] N number of particles in the mass transfer zone [-] Ra reaction rate [mole a/m3 s] RD interparticle distance, equation (1) [m] t time [s] x distance from gas-liquid interface [m]

Greek symbols

δ mass transfer zone near interface [m]

δp penetration depth [m] ε fraction dispersed phase [-] τ gas-liquid contact time [s]

Sub- and Superscripts a gas phase reactant a b liquid phase reactant b av average value bulk at bulk liquid phase conditions c continuous phase d dispersed phase exp experimental value F according to the film theory het heterogeneous (model) hom homogeneous (model) p physical absorption ref reference value * maximum solubility

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References

Al-Naafa M.A., Sami Selim M., 1993, Sedimentations and Brownian diffusion coefficients of interacting hard spheres, Fluid Phase Equilibria, 88, 227-238

Alper E., Wichtendahl B., Deckwer W.D., 1980, Gas absorption mechanism in catalytic slurry reactors, Chem. Engng. Sci., 35, 217-222

Alper E., Deckwer W.D., 1981, Comments on gas absorption with catalytic reaction, Chem.Engng.Sci., 36, 1097-1099

Beenackers A.A.C.M., Van Swaaij W.P.M., 1993, Mass transfer in gas-liquid slurry reactors, Chem.Engng. Sci., 48, 3109-3139

Brilman D.W.F., Goldschmidt M.J.V., Versteeg G.F., van Swaaij W.P.M., 1998, Heterogeneous mass transfer models for gas absorption in multiphase systems, (Chapter 6 of this thesis, to be published)

Bruining W.J., Joosten G.E.H., Beenackers A.A.C.M., Hofman H., 1986, Enhancement of gas- liquid mass transfer by a dispersed second liquid phase, Chem. Engng. Sci., 41, 1873-1877

Chesshire G., Henshaw W.D., 1990, Composite overlapping meshes for the solution of partial differential equations, J. Comp.Ph., 90, 1-64

Crank J., 1976, Mathematics of Diffusion, Oxford Univ. Press, Oxford

Ede C.J. van, Van Houten R. and Beenackers A.A.C.M., 1995, Enhancement of gas to water mass transfer rates by a dispersed organic phase, Chem. Engng. Sci., 50, 2911-2922

Geetha K.S., Surender G.D., 1994, Solid-liquid mass transfer in the presence of microparticles during dissolution of iron in a mechanically agitated reactor, Hydrometallurgy, 36, 231-246

Holstvoogd R.D., van Swaaij W.P.M., Dierendonck L.L. van, 1988, The absorption of gases in aqueous activated carbon slurries enhanced by adsorbing or catalytic particles, Chem.Engng.Sci., 43, 2182-2187.

Holstvoogd R.D., van Swaaij W.P.M., 1990, The influence of adsorption capacity on enhanced gas absorption in activated carbon slurries, Chem.Engng.Sci., 45, 151-162

Junker B.H., Wang D.I.C., Hatton A.H., 1990, Oxygen transfer enhancement in aqueous/perfluorocarbon fermentation systems: I. Experimental observations, Biotechn. Bioengng., 35, 578-585

Junker B.H., Wang D.I.C., Hatton A.H., 1990, Oxygen transfer enhancement in aqueous/perfluorocarbon fermentation systems: II. Theoretical analysis, Biotechn. Bioengng., 35, 586-597

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Kars R.L., Best R.J., Drinkenburg A.A.H., 1979, The sorption of propane in slurries of active carbon in water, Chem. Engng. J., 17, 201-210. Karve S., Juvekar V.A., 1990, Gas absorption into slurries containing fine catalyst particles, Chem. Engng. Sci., 45, 587-594

Littel R.J., Versteeg G.F. and Van Swaaij W.P.M., 1994, Physical absorption of CO2 and propene into toluene/water emulsions, A.I.Ch.E. J., 40, 1629-1638

Mehra A., 1988, Intensification of multiphase reactions through the use of a microphase-I. Theoretical, Chem. Engng Sci., 43, 899-912

Mehra A., Pandit A. and Sharma M.M., 1988, Intensification of multiphase reactions through the use of a microphase-II. Experimental, Chem. Engng Sci., 43, 913-927

Mehra A., 1990, Gas absorption in slurries of finite capacity microphases, Chem. Engng. Sci., 46, 1525-1538

Nagy E. and Moser A., 1995, Three-phase mass transfer: improved pseudo-homogeneous model, A.I.Ch.E. J., 41, 23-34

Nagy E., 1995, Three-phase mass transfer: one dimensional heterogeneous model, Chem. Engng. Sci., 50, 827-836

Nishikawa M., Kayama T., Nishioka S., Nishikawa S., 1994, Drop size distribution in mixing vessel with aeration, Chem.Engng.Sci., 49, 2379-2384

Tinge J.T., Drinkenburg A.A.H., 1995, The enhancement of the physical absorption of gases in aqueous activated carbon slurries, Chem. Engng. Sci., 50, 937-942

Vinke H., 1992, The effect of catalyst particle to bubble adhesion on the mass transfer in agitated slurry reactors, Ph.D. thesis, Municipal University of Amsterdam (The Netherlands).

Westerterp K.R., Van Swaaij W.P.M., Beenackers A.A.C.M., 1993, Chemical reactor design and operation, John Wiley & Sons

Wimmers O.J., Fortuin J.M.H., 1988, The use of adhesion of catalyst particles to gas bubbles to achieve enhancement of gas absorption in slurry reactors, Chem. Engng. Sci., 43, 303-312, 313- 319

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156 CHAPTER 6

Heterogeneous mass transfer models for gas absorption in multiphase systems

Abstract

Heterogeneous, instationary 2-D and 3-D mass transfer models were developed to study the effect of dispersed liquid phase droplets near the gas-liquid interface on the local gas absorption rate. It was found among other things that droplets (or particles) influence local mass transfer rates over an area exceeding largely the projection of the droplets on the gas-liquid interface. For a specific application particle-particle interaction was studied and could be described by a single parameter, depending only on the minimum interparticle distance. For gas absorption flux prediction an unit cell must be defined. The sensitivity of the absorption flux to the definition of the unit cell was investigated. Finally, a complete strategy to arrive at gas absorption flux prediction from single particle simulations has been proposed.

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2 Chapter 6

1. Introduction

In three phase reactors, gas-liquid-solid or gas-liquid-liquid, frequently the absorption rate of a (sparingly) soluble gas phase reactant to the reaction phase is rate determining (see e.g. Beenackers and Van Swaaij, 1993). The gas-liquid mass transfer rate may be enhanced significantly by the presence of a finely dispersed, liquid or solid, phase present in the bulk liquid phase. This was shown experimentally by among others Kars et al. (1979) and Alper and Deckwer (1981) for the addition of fine solid particles to a gas-liquid system. The addition of fine particles caused an enhancement of the specific gas absorption rate (per unit of driving force and interfacial area, based on the two- phase system), whereas larger particles showed almost no effect.

The increase of the specific gas absorption rate, at unit driving force and unit interfacial area, due to the presence of the dispersed phase can be characterized by an enhancement factor, E. This enhancement factor is defined as the ratio of the absorption flux in the presence of the particles (which can be solid particles or liquid droplets) to the absorption flux at the same hydrodynamic conditions and driving force for mass transfer without such particles respectively. Using this definition, possible effects of the presence of particles on the gas-liquid interfacial area and on local hydrodynamics are taken into account. For a complete and more detailed review the reader is referred to Beenackers and van Swaaij (1993).

The enhancement of the specific absorption flux due to the presence of fine particles has been explained by the so-called ‘grazing’- or ‘shuttle’- mechanism, see Kars et al. (1979) or Alper et al. (1980). According to this shuttle-mechanism particles travel frequently between the stagnant mass transfer zone (according to the film theory) at the gas liquid interface and the liquid bulk. Due to preferential absorption of the diffusing gas phase component in the dispersed phase particles the concentration of this gas phase reactant in the liquid phase near the interface will be reduced, leading to an increased absorption rate. After a certain contact time, the particle is returned to the liquid bulk where the gas phase component is desorbed owing to the local concentration differences and the particles are regenerated. This shuttle mechanism requires that the dispersed phase particles are smaller than the stagnant mass transfer film thickness, δF according to the film theory. For gas absorption in aqueous media in an intensely agitated contactor, a typical value for δp is approximately 10-20 µm, whereas for a (laboratory) stirred cell apparatus this value is typically about a few hundred microns.

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Table I Overview of experimental work on gas absorption enhancement for G-L-L systems and for some other systems Authors System System Apparatus Characteristics Geometric sizes Type

Mehra, G-L-L Absorption of isobutylene, stirred cell φ = 1-15 dd = 1-12 µm Sharma butene-1 and propylene in εdis = 0.02-0.30

≈ 2 µm (1985) emulsions of chlorobenzene in E = 1.5-26 δp ≈ 100 µm Mehra et al. aqueous solutions of sulphuric mR isobutene : 1617 (1988-II) acid 1-butene : 2014 propylene : 396

Bruining et G-L-L Oxygen absorption into stirred cell φ ≈ 0.2 dd ≤ 10 µm al. (1986) emulsions of hexadecane in εdis = 0.01-0.08 δp ≈ 23.5 µm sodium sulphate E = 1-1.4 mR = 11.6

Littel et al. G-L-L Physical absorption of CO2 and stirred cell εdis = 0.01-0.39 dd ≤ 3 µm (1994) propylene into toluene/water laminar E = 1-4.1 δp,st.cell ≈ 300 µm emulsions film mR: CO2 = 2.85 δp,lam.film ≈ 65µm propylene = 103

Venugopal, G-L-L Absorption of CO2 into stirred cell φ ≈ 6.4 dd = 5-8 µm Mehra (1994) emulsions of aqueous sodium εdis = 0.05-0.2 δp ≈ 400 µm hydroxide in 2-ethyl hexanol E = 2.4-3.8 mR, CO2 = 1.9

Van Ede et al. G-L-L Oxygen absorption into stirred cell φ ≈ 0.2 dd = 22 µm (1995) emulsions of octene in sodium εdis = 0.05-0.5 δp ≈ 25 µm sulphate E = 1.5-3.7 mR ≈ 18

Kars et al. G-L-S Absorption of propane in a stirred cell E ≈ 1.3 dd = 30-530 µm (1979) slurry of active carbon in water εdis = 0.5-5 wt% δp ≈ 20 µm

Alper et al. G-L-S Absorption of CO2 in an stirred cell φ ≈ 0.32 dd = 1-20 µm (1980) aqueous carbonate-bicarbonate εdis = 0-0.5 wt% δp ≈ 37.5 µm buffer with carbonic anhydrase E = 1.2-3.5 supp.on oxirane-acrylic beads φ ≈ µ Pal et al. G-L-S Oxidation of aqueous sodium stirred cell 2.7 dd = 1.7 and 4.3 m (1982) sulphite in the presence of εdis = 0.01-2.0 wt% δp ≈ 56 µm activated carbon E = 1.4-1.9

Mehra et al. S-L-L Alkaline hydrolysis of solid stirred cell φ = 0.4-1.9 d2,4-DCPB = 235 µm (1988-II) esters in emulsions of εdis = 0.005-0.20 dDCPB = 195 µm chlorobenzene in aqueous E = 1.7-12 dPB = 120 µm solution of potassium mR,: PB = 5170 dd = 1-12 µm hydroxide 2,4-DCPB = 8890

≈ 3-4 µm DCPB = 7085 δp ≈ 240 µm

Tinge et al. G-L-S Absorption of a mixture of stirred cell εdis = 0.01 dd = 40 - 63 µm µ (1987) propane and ethene in a slurry mR, ethene = 65 & 500 - 630 m of activated carbon in water δ µ mR, propane = 1500 p < 100 m

Rols et al. G-L-L- Oxygen absorption into fermentation εdis = 0.02-0.34 dd,solids = 0.5-5 µm broth (1990) S emulsions of n-dodecane and E = 1.1-3.5 dd,liquid = 0.5-50 µm perfluoro-carbon in water, in a mR, n-dodecane = 7.7 db = 500-5000 µm culture of aerobacter aerogenes mR, perfluoroc. = 17

Junker et al. G-L-L- Oxygen absorption in fermentation εdis = 0.1-0.95 dd = 50-100 µm broth (1989-I) S aqueous/perfluorocarbon E = 5-10 db ≈ 300 µm fermentation systems mR, perfluoroc.= 22 δp ≈ 15 µm

Van der Meer G-L- Oxygen absorption into fermentation εdis = 0.05-0.11 dd ≈ 0.5 µm broth et al. (1992) L-S emulsions of n-octane in water, E = 1.1-1.6 δp ≈ 5 µm in culture of pseud. oleovorans

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Owing to a particle size distribution also in applications where the mean particle diameter is relatively large, a significant enhancement of the gas absorption rate may be observed. This was confirmed experimentally by Tinge and Drinkenburg (1995), who added very fine particles to a slurry consisting already of larger ones and found that the enhancement of gas absorption to be similar to the enhancement of the gas absorption rate due to the addition of only the same amount of fine particles to a clear liquid. Such size distributions will certainly occur in case of gas absorption (or solids dissolution) in a liquid-liquid dispersion. Nishikawa et al. (1994) have shown for liquid- liquid systems that the effect of aeration is a broadening of the droplet size distribution, i.e. more fine droplets. This implies that especially for gas-liquid-liquid systems enhancement of gas absorption can be expected when, of course, the solubility of the diffusing component in the dispersed liquid phase exceeds the solubility in the continuous liquid phase.

Experimentally, the gas absorption enhancement phenomenon in mulitphase systems was frequently studied and a summary of relevant studies is given in Table I. Three types of (reaction) systems have been studied experimentally; physical absorption experiments, systems with a first order reaction for the diffusing component in the continuous phase and one for a first order reaction in the dispersed phase. No experimental study concerning the influence of an additional second liquid phase on the selectivity for multi-reaction systems has been found in literature.

All presented experiments show that mass transfer and chemical reaction in mass transfer limited gas-liquid systems can be significantly enhanced by the addition of a second dispersed liquid phase with a good solubility (mR ≥ 10) of the solute. Enhancement factors up to 26 have been found experimentally, though usually the enhancement factor E is within the range 1-5. Some typical experimental results of the enhancement factor vs. dispersed liquid phase hold up, as observed in G- L-L systems, are shown in Figure 1. Note that these results are all obtained using labscale equipment.

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30 1.5 E 25 E 1.4 20 1.3 15 1.2 10 5 1.1

0 1 0 0.05 0.1 0.15 0.2 0.25 0 0.02 0.04 0.06 0.08 dispersed phase fraction fraction dispersed phase a: Enhancement of butene-1 absorption in chloro- b: Enhancement of oxygen absorption in hexadecane/ benzene/water emulsions (Mehra 1985, 1988) sodium sulphate emulsions (Bruining et al., 1986)

E 3.5

2.5

1.5

1 0 0.1 0.2 0.3 0.4 0.5 Fraction dispersed phase c. Enhancement of oxygen absorption in octene/water + sulphite emulsion (van Ede et al., 1995)

Figure 1 Observed enhancement factors at increasing dispersed phase hold-up for G-L-L systems

Table II Classification of models

steady state models instationary models

Homogeneous models Mehra, Sharma (1985) Bruining et al. (1986) Mehra (1988) Littel et al. (1994) van Ede et al. (1995) Nagy, Moser (1995)

Heterogeneous models 3-D Holstvoogd (1988) 1-D Junker (1990) 3-D Karve, Juvekar (1990) Vinke (1992) Nagy (1995) Brilman (1998) 2-D (this work) 3-D (this work)

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In order to elucidate and/or describe the enhancement effect many theoretical models were developed. These can be categorized by using the model-characterizations ‘stationary’ or ‘instationary’ models and ‘(pseudo-) homogeneous’ models or ‘heterogeneous’ models. For the heterogeneous models a subdivision in one-dimensional, two-dimensional and three-dimensional models can be made, see Table II. In Table III the models presented in literature are summarized in more detail.

The advantage of the homogeneous models is their numerical simplicity (for simple cases they can even be solved analytically) and short computation times. For these homogeneous models the following assumptions are generally made. ⋅ the dispersed phase droplets are very small with respect to the mass transfer film thickness according to the film theory ⋅ the dispersed phase (a continuum) is homogeneously distributed throughout the continuous phase ⋅ there is no direct gas-dispersed phase contact ⋅ transport occurs only through the continuous phase ⋅ mass transfer resistances within the dispersed phase are neglected.

Clearly, some of these assumptions are questionable. The results obtained with these models, however, do predict the trend of the enhancement factor with changing operating conditions as the gas-liquid contact time, the relative solubility and the dispersed phase fraction qualitatively reasonably well.

Since the quantitative agreement of the homogeneous models with the results of the experimental studies is not completely satisfactory, several authors even adapted these models to fit their experimental data better. Van Ede et al. (1995) assumed the dispersed phase fraction in the mass transfer zone to increase with the distance to the gas-liquid interface from a zero fraction at the gas- liquid interface to the bulk phase holdup. Littel et al. (1994), on the contrary, assumed in their modeling a thin layer of the dispersed phase at the gas-liquid interface to account for the large differences between the experimentally observed enhancement factors using the stirred cell apparatus and the ones calculated with the homogeneous model. By using a laminar, falling, film apparatus Littel et al. (1994) were able to minimize the effect of gravity, i.e. to prohibit settling of the dispersed phase. In the latter set of experiments the (homogeneous) model predictions were already much better in agreement with experimentally determined absorption fluxes.

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Table III Overview of Mass Transfer Models relevant for microphase systems

Authors characteristics Application Model representation

Mehra, Sharma film model G-L-S (1985) stationary model

G mass transfer zone Lbulk Bruining penetration model G-L-L 1−ε et al. physical absorption =+⋅ε − ε (1986) Em11()R G-L interface δfilm

Holstvoogd unit cell approach G-L-S G Lbulk et al. N (=1,2,3) particles in a row effect of particle h (1988) stationary model -geometry instantaneous surface reaction h G-L interface h = δfilm / Nparticles in a row

G mass transfer zone L Mehra surface renewal model G-L-L bulk 1−ε (1988) instationary, 1storder reaction

reaction in both phases poss. effect ε, aLL ε

G-L interface δsurface renewal

Saraph, see: Mehra (1988) G-L-S, precipitation { see Mehra (1988) } Mehra (1994) (‘auto-catalytic effect’)

Venugopal, see: Mehra (1988) G-L-L, w/o emulsion, { see Mehra (1988) } Mehra (1994) fast reaction in the aqueous phase

J Junker et al. penetration model G-L-L 1 d (1989) 2 ‘plates’ in series (1D) physical absorption + J2 d 0th order reaction o/w || w/o transition GAS RD

G-L interface δ

Karve, unit cell approach G-L-S L Juvekar stationary model interparticle effect G bulk (1990) instantaneous surface reaction 1st order reaction

equal probability for particle effect ε, dp

position for dp/2 ≤ M(x) ≤ δ-dp/2 G-L interface δfilm

Rols et al. macrosc. absorption model (kLa)G→Lc + (kLa)G→Ld G L (1990) parallel transport via direct 1−ε gas-dispersed phase contact collision/break-up proposed ε for G-L-L systems G-L interface

8 Chapter 6 Authors characteristics Application Model representation

G L Vinke et al . stationary film model for G-L-S 1−α (1992) solid particles in the film effect of particle mass transfer zone adsorption capacity dp/4 dp/2 S α G parallel transport covered- & adhering properties Lbulk parallel G-L and uncovered surface and G-S particles represented by a transport slab (at x = d /4 - d /2) p p G-L interface δ (1D heterogeneous) film

Littel penetration model G-L-L optional dispersed phase G film at interface Lbulk et al. instationary idea of microscopic (suggested, not in model) (1994) phase separation 1−ε physical absorption effect ε interface > ε bulk ε

G-L interface δpenetration mass transfer zone

Nagy, Moser film-penetration theory G-L-L G mass transfer zone Lbulk (1995) (‘pseudo’-hom. model) 1−ε th st effect of L-L mass transfer 0 , 1 order reaction JLL & mass transfer inside drops ε

G-L interface δsurface renewal

JLL from

Nagy film-penetration model G-L-L (1995) (2 parameter model) physical absorption J1 RD 1D heterogeneous 0th, 1st order reaction Jav

δ G-L interface δ1 δ2 van Ede dispersed phase holdup varies physical absorption G mass transfer zone Lbulk et al. with distance to G/L interface 1st order reaction (1995) G

G-L interface δ

G-L interface δsurface re

2-D/3-D angular models

BrilmanInstationary heterogeneous models: G (this work) 1-D, 2-D and 3-Dimensional Rbubble Rbubble ⋅ introduction foreland ______Rdroplet Rdroplet ⋅ effect geometry factors (dp, L, Rb/Rd) ⋅ A particle interaction 2-D/3-D linear models B C ⋅ effect of choice of unit cell 1-D linear model

i δ

i δ ‘droplet capacity’

or Rdroplet / δpenetration

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Heterogeneous mass transfer models, taking into account the local geometry at the gas-liquid interface, will increase the level of understanding of the mass transfer enhancement phenomena at the gas-liquid interface. For gas-liquid-liquid systems one-dimensional, instationary, heterogeneous mass transfer models for one particle in the penetration film were developed by Junker et al. (1990) and Nagy (1995). Their models could be solved analytically for some specific cases as e.g. physical absorption. These were developed to describe mass transfer (+ reaction) in systems in which the dispersed phase drops are of the same size as the penetration film thickness. However, especially in these cases the sphericity of the gas bubble as well as the sphericity of the droplet may influence significantly the mass transfer rates. A numerical 1-D model, capable of handling more complex situation was presented by Brilman et al. (1998).

