THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF CHEMICAL ENGINEERING
DIFFUSION AND KINETIC STUDIES
IN THE CHLORINATION OF TOLUENE
DISSERTATION
Submitted in Partial Fulfilment of the Requirement for the Degree of Doctor of Philosophy in Chemical Engineering
FONG SECK KONG B. Sc. Hons. I January 1970. 0F KE,^30/^'
(, -x- KENSINGTON ) V * . This is to certify that the work presented in this thesis was carried out in the School of Chemical Engineering of the University of New South Wales, and has not been submitted to any other University or Institution for a Higher Degree. (Fong Seek Kong). 1 Acknowledgements The author wishes to record his sincere thanks to Professor J.S. Ratcliffe who suggested and supervised the work described in this thesis. His constant interest and discussions concerning the work have been an inspiration. The author is further thankful to Professor J.S. Ratcliffe and to Miss Chamberlain of the Commonwealth Office of Education and Science for their patient discussions and kind advice in difficult times. Thanks are due to the Commonwealth Government of Australia for the scholarship under the Commonwealth Scholarship and Fellowship Plan, and to the Government of Singapore for securing the award. Thanks are also due to the professional and technical staff of the School of Chemical Engineering for their assistance in the equipment construction and advice rendered, and to Mrs. V. Theodore for typing this thesis. Last, but not least, the author is greatly indebted to his family, whose days of austerity have to be prolonged, and to Miss Chew Ann Kheng for their encouragement and support. ii INDEX Page Acknowledgements i Abstract xv Nomenclature xvii Chapter One 1.1 Chemical Reaction Systems 1 1.2 Toluene and Its Reaction with Chlorine 6 1.3 Previous Investigations in Toluene Side-Chain Chlorination 13 1.4 Homogeneous and Heterogeneous Reaction Systems 19 1.5 Mass Transfer in Heterogeneous Systems 21 1.6 Mass Transfer and Chemical Reaction 28 Chapter Two 2.1 Gas-Liquid Contact Systems 57 2.1.1 Characteristics of the Gas Bubble Column 60 2.1.2 Mass Transfer Characteristics of the Gas Bubble Column 69 2.2 The Agitated Tank Reactor 75 2.2.1 Characteristics of the Agitated Tank 76 2.2.2 Mass Transfer and Interfacial Area in Agitated Tanks 79 iii Page Chapter Three 3.1 Experimental Programme and Equipment Design 84 3.2 Analytical Techniques 100 3.3 Experimental Procedure 110 Chapter Four Introduction 112 4.1 On a Gas-Liquid Absorption Followed by a First Order Reaction in the Liquid Reactant 114 4.2 Effect of Diffusion on Selectivity in Heterogeneous Consecutive Reactions 147 4.3 Unsteady State Chlorination of Toluene in a Laboratory Bubble Column Reactor 168 4.4 Bubble Behaviour in Chlorination of Toluene 169 4.5 Kinetics and Evaluation of Kinetic Data 180 4.6 Controlling Regime in Chlorine Absorption 214 4„7 Evaluation of Volumetric Mass Transfer Coefficients 220 4.8 Effect of Mass Transfer on Selectivity 243 4„9 An Evaluation of Specific Interfacial Area and Film Thickness 256 4.10 Chlorine Solubility Data - A Comparison of Experimental and Empirical Data 265 4.11 Experimental Investigation in the Agitated Batch Reactor 272 iv Page Chapter Five 5.1 Controlling Parameters on Conversion Rate 284 5.2 Effect of Diffusion on the Yield of the Intermediate in a Heterogeneous Consecutive Reaction 301 Chapter Six 6.1 Summary and Conclusions 318 6.2 Suggestions for Further Research 322 Appendix I A Computer Programme for Evaluation of Mole Fractions from Chromatogram 323 B Typical Result from Computer 327 II A Gas Liquid Heterogeneous Reaction-Solution of Differential Equations 328 B Selectivity in Heterogeneous Series Reaction-Solution of Differential Equations 331 C Selectivity in Homogeneous Series Reaction 336 D Maximum Yield of Intermediate in a Heterogeneous Series Reaction for S = 1.0 338 III A Evaluation of Diffusion Coefficients 341 B Estimation of Diffusion Parameter 345 V Page IV A Evaluation of Molar Chlorine Flow Rate 350 B Evaluation of Orifice Reynolds Number 352 V Concentration Units in the Evaluation of Data 353 VI Sample Calculations A Calculation of and k° 355 B Evaluation of Diffusion Regime Volumetric Mass Transfer Coefficient 357 C Evaluation of Gas/Liquid Interfacial Area and Film Thickness 358 VII Experimental Results Tables A1-A16 359 VIII References 378 vi List of Figures Page 101 Qualitative Effect of Chemical Reaction on the Profile of A in a Heterogeneous Pseudo First Order Reaction 29 1.2 Concentration Profile of A in a Fast Pseudo First Order Reaction 39 1.3a Concentration Profile of A in a Slow Pseudo First Order Reaction; High Interfacial Area 42 1.3b Concentration Profile of A in a Slow Pseudo First Order Reaction; Low Interfacial Area 43 1.4 Typical Concentration Profile of A and B in Infinitely Fast Chemical Reaction 49 3.1 G eneral Layout of Equipment 85 3.2 Sketch of Bubble Column Reactor 92 3.3 Sketch of Stirred Batch Reactor 95 3.4 Temperature Control-Electrical Circuit 97 3.5 Typical Gas-Liquid Chromatogram of Toluene, Benzyl, Benzal and Benzo-tri Chlorides 102 3.6 Calibration of Chromatographic Column 108 vii Page 4. la, Concentration Profiles at Interfacial Region. Slow 125, 4.1b Chemical Reaction 126 4.2af Concentration Profiles at Interfacial Region. Fast 129, Chemical Reaction 130 4.3 Concentration Profiles at Interfacial Region. Infinitely Fast Chemical Reaction 133 4.4a Effect of Diffusion Parameter on Chemical Acceleration Factor 141 g 4.4b Effect of 1/^ on Chemical Acceleration Factor 142 i 4.5 Typical Concentration Profile at Interfacial Region in a Heterogeneous Series Reaction 149 4.6 Effect of Diffusion of Selectivity. Slow Chemical Reaction 151 4.7 Effect of Diffusion on Selectivity. Fast Chemical Reaction 153 00 • Effect of Diffusion on Selectivity Fast Chemical Reaction 154 4.9 Effect of Diffusion on Selectivity. Fast Chemical Reaction 157 4.10 Effect of Diffusion of Selectivity. Infinitely Fast Chemical Reaction 159 4.11 Plot of Degree of Chlorination Against Time 184 4.12 Plot of Mole Fraction Toluene Against Time 185 viii Page 4.13 Time-Product Distribution Plot 190 4.14 Plot of log (Fraction Initial Benzal Chloride) Against Tim% 194 4.15 Plot of log (Fraction Initial Benzal Chloride) Against Time 197 4.16 Time-Product Distribution Plot 201 4.17 Arrhenius Equation Plot of and k^ 212 4.18 Deviation of Linear Absorption from Linearity 215 4.19 Plot of Degree of Chlorination Against Time in Diffusion Regime 222 4.20 Plot of Degree of Chlorination Against Time in Diffusion Regime 223 4.21 Typical Free Chlorine Accumulation Curve 228 4.22 Graphical Evaluation of Kinetic Regime Physical Volumetric Mass Transfer Coefficient 231 4.23 Plot of Physical Volumetric Mass Transfer Coefficient Against Molar Chlorine Flow Rate 237 4.24 Plot of Diffusion and Kinetic Regime Physical 241 Volumetric Mass Transfer Coefficient Against Temperature 4.25 Selectivity of Benzyl Chloride at 45°C 247 4.26 Selectivity of Benzyl Chloride at 80°C 249 4.27 Selectivity of Benzyl Chloride at 70°C 251 IX Page 4.28 Degree of Chlorination - Product Distribution Plot 254 4.29 Plot of Product Distribution Against Degree of Chlorination 255 4,30 Plot of Specific Interfacial Area and Film Thickness Against Temperature 261 4,31 Plot of Specific Interfacial Area and Film Thickness Against Chlorine Flow Rate 262 4.32 Comparison of Experimental and Empirical Chlorine Solubility Data 270 4.33 Plot of log (Fraction Initial Benzal Chloride) Against Time - Agitated Batch Reactor 273 4.34 Degree of Chlorination - Product Distribution Plot 275 4.35 Selectivity of Benzyl Chloride - Agitated Batch Reactor at 70°C 276 4.36 Effect of Agitation on Diffusion Regime Physical Volumetric Mass Transfer Coefficient 278 4.37 Effect of Agitation on Kinetic Regime Physical Volumetric Mass Transfer Coefficient 281 X Page 5.1 Determination of Transition Points 289 5.2 Effect of Chlorine Flow Rate on Free Chlorine Content 295 5.3 Effect of Chlorine Flow Rate on Chemical Acceleration Factor 2 96 5.4 Effect of Agitation on Free Chlorine Content 2 97 5.5 Effect of Agitation Rate on Chemical Acceleration Factor 298 5.6 Plot of Intermediate Yield Against (1-conversion) 305 5.7 Effect of Ratio of Reaction Rate Constants on Maximum Selectivity-limited Intermediate Yield 313 5.8 Effect of Ratio of Reaction Rate Constants on Maximum Yield of Intermediate 315 A1 Plot of Diffusion Coefficient Against Temperature 344 xi List of Tables Page Chapter Two 2.1 Summary of Some Published Literature on Bubble Columns 61 Chapter Four 4.1 Summary of Dye Dispersion Time and Orifice Reynolds Number for Bubble Column at 70°C 178 4.2 Specific Kinetic Constant, k at 70°C 196 O 4.3 Specific Kinetic Constant 199 4.4 Specific Kinetic Constants k^, k^, k^ 203 4.5 Analysis of Specific Kinetic Constant Variation with Temperature 211 4.6 Thermodynamic Constants of Reaction 213 4.7 Evaluation of Diffusion Regime Chlorine Physical Volu metric Mass Transfer Coefficient 225 4.8 Evaluation of Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficient 230 4.9 Summary of Evaluated Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficients and Chlorine Solubilities 233 4.10 Comparison of Diffusion Regime and Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficients 235 4.11 Variation of Chlorine Volumetric Mass Transfer Coefficient with Temperature 240 xii Page 4.12 Theoretical Selectivity of Benzyl Chloride under Diffusion and Non-diffusion Limitation at 45°C 246 4.13 Theoretical Selectivity of Benzyl Chloride under Diffusion and Non-diffusion Limitation at 80°C 248 4.14 Theoretical Selectivity of Benzyl Chloride under Diffusion and Non-diffusion Limitation at 70°C 250 4.15 Summary of Film Thickness and Specific Interfacial Area 260 4.16 Evaluation of Empirical Chlorine Solubility 2 68 4.17 Comparison of Experimental and Empirical Chlorine Solubility Data 2 69 4.18 Effect of Agitation on Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficient 282 Chapter Five 5.1 Summary of Transition Points from Diffusion Regime to Kinetic Regime 292 xiii Page Appendix 1 Diffusion Coefficients from Wilkie and Chang's Equation 343 2 Estimation of Diffusion Parameter 347 3 Molar Chlorine Flow Rates 351 A1-A16 Summary of Experimental Results 359 xiv Page List of Plates Plate I General Layout of Equipment 86 Plate II Chlorine Meter and Control Panel 88 Plate III Bubble Column Reactor with Chlorine Flow Rate at 0.4 lb/hr 170 Plate IV Bubble Column Reactor with Chlorine Flow Rate at 0.6 lb/hr 171 Plate V Bubble Column Reactor with Chlorine Flow Rate at 0.8 lb/hr 172 Plate VI Bubble Column Reactor with Chlorine Flow Rate at 1.0 lb/hr 173 XV Abstract The unsteady-state heterogeneous photochemical chlorination of the toluene side-chain in a bubble column reactor has been studied over a temperature range of 45°C to 80°C and chlorine flow rates of 0.4 lb/hr to 0.95 lb/hr. A diffusion controlled and a kinetic controlled chlorine absorption regime were distinguished. The reaction rate of benzal chloride to benzo-tri chloride was determined to be of first order with respect to benzal chloride, from which the kinetic constants and the kinetic equations of the consecutive reactions from toluene to benzo-tri chloride were evaluated. The theoretical equations which describe the simulta neous process of gas diffusion into a liquid and chemical reaction with a first order kinetic expression with respect to the liquid reactant were solved; this subject being found to have received little attention in literature. The controlling regimes were dis tinguished while the parameters which define these regimes were identified. Fast and infinitely fast heterogeneous gas-liquid chemical reactions have a diffusion parameter in excess of 2.0; and for these reactions, the absorption rate of the gas is controlled by the chemical diffusion rate. Slow reactions on the other hand have a diffusion parameter of less than 0.5; the absorption regime is dependent on the specific gas-liquid interfacial area, and on the xvi relative rates of the gas-diffusion and bulk liquid reaction. The heterogeneous photochemical chlorination of the toluene- side chain was estimated to have a diffusion parameter of less than 0.5 under the experimental conditions. From the theoretical equations developed, a diffusion regime and a kinetic regime volumetric mass transfer coefficient have been determined for the reaction. The calculated volumetric mass transfer coefficients varied linearly with chlorine flow rates and temperature. The effecfeof diffusion on the selectivity of an inter mediate in a gas-liquid consecutive reaction have been discussed qualitatively and quantitatively. Conditions which lead to a diffusion-limited selectivity (with a fall in the selectivity) have been described. The parameter that defines a diffusion-limited selectivity or otherwise is the diffusion parameter. A diffusion parameter in excess of 2.0 is a necessary condition for a diffusion-limited selectivity. The effect of the ratio of kinetic constants on a diffusion-limited and a non-diffusion-limited selectivity were discussed. The consecutive reaction of toluene to benzo-tri chloride had a non-diffusion-limited selectivity under the experimental conditions; experimental data correlated well with the theoretical values for a non-diffusion-limited selectivity. The photochemical chlorination of toluene was further investigated in a stirred batch reactor to evaluate the effects of agitation. Agitation was found to have no effect on the kinetic xvii constant and diffusion regime volumetric mass transfer co efficient evaluated previously. The kinetic regime volumetric mass transfer coefficient was shown to increase with agitation, but became approximately constant beyond a particular agitation rate. Theoretical equations and experimental data have been applied to define the transition from a diffusion regime to a kinetic regime, using a graphical method suggested. The transition point was a function of the gas flow rate and kinetic rate. The efficacy of the bubble column reactor was also discussed in re lation to the phase utilization factor, chemical acceleration factor and agitation effects. Generally, the bubble column reactor is a suitable reactor for the reaction studied. xviii Nomenclature Symbol Definition Units a Gas-liquid specific interfacial area cm * A Gas phase reactant: chlorine concentration (section 4.5-5.1) mole/mcqe B Liquid phase reactant; toluene concentration mole/moje C Liquid phase product; liquid phase intermediate product mole/mole benzyl chloride concentration (section 4.5- 5.1) D Liquid phase product; benzal chloride