For gas-liquid-solid systems some stationary 3-D heterogeneous models were developed by Holstvoogd et al. (1988) and Karve and Juvekar (1990). In both studies an unit cell approach was used, containing one single particle in the cell. The results of the heterogeneous models by Holstvoogd et al. (1988), Karve and Juvekar (1990) and the 1-D models of Nagy (1996) and Brilman et al. (1998) have shown that enhancement of gas-liquid mass transfer is dominated by the first particles near the gas-liquid interface. Further, it was shown by Holstvoogd et al. (1988) that local geometry strongly influences the enhancement factors found, indicating that a homogeneous description of the dispersed phase is not appropriate.

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2. Heterogeneous mass transfer models

From the short overview given above it is concluded, that instationary three dimensional mass transfer models are desired to investigate the importance of the geometrical factors involved in these multiple phase systems. It is necessary that the models to be developed are instationary in order to incorporate the effect of 'saturation' of the dispersed phase particles during the gas-liquid contact time. Next to the effects of near interface geometry and particle interaction also the translation of modeling results to actual absorption flux prediction will be discussed.

For the development of a three dimensional model in which local geometry is taken into account the characteristic geometrical size (or -) ratios should be measured or estimated. In general, bubbles are large with respect to the droplet size and the penetration film thickness. In these cases the interface can be regarded as a plane (in this work called ‘linear' or 'planar' models). For strong ionic solutions, at high power inputs in agitated systems or for a dissolving solid in a liquid-liquid system this is not necessarily the case and the bubble or solid particle size needs to be taken into account. This latter effect is taken into account in the so-called ‘angular models’, presented in this work. Therefore, a complete set of models has been developed and is presented schemetically in Figure 2.

2-D/3-D angular models

R Rbubble bubble R Rdroplet droplet

A 2-D/3-D linear models B C 1-D linear model

i δ

‘droplet capacity’ i δ

or R droplet / δ pen

Figure 2 Set of heterogeneous, instationary mass transfer models

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Depending on the geometrical size ratio Rbubble / Rdroplet and the relative ‘droplet absorption capacity’ one of these models will be most appropriate. Model A takes both the sphericity of the gas bubble and the drop into account. If the bubble size is much larger than the penetration film thickness the sphericity of the gas-liquid interface can be neglected. For very small particles with a low capacity the one dimensional model B may be found convenient and sufficient accurate, whereas for somewhat larger particles or particles with a higher capacity for the diffusing solute model C is most appropriate. In theory, in all the models described in Figure 2 the number, position and size of the drops etc. can be chosen arbitrarily.

For modeling mass transfer in multiple phase systems it is required that a fundamental mass transfer model like the Higbie penetration model or the film model is adopted. The Higbie model is applied in the present study, thus assuming that a package of the bulk liquid phase, including the dispersion droplets present within the package, is transported to the gas-liquid interface and remains there for a certain contact time τ, before returning to the liquid phase bulk. Additionally, it is assumed that the position and distribution of the dispersed phase droplets within the package remains unchanged. This is represented schematically in Figure 3.

Gas phase Liquid phase

Gas absorption flux J

Figure 3 Gas absorption (in a multiphase system) according to the penetration theory

An additional complication of the heterogeneous models for their practical applicability is the comparison of the modeling results for a particular situation with experimentally observed absorption rates. Since, in principal, an infinite number of distributions of the dispersed phase drops throughout the penetration film is possible, one needs to choose either a representative ‘average’ configuration or use a statistical averaging technique. Since it was shown (Brilman et

12 Chapter 6 al., 1998) with the one-dimensional model that among others the distance of the first droplet to the gas liquid interface has a major influence on the mass transfer enhancement, this aspect requires special attention. For 2-D and 3-D models the situation is even more complicated since particle-particle interactions are much more complex. After discussing the results for simulations with one dispersed phase particle, effects of particle-particle interaction will be investigated using 2-D multi-particle simulations. With these results, effects of different particle configurations in a liquid package (or unit cell) can be estimated.

2.1 The one dimensional model

G Ldis Lc

x = 0 x = δp

Figure 4 The one-dimensional, instationary, multi-particle model.

In Figure 4 a graphical representation of the one dimensional model is given. In Figure 4 the gas phase is on the left hand side, Lc represents the continuous liquid phase and Ldis the dispersed liquid phase droplets. The parameter δp is the penetration film thickness, as estimated by Higbie’s penetration theory for absorption in the continuous phase in the absence of the dispersed phase.

The actual penetration depth will, in general, be less than δp due to the larger absorption capacity of the dispersed phase droplets.

The equations describing diffusion of the gas phase solute in the stagnant continuous liquid phase and inside the dispersed phase (and chemical reaction if applicable) were solved numerically. The number of particles as well as their sizes, positions and composition can be varied arbitrarily. For more details on the model the reader is referred to Brilman et al. (1998).

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G Lc Ldis G Lc

y r x d

Ldis

(a) geometry of a grid on which (b) 3-D geometry as described (c) 3-D geometry described the model equations are solved by the equations of the by the equations of the 2-D linear model 3-D linear model

Figure 6 Transformation of the two-dimensional plane on which the mass balances for the 2-D and 3-D linear, heterogeneous models are solved into the three-dimensional situation that these equations represent.

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2.2 Two and three dimensional models

Ldis Gas Bubble

Figure 5 Two dimensional slice of a gas-liquid-liquid system

In Figure 5 a typical representation of a two or three dimensional model is given. In this figure the gas bubble is surrounded by a larger number of droplets. In this study both the gas bubble and the droplets are considered to be spherical. The partial differential equations describing diffusion with chemical reaction in such heterogeneous media can only be solved numerically. This requires the diffusion field to be covered by a computational grid on which the partial differential equations can be solved using a finite difference approximation.

The complex geometry of the heterogeneous medium is difficult to describe using a single global grid. In this work, a composite grid, consisting of simpler component grids, suitably chosen to describe a particular subdomain and overlapping where they meet, is chosen to solve this problem. This is illustrated below for the situation of one dispersed phase droplet located near the gas- liquid interface. For the 2-D and 3-D linear models (type C), the Base Composite Grid (BCG) used for solving the equations is represented by the x-y plane in Figure 6. More details on this Overlapping Grid Technique are given by Chesshire and Henshaw (1990).

In Figure 6-a the geometry of the BCG for which the equations are solved is represented. The equations for the 2-D models assume no variation in the z-direction, perpendicular to the x-y plane. The 3-D single particle models use the same BCG. However, now the three dimensional transport equations are solved. A large reduction of computational effort is hereby achieved by using the rotational symmetry around the line through the middle of the droplet, perpendicular to the gas- liquid interface.

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Constructing the Basic Composite Grid from the Component Grids

In the overlapping grid method a set of simpler, orthogonal component grids is used to cover the entire area to be considered. The diffusion with chemical reaction equations are solved on every 'component grid'. Now the most appropriate coordinate system (e.g. cylindrical coordinates for an annular grid) can be chosen for each component grid separately. On the overlap of the component grids interpolation can be specified. The component grids used in these simulations include:

⋅ a rectangular “background” grid

⋅ an annular “outer annulus” grid

⋅ an annular “inner annulus” grid

⋅ a rectangular ‘inner square” grid +

G-L interface

Basic Composite Grid x δ 1.5⋅δ (see Figure 6)

Figure 7 Construction of the basic composite (overlapping) grid from the component grids

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The composition of the composite overlapping grids of Figure 6 is clearly demonstrated in Figure 7. The “outer annulus” grid enables a numerically smooth overlap from the diffusion field around the droplet with the continuous phase diffusion field. The inner radius of the outer annulus grid and the outer radius of the inner annulus grid join precisely and constitute the phase boundary. At this phase boundary a user-defined boundary condition is implemented, accounting for continuity of fluxes and the instantaneous equilibrium distribution of the diffusing species between both phases at the interface (see equations 1-a and 1-b). A small square grid inside the drop is required to avoid very small grid sizes and a singularity at the center of the inner annulus.

The model equations for the 2-D and 3-D models are listed in Table IV. In all these equation Rcon

(or Rdis) is the source term due to chemical reaction. This term causes coupling of the mass balance of solute A to the mass balances of other component in case of multi-component reactions. The mass transfer resistance in the gas phase is neglected in this work.

The angular models (type A) differ from the linear models (type C) only via the background-grid. For the A-type models the background is chosen to be a fraction (≈ 1/6) of an angular grid. The equations describing diffusion with chemical reaction for the other component grids remain unchanged.

From Table IV-c it can be noted that boundary conditions at overlapping component grids do not need to be specified. The continuity of the concentration profile and the conservation of mass is accounted for by the interpolation and overlap algorithms within the Overture software package (Los Alamos Nat. Lab. (USA)). At the droplet surface the inner and outer annulus component grids do not overlap, but join precisely. Here, the boundary conditions need to be specified to ensure the continuity of fluxes and to account for the distribution if the solute between both liquid phases. The equilibrium at the interface is assumed to be instantaneously fast.

= Cdis mR Ccon (1-a)

 ∂C ∂C  − D dis = −D con  (1-b) dis ∂ con ∂  r r  = r Rd

17 Chapter 6

Table IV Mass balances and boundary conditions for the 2-D and 3-D Heterogeneous Mass Transfer Models

Table IV-a 2-D models; Instationary mass balances for diffusing gas phase component A

2D models instationary mass balances continuous phase ∂c ()x,,y t  ∂2c ()x,,y t ∂2c ()xt ,y,  con =++ con con  ∂t D con R con (rectangular 'Background' )  ∂x2 ∂y2  continuous phase 2) ∂θc ()r ,,t  ∂θ()∂θ2 () con bb 11∂  ccon rbb,,t  ccon rbb ,,t =++D   r   R (angular 'Background') ∂t con r ∂r b ∂r 2 ∂θ 2 con  b b b  rb b  continuous phase around ∂θc ()r ,,t  ∂θ()∂θ2 () con dd 11∂  ccon rdd,,t  ccon rdd ,,t 1) =++D   r   R dispersed phase droplet ∂t con r ∂r d ∂r 2 ∂θ 2 con  d d  d  rd d  ('outer annulus') dispersed phase 1) ∂θc ()r ,,t  ∂θ()∂θ2 () dis dd 11∂  cdis rdd,,t  cdis rdd ,,t =++D   r   R ('inner annulus') ∂t dis r ∂r  d ∂r  2 ∂θ 2 dis  d d d rd d  1) dispersed phase ∂ () 2 2 cdis x,,y t  ∂ c ()x,,y t ∂ c ()xt ,y,  =++D  dis dis  R ∂t dis dis ('inner square')  ∂x2 ∂y2 

Table IV-b 3-D models; Instationary mass balances for diffusing gas phase component A

3D models instationary mass balances continuous phase ∂c ()xt,y,  ∂2c ()xyt,,∂ ∂c ()xyt ,,  con =+ con 1 con  + ∂ Dcon ()y R con (rectangular 'Background') t  ∂x2 yy∂ ∂y  continuous phase 2)   ∂θc ()r ,,t ∂θc ()r ,,t  ∂θ2c ()r ,,t  con bb 1 ∂  2 con bb  1 ∂ con bb ∂ =+D   r  sinθ  +R (angular 'Background') t con  2 ∂r  b ∂r  2 θ ∂c  b ∂θ 2  con rb b b rbbsin ,con d continuous phase around ∂θ()   ccon rdd,,t ∂  ∂θc ()r ,,t  ∂  ∂θc ()r ,,t  =+1 2 con dd 1 θ con dd + 1) ∂ D   r  sin  R dispersed phase droplet t con  2 ∂r  d ∂r  r 2sinθ ∂θ  d ∂θ  con rd d d ddd d ('outer annulus') dispersed phase 1) ∂θc ()r ,,t  ∂θc ()r ,,t ∂θ2c ()r ,,t  dis dd 1 ∂  2 dis dd  1 ∂  dis dd  ∂ =+D   r  sinθ  +R ('inner annulus') t dis 2 ∂r  d ∂r  2 θ ∂c  d ∂θ 2  dis  rd d d rddsin dis d  1) dispersed phase ∂θ   c ()r ,,t ∂ ∂θc ()r ,,t ∂ ∂θ2c ()r ,,t dis dd 1  2 dis dd  1  dis dd  ∂ =+D   r  sin θ  +R ('inner square') t dis  2 ∂r  d ∂r  2 θ ∂c  d ∂θ 2  dis rd d d rddsin dis d

1) The center of the coordinate system is place at the center of the droplet.

2) The center of the coordinate system is place at the center of the gas bubble.

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Table IV-c 2-D and 3-D models; Initial and boundary conditions 3)

2D + 3D models boundary conditions continuous phase IC t = 0 x ≥ 0 ccon = 0 (or ccon = ccon,bulk)

(rectangular'Background') BC t > 0 x = 0 ccon = cgas ⋅ Mgl

x → ∞ ccon → 0 (or ccon → ccon,bulk) continuous phase IC t = 0rb ≥ Rb ccon = 0 (or ccon = ccon,bulk)

(angular 'Background') BC t > 0rb = Rb ccon = cgas ⋅ mGL

rb → ∞ ccon → 0 (or ccon → ccon,bulk) continuous phase around IC t = 0rd ≥ Rd ccon = 0 (or ccon = ccon,bulk) droplet ('outer annulus') BC t > 0rd = Rd cdis = ccon ⋅mR

Jcon = Jdis dispersed phase IC t = 0rd ≤ Rd cdis = 0 (or cdis = cdis,bulk)

('inner annulus') BC t > 0rd = Rd cdis = ccon ⋅mR

Jdis = Jcon dispersed phase IC t = 0 x ≥ 0 cdis = 0 ('inner square')

3) No boundary conditions are required at the overlap-boundaries: 'outer annulus' / 'Background' and 'inner square' / 'inner annulus'. The boundary condition at the droplet surface rd = Rd is defined in equations (1-a) and (1-b)

The result of the models described above consists of a concentration profile for the diffusing component(s) in the diffusion field (at every gridpoint) for both the continuous and the dispersed phase. From the model the time dependent specific rate of absorption per unit time and unit of gas-liquid interface, ϕ(t) in [mole/m2 s], and the average specific rate of absorption over the gas-

2 liquid contact time, ϕav(τ) in [mole/m s], are obtained at every y-position at the gas-liquid interface. The local enhancement factor E(y,t) is defined by the ratio of these fluxes to their equivalent for gas absorption under identical conditions without the presence of a dispersed phase ϕ ϕτ(,)y (,)yt τ av : Eyt(,)= , E(y,)=av (2-a, 2-b) D D c 2 c π t πτ

The enhancement factors E(y) mentioned refer always to the contact time averaged enhancement factor Eav(y,τ), unless mentioned otherwise. In the simulations the depth of the diffusion field was taken 1.5 times the penetration depth of the diffusing gas phase component (δπτpen= 2),D c

19 Chapter 6 thereby assuring that the concentration profile does not reach to the end of the diffusion field. The model was validated against analytical solutions for physical absorption and for absorption accompanied by a homogeneous first order chemical reaction in the continuous phase for situations without particles.

From these test cases it is concluded that the concentrations and fluxes calculated on overlapping grids are usually calculated within 1 percent deviation. Convergy orders in time- and space stepsize are consistent with the Euler explicit finite difference formula used to approximate the partial differential equations on the component grids. Extrapolation to infinitely small step sizes yielded deviations from the analytical solutions of less than 0.03% in the test cases.

Table V Input parameters

independent parameter values depending parameter values

-4 kL 1.16⋅10 [m/s] t 0.117332 [s] -9 2 -6 Dc 1.24⋅10 [m /s] dp 42.76⋅10 [m] -9 2 Dd 2.30⋅10 [m /s] DR 1.85 [-]

mR 103 [-]

-6 1) dp 3⋅10 [m]

1) Littel et al. (1994) mentioned that “the dispersed phase droplets were smaller than 3 µm.”

20 Chapter 6

3. Results of simulations with one dispersed phase particle

For the single particle simulations values for the various physico-chemical parameters need to be chosen. In this work the parameters taken from the experimental study of Littel et al. (1994) were chosen as a kind of default values, see Table V. A typical single particle model simulation result is given in Figure 8.

Local enhancement factors 1 Enhancement vs. position can be calculated gas side GAS y

1 Direction of diffusion into the liquid phase EnhancementE (y,τ)

Figure 8-a Typical simulation results: a concentration field around the droplet and the local enhancement factors, evaluated at the gas-liquid interface

3.8 3.4-3.8 E 3.4 3-3.4 2.6-3 3.0 2.2-2.6 1.8-2.2 2.6 1.4-1.8 1-1.4 2.2

1.8

1.4 1.0 0.8 1.0 0.6 t / τ 0.4 Y-position 0.2 0

Figure 8-b Typical simulation results: a concentration field around the droplet and the local enhancement factors, evaluated at the gas-liquid interface

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From Figure 8-b it is clear that the enhancement factor not only varies with the position along the gas-liquid interface, but also changes significantly with time. A maximum is observed due to counteracting effects. The initial increase of E(y,t) with time is due to the fact that the propagating concentration profile needs to reach the droplet, before its influence will become noticeable. However, as time propagates, the droplet will get ‘saturated’ with the diffusing solute. The local decrease of its concentration in the continuous phase near the gas-liquid interface will diminish, and with this the local enhancement factors will decrease, ultimately leading to E(y,t) = 1 at every y-position. Another important aspect which can be recognized from Figure 8-a is the interfacial area over which the influence of the mass transfer enhancement is noticeable. In this work, it is proposed to call this the ‘foreland’ of the droplet

For the single droplet case the influence of several process parameters was studied, and especially the distance of the front of the particle to the gas-liquid interface, the droplet diameter and the relative solubility mR were varied. Examples of results are given in Figures 9 a-e for 2-D simulations. The default parameter values used are given in Table V.