concentration, mole/mole (section 4.5-5.1) D Orifice diameter cm o Bubble diameter cm D Sauter mean bubble diameter s 2/ ■8 Diffusion coefficient cm /sec E Benzo-tri chloride concentration mole/mole £ Activation energy of reaction kcal/gm mole f Fugacity atm F Chemical acceleration factor dimensionless F. . Relative response factor of component dimensionless i/J i with respect to j (Chapter 3) Definition Units Surface renewal frequency in Danckwerts penetration absorption theory Gravitational constant acceleration (Equation 2.1, page 63 only) Peak height of chromatogram ins. -1 General reaction constant; sec Reaction constant for the reaction of -1 toluene to benzyl chloride sec (section 4.5-5.1) Reaction constant for the reaction of -1 benzyl chloride to benzal chloride sec (Section 4.5-5.1) Reaction constant for the reaction of -1 benzal chloride to benzo-tri chloride sec (Section 4.5-5.1) -1 Frequency factor sec Liquid phase physical mass transfer cm/sec coefficient Liquid phase chemical mass transfer cm/ / sec coefficient Diffusion regime physical volumetric -1 mass transfer coefficient sec Kinetic regime physical volumetric -1 mass transfer coefficient sec XX Symbol Definition Units in, logg Natural logarithm dimensionless m Mole fraction (Chapter Three) mole/mole n Impeller speed r. p.m. N Instantaneous specific absorption rate in penetration theories N Chemical specific absorption rate mole/mole2 sec. cm N° Physical specific absorption rate mole/ mola, sec. cm P Laplace paremeter dimensionless P Power consumption of impeller Ph Phenyl radical r Kinetic rate mole/^ole sec. R Overall absorption rate mole/mole sec. R Universal gas constant cals/gm. mole (Sections 4.5 and 4.10 only) Re Reynolds Number dimensionless s Solubility parameter (cals/c.c.)¥ xxi Symbol Definition Units S Selectivity factor, ratio of kinetic constants k dimensionless Sc Schmidt Number dimensionless Sh Sherwood Number dimensionless t Time sec. t* Time existence of liquid element on gas-liquid interface in Higbie's penetra tion theory -1 T Absolute temperature v Molar chlorine flow rate m mole/Jnole sec Superficial gas velocity Volume of dispersed phase Molar volume (Section 4.10) cc/qm mole x Mass fraction (Chapter 3 only) dimensionless x Distance in diffusion region of film theory cm X Degree of chlorination mole chlorine/ mole toluene Transition point from diffusion regime mole chlorine/ *r to kinetic regime (Section 5.1) mole toluene xxii Symbol Definition Units y Molar solubility of chlorine (section 4.10) mole/mole Z Height of undispersed liquid in bubble column Z Height of dispersed liquid in bubble f column Greek Symbols cx (alpha) Defined in equation 5.12, Chapter 5 dimensionless (beta) Defined in equation 5.14, Chapter 5 dimensionless Y (gamma) Surface tension § (delta) Film thickness in film theory cm 3 / 3 € (epsilon) Fractional hold-up cm /cm ^ (eta) Volume fraction of liquid (equation 3 , 3 4.52) cm /cm © (theta) Temperature °C (mu) Viscosity centipoise ^ (rho) Density cr (sigma) Phase utilization factor dimensionless xxiii Symbol Definition Units (sigma) Summation (p (phi) Diffusion parameter dimensionless f (psi) Age distribution function in Danckwert's Penetration Theory dimensionless Subscripts 1 gas Section 4.10 only 2 liquid A gas reactant chlorine (Section 4.5-5.1) B liquid reactant G gas phase i interface L liquid phase o initial state 1 CHAPTER ONE 1.1 Chemical Reaction Systems When a chemical substance undergoes a change that results in one or more chemical substances possessing different chemical properties from the parent substance, a chemical reaction is said to have occurred. In more precise terms, the parent substance is termed the reactant while the resultant substances are termed products. The more common chemical reactions particularly in industry involve more than one reactant, although reactions that involve only one reactant are by no means non-existant (e.g. thermal cracking of olefines). The stages of reaction that the reactants undergo is termed the reaction path or the reaction mechanism. Detailed studies of reaction mechanism have shown that mechanisms of many reactions are more intricate than is apparent in a stiochiometric equation, this being more so in organic chemistry In the more recent concepts of reactions, reactants that react under the physical conditions imposed on the reaction system are thermo dynamically unstable, and the process of thermodynamic equilibration brings the reactions to the stage of the thermodynamically stable products. Hence reaction can proceed only when the physical conditions imposed on the system induces the state of thermo dynamic instability. Similarly, different physical conditions can bring about a different system of instability in the reactants that leads to a varied reaction path and hence a different product. 2 The transition state theory appears to be the more accepted theory of reaction kinetics. An activated intermediate complex is postulated to form as a result of physical conditions imposed on the reactants. The complex has a higher energy than both the reactants and products and because it is unstable, its de composition can occur in both ways; to the initial state of reactants or the final state of products, which in both cases results in the evolution of energy. Inherent in the theory is therefore the reversi bility of a reaction and the fact that a reaction can be favoured by imposing conditions that affect the rate of decomposition of the complex. Competing reactions may give rise to different intermediates or one common intermediate in the reactions, which decompose in several ways to yield more than one product. Among many means of controlling a reaction path is one very important class of substances - catalysts. These are known to alter drastically the physical conditions required of thermodynamic instability that precedes a reaction, both positive and negative catalysts or inhibitors being known in this respect, although this classification is entirely arbitrary. Catalysts do not affect the thermodynamic equilibrium but rather affect the rate of a particular path of reaction leading to a favoured yield of a desired product. This is of particular important in series or parallel reactions as proper choice of a catalyst can significantly alter a product distribution. Despite a widespread use of catalysts, however, 3 the mechanisms of operation are still largely unknown. Although the transitional complex theory appears only to be conceptual its validity has been proven for several cases. Examples are the detection of the nitronium ion in a nitration mixture of concentrated sulphuric and nitric acids^ and the actual isolation of a stabilized intermediate in the triphenyl 3 methyl radical. 1.1.1 Chain Reactions It has been stated earlier that a chemical reaction is more involved than that suggested by its stiochiometric equations. Reactions in fact are often the gross effect of a number of elementary processes or reaction steps. The processes may occur concurrently in which case the reaction is termed a parallel complex reaction or it may occur in consecutive elementary stages in a series 4 complex reactions. Although such a mechanism is true in general, it is particularly true of a chain process or reaction. As the name suggests, the chain reaction is constituted of elementary processes acting in a chain which is continued by an active intermediate termed the chain carrier. A chain reaction starts with the production of the chain carrier through energy absorption by a molecule, thus: energy absorption X + X* initiation 4 This elementary process, essentially a decomposition through energy absorption is termed the initiation, which results in the chain carrier X*, typically an atom or radical. X* then reacts with a molecule to yield a product in a series of elementary reactions that leads to a regeneration of the chain carrier: X* + reactant Product + X* propagation This whole process is termed the propagation step. Because the chain carrier is very active, many parallel reactions can occur that lead to the destruction of the carrier, such a step being termed the termination step. X* + ...... * X* ...... termination The chain length is a term used to define the efficiency of a chain reaction. It may be defined as the number of propaga tion stages that arises from the generation of one chain carrier from an initiation step. The same may be defined as the number of cycles before the chain is interrupted. Both definitions are discrete and may not be numerically equal for a reaction, depending 5 on the reaction mechanism. 1.1.2 Photochemical Reactions The chain reaction describes in general reactions that involve activated molecules, radicals or free atoms. Energy sources of dissociation can be heat, chemical reaction or even radioactive radiation. When the source of energy is light, a very important class of reactions arises, termed photochemical reactions in general. In the Planck's Quantum Theory, light behaves as discrete photon particles, and each particle has inherently an energy equivalent to hi> where h = Planck's constant V = spectral frequency of the light radiation A photochemical reaction is therefore initiated by the bombardment with photons of a chain carrier source. The release of energy by the photon particle is absorbed with the formation of the chain carrier. Photochemical halogenation reactions, particularly chlorinations are rapidly becoming very important industrial reactions as the easiest means of manufacturing organic halides. Besides being useful chemical solvents, organic halides are 6 versatile starting materials in preparative chemistry. Some common industrial chlorinations include most olefines, allenes and aromatic compounds. A comprehensive survey of several industrial chlorinationg processes can be obtained from McBee and Unguade. From Planck's formula for the energy carried by a photon particle it is evident that a higher energy is carried by a light radiation of higher frequency, that is a shorter wavelength. In spite of the infinitely variable wavelength possible in light, only a relatively small portion of the spectrum is used which includes ultraviolet and visible light. This is not surprising because other than being sufficient as a source of free radical initiation the visible light sources are the most readily available. The efficiency of a photochemical reaction is generally measured by what is termed its quantum efficiency, defined as the molecules of product formed per quantum of light energy absorbed. In a photochemical substitution chlorination, a convenient measure would be the molecules of hydrogen chloride produced, since a substitution of one hydrogen atom in the organic molecule results in the formation of one hydrogen chloride molecule. 1.2 Toluene and its Reaction with Chlorine Toluene is the first member of the side-chain aromatic 7 hydrocarbons homologous series. Its molecular structure consists of a benzene ring nucleus with one hydrogen replaced by a methyl group. The structure may however be viewed from another angle, the toluene molecule being constituted of a methane molecule with a hydrogen replaced by a phenyl group. Hence it can be deduced that the toluene molecule will have both aromatic and aliphatic hydrocarbon properties, although its aromatic properties are more dominant; and toluene is generally regarded as an aromatic compound in reactions. When chlorine is bubbled into toluene, two well defined reactions are known to occur, dependent strongly on the conditions 7 of reaction. In the presence of a halogen chain carrier at low temperature of about 30-50°C, and in the absence of light, chlorine substitutes a hydrogen atom in the benzene ring to yield ortho- and para- chloro toluenes as first products. The halogen carrier plays a catalytic role in the reaction and easily polarizable compounds such as ferric, aluminium, stanuous, stannic chlorides and iodine are common halogen carriers. The mechanism of the reaction is essentially one of electro-philic substitution and will not be elaborated at length. When chlorine and toluene are contacted under a different set of conditions, however, an entirely different reaction ensues. In the absence of halogen carriers as catalysts, at elevated 8 temperatures above 50°C and under the radiation of light of sufficient spectral energy, photochemical chlorination occurs. The methyl side chain of toluene is involved and reaction pro gressively displaces the hydrogen atoms of the methyl group to yield benzyl chloride, benzal or benzylidene chloride and benzo- trichloride respectively. As a photochemical reaction the following general mecha nism will apply. A chlorine molecule on irradiation with light of sufficient spectral energy dissociates to two chlorine atoms following the fission of the molecular bond. h v Cl - Cl ------2 Cl . A chlorine atom is the active chain carrier in the photo chemical reaction and is capable of abstracting an hydrogen atom from the side-chain of toluene or any of the chlorinated side chain reaction products, forming hydrogen chloride and an active organic radical in the process. Ph . CH3 + Cl . ------► Ph. CH2 . + HC1 The organic radical can react in two ways. If it reacts with a chlorine molecule, a chlorine-substituted product is formed 9 with the regeneration of a chain carrier, thus completing a propagation cycle. hv Cl - Cl ------Cl . + Ph . CH3 Ph . CHr + HC1 n + Cl„ Initiation Propagation cycle Ph . CH2C1 -t Cl. If, however/ the organic radical reacts directly with a chlorine atom, the chloro-organic product is formed without a chlorine atom being regenerated, thus terminating the chain. A similar termination occurs in the combination of two chlorine atoms, reversing the initiation process. Ph. CH2 . + Cl ------* Ph . CH2C1 termination Cl . + Cl . ------ci2 The probabilities of a combination of the organic radical and a chlorine atom or the recombination of two chlorine atoms is 10 however largely reduced because of the low concentrations of these active radicals and atoms, although the low concen tration of the chain carrier may in fact be primarily the result of a very rapid reserval of the initiation process. Cl - Cl 2 Cl. The observation is further supported by the fact that chain reactions in photochemical chlorinationg have very high quantum efficiency, to the extent of 10 molecules in the photo g chemical chlorination of the toluene side chain, which must be the result of a very efficient and repetitive chain propagation cycle. Notwithstanding the complex intermediate mechanism, photochemical chlorination reactions