4 Distance to G-L interface E (y,τ) -6 3.5 1.707 [10 m]

3.31 ,,

3 4.91 ,,

2.5

1.5

1 -2.0E-05 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 Y-position [m]

Figure 9-a Effect of distance to gas-liquid interface (L)

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E [-] mR 4 2 10 103 3

1 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 1.0E-05 1.5E-05 y-position [m]

Figure 9-b Variation of relative solubility mR

4 t / 4* τ τ E (y, ) 0.005 0.01 0.02 3 0.08 0.16 0.32 1 2

1 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 1.0E-05 1.5E-05 y-position [m]

Figure 9-c E(y) at different contact times 0 ≤ t ≤ 4⋅τ

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E(y,τ) drop diameter in 10-6 m 6 2

3 5 6

4 10 24

1 -2.5E-05 -2.0E-05 -1.5E-05 -1.0E-05 -5.0E-06 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 y-position [m] Figure 9-d Variation of droplet diameter

4 E (y,t) Y-POSITION

3.5 0 -1.16E-06 -1.75E-06 3 -3.03E-06 -5.33E-06 2.5

1.5

1 0.001 0.01 0.1 1 t / 4*τ

Figure 9-e E(t) for 0 ≤ t ≤ 4⋅τ for 5 y-positions

Figure 9 Some typical (2-D) single particle simulation results showing the effects of several parameters (default values are given in Table V and default L value = 1.7 mm)

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Figure 9-c shows clearly that the width of the foreland changes in time and will depend on droplet diameter, relative solubility and the continuous phase diffusion coefficient (not shown in the figures). The distance of the droplet to the gas-liquid interface seems to have no significant influence on the foreland area (Figure 9-a), however, the enhancement factors obtained increase strongly with decreasing distance of the droplet to the gas-liquid interface. This latter result was also found for the 1-D model (see Brilman et al., 1998).

The importance of the radius of the foreland was further analyzed with the aid of Figures 10-a and 10-b. In Figure 10-a the local enhancement factors E (y,τ) at different radial positions from the projected center of the particle on the gas-liquid interface as well as the corresponding interfacial area represented for a 3-D simulation. In Figure 10-b these are combined to yield the relative contribution to the additional flux due to the presence of the droplet for every radial position. Note that for a 2-D calculation a similar representation can be constructed, but in these cases the differences in fractional surface ‘area’ (line pieces) of the gas-liquid interface, will be less pronounced.

17 16 τ E(y, 0- ) π 2 4 (y/ymax) [%]

13 12

9 8

5 Projected droplet 4

1 0 0.0 5.0 10.0 15.0 20.0 y-position [mm]

Figure 10-a Local enhancement factors at different y-positions

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10 100

8 80

6 60 -1}/{-1 ) τ)

4 40 * {E(y, enhancement (%)

totaal Projected droplet

2 20 Cumulative contribution to extra (dA/A Local contribution to the enhancement

0 0 0 5 10 15 20 25 radial position Y [µm]

Figure 10-b Contribution to mass transfer enhancement at different radial positions

Figure 10 Analysis of the contribution to mass transfer enhancement at different radial positions

In Figure 10-b it can be recognized that only about 1/3 of the additional gas phase component absorbed is accounted for in the area covered by the projection of the droplet on the gas-liquid interface, and thus 2/3 of the additional absorption occurs in the foreland outside this projection area.

The total amount of gas phase component which will be absorbed in addition to the amount absorbed by an equivalent liquid phase package without a droplet can be calculated by integrating the additional flux (which is equal to: J ph.⋅ (E(y,t)-1)) over the foreland area. It was found that the total amount of gas phase component absorbed in the dispersed phase droplet exceeds the additional amount absorbed through the gas liquid interface. In other words, the droplet acts as a sink for the diffusing gas phase component due to the local distribution of the gas phase component.

26 Chapter 6

4. Particle-particle interaction

Another important feature is that the presence of other particles in the vicinity of the particle considered may affect its influecne on the gas absorption. In this section it is investigated how the presence of additional particles influences the overall absorption flux. In these simulations the default physico-chemical parameter values are taken equal to those presented in Table V, only the number of particles and their position is varied.

Interaction between the enhancing effect of particles occurs when the total effect of the particles differs from the sum of the individual contributions of the separate particles if no other particles were present. This interaction is studied for several particle configurations, using the two- dimensional model. First, interactions between two particles were considered as schemetically shown below :

2 2

w ∆x

1 2 ∆y L

Gas-Liquid interface

Figure 11 Two particle configurations

Some results of these simulations are shown in Figures 12 . In these figures the calculated local enhancement curve for the two particle configuration as well as the individual contributions of the particles respectively and the summation of the their contributions is presented. For particles located directly behind each other (with respect to the interface, see Figure 12-c) it is found that the particles located directly behind the first one contribute marginally to the mass transfer enhancement. This is not only due to the larger distance to the interface for the second particle, but mainly to the shielding effect of the first particle.

27 Chapter 6

5 Two particle simulation E1 , single particle result E (y, t) E2 , single particle result E1 + E2 -1

1 -2.00E-05 -1.00E-05 0.00E+00 1.00E-05 2.00E-05 3.00E-05 4.00E-05 y-position [m]

Figure 12-a 2-D simulations for two particles an interparticle distance of 17 µm

5 result two particle simulation E(y,τ) E1 + E2 - 1 E1, single particle result 4 E2, single particle result

1 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 y-position [m]

Figure 12-b 2-D simulations for two particles an interparticle distance of 2 µm

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5 Two particle simulation E (y,τ) E1, single particle simulation first particle E1 + E2 - 1 4

2 ∆x

1 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05

y-position [m]

Figure 12-c 2-D simulations for two particles directly behind each other

5 Two particles simulation E (y,τ) E1 + E2 - 1 E1 4 E1

1 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05

y-position [m]

Figure 12-d 2-D simulations for a 2µm and a 3µm particle located at the same distance to the G-L interface

As it may be expected, the interaction (in fact the deviation between the two particle simulation and the sum of both single particle contributions) increases with decreasing distance between the particles considered. For three particle simulations similar results were found, see Figures 13 a-d.

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The interaction may be quantified by defining an interaction factor I as the ratio of the actual enhancement factor to the summation of the contributions of the particles separately;

N ∑ E(y) − (N − 1) = I(y) = i 1 (3) E Nparticles(y)

The value found for this interaction factor will vary with the y-position along the gas-liquid interface. For the simulation case of Table V, the interaction factor I decreases strongly (and thus interaction becomes increasingly important) at interparticle distances below 5 µm. At interparticle distances exceeding 5 µm the particle-particle interaction may be neglected (deviations less than 3%). For other sets of physico-chemical parameters the mentioned threshold value of 5 µm will be different, e.g. for larger values of Dcon the treshold value will be higher.

Since the number of multi-particle configurations possible is infinite, it would be advantageous if the enhancement factors for a specific multi-particle configuration could be described on beforehand from the results for single particle simulations. It was found that the calculated local enhancement factors for the two- and three particle curves can be described satisfactory accurate well using the following correlation, in which all binary particle-particle interactions are accounted for :

  N −  N−1 N  (N 1)  C(wi→j)  E (y) = ∑ E (y) − ⋅ ∑ ∑ (E (y) ⋅E (y)) (4) Nparticles i 1 ⋅ ⋅ −  i j  i=1 2 N (N 1)  i=1 j=i+1   i≠ j 

In this correlation the only remaining (fit)-parameter is C, which is a function of the interparticle distance (surface to surface) ∆w i→j. For the parameter set of Table V the correlation of C with w is found to be :

-6 w ≤ 5 µm C = 0.1 + (5.0⋅10 - wi→j) ⋅ 0.05/wi→j (w i→j in [µm]) w > 5 µm C = 0.1

30 Chapter 6

6 Three particle simulation E(y,t) E1 + E2 + E3 - 2 E1 5 E2 E3

1 0.0E+00 5.0E-06 1.0E-05 1.5E-05 2.0E-05 2.5E-05 3.0E-05 3.5E-05 4.0E-05 y-position [m]

Figure 13-a Three identical particles at equal distance from the gas-liquid interface and an interparticle distance of 2 µm

5 Three particle simulation E1 E (y,t) E2 E3 E1+E2+E3 - 2 4

1 -1.0E-05 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05 5.0E-05 Y-position [m]

Figure 13-b Three particles, at equal distance from the G-L interface. Interparticle distance : 7 µm.

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5 Three particle simulation E3 E (y, τ) E2

4 E1 E1 + E2 + E3 - 2

1 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05 y-position [m]

Figure 13-c Three particles, the outer particles are located more close to the gas-liquid interface.

11 Three particle simulation E (y,τ) E1 + E2 + E3 - 2 9 E3

7 E1

1 0.0E+00 1.0E-05 2.0E-05 3.0E-05 4.0E-05 y-position [m]

Figure 13-d Three particles, the middle one is located closer to the gas-liquid interface

For the considered set of parameter values, this particle interaction description was tested for a 5 particle configuration. The results are given in Figure 14. From these results it is concluded that the E(y,τ) profile is predicted reasonably accurate from the single particle simulations.

32 Chapter 6

6 5 particle simulation E (y,τ) Particle 1 Particle 2 5 Particle 3 Particle 4 Particle 5 4 E, without interaction E, with interaction

1 2.0E-05 3.0E-05 4.0E-05 5.0E-05 6.0E-05 7.0E-05 8.0E-05 y-position [m]

Figure 14 Five particle simulation; testing the interaction correlation

5. On the prediction of absorption fluxes

For calculating the overall gas absorption fluxes into emulsions or liquid-liquid dispersions using a heterogeneous model all the possible particle configurations at the interfaces must be taken into account and the enhancement factors for these situations should be calculated. Alternatively, an unit cell may be defined in which the particle configuration is such that the absorption flux for this unit cell represents the average absorption flux for the particular system and all interactions are corrected for. Holstvoogd et al. (1988) arbitrarily choose to place one particle in the center of a unit, cubic, cell (see Table III). Karve and Juvekar (1990) took a cylindrical unit cell with one particle (see Table III). However, this unit cell, implemented with a symmetry boundary at the cylindrical wall overestimates the dispersed phase hold-up surrounding this unit cell, owing to the cylindrical geometry.

Single particle calculations have shown that especially those particles located most closely to the interface contribute to the mass transfer enhancement. Particles lying directly behind other

33 Chapter 6 particles hardly contribute to the calculated mass transfer enhancement. The interaction algorithm, taking the binary particle-particle interaction pairs into account, was found to describe reasonably well the local enhancement factors for the 2-D cases considered. With this, the effect of interaction of different particle configurations can now be evaluated. Since it is impossible to evaluate every possible configuration, the sensitivity of the average absorption flux in a multi- particle cell to the particle configuration is studied. From this it might be ultimately possible to arrive at a representative unit cell configuration.

For this purpose a multi-particle cell was defined, with 12 particles present in a certain area in combination with various combinations. The area was chosen such that the hold-up (by surface for the 2-D model) was equal to 3.4 %. The area δp × ∆Y was divided (in 6 different ways) in 12 equally sized rectangular single particle cells, which, on the average, will contain each one single particle (so-called ‘single particle cells’). Examples of these subdivisions are given in Figures 15.

gas-liquid interface gas-liquid interface ∆Y

1/3 δp

1/3⋅δp δ p (b) (c) (d)

Some configurations used δp (a) 12 particles in ∆Y×δp

Figure 15 Some particle configurations used in the sensitivity study

For these configurations one single particle cell located at the gas-liquid interface was considered and the local enhancement curves E(L,y,τ) were integrated and averaged over all possible particle positions within the cell, on the centerline perpendicular to the gas-liquid interface, to yield

E L(y,τ). To allow analytical integration, the E(L,y,τ) curves were fitted (without significant loss in accuracy) using a Cauchy distribution function E(L,y,τ) = 1 + A/(1+(y/B)2) in which the parameters A and B depend only on L.

34 Chapter 6

L=dspc −1/ 2 dp ∫ E(L, y, τ)dL τ = L=0 E L (y, ) (5) L=dspc −1/ 2dp ∫ dL L=0 In the next step, the interaction between particles in adjacent cells was taken into account via equation (4), using the L-averaged enhancement relations from Eq. (5). By doing so, it is assumed τ that the interaction of the EyL (,) curves for the separate particles is a good approach to averaging over all possible configurations, each with its own interaction characteristics. This assumption was supported by test calculations with three adjacent cells. In each of these cells 20 particle positions on the centerline were chosen. The average E(y,τ) relation for these 20×20×20 situations was found to be equal to the E(y,τ) relation obtained by the interaction of the three τ EyL (,) relations. In another test the assumption of locating all particles at the centerline of their respective single particle cell was tested by allowing 45 positions (3 lines ×15 positions per line) per cell, again for three adjacent cells. All tests showed that these assumptions cause little error (< 5%).

Single particle simulations have shown that droplets located at L > 1/3⋅δp have no significant influence on the flux enhancement, see also Brilman (1998). Therefore, for those configurations where the depth of the single particle cell exceeds this value, the cells behind the cell adjacent to the gas-liquid interface were neglected. However, this is not the case for configurations like in Figure 15-d, where also the second row of single particle cells will contribute to the mass transfer enhancement. However, a maximum shielding effect is obtained if the particles are located directly behind one another, as will be clear from Figure 12-c. To avoid this, the second row is shifted half-a-cell position aside. This is represented in Figure 16. When N rows should be taken into account, each row is shifted 1/N-th part aside. After this, the contribution of the second row of cells, taking into account the interaction terms, was also included.

gas-liquid interface gas-liquid interface

δ 1/3 δp 1/3 p

(a) (b) Figure 16 "..shifted half-a-cell position aside to avoid the maximum shielding effect.."

35 Chapter 6

Physico-chemical input parameters mR, DR, Dc τ ε process parameters: dp, (or kL), hold up Determine particle Single particle simulation result

4.5 interaction factors

3.5 E E 3

2.5 E (L, y, τ) 2 1. 5

1 y-position y-position FA

calculate the single particle cell size 1/3⋅δp δp from dp, ε (+ choose configurations)

1/3 δ pen no.of rows configuration of single particle cells 1/3 δ pen

E (y,τ) for each s.p.c. L L Averaging over L-position

d s.p.c. Sum of all contributions to E(y,τ) in the 1/3 δ central single particle cell; pen particle interaction with neighbouring particles in the same and in lower rows Taking into account the width of the foreland and all particle-particle interactions E E s.p.c. (y,τ)

y-position Averaging over s.p.c. width

E (τ)

Figure 17 Procedure for calculating the average enhancement factor from heterogeneous, single particle models {s.p.c. = single particle cell }

36 Chapter 6

The 2-D single particle results (for 3 µm and for 2 µm droplets) were used to evaluate the different single particle cell configurations. The results are presented below.

Table VI Effect of single particle cell configuration

Configuration Eav,cell (3 µm) Eav,cell (2 µm) 1x12 1.73 2.14 2x6 1.71 2.09 3x4 1.72 2.05 4x3 1.76 2.10 1x12 2x6 3x4 6x2 1.77 2.10 12x1 1.88 2.15

4x3 6x2 12x1

From these results it is concluded that the configuration of the unit cell does not influence significantly the overall enhancement factor calculated, if the configuration of the single particle cell is chosen not too extreme. In Figure 16 the complete procedure for flux prediction from single particle simulations using particle-particle interaction is represented.

This procedure is used to evaluate the average enhancement factor using the 3D simulations for the parameter set of Table V, representing the measurements of Littel et al. (1994). Using these 3D single particle simulations and the strategy proposed in Figure 17 the results of the Figure 18 were obtained.

From the results of Figure 18 it can be seen for the results of the 3-D heterogeneous model that inclusion of the particle interaction leads to a more logarithmic shape of the E-ε curve, which is also predicted by the homogeneous models. This was not found for the 1-D model, because in the latter model particle interaction is negligible (all particles lie behind one another) and an increase in the dispersed phase hold-up only leads to a smaller distancer of the first particle to the gas- liquid interface.

37 Chapter 6

8 experimental (Littel et al. 1994) E (τ) homogeneous model 1-D Het. model µ 3-D Het. model 3-D Het. model, dp = 3 m without interaction ! 6 3-D Het. model, without interaction µ 1-D Het. model, dp = 3 m

homogeneous model

µ 3-D heterogeneous models, dp = 3 m 4

0 0 0.1 0.2 0.3 dispersed phase hold up ε

Figure 18 Comparison of results obtained with the 1-D and 3-D instationary heterogeneous models with a homogeneous model and experimental data by Littel et al. (1994)

With respect to the simulation of the data by Littel et al. (1994) it can be concluded that the average droplet size is indeed smaller than 3 µm. However, since the exact dropsize (distribution) is not known, no further validation is possible.

The 3-D simulation data presented in Figure 18 were calculated for different numbers of rows and for different aspect ratios of the unit cell. The latter effect was negligible, whereas the number of rows had a minor influence (< 5%) at higher hold-ups. This is believed to be caused by the limitations of the fit of the simulation data at small distances to the gas-liquid interface. More single particle simulations under these conditions could resolve this influence.

38 Chapter 6

6. Discussion and conclusions

Heterogeneous mass transfer models have been developed to study the effect of particles near the gas-liquid interface on the gas-absorption rate. Using the developed models the relative importance of particle capacity parameters and particle position are now clear from single particle simulations. Particle interaction was studied extensively for the 2-D models, and to a lesser extent for the 3-D models. An interaction algorithm valid for the specific set of parameters considered (Table V) was identified and gave good results in predicting the absorption fluxes for multi-particle simulations. However, for other sets of physico-chemical parameters the (coefficients used in the) algorithm should be determined again by fitting another set of simulations (multi particle simulations or 2-D single particle simulations using symmetry at the boundaries of the single particle cell). Taking all particle interactions into account, the shape of the single particle cell (the size is already determined by the holdup) can be chosen rather arbitrarily. A procedure for predicting the absorption flux for gas absorption in heterogeneous media has been proposed in Figure 17.

From the results of Figures 18 for the variation of the enhancement factor at increasing holdup, it is clear that particle-particle interaction should be taken into account in the heterogeneous models in order to be able to describe the enhancement factor leveling off at higher hold-ups. Note, that at higher holdups also other hydrodynamic parameters (like the characteristic surface renewal time) may have changed in the experiments and even direct gas-dispersed liquid phase contact may become important.

The results obtained using the models developed and the strategy proposed seem to follow the general experimental trends and described reasonably well the data by Littel et al. (1994). However, accurate comparison is difficult since no accurate data on dispersed phase droplet size and - distribution were reported. Further validation of the model is desired and awaiting new, accurately defined experiments.

Acknowledgments The author wishes to acknowledge W.D. Henshaw (Los Alamos Nat. Lab., U.S.A.) for providing the Overture Overlapping Grid software and M.J.V. Goldschmidt and S. Maas for their contributions to the development, testing and applications of the models.