have an overall bimolecular 9 kinetics as in the chlorination of methane, A classic exception to a bimolecular kinetics for photochemical reactions is that reported by Bodenstein'*’^ for the hydrogen-bromine photo chemical reaction. The reason for a bimolecular mechanism is due to the rate controlling step in the reaction of the organic radical with 11 chlorine, R. + Cl2 ------R - Cl + Cl. with overall rate r, given by r = k [R.J [Cl2] Because [r.J is proportional to the concentration of the organic derivative of R. , a second order reaction is observed. Overall, the reaction of chlorine in the toluene under the radiation of light may be summarized as the substitution of side- chain methyl hydrogen to given the resultant chlorides of benzyl chloride, benzal chloride and benzo-trichloride progressively with a molecule of hydrogen chloride evolved simultaneously for each hydrogen atom substituted. The reaction is represented schematically below: 12 Ph.CH3 + Cl2 —---- * Ph.CH Cl + HC1 toluene benzyl chloride Ph.CH. Cl2 + HC1 benzal chloride + Cl 2 hp Ph CC13 + HC1 ben zo-trichloride The two different reactions that occur under the different conditions imposed on the same reaction system already illustrate the dual nature of toluene as an aromatic and aliphatic hydrocarbon. As an aromatic, it undergoes electro-philic substitution, characteristic of the aromatic nucleus. As an aliphatic, however, it can undergo a photo chemical chlorination with displacement of the methyl hydrogens. In fact, under any condition, both paths of reaction do occur, except that under specific controlled conditions, one particular 13 reaction path becomes predominant to the virtual exclusion of the other. It can be appreciated therefore that the chlorina tion of toluene with two parallel consecutive reactions can be complex. The present study is concerned with the chlorination of the side-chain in toluene. Under carefully controlled conditions, however, almost complete dominance of the desired Q reaction is achieved. Ratcliffe confirmed the absence of nuclear chlorination products with the Beilstein test in his side- chain chlorination of toluene conducted at 111°C. Harring and Knol^ however obtained a high boiling residue when a re action product mixture was separated using a distillation technique. Although they did not detect simpler nuclear chlorination products with a gas liquid chromatograph the residue was accounted for as poly-nuclear chlorides. In the absence of details on the nature of these chlorides, the possibility that the high boiling residue is actually the product of thermal decomposition of side chain chloro toluenes cannot be excluded. 1.3 Previous Investigations in Toluene Side-Chain Chlorination The literature available contained only a scant amount of information on the chlorination of the toluene side chain. It is not surprising, however, if it is remembered that such studies have been included in the work on photochemical chlorinations 14 of hydrocarbons as a whole. As a result, there is only a little or no evidence on the mechanism and kinetics of the reaction, although it would be expected to conform to the general mechanism for hydrocarbon chlorinations. 12 o Book and Eggert chlorinated liquid toluene at 105-10 C and reported of the sole product as benzyl chloride irrespective of the presence or absence of light radiation, provided halogen carriers were excluded. At -80°C reaction was negligible in the dark but with suitable light illumination, reaction produced benzyl chloride and chloro-toluene with a quantum yield of 25 13 molecules. Bergel concluded from the reports of Book and Eggert that the latter authors had questioned the efficacy of light in catalysing the side-chain chlorination of toluene. From experimental work conducted, Bergel concluded that sunlight did 14 materially affect the side-chain chlorination. Book and Eggert however reiterated from their earlier work that at 105-10°C, reaction was predominantly chemical rather than photochemical, whereas at -80°C, the chemical reaction is ten times less than the photochemical reaction. Calculation from the same work did not contradict the conclusions of Bergel. Ritchie and Winning^ studied the vapour phase chlorina tion of toluene, with light and thermal initiation of the reaction. In both cases, reaction rate was extremely rapid, and influenced strongly by wall reactions. The authors further concluded that 15 the photochlorination reaction occurred for a light source of wavelength 3650 and 4060 angstroms. Oxygen was found to inhibit the reaction markedly, being even more effective in the thermal initiated reaction. The influence of oxygen in inhibition of the toluene side chain chlorination is not specific to the reaction. Oxygen and a great number of other compounds including phenols, ethers and amines act in the same manner for most chain re actions . The organic radical in chain reactions combine with 16 oxygen to form a peroxide radical. Further, Port and Wright showed thfet oxygen and chlorine react to give a transient species CIO, which subsequently decomposes bimolecularly to chlorine and oxygen. This destroys the active chlorine atom. Cl* + o ------► CIO 2C10 ------► Cl2 + 02 An inhibitive capacity in oxygen in chlorination of the toluene side chain was also observed by Harring and Knol"/ Ritchie and Winning^ had indicated the possibility of thermal energy as a source of energy to initiate the chlorination 16 of the toluene side chain. Firth and Smith conducted a chlorination of toluene at its boiling point in complete absence of light. The yield of side chain substitution products were increased by the addition of activated (sugar) charcoal. The catalytic activity of the same was increased if it had previously absorbed iodine. Blood charcoal showed an even greater activity, although addition of iron to this catalyst affected in no way its activity. Iron-impregnated silica-gel however induced chlori nation of the nucleus. 18 Willey and Foord utilized an electrical discharge through chlorine as a means of chain initiation. An overall chlorination product increase of ten per cent was reported although ring substitution was not materially affected. Traces of atomic chlorine formed in the discharge were deemed responsible for the subsequent increase of chlorinated products. Of a more academic nature is perhaps the report by 19 V Harmer et al of the chlorination of toluene under a \ - ray radiation. Two sources of V - rays were used, of 300 and 3000 curies respectively. Product distribution in the experiments differed from those using photo-chemical activation, both side- chain and ring substitution being observed. As a result of the wide availability of toluene from processes developed in the last world war, there appears to be a 17 rejuvenated interest in the studies of the toluene side-chain chlorination with an industrial bias. 20 Benoy and Maeyer conducted experiments with a view to obtaining optimal yield of benzyl chloride from the chlorination of toluene. An experimental reactor was made up of a toluene boiler, a packed tower with an fractionation efficiency of five to six theoretical plates, a reaction chamber and a condenser. Toluene vapour from the boiler rose through the packed tower into the reaction chamber where it reacted with chlorine under the catalytic effect of ultra violet light at 120°C. Reaction products and hydrogen chloride were removed from the condenser, with an overall chlorination of 70%. The authors obtained an optimal yield with sulphuryl chloride catalyst in the fluid phase or phosphoryl chloride in the gas phase. Arsenious oxide retarded thermal decomposition of the product chlorides. g Ratcliffe studied the commercial feasibility of conducting the reaction in a constant stirred tank reactor, CSTR in short. From calculations, he showed that a light source of 0.05 watts would have been sufficient to initiate the photochlorination of g toluene, a reaction with a quantum efficiency of 10 molecules. Although a constant flow reactor would result in a decreased yield of intermediate compounds (benzyl and benzal chloride), a 18 phenomenon well supported in theory and experiments, Ratcliffe concluded that with a low level of chlorination, the operating advantages of the continuous reactor would outweigh the slight loss of intermediate yield in comparison with a batch reactor. No details of kinetic measurements were, however, forwarded by Ratcliffe. Although the wavelength of light suitable for photo chemical reactions is ill defined, it is widely accepted that light in the human-visible spectrum is practically sufficient for industrial applications. The use of ultraviolet light was deemed more efficient because of the higher energy per quanta, resulting in increased yield from chlorine chain carrier. In this respect Harring and Knol^ studied the side-chain chlorination of toluene under the irradiation of light sources of varying spectral energy in a laboratory continous reactor. However, as will be discussed in full in Chapter Four, the calculation of kinetics used by the authors proved to be suspect. Nevertheless, the kinetic constants showed an orderly trend, increasing as the spectral energy of the light source varied from red to blue, falling thereafter for ultraviolet light. The lower efficiency with ultraviolet light was explained by the non-transparency of Pyrex glass to the light and to its poor absorption by the green-yellow coloured solution of chlorine in toluene. Blue light on the other hand penetrated the chlorine solution best, thus proving to be 19 the optimum source of light for this reaction. In the chlorination of toluene, reaction in the first stages proved very rapid, all chlorine being absorbed in reaction. Kinetics were therefore evaluated only when reaction slowed down with an appreciable concentration of chlorine in the Hcpid phase. Ring chlorination was reported to increase at 40°C over the same reaction at 100°C. 1.4 Homogeneous and Heterogeneous Reaction Systems Although the known and possible reactions would amount to an astronomical figure, common characteristics exist among many reactions. Such a common characteristic is therefore most conveniently employed in the classification of chemical reactions according to purpose. Classification may be based on reaction mechanism (e.g. chain reactions, electro-philic substitution reactions) or a common reactant may form the basis of classification (such as chlorination, hydrogenation and the like). In chemical engineering design, a most important classifi cation appears to be a differentiation of all reaction systems into homogeneous and heterogeneous types, with the reaction and its mechanism assuming a secondary importance.^ A homogeneous reaction system is defined as one in which all the reactants active in a chemical reaction including 20 catalysts occur in one phase. Even when reactants are present in different phases prior to mixture, the requirements of the homogeneous reaction system stipulates that the phases must merge into one, to the total exclusion of an interface. A heterogeneous reaction system on the other hand describes one in which reactants are present in different phases that do not merge on contact. A diffusion process is therefore necessary to bring reactants across an interface in order to sustain a chemical reaction. In contrast to the homogeneous system therefore, not all reactants present in the system are available for reaction. As a further differentiation, if reaction occurs in one or more phases of the heterogeneous system the reaction system may be termed a heterogeneous system with a homogeneous reaction. Whereas, if reaction were to occur at an interfacial region with reactants fed from the main phases, the reaction system becomes 22 a heterogeneous reaction system with a heterogeneous reaction. Even in a homogeneous reaction system, however, kinetic rate is not uniform throughout the system. Such variation is due to incomplete mixing and the existence of dead space in reactors. In more extreme cases, micro kinetics no longer can be applied with a high degree of confidence and macro kinetics considerations apply. 21 1.5 Mass Transfer in Heterogeneous Systems The general purpose in contacting two phases in a heterogenous system is to bring about mass transfer between the phases with a subsequent chemical reaction. A theoretical analysis of the mass transfer process is developed largely for the gas-liquid system, but the results are equally applicable to any fluid-fluid system. Although the elementary equations are developed on a physical absorption of a gas by a liquid a strictly physical absorption process in this respect is almost non existent since some form of chemical reaction always occurs 23 after the absorption. 1.5.1 Physical absorption in Gas-liquid Systems The rate of mass transfer in a physical gas-liquid absorption is largely dependent on two sets of factors. i) Physico-chemical variables such as solubility and diffusivity of the gas in the liquid. For absorption followed by chemical reactions the kinetic rate will also have to be considered. ii) Hydrodynamic factors such as geometry and scale of equipment, viscosity, density, flow-rate of fluids and external agitation. 22 Consider the two phases in a heterogeneous system under agitation caused either by the introduction of the fluid phases at high velocities or external agitation or a combination of both. Within the main body of both phases, turbulence due to agitation would render the contents homogeneous throughout. Whether this turbulence and homogeneity would be developed to the interface is debatable. One postulate conceives the turbulence to be progressively damped towards the interface and at the interface laminar conditions may be assumed. Such a concept has supporting evidence in fluid flow through pipes where the turbulence is known to develop away from the walls of the pipe. Turbulence within the bulk of the fluid establishes a mechanism of mass transfer through eddy diffusion, and because of the concept of fluid homogeneity, no resistance to mass transfer will exist. At the region of the interface, however, mass transfer must occur through the process of diffusion with the establishment of a concentration gradient. Between the extreme turbulent and laminar regions will exist a layer that is inter mediate in hydrodynamics which offers an appreciable resistance to diffusion. A second hydrodynamic model however considers the turbulence to be developed to the interface; the latter consisting of small fluid elements which are continually renewed by the turbulence. During their existence at the boundary, the elements 23 absorb solutes by an unsteady state process. Since a critical analysis of the actual diffusion process is difficult, accepted theories tend to idealize the above two models. 