39 Chapter 6

Notation A area [m2] BCG Basic Composite Grid c concentration [mol/m3] D diffusion coefficient [m2/s] DR relative diffusion coefficient { Dd / Dc } [-] d characteristic particle diameter [m] dp particle diameter [m] dd drop diameter [m] E enhancement factor [-] G gas phase I interaction parameter [-] J mass transfer flux [mol/m2 s] kL liquid side mass transfer coefficient [m/s] L distance to the gas-liquid interface [m] 3 3 mR relative solubility or distribution coefficient { [mol/m ]LII / [mol/m ]LI } [-] N number of particles [-] r radial position [-] R chemical reaction rate [mole/m3 s] Rd, Rb radius of droplet and bubble respectively [m] spc single particle cell t time [s] w minimum (surface-to-surface) distance between particles [m] x position perpendicular to gas-liquid interface [m] y position along the gas-liquid interface [m]

Greek symbols δ mass transfer zone near interface [m]

δp penetration depth [m] εdis fraction dispersed phase [-] φ Hatta number [-] τ gas-liquid contact time [s]

Sub- and Superscripts av average value b bubble bulk at bulk liquid phase conditions con continuous phase ddroplet dis dispersed phase film according to the film theory gas gas phase het heterogeneous (model) hom homogeneous (model) p physical absorption

40 Chapter 6

References

Alper E., Wichtendahl B., Deckwer W.D., 1980, Gas absorption mechanism in catalytic slurry reactors, Chem. Engng. Sci., 35, 217-222

Alper E., Deckwer W.D., 1981, Comments on gas absorption with catalytic reaction, Chem.Engng.Sci., 36, 1097-1099

Bhagwat S.S. and Sharma M.M., 1988, Intensification of solid-liquid reactions: Microemulsions, Chem. Engng Sci., 43, 195-205

Beenackers A.A.C.M., Van Swaaij W.P.M., 1993, Mass transfer in gas-liquid slurry reactors, Chem.Engng. Sci., 48, 3109-3139

Brilman D.W.F., 1998, A one-dimensional instationary heterogeneous mass transfer model for gas absorption in multiphase systems (accepted for publication in Chem.Eng. & Proc.) (Chapter 5 of this thesis)

Bruining W.J., Joosten G.E.H., Beenackers A.A.C.M., Hofman H., 1986, Enhancement of gas- liquid mass transfer by a dispersed second liquid phase, Chem. Engng. Sci., 41, 1873-1877

Chesshire G., Henshaw W.D., 1994, Composite overlapping meshes for the solution of partial differential equations, J. Comp.Ph., 90, 1-64

Ede C.J. van, Van Houten R. and Beenackers A.A.C.M., 1995, Enhancement of gas to water mass transfer rates by a dispersed organic phase, Chem. Engng. Sci., 50, 2911-2922

Holstvoogd R.D., van Swaaij W.P.M., 1990, The influence of adsorption capacity on enhanced gas absorption in activated carbon slurries, Chem.Engng.Sci., 45, 151-162

Junker B.H., Wang D.I.C., Hatton A.H., 1990, Oxygen transfer enhancement in aqueous/perfluorocarbon fermentation systems: I. Experimental observations, Biotechn. Bioengng., 35, 578-585

Junker B.H., Wang D.I.C., Hatton A.H., 1990, Oxygen transfer enhancement in aqueous/ perfluorocarbon fermentation systems: II. Theoretical analysis, Biotechn. Bioengng., 35, 586-597

Kars R.L., Best R.J., Drinkenburg A.A.H., 1979, The sorption of propane in slurries of active carbon in water, Chem. Engng. J., 17, 201-210

Karve S., Juvekar V.A., 1990, Gas absorption into slurries containing fine catalyst particles, Chem. Engng. Sci., 45, 587-594

41 Chapter 6

Littel R.J., Versteeg G.F. and Van Swaaij W.P.M., 1994, Physical absorption of CO2 and propene into toluene/water emulsions, A.I.Ch.E. J., 40, 1629-1638

Meer A.B. van der, Beenackers A.A.C.M., Burghard R., Mulder N.H., Fok J.J., 1992, Gas/liquid mass transfer in a four-phase stirred fermentator: effects of organic phase hold-up and concentration, Chem. Engng Sci., 47, 2369-2374

Mehra A., Sharma M.M., 1985, Absorption with reaction: effect of emulsified liquid phase, Chem. Engng Sci., 40, 2382-2385

Mehra A., 1988, Intensification of multiphase reactions through the use of a microphase-I. Theoretical, Chem. Engng Sci., 43, 899-912

Mehra A., Pandit A. and Sharma M.M., 1988, Intensification of multiphase reactions through the use of a microphase-II. Experimental, Chem. Engng Sci. 43, 913-927

Mehra A., Sharma, 1988, Simultaneous absorption of two gases with chemical reactions: selectivity variation in microheterogeneous media, Chem. Engng Sci., 43, 2541-2543

Mehra A., 1989, Intensification of heterogeneous reactions through the use of water-in-oil media, Chem. Engng Sci., 44, 448-452

Mehra A., 1990, An overview of microphase catalysis, Current Science, 59, 970-979

Mehra A., 1990, Gas absorption in slurries of finite capacity microphases, Chem. Engng. Sci., 45, 1525-1538

Mehra A., 1991, Diffusion accompanied by chemical reaction in water-in-oil media, Current Science, 60, 350-354

Nagy E., Moser A., 1995, Three-phase mass transfer: improved pseudo-homogeneous model, A.I.Ch.E. J., 41, 23-34

Nagy E., 1995, Three-phase mass transfer: one dimensional heterogeneous model, Chem. Engng. Sci., 50, 827-836

Pal S.K., Sharma M.M., Juvekar V.A., 1982, Fast reactions in slurry reactors: catalyst particle size smaller than film thickness: oxidation of aqueous sodium sulphide solutions with activated carbon particles as catalyst at elevated temperatures, Chem.Engng.Sci., 37, 327-336

Pradhan N.C., Mehra A., Sharma M.M., 1992, Intensification and selectivity modification through the use of a microphase: simultaneous absorption of two gases with chemical reaction, Chem. Engng Sci., 47, 493-498

Rols J.L., Condoret J.S., Fonade C., Goma G., 1990, Mechanism of enhanced oxygen transfer in fermentation using emulsified oxygen-vectors, Biotechn. and Bioengng., 35, 427-435

42 Chapter 6

Rols J.L., Condoret J.S., Fonade C., Goma G., 1991, Modeling of oxygen transfer in water through emulsified organic liquids, Chem. Engng Sci., 46, 1869-1873

Saraph V.S., Mehra A., 1994, Microphase autocatalysis: importance of near interface effects, Chem. Engng Sci., 49, 949-956

Sharma M.M., 1988, Multiphase reactions in the manufacture of fine chemicals, Chem. Engng Sci., 43, 1749-1758

TableCurve version1.0, Jandel Scientific.

Tinge J.T., Mencke K., Drinkenburg A.A.H., 1987, The absorption of propane and ethene in slurries of activated carbon in water - I, Chem. Engng Sci., 42, 1899-1907

Tinge J.T., Drinkenburg A.A.H., 1995, The enhancement of the physical absorption of gases in aqueous activated carbon slurries, Chem. Engng. Sci., 50, 937-942

Venugopal B.V., Mehra A., 1994, Gas absorption accompanied by fast chemical reaction in water-in-oil emulsions, Chem. Engng Sci., 49, 3331-3336

Vinke H., 1992, The effect of catalyst particle to bubble adhesion on the mass transfer in agitated slurry reactors, Ph.D. thesis, Municipal University of Amsterdam (The Netherlands).

Westerterp K.R., Van Swaaij W.P.M., Beenackers A.A.C.M., 1993, Chemical reactor design and operation, John Wiley & Sons

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44 CHAPTER 7

Experimental study of the effect of bubbles, drops and particles on the product distribution for a mixing sensitive, parallel-consecutive reaction system

Abstract

For stirred multiphase reactors the effect of a dispersed (gas, liquid or solid) phase on the product distribution for a mixing sensitive reaction was tested. Turbulence modification due to the presence of dispersed phase particles has been reported frequently in literature, but the extent of the effect in a stirred multiphase reactor was not clear. In this work the well-known mixing sensitive diazo-coupling reaction system was selected to investigate the influence of the changes in the turbulent kinetic energy spectrum on the product distribution. This reaction system was found to be suitable to study the influence of a dispersed (gas, liquid or solid) phase. The Engulfment model could describe the single phase experiments and describes reasonably well the multiphase experiments when the effective dispersion properties are implemented. For the liquid-liquid dispersions effects of de-localization of the reaction zone were encountered, due to Naphthol extraction by the dispersed phase. The Engulfment model was extended to incorporate mass transfer and the first experimental and simulation results are promising. Additional, experimental and theoretical, research studying the combined effects of the mass transfer rate and the mixing rate for the liquid-liquid dispersions is highly desired.

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202 Chapter 7

1. Introduction

In multiphase reaction systems with multiple, (ir-)reversible, chemical reactions mass transfer, mixing and chemical reaction rate determine in an open competition the conversion rate and also the final product distribution. An example of such a complex multiphase reaction system is the Koch carbonylation of olefinic compounds to produce carboxylic acids (Falbe, 1980). This complex gas-liquid-liquid reaction system is operated on industrial scale in a stirred liquid phase, pressurized reactor. Apart from the desired reaction, the acid-catalyzed addition of carbon monoxide to an olefin, undesired olefin polymerization may occur. On analyzing this situation, the question rose to what extent the mixing in the continuous liquid phase near the feedpoint of the olefinic reactant (and with this, the product distribution) was affected by the presence of a dispersed (liquid) phase. A second important issue is the interaction between mixing and mass transfer between the continuous liquid phase and the dispersed liquid phase in the zones neighboring the feedpoint. An experimental study investigating the extent of these influences, also at higher volume fractions dispersed phase, using a well known model reaction system, as the diazo coupling reaction proposed by Bourne et al. (1981), was considered suitable to study these (micro-)mixing phenomena.

For a complex reaction system with fast chemical reactions in a parallel-consecutive reaction scheme as e.g.: A + B → P, P + B → X the production of component X depends on the local concentrations of B and P in the reaction zone. In case of poor mixing characteristics at the molecular scale local concentrations of B near its feedpoint in the reactor may differ significantly from its (bulk phase) average value, leading to an increase of the production of the consecutive reaction product X.

The micromixing process can be studied experimentally by using chemical test reactions. The diazo-coupling reaction of Bourne et al. (1981), for which the reaction kinetics are well established (Bourne et al., 1990), is frequently used for this purpose. This reaction system consist of a set parallel, consecutive instantaneously fast, irreversible reactions, see equations 1 and 2 :

k AB+1,o → oR A = 1-Naphthol (1-a)

k1,p AB+ → pR B = diazotized sulfanilic acid (1-b)

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k oR+ B2,o → S oR = mono-azo coupling product (ortho) (2-a)

k2,p pR+ B → S pR = mono-azo coupling product (para) (2-b) S = bis-azo coupling product

Usually the reaction system is operated semi-batch wise. Reactant B is added slowly to the reaction mixture, containing an excess of reactant A, where B is rapidly converted into the mono- azocompounds (oR, pR) and the bis-azocompound S. The product distribution is uniquely characterized by the product ratio XS, representing the selectivity of component B towards product S, given in equation 3. 2[]S X = (3) S 2[]SoRpR++ [ ] [ ]

Mixing may affect the product distribution parameter XS, significantly. In a well mixed reactor (at high energy dissipation levels) almost exclusively mono-azo coupling products will be formed and, as a consequence, the XS value will be low.

The process of mixing a reactant into a bulk phase can be considered at different scales, starting with the spatially distribution of feed lumps through the bulk phase (macromixing), followed by reduction of the scale of the unmixed lumps by breakage without influence on molecular mixing (mesomixing). The smaller fluid elements are subjected to laminar strain and molecular diffusion becomes more and more important with decreasing characteristic length scale (micromixing). Finally, homogeneity at the molecular scale is rapidly attained through molecular diffusion.

The mixing process can be related to turbulent energy spectrum (the distribution of turbulent energy over the eddy length scale) of the bulk liquid phase, see e.g. Baldyga and Pohorecki (1995) for an overview. The viscous-convective deformation of fluid lumps, which increases the effect of concentration variance dissipation by molecular diffusion, is considered to be the most important micromixing feature.

The reactant concentration in the reaction zone can be influenced by macro-, meso and microscale effects. To interpret the experimentally determined product distribution in terms of micromixing characteristics, the macroscale and mesoscale mixing effects need to be excluded. This can be checked experimentally by varying the feed time of the (fixed amount of) reactant B containing solution. For a semi-batch reactor a critical feed time can be observed, above which the product

204 Chapter 7 distribution is no longer sensitive to the feed time (Bourne and Thoma, 1991). Under these conditions the product distribution is determined by the micromixing processes of fluid element deformation and molecular diffusion in the viscous-convective and viscous-diffusive subranges of the turbulent energy spectrum. Since these processes are governed by the energy dissipation rates and fluid viscosity, local energy dissipation rates can be determined.

2. Theory

2.1 Single phase systems The micromixing process is determined by viscous deformations of fluid feed lump elements and molecular diffusion. The rate of viscous deformation of the fluid elements is generally assumed to

½ be proportional to (ε/ν) , the Kolmogoroff rate of strain in the viscous subrange. Due to turbulent vorticity the long thin slabs of the deforming fluid lump are twisted and fluid from the environment is incorporated. Now thin lamellar structures are formed in which high concentration gradients are formed by viscous deformation. In these structures, concentration variances are rapidly dissipated by molecular diffusion, thereby losing the lamellar character. For not too high Schmidt-Numbers (Sc) the diffusion process is faster than the rate of incorporation of fluid from the environment, called ‘Engulfment’, and this engulfment process is dominating micromixing.

Vortices of the scale of approximately 12⋅λK (λK being the Kolmogoroff length scale) are considered to be stable, since the amount of energy dissipated by these vortices balances the work done by stretching the elements (Baldyga and Pohorecki, 1995).

The single phase experiments with the diazo coupling test-reaction presented in this work are conducted in the regime where the Engulfment model, E-model, (Baldyga and Bourne, 1989) can be used to describe the micromixing process. Due to incorporation of fluid from the environment the feed lumps grow at the expense of the environment and the concentration in the reaction zone changes due to chemical reaction and mixing with bulk fluid phase elements of equal volume.

dc i =⋅Ec() − c − R (4) dt bulk, i i i

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The engulfment rate, E, is the main parameter in this model and is related to the local energy dissipation rate by :

ε05. ερ05. ≈   =   E 0.. 058ν 0 058 µ  (5)

From experimentally determined product distributions (XS values), using the E-model by Baldyga and Bourne (1989), the local energy dissipation rates in the reaction zone can be derived. Since the relative energy dissipation in an agitated vessel may vary strongly with position, it is important to ensure that the reaction is completed in a zone of more or less homogeneous energy dissipation rate. Otherwise, the trajectory of a feed lump through zones of different energy dissipation levels needs to be considered (Baldyga and Bourne, 1988).

2.2 Turbulence modification by particles For multiphase systems, the presence of dispersed phase particles may influence the macroscale continuous phase hydrodynamics as well as the turbulent energy spectrum, and thus mixing at different scales. Depending on holdup, particle size and -density, the particles may interact with the macro-scale fluctuations thereby extracting energy from the average flow and increasing high- frequency turbulence by vortex-shedding (‘turbulence production’). Small, light particles will tend to interact with high frequency micro-scale fluctuations. Turbulent kinetic energy is dissipated through the acceleration of dispersed phase particles (‘turbulence damping’).

Effects of particles on the turbulent energy spectrum of the continuous phase have been studied frequently, mainly for gas-solid systems at (very) low volume solids fractions. Usually, physical techniques like Laser Doppler Velocimetry have been used to determine continuous phase velocity fluctuations. From these measurements, turbulence intensity was calculated and the effect of the particles on the turbulent energy spectrum was studied.

Gore and Crowe (1989) and Hetsroni (1989) reviewed the limited amount of available experimental data on turbulence modification by (dispersed) particles. These results, mainly obtained for gas-solid and a few for gas-liquid systems at low particle loadings, were interpreted differently. Gore and Crowe (1989) proposed that the way in which the turbulence level is modified solely depends on the particle size; ‘small particles’ with respect to the turbulence length scale pick up energy from the turbulent eddies and thus decrease the turbulence level, whereas ‘large particles’ cause significant vortex shedding, thereby increasing the turbulence. From their

206 Chapter 7 data-correlation it seems that the turbulence damping effect is marginally, whereas the turbulence increase by larger particles is more pronounced. Hetsroni (1989) used the particle Reynolds number to correlate essentially the same set of data. Particles with small Reynolds numbers (< 400) where considered to suppress turbulence, whereas particles under high particle Reynolds number increase the turbulence levels.

Modification of the turbulence kinetic energy spectrum for a continuous liquid phase by solid particles has been studied experimentally very scarcely. Kada and Hanratty (1960) studied the effect of solid particles on turbulent diffusion of injected KCl pulses for slurry systems falling through a vertical pipe. They concluded that solids did not have a large effect on the turbulence level, except for solids having an appreciable slip velocity (high density and/or relatively large, for glass spheres > 300 µm, and at sufficiently high solids concentrations (2-3 vol% for glass spheres). At these conditions the turbulent eddy diffusivity calculated increased 2.5 fold.

Schreck and Kleis (1993) presented a comprehensive study on the effect of solid spherical

3 3 particles (600-700 µm, plastic (ρp = 1049 kg/m ) and glass (ρp = 2500 kg/m )) on grid-generated liquid phase turbulence. In their study a monotonic increase in energy dissipation rate with particle concentration was observed. The additional energy dissipation rate for the glass particles was almost two times that of the light plastic particles. From the literature overview by Schreck and Kleis (1993) it is clear that the addition of solid particles may indeed modify the turbulence spectrum (and thus affect mixing). For gas-solid two phase flow, experimentally both the effects of increasing turbulence for large particles (≈ 1 mm) and decreasing turbulence for small particles (≈ 200 µm) have been reported (Tsuji et al., 1984). For turbulent pipeflow it was found that intermediate sized particles (≈ 500 µm) increased turbulence at the pipe centre and reduced it along the wall. Both from the work of Schreck and Kleis (1993) and of Tsuji et al. (1984) for gas-solid two phase flow it is clear that the isotropy of the flow is enhanced due to the presence of particles.

Elgobashi (1994) presented a regime map for turbulent fluid-solids flow to discriminate between regimes in which turbulence is enhanced and suppressed, based on the solids holdup and the ratio of the particle response time τP and the Kolmogoroff time scale τK (turbulence enhancement for

2 τP/τK > 10 ). Turbulence enhancement by vortex shedding will occur at high particle Reynolds numbers (> 400), requiring relatively large particles and high density differences. Turbulence

207 Chapter 7 damping may be caused by energy dissipation through fluid-particle interaction (energy required for suspending and oscillating the particles due to continuous phase turbulence, 'two way coupling'), particle-particle interaction (so-called 'four way coupling') and due to the fact that in dense solutions a significant fraction of the fluid is present as low turbulent added mass, moving with the particles. According to Elgobashi’s classification all the results presented in this present study were carried out in the four-way coupling regime (dispersed phase hold up > 0.1 vol% ). Summarizing, it can be concluded that particles modify the turbulence energy spectrum, e.g. by facilitating energy transfer from large to smaller eddies and promoting isotropy of the turbulence. However, the effect on the energy dissipation rate and mixing on a scale, which is relevant to a complex chemical reaction, can not be derived from these studies.

In a few studies the aspect of the influence of particles on the product distribution for a mixing sensitive (homogeneous) chemical reaction has been considered. Bennington and Bourne (1990) used the diazo-coupling reaction of Bourne et al. (1981) to study the effect of suspended nylon fibers on macro- and micromixing in a stirred tank. The fiber suspension was found to behave like a pseudo-plastic fluid at higher volume fractions of fibers, causing the occurrence of a well mixed zone near the stirrer and more stagnant zones at the outer radius of the vessel. Bennington and Thangavel (1993) showed in a consecutive publication that fibers, irrespective of changes to macroscopic flow patterns, dampen the observed turbulence level (an increase in the experimentally determined XS values), which was assumed to be caused by network-formation by the fibers.

Villermaux et al. (1994) used a parallel (Iodine-Iodate) reaction system to study the effect of suspended solids and inert bubbles on micromixing in stirred reactors. Preliminary results showed that the effect of solids (< 40 µm) was however considerable. Micromixing in the presence of these small particles seemed to be enhanced significantly; a strong increase of micromixedness was observed at only 4 wt% addition of solid particles. In a consecutive publication by Guichardon et al. (1995) the preliminary results of Villermaux et al. (1994) were considered to be invalid. After checking the mass balance more precisely and re-investigation of the reaction kinetics only a minor effect of the presence of particles in this latter paper remained. This example illustrates that especially for multiphase systems the reaction kinetics for the test system as well as effects of product adsorption or absorption in the dispersed phase should be known. Guichardon et al. (1995) stressed the need for a study of more concentrated suspensions.

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More recently, Barresi (1997) studied the influence of solid particles on the product distribution obtained for a fast, parallel reaction scheme. Two preliminary conclusions were presented, the first being that the particles had only an effect at relatively high volume fractions (> 10 vol%) and, secondly, it was found for three experiments at constant volumetric holdup that large glass particles (425-500 µm) exhibited a significant influence on the product distribution, whereas fine glass particles (100-177 µm) and PET beads (having a equivalent diameter of 3 mm) had a minor effect and no effect on the product distribution respectively.

In the present study attention will be focused at high dispersed phase holdups. Since for a dispersed liquid phase mass transfer may be important, an inert solid and gas phase were also used, to study the effect of dispersed holdup and ‘particle’ size. Macroscopically, the effects of a dispersed phase on turbulence may be noticeable via e.g. the effective viscosity and density of the dispersion. In interpreting the experimental data the E-model, valid for a single phase situation, is used to see if macroscopic physical properties for the dispersion are able to describe the observed trends in the product distribution with increasing holdup.