1.5.2 Whitmarfs Film Theory^ The earliest of three theories to be discussed the Whitman's film theory idealizes the former model by postulating a laminar film to exist at an interface, with a thickness of, say, £ . Within the film, laminar conditions prevail while outside the film^the fluid discretely changes to a fully developed turbulence. All resistance to diffusion is accounted for by the laminar film and this will have a negligible capacity. For physical absorption the concentration gradient of an absorbing component A will have a linear profile so that d A fri' al} 1.1 dx s Hence, the specific physical absorption rate of A is given by o N 1.2 A V V in the film theory. 24 1.5.3. Penetration Theories The penetration theory is based on an idealized surface renewal hydrodynamic model. Liquid elements at the interface, during their existence at the interface, may be considered to behave as a stagnant layer of infinite depth. Concentration of a solute gas in an element may be assumed to be everywhere equal to the bulk liquid concentration when the element is brought to the surface. Absorption of a gaseous component A is then governed by an unsteady- state rate given by the dif ferential equation derived from Fick's Law: d2 A dA 1.3 dt with the boundary conditions t = 0 x = 0 A = A. l x —♦ oo A is bounded 1.4 It is evident that the amount of solute absorbed by any element is dependent on the life of the element, and the net absorption of all elements on the surface will therefore depend on the age T 25 distribution of the surface elements. In this respect, Higbie proposed that the surface elements have a systematic renewal 25 so that each has a life span of t* at the surface. Integration of equation 1.3 w ith the boundary conditions gave the instantaneous rate of absorption of A as N _2} ,dA, (A.-Al) 1.5 A W . x=0 w hence the overall rate for a surface element of life t* is 2 (VAi> 1.6 Danckwerts rejected the concept of a systematic surface renewal, but instead proposed a penetration theory based on random surface renewal. In essence, the age distribution of surface elements is described by the distribution function ^ ( t ) dtr the fraction of surface elem ents with an age between t and (t + dt), which satisfies the integral o Further, in Danckwerts' concept, the rate of renewal 26 of a surface element of any age is proportional to the nurrber of elements of that age, hence 1.8 where g is a proportionality constant. Integration of equation 1.8 yields = g e ('a4 > 1.9 With both assumptions, the overall rate of absorption is given by (A. - AL) ( t ) dt 1.10 or W 1.11 The constant g thus has the significance of surface renewal frequency, hence 1/g will indicate the average life of surface elements. 27 Comparison of the three theories will indicate that the rates of absorption derived from each contain a common term for driving force, (A. - A ). If the remainder of the terms 1 J-i I in each rate is equated to the physical mass transfer coefficient then T> & - Whitman's Theory z>, Higbie's Theory 7T t 25 Danckwerts* Theory The film theory therefore predicts that while the penetration theories predict Experimental evidence indicates the penetration theories are the mathematically more correct model. However, a more 28 rigorous analysis will reveal that both models are only extremes of actual hydrodynamic conditions existing in any 27 system. Toor and Marchello proposed a film-penetration model which requires k° to be proportional to raised to a power intermediate between 0.5 to 1.0. For long time intervals the film model is approximated while for short time exposures, the penetration theories become mathematically valid. In a systematic analysis of the film and penetration theories applied to several cases of gas-liquid absorption with 2 8 chemical absorption, Danckwerts and Kennedy conclude that the three theories lead essentially to similar derivations, and all are equally valid as mathematical descriptions. When the difficulty in assessing the life time of the surface elements is taken into consideration, the film theory offers the great advantage of being the simplest mathematically. Although it lacks rigor, it has been found to be adequate for engineering calculations, as evidenced by its wide adoption in practice. 1.6 Mass Transfer and Chemical Reaction 1,6.1 Qualitative Analysis In an absorption of a gaseous solute followed by chemical reaction, the total liquid phase may be considered the reaction 29 Interface Diffusion Bulk Slow chemical reaction; Region Region little reaction of A in diffusion region. al At ~ A.. L 1 (a) Moderately fast chemical reaction; A partly reacted in diffusion region. (b) Fast chemical reaction; A completely reacted in diffusion region. (c) Figure 1.1. Qualitative Effect of Chemical Reaction on the Profile of A in a Heterogeneous Pseudo First Order Reaction. 30 phase. Further the reaction phase may be divided into the boundary region (or diffusion region) within which the process of the gas and liquid diffusion with a simultaneous chemical reaction occurs, and the bulk (liquid) region within which the contents are homogeneous. Any reaction in the bulk region will occur as a homogeneous reaction. The absorption of a gaseous solute simultaneously with a chemical reaction reduces the active concentration of the solute, hence the absorption rate by the liquid body is increased. In terms of the film theory, the solute A is reacted as it diffuses along the path of the film. When reaction is fast, conversion of A is very rapid and its profile in the diffusion region therefore drops much more rapidly than the profile for physical absorption alone. In the extreme case conversion of A is complete within the diffusion region, with A falling to zero concentration within the region. (Figure 1.1 c). On the contrary, when reaction is slow, the depletion of A along its diffusion path is not appreciable, and approximately equals the physical rate profile. Absorption rate may be approximated by the physical rate. (Figure 1.1a) In the case of an infinitely rapid reaction between the gaseous solute and the liquid, the reactants cannot co-exist . Reaction takes place on a plane situated in the diffusion region. 31 When reaction is rapid, an intermediate product in a consecutive reaction may not be able to leave the diffusion region rapidly enough. A high conversion of the intermediate thereby occurs with a resultant decrease in the selectivity of the intermediate. Mathematical description of this is treated in Chapter Four. Two quantitative measures are available to describe the effect of chemical reaction on absorption. If the basis of 29 treatment is the chemical reaction rate, the utility factor is defined as the ratio of the heterogeneous reaction rate to the reaction rate when the liquid phase is in equilibrium with the interface. Since the general effect of diffusion is to retard the chemical reaction, the utility factor is always less than unity. Based on the absorption rate, the chemical acceleration 22 factor is defined as the chemical absorption rate increase over the maximum physical absorption rate. Since reaction increases absorption rate, the enhancement factor is often greater than unity, particularly in fast reactions. For analytical purposes, the following regimes of absorption may be defined in extreme cases: (a) Mass transfer control - diffusional regime, occurring when: i) mass transfer is followed by instantaneous chemical reaction 32 ii) reaction rate is rapid compared to the diffusional rate. Mathematical analyses show this to apply if the interfacial area is small. (b) Mass transfer and chemical reaction both important, occurring when reaction rate and mass transfer rate are of comparable order. (c) Chemical reaction control - kinetic regime occurring when reaction rate is low. Mathematical analyses show that the regime is applicable when interfacial area is large. 