2.3 Interpretation of experimental results for multi phase systems using the E-model Although the E-model is derived for single phase systems, the model will be used to interpret the experimental data for the multiphase systems used. It will be tested if the E-model, using the apparent slurry viscosity and -density, can be used to describe the obtained product distributions at changing operating conditions, like dispersed phase holdup. The power input via the impeller and the average energy dissipation rate ε [W/kg] are given by :

=⋅ρ 35 PCeff Nd st [W] (6)

P CNd⋅ 35 ε = = st [W/kg dispersion] (7) eff ρ ⋅ ()eff V V For the kinematic viscosity ν [m2/s] = µ/ρ, the change in viscosity was taken into account via correlations for the relative dynamic viscosity (µr) of liquid-solid and liquid-liquid dispersions at different volumetric holdups. For modeling the liquid-solid dispersions the correlation of Graham

(1981) was used for estimating µr. For the effective viscosity of liquid-liquid dispersions the correlation of Vermeulen (Perry (1988); eq. 21-32) was compared with the Graham-correlation, which may be applicable at low holdups since the droplets are small and rigid and will probably behave as solid spheres.

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The density ρ in equation (5) was taken equal to the effective dispersion density and equal to the continuous phase density, leading to two definitions of the Engulfment parameter E which were used in the simulations :

 3 5   ε ε   ε CN d ρ  E(I) = 0.058 R av  = 0.058 R st eff (8) ν  µ     V eff 

 3 5   ε ε   ε CN d ρ  E(II) = 0.058 R av  = 0.058 R st (9) ν  µ     V eff 

For the experiments with a dispersed liquid phase the E-model was extended to incorporate mass transfer between the bulk of the continuous liquid phase and the dispersed liquid phase, both considered to be ideally mixed. The set of additional mass transfer model equations is:

dc  c  c,i = ⋅ d,i −  Vbulk k LLALL  cc,i  (continuous phase) (10) dt  mi 

dc  c  d,i = ⋅  − d,i  Vd k LLALL cc,i  (dispersed phase) (11) dt  mi 

In the present contribution, mass transfer was accounted for discontinuously by calculating the exchange between the two liquid phases after each (of the σ) feed lump(s) during tfeed/σ [s]. The overall mass transfer coefficient kLL was estimated conservatively from the partial coefficients for

2 mass transfer inside and outside the droplets by assuming stagnant media; thus Shinside = 2π /3 is used for mass transfer inside the droplets and Shoutside = 2 for the external partial mass transfer coefficient, thereby using D = 1⋅10-9 m2/s as typical liquid phase diffusion coefficient. The interfacial area ALL was calculated using ALL = 6⋅Vd / dp and the correlation of Calderbank for the drop size.

The effect of mass transfer can be estimated by comparing the timescale for mass transfer

(kLLALL/Vbulk) with the time for complete engulfment of a feedlump. Depending on initial conditions and the distribution coefficients for Naphthol mass transfer from the dispersed phase may become the limiting process. In that case the current method of solving the equations must be adapted.

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3. Experimental

For the mixing experiments a baffled, flat bottom, stirred tank was used as reactor, equipped with a six blade Rushton-like turbine (see Figure 1). The feed points are indicated in the figure, as well as all relevant dimensions. Feedpoint A is located at the top of the plane of the stirrer (radial flow zone). Feedpoints B, C and D are located just above the stirrer, in the suction stream to the impeller zone. Feedpoint E is located in a stream leaving the stirrer zone, where axial flow dominates. To avoid backmixing of bulk reaction liquid into the feedpipe a small diameter of the feedpipe was chosen (inner diameter : 1 mm). This diameter was shown to be sufficient small using the criteria presented by Baldyga and Pohorecki (1995).

Wb = 8.2 mm

Liquid level 700 ml

Liquid level 500 ml ε ⋅ D Feedpoint R C C A40 H = 200 mm B B 8 E A C 6 D 4 h =51.6 mm E 50 dst = 45 mm.

Cooling jacket 10.0 mm D = 82 mm

15.0 mm 10.4 mm db = 1.5 mm 13.0 mm

E Stirrer and baffles: SS-316 Reactor: Boorsilicate glass

Figure 1 Experimental Set up

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3.1 Development of the test reaction system In most experiment series the 1-Naftol reaction system, represented by equations (1) and (2) is used. For some experiments the extended reaction system of Bourne et al. (1992), developed for high energy dissipation rates was used. This system encompasses the reactions (1) and (2), as well as a parallel reaction of 2-Naphthol (AA) with diazotized sulfanilic acid.

k3 AA+→ B Q (12)

The product distribution is then characterized by XS’ and XQ, which are defined below.

2[]S []Q X = , X = (13-a, 13-b) S' [][]oR+++ pR2 [][] S Q Q [][]oR+++ pR2 [][] S Q

Before using the reaction system of Bourne et al. (1981), the UV-extinction coefficients as reported by Lenzner (1991) were verified. Therefore the reaction product p-R was synthesized, identified by NMR and purified by several washing and recrystallisation steps. The UV-extinction coefficients as reported by Lenzner (1991) were confirmed for p-R. From other syntheses the products o-R, S and Q were obtained at purity levels of 90-95% by element analysis, but it turned out to be difficult to improve on the purity. The UV-extinction coefficients were, however, conform the purity level and the extinction coefficients reported by Lenzner (1991), thus justifying the use of these extinction coefficients.

Naphthols (1- and 2-) and sulfanilic acid of 99+% purity were purchased from Acros Organics, as well as the Sodium Carbonate and Sodium Bicarbonate for the buffer solution (pH = 9.9). The reactant B (diazotized sulfanilic acid) was obtained almost quantitatively, according to a test based on the Sandmeyer reaction. The occurrence of degradation of reaction products, diluted 50× for UV analysis, was found to be negligible. Stability was also tested for 1- and 2-Naphthol solutions and for a solution of freshly synthesized diazotized sulfanilic acid. The 2-Naphthol solutions (1% degradation in 20 hours) was found to be much more stabile than the 1-Naphthol solutions (5% in 6 hours) and the 1- + 2-Naphthol mixtures. When sparging nitrogen through the solution, degradation could be reduced to almost zero. 1-Naphthol was dissolved for each experiment in a series separately just before the experimental usage. By storing the diazotized sulfanilic acid solutions in an ice-bath the degradation of diazotized sulfanilic acid during one experiment series (ca. 5 hours) could be reduced to ca. 1%.

212 Chapter 7

3.2 Analysis Multicomponent regression (over the range of 400 - 600 nm) was used to obtain the individual component concentrations from the recorded UV spectrum (HP 8452A spectro photometer). The regression coefficients were usually better than 0.9995. Tests with small shifts in the UV spectrum showed that the o-R / p-R distribution is relatively sensitive to this, however, the segregation index XS remains almost unaffected. The presence of small amounts of 1-octanol and heptane in the analysis samples (reactor samples, diluted 50× with buffer solution) did not affect the UV- analysis. For single phase experiments no effect was found in experiments in which the Naphthol / buffer solution was saturated with heptane or 1-octanol.

3.3 Accuracy

Reproducibility of the XS value for experiments within a series (measured at sequentially) at the same feedpoint was tested for the 1-Naphthol and 1-+2-Naphthol system. Standard deviation values for a series of experiments under identical conditions revealed that XS ≈ 0.092± 0.002, XQ

≈ 0.284 ± 0.005, ∆XS’ ≈ 0.050±0.001, mainly due to uncertainties in the analysis-part. Therefore, for each experiment three reactor samples were taken, diluted with buffer solution and analyzed. The reproducibility between series of experiments was somewhat less (± 0.005), due to possible variations in the synthesis of the reactants, small temperature differences or a slightly different feedpoint position. Mass balances (for B) were checked and were found to be accurate (± 98% was recovered in the products) for the experiments in aqueous buffer solutions.

3.4 Experimental conditions Typical reaction conditions are listed in Table I. For the suspension experiments with varying holdups, the total volume of the dispersion was kept constant. The suspensions of glass beads were prepared by adding the appropriate amount of solids to the Naphthol solutions. In order to keep the total molar ratio of A and B constant, the amount of B-solution fed to the reactor had to be adapted. For the glass beads sieved fractions were used with a rather narrow distribution (see Table II), as determined with a Microtrax X100 Particle Analyzer. Adsorption of reactants and products on the glass beads was found to be negligible and, therefore, did not influence the observed product distribution. This was checked by ‘extracting’ typical, well known, reaction mixtures with the glass beads concerned and analyzing again the reaction mixture. The distribution coefficients were roughly estimated to be in the order of magnitude of 1-5⋅10-8 mol/m2 glass beads and S appears to be slightly preferentially absorbed. For a typical experiment the XS

213 Chapter 7 values will be underestimated by some 0.0001 unit due to adsorption. Therefore, no disturbing effect on the results is to be expected owing to adsorption phenomena on the solid particles.

Table I Typical reaction conditions

Temperature 298 [K] pH 9.9 [-] Volume Naphthol solution 500 - 1000 [ml] 750 [ml] (for 1-/2-Naphthol exp.) Injected volume B-solution 10 [ml] Feed rate reactant B 30 [ml/hr] 3 Concentration CB,o 40 60 57 [mole/m ] 3 Concentration CA,0 1.04 1.32 0.87 [mole/m ] 3 Concentration CAA,o - - 0.87 [mole/m ] Stirrer speed 100 - 1200 [rpm]

The liquids selected for the dispersion study were 1-octanol and heptane, because of their difference in naphthol solubility. Distribution coefficients for the individual components were obtained from extraction experiments, however, the accuracy of the separate coefficients for both o-R and p-R respectively was relatively low. Therefore, the mono-azo compounds were regarded as one component in the analysis.

Table II Particle size distribution (PSD) of sieved glass beads fractions

Sample particle diameter size range % (v/v) 20 ID. (dp)4,3 [mm] [mm]

15 ‘70’ 69 40 - 114

‘110’ 110 80 - 148 10 ‘180’ 182 135 - 228 ‘290’ 294 228 - 332 5 ‘500’ 502 418 - 592 0 26 31 37 44 52 62 74 88 ‘700’ 700 590 - 800 dp [µm] 105 125 148 176 209

Example: PSD of “70” [µm] fraction

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4. Results

4.1 Critical Feed Rate First, the critical feed times for the operation conditions of Table I were identified. The critical feed time is within the range 200-500 s for all conditions considered. A feed time of 1200 s (corresponding with a feed rate of 30 ml/hr) was chosen safely above the critical feed times determined. Typical results for some of the single phase and multiphase experiments are presented in Figure 2.

0.25 N = 700 (1/min) 3 [A]o = 1,32 mol/m XS 3 [B]o = 60 mol/m 0.2

0.15

... + 10 vol% heptane 0.1

single phase 0.05

0 0 300 600 900 1200 1500 Feed time [s]

Figure 2 Critical feed time curves for a single phase system and a liquid-liquid dispersion

4.2 Single phase experiments Before the start of the multiphase experiments several series of single phase experiments were performed. The Engulfment model by Baldyga and Bourne (1989) was used to recalculate local energy dissipation rates from experimentally determined XS and XQ values at different stirrer speeds. It was found that for N > 500 rpm the relative energy dissipation rate, i.e. the ratio

3 5 between the calculated and the average energy dissipation rate (εav = C⋅N ⋅dst /VL) remains essentially constant, indicating that the reaction is localized in a zone of more or less homogeneous energy dissipation. Indications of the thus derived relative energy dissipation rates are presented in Figure 1.

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4.3 Two phase experiments: Effect of a dispersed gas phase The effect of the presence of gas bubbles on the product distribution was not clear on beforehand. Fort et al. (1994) found a suppression of the energy dissipation rate in the impeller discharge flow and an increase in the remaining part of the agitated vessel. This would imply a position dependent effect of sparging on the XS value obtained. Gas sparging experiments were performed for two different feedpoints, using Nitrogen and SF6 as dispersed phase, see Figure 3.

0.200

0.150 3 CA,o = 1.32 mol/m Feedpoint C 3 CB,o = 60 mol/m

0.100

3 CA,o = 1.32 mol/m Feedpoint A 3 CB,o = 60 mol/m 0.050 3 Feedpoint A CA,o = 0.74 mol/m 3 CB,o = 40 mol/m 0.000 0.1 1 10 100 1000 Gas Flow [ml/s]

gas phase = N2 , N = 700 rpm, VL = 700 mL, εG = 1 - 7 vol%

gas phase = SF6 , N = 900 rpm, VL = 700 mL, εG = 1 - 3 vol%

gas phase = N2 , N = 900 rpm, VL = 700 mL, εG = 1 - 3 vol% XS values homogeneous liquid phase

Figure 3 Effect of gas bubbles

The effect of sparging or gas entrainment, thus the presence of gas bubbles, on the product distribution for the mixing sensitive test reaction seems to be limited from the results of this work.

The minor effects found are in accordance with the results of Fort et al. (1994); the XS value for feedpoint C slightly decreases (thus suggesting a slightly increased local energy dissipation rate),

-2 whereas the XS value for one of the series at a superficial gas velocity of 2.8⋅10 m/s for feedpoint A just above the stirrer increased from 0.061 to 0.063 (ca. 3% increase), corresponding to a decrease of approximately 1.7 W/kg (ca. 7%) in the apparent local power input, as was recalculated using the E-model. This latter result is in line with the expected reduced power input by agitation due to the decreased density of the dispersion. The decrease in the apparent local

216 Chapter 7 power input corresponds with the gas holdup, which was also estimated to be 7%, using the correlation of Takenaka and Takahashi (1992).

4.4 Two phase experiments: Effect of a dispersed solid phase In Figure 4 the results are presented of experiments with different holdups of solid particles at constant total volume for two different particle-sizes. By using effective properties for viscosity and density for the slurries in the E-model it was investigated if the measured variation in product distribution at increasing holdup can be described.

0.05 500 µ m, (700 700 rpm) RPM ∆XS 290 µ m, (700 700 rpm)RPM 0.04 290 µ m, (500 500 rpm) RPM 70 µ m, (500 500 rpm) RPM E-model using E = E(II) eps_eff, visc_eff, dens_eff 0.03 eps_eff en visc_eff

E-model using E = E(I) 0.02

0.01

0 (no effect)

-0.01 0 5 10 15 20 25 30 35 40 45 50 hold up [wt%]

3 Figure 4 Glass beads holdup variation for feedpoint C, 1-Naphthol system, cA,o = 1.04 mol/m , 3 cB,o= 40 mol/m . Solid and dashed line are E-model simulation results using equations (9) and (8) respectively.

The series with the 290 µm particles at 500 rpm (and 500 ml total volume) seems to differ significantly from the other series, since no effect on XS was found. This may be explained by insufficient suspension of these solid particles at these conditions. Since the feedpoint is located above the stirrer probably the local solids holdup was insufficient to produce any effect. It appears that a reasonable prediction of the experimental trend for the other three series is obtained by just implementing the effective viscosity, thus using E = E(II) (eq. 9). This result was confirmed for a duplicate series using the 1-Naphthol + 2-Naphthol system (see Figure 5).

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0.020 100∆X mm, (series DXQ 1) (series 1) ∆X Q Q ∆ 100XQ mm, (series DXQ 2) (series 2) 0.016 E-model, E = E(I) E-model, E = E(II)

0.012

0.008

0.004

0.000 0 5 10 15 20 25 30 Holdup [wt%]

Figure 5 Glass beads (dp = 100 µm) holdup variation for feedpoint D, 1- + 2-Naphthol system for conditions see Table I) and E-model simulation results.

Experimental series like those presented in the Figures 4 and 5 respectively are measured using a freshly prepared stock of diazotized sulfanilic acid per series and the experiments within a series are performed in random order of holdup, starting and ending with a blank run (zero holdup), in order to exclude time dependent trends. Mass balances were found to be satisfied within 0-4% deviation of the theoretical maximum amount of B injected. For a single data series (not shown in the figures) with 3 mm particles the XS-value was found to decrease (from XS = 0.07 at zero 3 3 holdup to 0.06 at 5 wt% holdup and 990 RPM, CA,o = 1.32 mol/m , CB,o = 60 mol/m , VA,o = 500 ml, VB,o = 10 ml at feedpoint E).

The average particle size has been varied at constant holdup. Results for the 1-Naphthol system are presented in Figure 6. With the 2-Naphthol system similar results were found (not shown), though the accuracy is somewhat less. The trend observed, represented by the dashed line, is approximately within the experimental accuracy, however, the presented trend could be recognized clearly for all individual series.

218 Chapter 7

0.015

∆ XS

0.010

0.005 trend

0.000 (no effect)

feedpoint C, 500 rpm, 12.6 wt% feedpoint C, 700 rpm, 23.1 wt% -0.005 feedpoint C, 700 rpm, 23.1 wt% feedpoint A, 700 rpm, 23.1 wt%

-0.010 0 100 200 300 400 500 600 700 800 µ dp [ m]

Figure 6 Solids particle size variation at constant holdup, VL = 500 ml, cA,o = 1.04 mol/m3, 3 cB,o= 40 mol/m

The experiments were, as stressed before, conducted in random order with respect to particle size. For very small particles the dispersion behaves as a pseudo-fluid with the appropriate effective (density and viscosity) properties. Energy is probably mainly dissipated by particle- particle interaction. This will decrease due to a strong reduction in the number of (‘near’-) collisions with increasing particle size, at constant holdup. In the classification by Elgobashi (1994) for the two-way coupling regime the regime-transition between 'particles enhancing energy

2 dissipation' and 'particles enhancing energy production' is approximately given by τP/τk ≈ 10 . For the glass beads used under the experimental conditions applied, the transition is located at approximately 150 µm. This is in agreement with the experimentally determined decrease in the

XS value going from particles of 50 to 150 µm, as shown in Figure 6. However, the volume fractions used in this study are such that all experiments are conducted in the 'four way coupling' - regime, according to Elgobashi (1994).

The increase at higher particle sizes may be caused owing to the fact that the particles are being less able to follow fluid motion (an increase in particle response time) and more energy is required to (re-) suspend the particles (see e.g. Zwietering, 1958) and more energy is dissipated in particle-

219 Chapter 7 particle collisions and particle-wall collisions. Another explanation may be an increase in the amount of stagnant liquid moving with the particles. A similar result for the turbulence intensity at different particle diameters has been presented in an overview by Zakharov et al. (1993) for gas-solid two phase flow at low concentrations (< 1 vol% solids). In their study friction drag due to the flow of a dispersion was studied at constant dispersed phase holdup for different particle size. It was found that first the drag was reduced with increasing particle diameter and, with a further increase in diameter the drag started increasing again. The particle regime for which friction reduction may occur was estimated in their study using the Owen theory, assuming that (quote:) "friction reduction is possible in a flow laden with particles having a relaxation time which is higher than the characteristic time of the energy-containing vortices, but which does not exceed the characteristic time of the maximum possible vortices”. Applying these criteria to the conditions of current investigation, glass particles of 150-1000 µm may "decrease the friction", implying that for these particles the turbulence intensity will be increased or less reduced.

The results of this study are in accordance with those presented by Guichardon et al. (1995), who

3 found a negligible influence of solid particles (ρ = 2500 kg/m , dp = 27, 201, 1250 µm) on the micromixing index for their (Iodide-Iodate) test-reaction in the range 1-6 wt%. The scatter of the experimental data of Barresi (1997) in combination with the limited effect of solids makes comparison with the results of the present study difficult, though the results are not necessarily conflicting. Scouting experiments in this study with 5 wt% solids of different density (not shown in figures), comparing glass beads with polystyrene, polypropylene and poly methyl methacrylate beads of the same size at 5 wt% holdup, showed no significant influence of particle density within the experimental error, which was larger due to product adsorption on the plastic beads.

4.5 Two phase experiments: Effect of a dispersed liquid phase A dispersed liquid phase may influence the obtained product distribution in different ways. Besides possible effects on the state of local mixing, which can be significant as was shown in experiments with the solid particles, mass transfer can be important and macroscopic hydrodynamics may change. In this work the results of scouting experiments with two different liquid phases are reported. As dispersed phase a solvent-grade heptane containing heptane isomers (82%), octane (15%) and toluene (3%), analytical grade (99+% purity) heptane and 1- Octanol (99+% purity) were used. For these solvents the (approximate) distribution coefficients

220 Chapter 7 for the reactants and products were determined by extraction experiments. The (approximate) distribution coefficients determined are given in Table III. Heptane was selected for its low affinity for 1-Naphthol (thus essentially excluding mass transfer effects), whereas 1-octanol was chosen as a solvent showing a high Naphthol affinity.

Table III Distribution coefficients for reactants and products

(m = Cdisp.phase/Cbuffer) Heptane 1-Octanol

1-Naphthol 1 2⋅102 o-R 0.12 1.1 p-R 0.0010 0.06 R (o-R + p-R) 0.020 0.2 S 0.19 0.09

In Figure 7 two sets of experiments for different holdups of heptane are presented. Optically, the dispersed phase was distributed homogeneously throughout the dispersion volume for stirrer speeds exceeding 450 rpm.

0.16 Heptane data Wim (feedpoint H. A) mhu_r=R2 E-model,E-model, EE == E(II), E(II), µ µ == = µ (II)µ(II)(II) XS µ µ E-model. E-model,E-model, E E= EE E(II)= == E(II), E(II),E(II), µ µ= = = (I) µ(I) E-model, E-model,E-model, E E=E E(I) == E(I),E(I), µµ == µ(I) 0.12 Heptane Heptane (feedpoint (feedpoint E) µ µ E-model,E-model, E E = =E(II) E(II), = (I) ... + trajectory of reaction E-model, inhomogeneous model zone

0.08

no effect

0.04

no effect

0 0 0.1 0.2 0.3 0.4 Heptane Holdup [-]

Figure 7 Experiments with heptane as dispersed phase at different volume fractions

3 3 Series I: Feedpoint A, CA,o = 1.04 mol/m , CB,o = 40 mol/m , 700 ml, 1000 rpm 3 3 Series II: Feedpoint E. CA,o = 1.32 mol/m , CB,o = 60 mol/m , 500 ml, 500 rpm

Simulation input: µ (I) => relative viscosity according to Graham (1981) µ (II) => relative viscosity according to Vermeulen (Perry (1988); eq. 21-32)

changing εR along trajectory of reaction zone according to Yu (1993)

221 Chapter 7

From simulations for the series at feedpoint A, it seems that taking the effective viscosity (for solid spheres !) according to Graham's relation (1981) yields better results for these conditions than the correlation by Vermeulen (Perry, 1988) for liquid-liquid dispersions in baffled agitated tanks. Conclusions with respect to the effective viscosity for liquid-liquid dispersions at higher holdups can, however, not be drawn from these results, considering the assumptions by using the E-model extended with mass transfer. This is especially true for the 1-octanol data series, where de-localization of the reaction zone dominates.

For the experiment series at feedpoint E the simulation results started deviating from the experimental data at higher holdups. This is most likely caused by a de-localized reaction zone. Due to the distribution of Naphthol over both liquid phases the number of engulfments required for complete reaction of a feedlump slightly increases, causing the reaction to take place in zones of different energy dissipation. This effect is more important for feedpoint E in the radial flow leaving the impeller zone than for feedpoint A in the suction stream to the impeller zone. This effect is even more pronounced in case 1-octanol is used. Figure 8 shows two 1-octanol data series for different feedpoints. Since Naphthol is extracted to a large extent by the 1-octanol, the number of engulfments required for complete reaction of a feedlump is such, that the average energy dissipation rate, as experienced by the reaction zone, is essentially the average energy dissipation rate for the complete tank, εav.

Assuming this, the E-model extended with mass transfer was used to see if the experimental results could be described. Although the set of experimental data is limited, the results seem promising. Using the effective dispersion viscosity in the Engulfment model seems to yield reasonable description of XS values at increasing holdup, both for the viscosity correlation's of Graham (1981) and Vermeulen (Perry, 1988). It should be noted that in the experiments described the mass transfer rate is relatively unimportant (as the "equilibrium model", i.e. the model without mass transfer limitations by using an extremely high mass transfer coefficient kLL in the model and presented by the dotted line in Figure 8, gives almost identical results as the model including mass transfer), due to the low feed rate of reactant B. More (and dedicated) experiments are required to investigate (or validate) the mass transfer description.

222 Chapter 7

0.7

XS 0.6

0.5

Octanol (feedpoint C) 0.4 OctanolOctanol ++ N2N2 (125 ml/s) (G-L-L) Octanol (feedpoint E) 0.3 E-model,E-model +tot L-L 80% mass transfer

0.2 E-model,E-model, tot"equilibrium 80%, zonder model" SO lim. Heptane (feedpoint E) 0.1 E-model, inhomogeneous model E-model, E = E(II) 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 volume fraction dispersed liquid phase [-]

Figure 8 Experiments with 1-octanol and heptane as dispersed phase at increasing holdup 3 3 and CA,o = 1.32 mol/m , CB,o = 60 mol/m , 500 ml, N = 500 rpm and simulation results assuming mA = 100, εR =1 and using the viscosity correlation according to Graham (1981) and E= E(II), see eqn. (9), for the E-model.

5. Discussion and Conclusions

In this study for a limited set of experimental conditions the effect of the presence of bubbles, drops and solid particles on the product distribution for the (micro-)mixing sensitive diazo- coupling reaction (Bourne et al., 1981) is investigated. The diazo-coupling reaction system can be used conveniently for this purpose. Adsorption on glass beads is found to be negligible and the dispersed phases used do not seem to affect the intrinsic reaction kinetics and product analysis.

The single phase experiments could be satisfactory described using the Engulfment model, and this model was tested on its applicability in the multiphase systems. In the presence of gas, liquid and solid particles in the continuous liquid phase, the product distribution could reasonably well be described by the Engulfment model, if effective dispersion slurry properties are implemented.

223 Chapter 7

Modification of local liquid phase turbulence, or the kinetic energy spectrum, at a scale relevant for the test reaction, is then accounted for.

For the liquid-liquid dispersions the viscosity correlation seems less established. From the limited set of experiments, it appears that application of the viscosity correlation of Graham (1981) for liquid-solid applications yields acceptable results for heptane-buffer dispersions at the conditions considered in this work (a.o. heptane holdup ≤ 40 vol%). Additional experimental work is, however, recommended.

In the work presented, the mass transfer rate was relatively unimportant for the liquid-liquid dispersions and only preliminary experimental results and a simple mass transfer model have been presented. Further research of the combined effects of the mass transfer rate and mixing rate is desired for the development of multiphase reactor models.

Acknowledgments The authors wish to thank B. Knaken for constructing the experimental setup and A.K. Jellema and W. Hesselink for their valuable contribution to the experimental work. The Shell Research and Technology Centre, Amsterdam (The Netherlands) is acknowledged for the financial support.

224 Chapter 7

Notation

2 ALL Interfacial area [m ] c concentration [mole/m3] C configuration dependent power constant [-] D Diffusion coefficient [m2/s] dp particle diameter [m] dst stirrer diameter [m] E Engulfment rate [1/s] ki partial mass transfer coefficient [m/s] kLL Overall liquid-liquid mass transfer coefficient [m/s] mi distribution coefficient (cd,i /cc,I) equilibrium [-] N stirrer speed [1/min] 3 Ri source term for chemical reaction [mole i/m s] Sh Sherwood Number ki⋅dp/D [-] Sc Schmidt Number ν/D [-] t time [s] tfeed feed time of a fixed amount of reactant solution [s] V volume [m3] XS product distribution parameter (defined in eq. (3)) [-]

Greek

εav average energy dissipation rate [W/kg] εR relative energy dissipation rate ε/εav [-] 3 ¼ λK Kolmogoroff length scale (ν /ε) [m] µ dynamic viscosity [kg/m s] ν kinematic viscosity [m2/s] ρ density [kg/m3] σ number of feed lumps in E-model [-] ½ τΚ Kolmogoroff time-scale (ν/ε) [s] 2 τP particle response time ρp dp / (18⋅ρc⋅ν)[s]

Super- and subscripts A 1-Naphthol AA 2-Naphthol B diazotized sulfanilic acid c continuous liquid phase d dispersed phase eff effective dispersion property inside inside o initial value outside outside p particle r effective

225 Chapter 7

References

Baldyga J., Bourne J.R., 1988, Calculation of micromixing in inhomogeneous stirred tank reactors, Chem.Eng.Res.Dev., 66, 33-38

Baldyga J., Bourne J.R., 1989, Simplification of micromixing calculations: 1. Derivation and application of new model, Chem.Eng.J., 42, 83-92

Baldyga J., Pohorecki R., 1995, Turbulent micromixing in chemical reactors - a review, Chem.Eng.J., 58, 183-195

Barresi, A.A., 1997, Experimental investigation of interaction between turbulent liquid flow and solid particles and its effects on fast reactions, Chem.Engng.Sci., 52, 807-814

Bennington C.P.J., Bourne J.R., 1990, Effect of suspended fibers on macro-mixing and micromixing in a stirred tank reactor, Chem.Eng.Comm., 92, 183 - 197

Bennington C.P.J., Thangavel V.K., 1993, The use of a mixing-sensitive chemical reaction for the study of pulp fiber suspension mixing, Can. J. Chem. Eng., 71, 667-675

Bourne J.R., Kozicki F., Rys P., 1981, Mixing and fast chemical reaction - I : Test reactions to determine segregation, Chem.Engng.Sci., 36, 1643-1648

Bourne J.R., Kut O.M., Lenzner J., Maire H., 1990, Kinetics of the diazo coupling between 1- Naphthol and diazotized sulfanilic acid, Ind.Eng.Chem.Res., 29, 1761-1765

Bourne J.R., Thoma S.A., 1991, Some factors determining the critical feed time of a semi-batch reactor, Trans.I.Chem.E., 69, Part A, 321-323

Bourne J.R., Kut O.M., Lenzner J., 1992, An improved reaction system to investigate micromixing in high-intensity mixers, Ind.Eng.Chem.Res., 31, 949-958

Elgobashi, S., 1994, On predicting particle-laden turbulent flows, App.Sci.Res., 52, 309-329

Falbe J., 1980, ‘New synthesis with carbon monoxide; Ch. V.: Koch Reactions (H. Bahrmann)’, Springer-Verlag, Berlin

Fort I., Machoñ V., Kadlec P., 1994, Distribution of energy dissipation rate in an agitated gas- liquid system, Chem.Eng.Technol., 16, 389-394

Gore R.A., Crowe C.T., 1989, Effect of particle size on modulating turbulent intensity, Int.J.Multiphase Flow, 15, 279-285

Graham A.L., 1981, On the viscosity of suspensions of solid spheres, App.Sci.Res., 37, 275-286

Guichardon P., Falk L., Fournier M.C., Villermaux J., 1995, Study of micromixing in a liquid- solid suspension in a stirred reactor, AIChE Symposium Series 305, 91, 123-130

Hetsroni G., 1989, Particle-turbulence interaction, Int.J.Multiphase Flow, 15, 735-746

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Kada H., Hanratty T.J., 1960, Effects of solids on turbulence in a fluid, AIChE J., 6, 624-630

Lenzner J., 1991, Der Einsatz Rascher Kompetitiver Reaktionen zur Untersuchung von Mischeinrichtungen, Ph.D. Thesis No. 9469, ETH Zürich

Perry R.H., Green D.W., 1988, Chemical Engineers Handbook, Mc.Graw-Hill, New York

Schreck S., Kleis S.J., 1993, Modification of grid-generated turbulence by solid particles, J.Fluid Mech., 249, 665-688

Takenaka K., Takahashi K., 1992, Local gas holdup and gas recirculation rate in aerated vessel equipped with a Rushton turbine impeller, J.Chem.Eng.Japan, 29, 799-804

Tsuji Y., Morikawa Y., Shiomi H.H., 1984, LDV measurements of an air-solid two-phase flow in a vertical pipe, J.Fluid Mech., 139, 417-434

Villermaux J., Falk L., Fournier M.C. , 1994, Potential use of a new parallel reaction system to characterize micromixing in stirred reactors, AIChE Symp.Ser. 292, 90, 50-54

Yu S., 1993, Micromixing and parallel reactions, PhD. Thesis No. 10160, ETH Zürich

Zwietering Th. N., 1958, Suspending of solid particles in liquid by agitators, Chem.Engng.Sci., 8, 244-253

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228 Chapter 8

On the Koch synthesis of Pivalic Acid from tert- butanol and isobutene using sulfuric acid as catalyst

Abstract

The synthesis of carboxylic acids according to the Koch process is usually carried out in a stirred gas-liquid-liquid multiphase reactor. In the present contribution the reaction of tert- butanol and of isobutene to Pivalic Acid, using 96 wt% sulfuric acid as catalyst solution, is studied at varying operating conditions. Both the desired carbonylation reaction as well as undesired oligomerisation are found to be fast with respect to gas-liquid mass transfer and mixing. The addition of an immiscible liquid, heptane, phase to the catalyst phase increased the product yield significantly. This is most likely due to an increase in gas-liquid mass transfer. More work on this challenging reaction system is, however, required.

229 Chapter 8

230 Chapter 8

1. Introduction

The production of sterically hindered carboxylic acids through the Koch synthesis is an example of a complex reaction system with challenging chemical reaction engineering aspects. The production of these Koch acids is generally characterized by the presence of two liquid phases and one gas phase, a parallel/consecutive reaction scheme with fast, equilibrium reactions and fast, undesired, side reactions. This makes the overall reaction system complex to describe.

The acid yield and the product distribution obtained for this process depends on a number of process parameters, e.g. temperature, carbon monoxide partial pressure, agitation intensity (liquid mixing), and composition of the catalyst solution. Additional to the desired reaction steps also oligomerisation, isomerisation and disproportionation reactions may occur. In this study, attention will be focused to the effect of some of the process parameters on the acid yield and product composition in the production of the smallest Koch Acid, i.c. Pivalic Acid, using sulfuric acid as catalyst solution.

In the industry usually agitated tank reactors are applied and the hydrocarbon reactant and the carboxylic acids produced constitute a dispersed organic liquid phase. The effect of an immiscible organic liquid phase is investigated by using heptane as immiscible phase. By doing so, the effects of an immiscible (inert) liquid phase and the effect of the presence of Pivalic Acid (which affects the reaction kinetics as shown in Chapter 3, can be separated. By variation of the process parameters the effects of gas-liquid mass transfer and liquid phase mixing on the product distribution is analysed. As hydrocarbon reactants tert-butanol and isobutene are used.

231 Chapter 8

2. Reaction mechanism and reaction kinetics

The generally accepted mechanism for the Koch reaction (see Figure 1) includes four reversible reaction steps (Koch, 1955; Falbe, 1980).

R= + (I) formation of a carbocat ion from an alkene or alcohol RCOOH R + CO H (II) addition of carbon monoxide (III) addition of water + + RCOOH 2 RCO (IV) deprotonation of the carboxylic acid formed H O 2

Figure 1 Reaction mechanism

The protonation of olefins is frequently studied in literature. For isobutene, literature data was recently reviewed and updated by Brilman et al. (1997). Fast to extremely fast reaction rates were found, strongly depending on the apparent Hammett acidity of the catalyst solution. For isobutene the apparent first order forward reaction rate constant can be estimated by :

10 log k1,app = -1.35⋅Ho - 3.3 (1)

In this equation k1,app is the apparent first order reaction rate constant for the protonation of isobutene. The rate of dehydration of tert-butanol in strong sulfuric acid solutions is not known from literature. Since the k1,app value for the deprotonation reaction for alcohols in aqueous acid solutions generally shows a log-linear dependency with the Hammett (or equivalent) Acidity scale (Ho), the dehydration kinetics for tert-butanol at high acid concentrations can probably be estimated by extrapolation of dehydration kinetics, measured via the CO consumption rate, at lower acid concentrations.

The results of the initial CO consumption rates in these experiments with tert-butanol as reactant are presented in Figure 2 and compared with the protonation kinetics of isobutene and the dehydration rates of other tertiary alcohols. The experimental procedures and setup used are identical to those applied in Chapter 3, (Brilman, 1998). It appears that the reaction rate constant indeed depends strongly on the Ho value. The reaction rates found are considerably slower than was expected from the t-pentylalcohol and 2-phenyl-2-propanol dehydration rates and the 18O exchange rate data (Deno et al., 1965; Boyd et al., 1960). Several possibilities may account for this effect. First, the carbonylation step may be rate determining. However, considering the log-

232 Chapter 8 linear relationship with the catalyst solution acidity and the reported carbonylation rates in other media (Hogeveen et al., 1970) this seems not very likely. Secondly, the reaction kinetics as determined by CO consumption are not merely determined by dehydration or carbonylation rate, but additionally by the interference of an equilibrium reaction. This equilibrium reaction can be the dehydration reaction itself, or it can be an equilibrium reaction in which another intermediate reaction component is involved. These situations are not easily differentiated from the current kinetic data, but may be analyzed through additional experiments and using more sophisticated techniques (Cox, 1987). At this point, it is assumed that equilibrium position for the dehydration reaction causes the relatively slow CO consumption rate. Attention will be focused in this work on the effects of the addition of an immiscible, inert, liquid phase on the product distribution.

10 2-phenyl-2-propanol (Deno et al., 1965) t-pentylalcohol (in HNO3) (Boyd, Taft, 1960) 8 trans-2-butene (Brilman et al., 1997) 10 isobutene (Brilman et al., 1997) Log k1 6 ethylene (Chwang et al., 1977) propylene (Chwang et al., 1977) 4 iso-butanol (Chapter 3) tert-butanol O-exchange rate (Boyd et al, 1960) tert-butanol, CO consumption (this work) 2 Extrapolation (tert-butanol, this work)

-2

-4

-6

-8

-10 -2024681012 -Ho

Figure 2 Apparent first order dehydration constant for tert-butanol in H2SO4 solutions from CO absorption kinetics. Conditions: 9 g t-butanol, 210 ml H2SO4, 293 K, 40 bar CO, 1800 rpm

For isobutene the protonation reaction is very fast. Even for moderately strong acid concentrations and conditions were the carbocation formation cannot be followed with by the carbonylation, reactions like e.g. oligomerisation and hydration turn out to dominate over carbonylation. In this system the rate of carbonylation of the carbocations formed may become the rate determining reaction step in the mechanism of Figure 1. The reaction rate for this reaction step may be estimated from experimental data for the carbonylation reaction of the

233 Chapter 8

3 t-butyl cation in superacidic media (kcarbonylation ≈ 1.0 [m /mole s], Hogeveen et al. (1970)).

Important side reactions affecting the product distribution include the formation of stable polyalkyl-cyclopentyl cations at acid concentrations exceeding 90 wt% and products due to oligomerisation and consecutive reactions including isomerisation, disproportionating and carbonylation (forming higher acids). The kinetics for these reactions are, however, not known. An overview of the most important competing reactions is presented in Figure 3.

tert-butanol

+H+ - H O 2 + H+ CO H2O -H + + + C COOH isobutene C4 C4CO C4COOH2 4 = (C4 ) (Pivalic Acid) CO = (C4 ) + (C4’) isomers

H+ diisobutenes + + C8 CO H2O -H = + + (C8 ) C8CO C8COOH2 C9 acids

= + (C4 ) (C8’) isomers

+ CO H2O -H + + C13 acids C12CO C12COOH2 + C12

CO, H2O + + C5 + C7 (disproportionation) C6 + C8 acids -H+ R R R + + alkanes (Polyalkylcyclopentyl cations R + alkane fractions) R

Figure 3 (Simplified) Scheme of competing reactions in the Koch synthesis of Pivalic Acid

From Figure 3 it can be concluded that at high dehydration rates of tert-butanol (or high protonation rates of isobutene) transport of CO to the reaction zone and mixing to avoid locally = high C4 concentrations are essential. Attention will therefore be focused on these topics.

234 Chapter 8

3. Experimental

Equipment The experiments were carried out using a high pressure autoclave. The experimental setup is shown schematically in Figure 4. The high pressure autoclave usually was operated semi-batch wise. The reactor used (0.5 L) is made of Hastelloy C-22 and could be pressurized up to 60 bar.

Reactant

MFC storage vessel bypass line

Injection dump vessel vessel

CO Storage vessel Injector

T To vent and P vacuum pump

Reactor feedpoint injection vessel feedpoint injector internal diameter internal diameter

10.0 mm top view

baffle = injection point

10.4 mm

13.0 mm

45 mm 65 mm

Figure 4 Experimental setup 235 Chapter 8

Experimental procedures Prior to an experiment, the thermostated reactor was filled with a sulfuric acid catalyst solution. The solution was degassed by applying vacuum while stirring. When the injection vessel is used for feeding the hydrocarbon reactant, the injection vessel was filled with the liquid phase reactant, in most experiments presented a mixture of t-butanol containing 8wt% of heptane to keep the tert-butanol in the liquid phase at 293 K. Then the reactor was pressurized via a pressure reducer at the desired reaction pressure via the bypass line. Afterwards, the bypass line is closed and the (gas inducing) stirrer is started. Meanwhile, the CO solubility as well as the volumetric gas-liquid mass transfer parameter could be determined when the pressure and temperature vs. time data are recorded. After saturation of the catalyst solution with CO, stirring was stopped and the reactor pressure was reduced by 1.5 bar by opening the valve to the (initially 30 bar CO containing) dump vessel. In this way a pressure drop over the injection vessel is created. Data acquisition is (re-)started and the relevant pressures and temperatures are recorded (these are indicated in Figure 3). The gas inducing stirrer is started again. Both valves of the injection vessel are opened and the carbon monoxide flow is used to inject the reactant. The CO pressure in the reactor is initially kept constant by the pressure reducer. If the CO consumption rate is low, the pressure regulation is switched to a pressure regulating system, consisting of a PC + PID controller system using the Mass Flow Controller to regulate the reactor pressure (± 0.01 bar). Data acquisition is stopped when no longer CO is consumed and minimally after 45 minutes. From the pressurized reactor a sample of about 100 grams from the reaction mixture is directly quenched on 200 grams of ice-water under stirring. After this, the reactor pressure is relieved, the reactor is emptied and cleaned several times with water, dried and closed under a nitrogen atmosphere.

In the experiments with the reactant injector, the reactor is kept at 40 bar CO partial pressure and the injection time could be varied separately. The minimum injection time for a 13 ml of tert- butanol / heptane solution (containing ca. 9.5 g of tert-butanol) is approximately 16 s in the setup used.

Analysis of reaction products A sample of the reactor contents (≈ 100 g) is quenched (at 10 bar CO pressure in the reactor) on icewater (≈ 200 g) and was extracted in four steps with about 60 g heptane (99.9+ %, Merck, pro analyses). The organic layer was analyzed by gas chromatography using a Varian 3400 GC (FID

236 Chapter 8

detector, 250°C, DB-FFAP column 30 m × 0.258 mm, 0.25 µm film, split injection, He or N2 as carrier gas). The organic layer was also titrated to determine the total concentration of weak acids. Further, the consumption of carbon monoxide during the reaction was recorded and used for calculating of the total amount of CO containing products (acids) formed.

The analyses of the organic layer retrieved after extraction on the total amount of acids using GC and titration are generally in good agreement, see Figure 5. When compared with the CO consumption it is usually found that the trends are identical, however, the acid yield by CO consumption is somewhat higher. This may be due to uncertainties in the parameters of CO mass balances (like e.g. reactor volumina and the CO solubility in the catalyst solution with and without products), but also some CO containing (intermediate) products could decompose (retro-Koch) during sampling or they may not be extracted into the organic layer. By titration no weak acids were found in the extracted acid phase. Extraction of carboxylic acids therefore appears to be complete.

100

40 Acid Yield (by GC analysis)

[mole acid / mole reactant *100%] 20 GC CO (titration) 0 0 20406080100 Yield (by titration) [mole acid / mole reactant *100% ]

Figure 5 Total acid yield by titration and GC analysis for a.o. the data series presented in Figure 6

In two experiments Pivalic Acid was added to 380 g, 96 wt% H2SO4 catalyst solution at 5 and 40 bar CO respectively. After one hour samples were taken to determine to what extent e.g. the retro-Koch reaction had occurred and side products were formed. In these experiments 64 and

237 Chapter 8

81% respectively (by GC analysis and titration) of the original injected Pivalic Acid were retrieved as Pivalic Acid in the organic phase after (the standard 4-step) extraction of the quenched reactor sample with heptane. In a fifth extraction step no additional Pivalic Acid was found. In these samples a negligible amount of higher acids was detected. The higher acids found in the reaction product are therefore not formed by a retro-Koch reaction of Pivalic Acid under the conditions used in this study.

The stability of C9 acids formed during reaction was tested in a separate run in which 18.4 g of a mixture of C9 acids (Versatic-9, kindly provided by SHELL RTC, Amsterdam) was injected at 293 K and 40 bar carbon monoxide partial pressure in 380 g, 96 wt% of sulfuric acid catalyst solution. After 6 hours a reactor sample was taken and quenched in the usual manner. It was found by GC analysis that only 1.8 % of the injected C9 acids was converted to Pivalic Acid. No other acids than C9 acids and Pivalic Acid were found.

For the product analysis by GC the following yield parameters are defined. The acid yield YA is the yield on carboxylic acids on a molar basis; YA = mole of acid formed per mole reactant used

(tert-butanol or isobutene). Further, the carbon yield parameter YC is used in this work. The yield ()xYC−⋅1 () parameter Y (C ) is defined as follows : YC()= Ax C x Cx 4

The factor 4 in the above equation originates from the C4 reactants used (tert-butanol as well as isobutene). YC (Cx) now represents the carbon atom yield on Cx acids based on the total amount of injected carbon atoms as hydrocarbon. Note that for the production of e.g. a C9 acid exact two

C4 reactant molecules are required.

Since attention is focused on the total acid yield and the selectivity towards the primary product Pivalic Acid at different process conditions, the higher acids formed were not analysed in great detail for their isomers.

238 Chapter 8

4. Experimental results

In this study subsequently the effects of the reactant feed rate, stirring rate and the presence of an immiscible liquid phase on the total acid yield and on the product distribution will be presented.

4.1 Effect of injection rate and injection method From Figure 6 it can be seen that the injection rate has a very strong effect on the acid yield and on the product composition obtained. The acid yield for the experiments using the injection vessel seems somewhat higher than for the experiments using the injector at the same reactant feed rates. Probably, this difference can partially be attributed to CO dissolved in the reactant solution, when using the injection vessel. In the latter technique CO is used to inject the reactant solution, see Figure 4, and (partial) saturation of this solution with CO is unavoidable. This aspect will be discussed in more detail in the next section. An alternative explanation could be a difference in the local mixing characteristics (energy dissipation rate) around the feed inlet points.

100 Acid Yield [%]

YA ( by titration ) 80

20 Injector Injection vessel

0 1.0E-04 1.0E-03 1.0E-02 1.0E-01 t-butanol injection rate [mole/s]

6-a) Effect of injection rate and - method

239 Chapter 8

100%

Yc unidentified [mole %] > C9 acids [mole %] 75% C9 acids [mole %] C8 acids [mole %] C6 acid [mole %] Pivalic Acid [mole %] 50%

25%

0% 0.0004 0.0009 0.0020 0.0033 0.0036 0.0046 0.0085 0.0161 0.0329 tert-butanol injection rate [mole/s]

b) Product composition at different injection rates (injector series)

Figure 6-a,b Effect of the t-butanol injection rate on the acid yield YA and the product composition YC Conditions: P = 40 bar CO, T = 293 K, 380 g of 96 wt% H2SO4 solution, N = 1800 rpm

At lower feed rates the formation of oligomers seems to be suppressed and the selectivity to Pivalic Acid increases. The ‘unidentified products’ in Figure 6-b involve a.o. acid soluble polyalkylcyclopentyl cations and accompanying alkane fractions (Deno et al., 1964). Comparing the GC diagrams at high and low tert-butanol feed rates, it is found that in the first case a large number of small peaks with low retention times appeared on the GC diagram. These were not taken into account (although their cumulative area may account for at least 30% of the tert- butanol injected) and are not further identified, but judging by the position in the GC diagram it is likely that these are small, high weight alkane fractions. Most likely these peaks represent the products simultaneously formed with the polyalkylcyclopentyl cations (Deno et al., 1964). Additionally, acid soluble components like alkylsulfates may be formed.

4.2 Effect of stirrer speed The influence of gas-liquid mass transfer and liquid phase mixing cannot be separated completely by varying the stirrer speed in the setup used, since a gas-inducing stirrer was applied.

240 Chapter 8

Nevertheless, the effect of the stirrer speed on product yield is shown in Figure 7. The feed rates varied slightly within this series, and the actual values are reported in Table I. The product composition for the series at low injection rates in presented in Figure 7-b.

100 0.023 mole/s, GC 100% Acid Yield 0.023 mole/s, titration Yield Yc YA [%] 0.0009 mole/s, titration on total acids 80 0.0009 mole/s, GC 90%

60 80%

40 70% > V9 [%] V9 [%] 20 60% V8 [%] V6 [%] V5 [%]

0 50% 100 1000 10000 800 1050 1400 1800 N [rpm] N [rpm]

(a) (b) Figure 7-a,b Effect of stirrer speed on acid yield 9 g of tert-butanol (10 M), injection vessel, 40 bar CO, 293 K, 380 g, 96 wt% of H2SO4

Table I Effect of stirrer speed Acid yield YA

Agitation speed vinj CO GC titration kLa N [rev/min] [mole/s] [%] [%] [%] [1/s] low : 800 0.015 25 19 22 0.08 1050 0.023 30 22 24 0.10 1400 0.022 34 23 26 0.12 1800 0.032 38 27 27 0.15 high : 800 0.0008 66 91 64 0.08 1050 0.0009 82 76 77 0.10 1400 0.0009 82 73 77 0.12 1800 0.0009 83 74 76 0.15

For the high injection rates it can be seen that the acid yield increased significantly with the stirrer speed. The product composition for this series did not change significantly with stirrer speed. Only the formation of the polyalkylcyclopentyl cations seems to be suppressed more effectively at

241 Chapter 8 higher stirrer speeds. However, as mentioned above, from these experiments the effect of CO transport and mixing cannot be separated completely. 4.3 Effect of an immiscible liquid phase Industrially, the process is usually operated as gas-liquid-liquid reaction system. The presence of a second liquid phase may have some influence on the mixing and especially on the CO transport towards the reaction zone. The role of such a dispersed liquid phase on the product distribution has been studied in this reaction system by taking heptane as immiscible organic liquid phase. The volumetric carbon monoxide solubility is approximately 3.5 times higher in heptane than in the catalyst solution. To check separately the inertness of heptane, in one of the experiments no reactant (tert-butanol or isobutene) but only heptane was injected. It was found that no CO was consumed due to reaction and no products in the organic layer after extraction were found neither by titration nor by GC analysis of this layer. In Figure 8-a the results at different holdups of heptane initially present in the reactor are shown for experiments at 1800 rpm. The injection vessel was used to introduce the reactant in these experiments.

100% Yield Yc 80 on acids Acid yield 80% YA [%]

60 60%

40 40%

> C9 acids [mole %] CO 20 20% C9 acids [mole %] GC C8 acids [mole %] P = 5 bar C6 acid [mole %] Pivalic Acid [mole %] 0 0% 0 1020304050 0 6 11 15 18 23 28 33 42 49 Φ v [vol%] vol% heptane

Figure 8-a,b Effect of an immiscible heptane phase on the acid yield YA for tert-butanol, injection vessel 9 g tert-butanol (10M), 380 g 96 wt% H2SO4, 1800 rpm, 40 bar CO, 293 K, 0.015-0.03 mole/s ( two datapoints at 5 bar, further identical conditions)

From Figure 8-a an increase in the acid yield can be observed within the range of 0 - 30 vol% heptane. For one pair of experiments at 5 bar and at an injection rate of 0.032 mole/s it was tested if again an increase in the acid yield is found on addition of 25 vol% of heptane. For the

242 Chapter 8 experiments at 5 bar the acid yield indeed increased from 5 to 7.5 %. The decrease in acid yield going from the 40 bar CO experiments to these 5 bar experiments is almost proportional to the decrease in reactor pressure, indicating that the yield is indeed limited by the CO transport to the reaction zone. From Figure 8-b, the product composition for the detected carboxylic acids seems, however, not to be influenced by the heptane present.

100 100% Acid yield YA [%] Yield Yc on acids 90 90%

80%

GC > C9 acids [mole %] CO 70% C9 acids [mole %] 60 C8 acids [mole %] Titration C6 acid [mole %] Pivalic Acid [mole %]

50 60% 0 102030405060 0 14283550 Φ v [vol%] vol% heptane

Figures 8-c,d Effect of an immiscible heptane phase on the acid yield YA for tert-butanol, injector, 9 g of tert-butanol (10M), 380 g 96 wt% H2SO4, 1800 rpm, 40 bar CO, 293 K, 0.001 mole/s

In Figures 8-c and 8-d a similar set of data is presented for low injection rates. Also in this case an increase in the acid yield with increasing heptane holdup up to 30 vol% can be observed.

In a second set of experiments at 800 rpm the dispersed phase hold-up initially present in the reactor has also been varied. The results are shown in Figures 9-a and 9-b. From these figures it is clear that under these conditions the total acid yield increases clearly with increasing dispersed phase hold-up (Figure 9-a). The selectivity towards Pivalic Acid is hardly affected, and the variation in the acids -product distribution shown in Figure 9-b is probably caused by accidental variations. Although the hydrodynamics of the reaction systems may have also changed significantly at 30-50 vol% heptane, no dramatic effects due to a possible phase inversion or a change in dispersion viscosity have been observed.

243 Chapter 8

For the experiment at 0 vol% again a large number of small peaks with low retention times appeared on the GC diagram, most likely representing the products simultaneously formed with the polyalkylcyclopentyl cations (Deno et al., 1964). In this case the acid layer was tested for the presence of the UV/VIS absorption at 302 nm, characteristic for the PACP cations, and this was indeed found.

100%

50 50 Yield Y Pivalic Acid C Yield Yield YA on total C6 acid acids[-] YC [%] [%] C8 acids

40 C9 acids 40 75% > C9 acids Ya (CO consumption) Ya (titration) 30 30

50%

20 20

25% > C9 acids C9 acids 10 10 C8 acids C6 acid Pivalic Acid 0 0 0% 0 7 13 25 38 48 0 7 13 25 38 48 heptane [vol%] Heptane [vol%]

Figure 9-a,b Acid yield and product composition vs. dispersed phase fractions, 293 K, 40 bar, 9.5 g tert- butanol (10 M), 380 g 96wt% H2SO4, injection rate 0.028 mole/s, 800 rpm, injection vessel

244 Chapter 8

5. Discussion

5.1 CO transport The CO transport to the reaction zone seems to be an important factor in these experiments. In view of this, it is important to estimate the amounts of CO already present in the catalyst solution, the CO introduced via the reactant solution (when using the injection vessel) and the rate of gas- liquid mass transfer in order to understand the observed trends. The solubility of CO in the sulphuric acid catalyst solution has been determined experimentally and was compared with the limited amount of data already available from literature. At 40 bar CO and 293 K the solubility is approximately 1.5⋅102 mol/m3. For a saturated catalyst solution and 9 g of tert-butanol this implies that the amount of CO dissolved in the catalyst is sufficient for the production of about 25% acid yield. This is in accordance with the results in Figure 6-a. The gas-liquid mass transfer rate can be determined from the rate of saturation of the catalyst solution with carbon monoxide. The approximate kLa values thus calculated for the sulfuric acid/heptane dispersions increased slightly with the heptane volume fraction. Since the stirrer was stopped shortly during pressurizing the reactor at the start of the experiment and settling may have occured partially during this time, the kLa values presented in Figure 10 should be regarded as first approximations.

0.3

kLa [1/s]

1800

0.2

800 RPM

0.1

0 0 1020304050 volume fraction heptane [%]

Figure 10 Gas-liquid mass transfer coefficients in the presence of heptane as second liquid phase

245 Chapter 8

Considering, however, that the CO capacity of the dispersion increases with the heptane volume fraction, the gas absorption rate is even stronger affected if the mass transfer path is gas → sulfuric acid solution → heptane. This implies that e.g. for the experiment at 1800 rpm and 48 vol% heptane the maximum CO mass transfer rate is approximately 3 times the mass transfer rate at 0 vol% heptane.

The importance of the reactant feed rate was clearly illustrated by the results shown in Figure 6 (and again in Figure 11). The observed trend will be determined (amongst other things) by the CO transport rate and the CO consumption rate. At higher injection rates the CO mass transfer rate in the agitated reactor is insufficient to keep the catalyst solution saturated (Regime III). If the reaction kinetics for both the carbonylation reaction and the oligomerisation/isomerisation reactions are faster than the gas-liquid mass transfer rates, the acid yield is then determined by the amount of CO initially dissolved in the catalyst solution. This explains that the acid yield curve levels off at high injection rates.

100 Acid Yield [%] Regime I Regime II Regime III YA ( by titration ) 80

40 Injector Injection vessel Injector, Isobutene 20 1.0E-04 1.0E-03 1.0E-02 1.0E-01 t-butanol injection rate [mole/s]

Figure 11 Regimes of gas-liquid mass transfer in competition with side reactions data for tert-butanol (Figure 6-a,b) and for isobutene (20 bar CO, 293 K, 2150 rpm,8 g of isobutene)

246 Chapter 8

At low injection rates (Regime I) the CO transport from the gas phase to the bulk of the catalyst solution is sufficiently large. Macroscopically, the catalyst solution will be almost saturated with CO at all times. However, locally around the feedpoint still some CO depletion may occur. In this regime micromixing effects around the feedpoint may dominate the final acid yield obtained. Since the acid yield using isobutene as reactant is significantly lower than the one for tert-butanol under almost identical conditions, this mixing effect may very well cause the difference in yield.

In the intermediate region (Regime II) the macroscopic gas absorption rate becomes more and more limiting with increasing feed rate. Using the apparent kLa value (Figure 10) the maximum CO mass transfer rate for the conditions of Figure 11 can be estimated to be approximately 5⋅10-3 mole/s, which is approximately at the inflection point of the curve in the transition regime. From the existence of these regimes, it is concluded that both the carbonylation reaction and the competing reactions in which the byproducts are formed, and especially the PACP cations, are indeed very fast. In addition, it is found that the latter one is essentially irreversible. In the experiments with heptane as an immiscible liquid phase, the CO depletion in the bulk of the

H2SO4 solution may be reduced by CO transport from the initially saturated organic phase to the catalyst phase, since liquid-liquid mass transfer is usually significantly faster than gas-liquid mass transfer due to the smaller droplet size when compared to the gas bubble size.

When the CO capacity of the H2SO4/heptane dispersions at varying initial holdup of dispersed organic liquid phase already present in the reactor is considered, it can be calculated that the CO capacity increases from an amount sufficient for 25% conversion of the injected tert-butanol to 100% conversion at 48 vol% heptane for the conditions of the experiments shown in Figures 8-a and 9-a. The experimentally determined acid yield was, however, generally not more than 50%. Both the 1800 and 800 rpm series show an increase in the acid yield with increasing heptane volume fraction which is less that the corresponding increase in CO capacity of the dispersion. Mixing and liquid-liquid mass transfer of CO is in the experiments with high volume fractions of heptane at 1800 rpm therefore not fast enough to ensure very high acid yields.

5.2 Effect of tert-butanol concentration To investigate the importance of local reactant concentrations at the feed inlet point the reactant concentration was varied at equal reactant feed rates (0.0028 mole/s). The results for the acid yield and the product composition are shown in Figure 12. It was expected on beforehand that diluting the reactant feed might suppress the formation of higher oligomers and PACP cations. It

247 Chapter 8 appears that the total yield indeed slightly increases with decreasing reactant concentration. Especially the formation of higher acids is suppressed at lower reactant concentrations.

100

100% Acid yield

YA [%] Yield Yc on acids

90% 80

80%

60 > C9 acids [mole %] CO 70% C9 acids [mole %] C8 acids [mole %] Titration C6 acid [mole %] GC Pivalic Acid [mole %]

40 60% 024681012 34710 t-butanol concentration [M] tert-butanol concentration [M]

Figure 12-a Acid yield at various tert-butanol concentrations 12-b Acid product composition

9 g of t-butanol, injector, 380 g 96 wt% H2SO4,vinj = 0.0028 mole/s, 1800 rpm,40 bar, 293K

In Figure 12-a the acid yield at different reactant concentrations but identical feed rates has been presented for experiments with the injector. In these experiments no CO is transported along with the reactant and the differences in the yields obtained can therefore be attributed to the different local reactant concentrations in the reaction zone. Although significant, the effect appears to be rather limited for the tert-butanol experiments. This is probably due to the fact that for oligomerisation two tert-butanol molecules should react and both of them have to be dehydrated. The apparent reaction rate constant for this dehydration reaction is approximately 1⋅101 [1/s] (extrapolated from Figure 2). In the case of isobutene, however, the protonation reaction is much faster and only one of the reactants needs to be protonated. A much stronger effect of liquid phase mixing and reactant concentration is therefore expected when isobutene is used as reactant.

In a similar set of experiments as in Figure 12, but now using the injection vessel, the acid yield increased more strongly with decreasing reactant concentration, especially in the experiments in which less reactant was used, see Figure 13 and Table II. The increase in acid yield is most likely to be caused by CO dissolved in the heptane diluent, which is transported along with the tert- butanol.

248 Chapter 8

100 Molarity g t-BOH anal. Acid yield increasing yield with 10 M 9 g t-BOH titration, GC YA [%] decreasing tert- butanol concentration 4 M 9 g t-BOH titration, GC 80 ,, CO

2.1 M 8 g t-BOH titration, GC

,, CO 60 2 M 9 g t-BOH titration, GC

,, CO

2.1 M 4 g t-BOH GC 40 10 M, 9 g t-BOH, CO ,, CO

10 M, 9 g t-BOH, 1.1 M 4 g t-BOH CO GC/titration 0.8 M 4 g t-BOH CO 20 0.0001 0.001 0.01 0.1 tert-butanol injection rate [mole/s]

Figure 13 Effect on the acid yield of CO transported along with the reactant by the heptane diluent.

This is supported by comparing the acid yield with the (maximal) amount of dissolved CO in the reactant solution, see Table II. Although the analysis of the small reactor samples causes some more uncertainty in the absolute yields obtained for small amounts of reactant, the beneficial effect of transporting CO along with the hydrocarbon reactant is clear.

Table II Effect of CO capacity of the reactant feed on the acid yield (all experiments at 40 bar CO, 293 K, 1800 rpm, 380 g 96 wt% H2SO4)

dissolved CO Product yield

t-BOH t-BOH injection vinj H2SO4 feed total CO GC titration [M] [g] method [mole/s] (% of max. yield) [%] [%] [%] 0.8 4.0 inj. vessel 0.0035 57 58 115 87 88 - 1.1 3.9 inj. vessel 0.0035 59 43 102 86 95 - 2.1 3.8 inj. vessel 0.0060 58 46 104 84 95 - 2.0 5.6 inj. vessel 0.0016 40 25 65 98 79 78 2.1 8.2 inj. vessel 0.0092 28 22 50 75 51 56 4.0 8.4 inj. vessel 0.0038 25 11 36 84 71 70 10 8.8 inj. vessel 0.0037 24 2.5 27 72 57 63 3.0 9.3 injector 0.0030 24 0 24 81 65 72 4.0 9.3 injector 0.0027 24 0 24 76 68 74 7.0 9.3 injector 0.0028 25 0 24 77 64 65 10 9.3 injector 0.0026 25 0 24 71 65 67

249 Chapter 8

5.3 Acid product composition

When comparing the relative concentrations of the detected C5-C9 acids in the products obtained for tert-butanol and isobutene for the different conditions used in this study, the product ratio YC

(C6) : YC (C8) was found to be more or less constant (approximately 3 : 2), irrespective of the absolute yield of these components. It is not surprising that the yields of both components seem to be coupled, since they are likely to be both products from a disproportionation reaction, e.g. a

C12 precursor which may result on disproportionation in a C5 and C7 cation to yield finally a C6 and C8 acid on carbonylation. Further, the YC (C9) :YC (C6) ratio was found to be at least 3 : 2 and increases with decreasing reactant feed rate (or increasing acid yield). This ratio is in fact indirect an indication for the ratio of triisobutene oligomers (which may yield C6 acids via disproportionation) and diisobutene oligomers in the reaction zone. It may therefore be an indication of the reactant concentration in the reaction zone near the feedpoint.

5.4 Product extraction In case of an immiscible heptane phase present in the reactor, the carboxylic acids produced could be extracted by the heptane phase. This may be advantageous, since the presence of Pivalic Acid in the catalyst solution reduces the solution acidity, and with this, the reactivity of the catalyst solution (see Chapter 3). It was found, however, that the extraction of Pivalic Acid by heptane did not occur to a significant extent for a 96 wt% sulfuric acid catalyst solution under the conditions applied in this study. Pivalic Acid and especially higher acids were indeed extracted by the heptane layer as was found in a limited set of experiments at 85 wt%. As the acid strength will be reduced significantly due to the presence of the reaction products in the backmixed reactors used for large scale production, this effect may become important. For Koch Acids with substantially higher molar mass compared to Pivalic Acid a much more pronounced beneficial effect could be realised.

In a single set of experiments at 85 wt% H2SO4 it was found that the addition of heptane to a loaded catalyst solution indeed caused an increase in the observed carbon monoxide consumption rate on addition of tert-butanol reactant, when compared to an experiment in which the same catalyst composition was used but without the addition of a heptane phase. Further study on this topic is therefore recommended.

250 Chapter 8

6. Concluding remarks

For the production of Pivalic Acid from tert-butanol and isobutene in a lab-scale high pressure agitated tank reactor the CO transport was found to be the major parameter determining the acid yield. Both the carbonylation reaction step and the undesired oligomerisation reactions are fast with respect to the dehydration of tert-butanol in the 96 wt% sulfuric acid catalyst solutions used.

For isobutene the protonation reaction is much faster than the dehydration of tert-butanol and the CO transport to the reaction zone as well as the mixing intensity at the feed inlet are therefore even more important. More experimental work using isobutene is therefore required, especially on the reaction kinetics and equilibria of the oligomerisation reactions, in order to be able to predict the product distribution at other process conditions.

In the experiments with tert-butanol the presence of a dispersed organic liquid phase in the reactor increased the acid yield, especially at lower stirring rates. This is caused by the increased amount of CO dissolved in the dispersion and an increased gas absorption rate. Relatively high yields are obtained in case the tert-butanol reactant feed already contains sufficient CO for the carbonylation reaction. Further, the effect of an immiscible liquid phase at lower acid strengths may yield interesting results through the extraction of reactants and products.

The analysis of the reaction system is not completely conclusive with this work. Effects of reaction temperature, CO pressure and, especially, catalyst solution composition have not been considered yet. For the development of a reactor model, attention should be focused on the feed inlet conditions. However, the results obtained in this study indicate that the use of the industrially frequently applied agitated tank reactors for this reaction system should be reconsidered.

Acknowledgements The author wishes to acknowledge B. Knaken for constructing the setup used. G.B. Meijer and N.G. Meesters are acknowledged for their valuable experimental work. A. Hovestadt is acknowledged for the assistance in the analysis. This research was supported financially by the SHELL Research and Technology Centre, Amsterdam (The Netherlands).

251 Chapter 8

Notation

Cx alkyl group or acid with x carbon atoms Ho Hammett Acidity Function kLa volumetric gas-liquid mass transfer coefficient [m/s] N stirrer speed [rpm] P pressure [bar] PACP polyalkylcyclopentyl cations tinj injection time (for the reactant isobutanol) [s] R indication of an alkyl group (Figure 1) R= alkene (Figure 1) [-] T temperature [K] vinj feed rate of reactant [mole/s] YA acid yield (moles of carboxylic acid per mole tert-butanol) [-] YC (Cx) carbon yield (fraction of tert-butanol retrieved as Cx acid) [-]

Super- and subscripts

CO carbon monoxide + carbocation

252 Chapter 8

References

Brilman D.W.F., Swaaij W.P.M. van, Versteeg G.F., 1997, On the absorption of isobutene and trans-2-butene in sulfuric acid solutions, Ind. & Eng. Chem. Res., 36, 4638-4650

Brilman D.W.F., 1998, The Koch synthesis of Pivalic Acid from isobutanol using sulfuric acid as catalyst, Chapter 3 of this thesis

Chwang W.K., Nowlan V.J., Tidwell T.T., 1977, Reactivity of cyclic anc acyclic olefinic hydrocarbons in acid-catalyzed hydration, J.Am.Chem.Soc., 99, 7233-7238

Cox R.A., 1987, Organic reactions in sulfuric acid: The Excess Acidity method, Acc.Chem.Res., 20, 27-31

Deno N.C., Boyd D.B., Hodge J.D., Pittman C.U., Turner J.O., 1964, Carbonium Ions XVI. The Fate of the t-butyl cation in 96% H2SO4, J.Am.Chem.Soc., 86, 1745-1748

Deno N.C., Kish F.A., Peterson H.J., 1965, The intermediacy of carbonium ions in the addition of water or ethanol to arylalkenes, J.Am.Chem.Soc., 87, 2157-2161

Falbe J., 1980, ’New synthesis with carbon monoxide' ; Ch. V.: Koch Reactions (H. Bahrmann), Springer-Verlag, Berlin

Koch H., 1955, Carbonsäure-Synthese aus Olefinen, Kohlenoxyd und Wasser, Brennstoff- Chemie, 36, 21/22, 321-328

253 Chapter 8

254 Dankwoord

Een proefschrift is indirect het product van de inzet van velen, zoals mag blijken uit dit dankwoord. Een ieder die tot de totstandkoming van dit proefschrift heeft bijgedragen wil ik daarom bij deze hartelijk bedanken voor de vaak belangeloze inzet. De inzet van een aantal personen wil ik echter niet ongenoemd laten.

Allereerst wil ik graag mijn promotoren Geert Versteeg en Wim van Swaaij bedanken. Zij hebben mij de mogelijkheid geboden het in dit proefschrift beschreven onderzoek naar eigen inzicht in te richten en uit te voeren. Geert was daarbij de afgelopen jaren niet alleen het wetenschappelijk geweten, maar vooral ook een goede coach. Zijn enthousiasme en optimisme, gekoppeld aan een efficiënte en doelgerichte werkwijze en oprechte belangstelling zijn een voorbeeld voor mij en zorgden voor een prettige sfeer. Aan de wetenschappelijke discussies met Wim van Swaaij en zijn aanstekelijk enthousiasme voor onconventionele, conceptuele, experimenten bewaar ik goede herinneringen.

Het contact met Leo Petrus (SHELL) heb ik altijd zeer prettig gevonden en zijn kritische, maar altijd opbouwende, opmerkingen heb ik erg gewaardeerd. SHELL Amsterdam (SRTCA) wil ik hierbij danken voor de beschikbaar gestelde financiële middelen.

Hans Kuipers wil ik bij deze graag bedanken voor zijn goede adviezen op numeriek gebied binnen dit onderzoek. Daarnaast heeft hij, maar ook Bert Heesink en Wolter Prins, extra inspanningen in de afgelopen jaren geleverd, waardoor ik meer tijd aan mijn promotieonderzoek kon besteden. Ik ben hen dankbaar voor de getoonde collegialiteit.

Het experimentele werk beschreven in dit proefschrift werd écht mogelijk gemaakt door met name Benno Knaken. Niet alleen heeft hij elk van de beschreven opstellingen snel en accuraat gebouwd, ook het meedenken bij het ontwerp en het eigen initiatief om bepaalde aspecten van de opstellingen nog verder te verbeteren heb ik zeer gewaardeerd. Maar ook de talloze bijdragen van Wim Leppink, Henk Jan Moed, Gerrit Schorfhaar en Olaf Veehof waren onmisbaar. Robert Meijer vond vaak de juiste oplossing bij problemen met elektrische schakelingen en de data- acquisitie systemen. In het startfase van het project heeft Sjoerd Kuipers een belangrijke bijdrage geleverd bij het intrinsiek veilig ontwerpen van de opstelling. Rik Akse heeft als zaalchef een belangrijke rol gespeeld bij de handhaving hiervan en als hét aanspreekpunt voor veiligheidskwesties. Daarnaast heeft Rik de financiën van het project uitstekend beheerd. Administratieve zaken werden prima verzorgd door Gery Stratingh en Nicole Haitjema.

De mensen van Chemische Analyse, en met name Adri Hovestad en Wim Lengton, waren onmisbaar voor hun steun bij de analyse van de produktmengsels. Voor reparaties van met name de GC kon ik altijd bij Bert Kamp terecht, waarvoor mijn hartelijke dank. De glasblazerij, en in het bijzonder Gerrit Mollenhorst en Jan van Veen, hebben wanneer nodig glazen onderdelen gerepareerd dan wel vervangen. Jan Heezen en Marc Hulshoff stonden altijd klaar voor vragen en problemen met de PC, het netwerk of aanverwante zaken. Bestellingen van artikelen en de aanschaf van de hoge druk reactoren werden verzorgd door de inkoopafdeling van de faculteit der Chemische Technologie. Wim Platvoet, Jan Jagt en wijlen Ben Haafkes hebben hierbij een belangrijke rol gespeeld. De mensen van Organische Chemie wil ik bedanken voor hun inzet en het gebruik van het UV-apparaat.

Daarnaast hebben nog vele anderen binnen de faculteit Chemische Technologie hun steentje bijgedragen, zoals de portiers, de mensen van de bibliotheek, het chemicaliën magazijn etc. Zonder de anderen tekort willen doen, wil ik met echter met name Wim Verboom, Louis van der Ham, Bert Heesink en Tony van den Boogaard bij deze hartelijk danken voor hun bijdragen in de vele Doctoraalcommissies.

Onmisbaar was echter de experimentele inbreng, de discussies, het enthousiasme en de gezelligheid die de afstudeerders met zich meebrachten. Alex Benschop (TBK) verkende in de eerste 'pioniers'-fase zowel theoretisch als experimenteel de mogelijkheden voor het bestuderen van de reactiekinetiek van de Pivalinezuur synthese via simultane CO / isobuteen absorptie. Femke de Jager (TBK) heeft de belangrijke eerste metingen van de absorptieflux van isobuteen in zwavelzuur oplossingen gedaan, terwijl Cris Freriks (HTS) oplosbaarheids-metingen heeft verricht. In het kader van een keuze-praktikum heeft Bart Oosterlee een meet- en regelsysteem voor de geroerde cel opstelling ontworpen, gebouwd en getest, waarmee later de gasabsorptie metingen nauwkeurig konden worden uitgevoerd. Ook de hoge druk opstelling is later met dit regelsysteem uitgerust. Kristian Leer verrichte met behulp van een beschikbare autoclaaf met een op en neergaande "roerder" de eerste Pivalinezuur syntheses onder verhoogde CO druk, op basis waarvan een meer geschikte opstelling werd ontworpen. Een uitgebreide studie naar de protonering van isobuteen werd verricht door Lars Oberink. Aram de Ruiter (TBK) heeft een verkennende literatuurstudie gedaan naar hydrodynamische aspecten van geroerde G-L-L systemen.

Vervolgens kwam het 'Dream Team' het project versterken. Erik Jan Kant heeft met de nieuwe hoge druk opstelling de Pivalinezuur synthese vanuit isobutanol onderzocht. De experimentele bepaling van de protoneringskinetiek van trans-2-buteen alsmede de modellering van dit absorptieproces is verricht door Ivo Lemmens. Voor de interpretatie van de absorptiefluxen voor deze systemen heeft Diederik Zwart de benodigde fysisch-chemische data uitgezocht met behulp van een isobuteen-isobutaan analogie en metingen met een membraan diffusie cel. Roy Antink heeft in een gedegen studie de benodigde kennis en kunde opgebouwd voor het meten van micromenging met behulp van de diazokoppelingsreactie. Eric van Dijk wist de botsende bellen en druppels in een G-L-L systeem te bewegen om 'complexen' te vormen in een dynamische situatie en dit toch vast te leggen op de video. De invloed van disperse fase druppels op de gas absorptiesnelheid is uitgebreid bestudeerd en gemodelleerd door Mathijs Goldschmidt. Mede door zijn doortastend optreden is het mogelijk geworden om daadwerkelijk een instationair, heterogeen stofoverdrachtsmodel te realiseren. At this point I also like to thank William Hensham (Los Alamos Nat.Lab., U.S.A.) for his help and for providing us with the Overture software package.

Susan Maas heeft de heterogene stofoverdrachtsmodellering van één-deeltjes simulaties uitgebouwd naar meer-deeltjes situaties en een concrete methode voor het voorspellen van absorptiefluxen ontwikkeld. Ivo Kooijman heeft de invloed van Pivalinezuur op de zuurgraad van de zwavelzuuroplossing onderzocht. Eigenschappen van emulsies werden bestudeerd door Rolf de Wit (TBK). Anne Klaas Jellema heeft nauwgezet de mengeffecten in geroerde meerfasen reactoren experimenteel onderzocht. Dit werk werd voortgezet door Wim Hesselink. Theoretisch en experimenteel werk aan gas absorptie in geroerde G-L-L systemen werd verricht door Annemarie Hessels, Brigitte Wolffenbüttel en Thea van der Sar. Hun pionierende werk is in dit proefschrift nog nauwelijks aan bod gekomen, maar zal zeker in de toekomst uitgebreid en gepubliceerd worden. Gerben Meijer onderzocht de Koch synthese van Pivalinezuur vanuit tert- butanol en het effect van een 2e vloeistoffase daarop. Dit onderzoek werd verder uitgebouwd in een vervolgstudie door Niko Meesters, die bovendien experimenteel op een andere aantal plaatsen nog even de puntjes op de i wist te zetten.

Veel van de gezelligheid in en om de vakgroep in de afgelopen jaren is te danken aan mijn (oud-)collega promovendi. Met name de PK-zeilweekenden, het zaalvoetballen en de dart-en stapavonden waren daarbij hoogtepunten.

De paranimfen Mathijs Goldschmidt en Ivo Kooijman wil ik hierbij bedanken voor hun inzet en enthousiasme.

Ik wil bij deze graag mijn ouders en familieleden bedanken voor hun onvoorwaardelijke steun in allerlei opzichten die ik in al die jaren heb mogen ontvangen. Tot slot wil ik Sandra bedanken voor haar steun, geduld en vertrouwen. Curriculum Vitae

Wim Brilman werd op 19 februari 1968 geboren in Meppel. Na de openbare lagere school te Eelde-Paterswolde bezocht hij het Zernike College te Groningen, alwaar hij in 1986 het Atheneum diploma behaalde. Aansluitend begon hij met de studie Chemische Technologie aan de Universiteit Twente. Na een stageperiode van oktober tot en met december 1990 bij Bayer A.G. te Leverkusen (D.), studeerde hij in oktober 1991 cum laude af. Het afstudeeronderzoek was getiteld: “De sulfidatie van kalk; een onderzoek naar het mechanisme en de ontwikkeling van een mathematisch model”.

Na het behalen van het ingenieursdiploma startte hij in oktober 1991 met de Ontwerpers-opleiding Procestechnologie van de Universiteit Twente in samenwerking met de Rijksuniversiteit Groningen. Binnen het kader van de jaaropdracht van deze opleiding is een ontwerp gemaakt van een reactor voor de produktie van Versatic Acids. In oktober 1993 ontving hij het getuigschrift van de Ontwerpersopleiding Procestechnologie, alsmede de Hoogewerff Ontwerpersprijs voor de jaaropdracht.

Aansluitend is hij in dienst getreden als Universitair Docent bij de faculteit Chemische Technologie, vakgroep Proceskunde, van de Universiteit Twente. Tegelijkertijd werd het promotieonderzoek o.l.v. Prof.dr.ir. G.F. Versteeg en Prof.dr.ir W.P.M. van Swaaij gestart, waarvan de resultaten in dit proefschrift zijn beschreven.