1.6.2 Mathematical Analysis The phenomenon of simultaneous mass transfer with chemical reaction in a heterogeneous reaction system is expressed by the differential equation for any component i as <}2c. 3c. 9c. i J-f- = u tV + ~ar +ri U12 X In equation 1.12 the term on the left signifies the molecular transport while the three terms on the right have the significance of convection, accumulation and reaction rate respect ively. The factor, u , has the physical significance of the relative velocity of a surface element with respect to the system of 33 coordinates, and t has the significance of the time elapsed from the time when a surface element is renewed. Complete solution of equation II2 can be extremely difficult. In idealized cases, simplifications can be made however, and these allow solution of the equation for relatively simple reaction rate expressions. Idealized hydrodynamic models assumed by the film and penetration theories also assume inherently that the surface behaves as a rigid body so that u = 0. The accumulation term which governs the unsteady static conditions prevailing at a constantly renewed surface also becomes zero for the film theory. Equation 1.12 therefore simplifies to i ci & . * 1.13 i a x2 - <31 + ri for the penetration theories, and to 1.14 0> 2 X for the film theory. Equations 1.13 and 1.14 can be solved only for a simple dependency of the kinetic rate m. Rigorous 34 solutions appear possible only for first order and zero order rates, the higher order reaction rates being soluble only by approximate methods. Most of the solutions that have appeared in literature deal with a first order reaction with respect to the gaseous reactant in a gas-liquid system. These will be reviewed here. In Chapter Four, equation 1.14 is solved for a kinetic rate which is of first order with respect to the liquid reactant; a mechanism which has been shown to apply for the photochemical chlorination of benzal chloride to benzotrichloride. Consider a bimolecular heterogeneous reaction re presented schematically. A + B ------► C gas phase liquid liquid phase phase with the homogeneous kinetic rate expressed by r = kx [a][ b] The simultaneous diffusion and reaction of A and B is expressed by 35 d2A 2) ' II > TO — i A dx2 1.14a a d2B = k i A B B dx2 in the steady-state (film) theory with the boundary conditions of o X II A = A (a) X II -a A = Al (c) for A, 1.15 and, o X II = 0 (a) dx II X B = B (b) 1.16 for B. The expression of the boundary condition 1.15(b) describes actually the homogeneous liquid reaction, with the volume of the 36 bulk region as ( €: - a 5 ). Solution of equations 1.14a J-j however cannot be undertaken unless a pseudo first order reaction rate is assumed, with either A or B being assumed constanto Assuming B to be equal to B (constant) Lj throughout, the equations simplify to klABL 1.14b k. A B, B Mathematical solution of equation 1.14b is given in Appendix II. The resulting equation which describes the con centration of A with respect to the diffusion length x for 0 < x < + tanh A_ cosh -j- ■ Equation 1.17 contains two important dimensionless parameters. The first, ^ , is termed the diffusion parameter and 37 is defined as S ki bl k.BT A. 1 L i $ is the ratio of the maximum conversion of A in the diffusion region per unit interfacial area (k B A. &) to the -L JLi 1 maximum diffusional transport of A into the same. The second dimensionless parameter 6/acT is the J-i ratio of the total volume of the liquid reaction phase per unit volume of the heterogeneous reaction system (which is equal to the fractional liquid hold up) to the volume of the diffusion region. Differentiation of equation 1.17 yields $ / . , x j ’+ tanh ^ A cosh dx i T—I sinh^-9 ‘ Tc ------\ o o o L/ac5-l/cj>tanh (j) + l OMX Hence the rate of diffusion of A into the reaction phase, N is 38 given by ^ L/ac5 -1) $ + tanh (f> N A x=0 (^L/a 1.6.3 C ontrolling Parameters in Absorption Rates The effect of mass transfer on the overall absorption rate, and hence conversion rate, can be dealt with mathematically. Pertinent equations are equation 1.17 with x= 3 , and equation 1.19. .17a .19 The controlling parameters on the absorption rate are the diffusion parameter (p and the parameter ^L/a(5 * Three cases can be distinguished. 39 F irst P seudo F ast a in A of P rofile Reaction Order Concentration 1 .2 . Figure 40 i) When the diffusion parameter (p is greater than two, a rapid reaction rate relative to the diffusion rate is indicated. For (p > 2.0, the following approximations are valid. cosh (a) The concentration profile of A in the diffusion region becomes an independent function of , and A aS approximates to zero in equation 1.17a, or in other words, A is reacted completely in the diffusion region, a situation illustrated in Figure 1.2. (b) The absorption rate of A is obtained by equating tanh<£ to 1.0 in equation 1.19, from which na The absorption rate of A is a diffusion controlled process Conversion of A (and B) is limited by diffusion, and is dependent on the specific interfacial area since a A. l 41 A chemical mass transfer coefficient may in fact be defined such that k a A La i with A ii) When the diffusion parameter is less than 0.5, a slow reaction rate relative to the diffusion rate is indicated. For cosh sinh (p k <*> tanh (a) The concentration profile of A in the diffusion region is obtained from equation 1.17 with the values of cosh ^ sinh ^ and tanh^ above. From equation 1.17a, the bulk chlorine concentration A is expressed as i-j (^L/a<£ - l) 4 + ft (€L/aS - l)(f>2 + 1 42 Area Pseudo Slow a UJ in Interfacial I co A r—H High of A < Profile ro Reaction; O hJ Order V First Concentration CO - -r-H c u o fO -I-H l+-j +-* o CD +-> CO 1 .3 a . a CD -rH i-i JO £ o Cn Figure 43 O rder F irst P seudo Slow a in Area A of Interfacial Profile Low Reaction; Concentration 1 .3 b . Figure 44 or = 1.20 Ai (%£ -l)f>2 + 1 In contrast to the case of (p > 2.0, A is a function £ i_j of the parameter L/a£ . Two extreme cases arise. (i) When the specific interfacial area is high, so that £Va —— =1.0 or A = A A. L i 1 A low conversion of A in the diffusion region is indicated, while the reaction phase concentration of A is in equilibrium with that concentration at the interface, a situation dep icted in Figure 1.3a. (2) However, as the parameter ^*L/a A limiting case is obtained when 1. The denominator on the right hand side in equation 1.20 becomes very large. A then assumes a negligible J-i value, indicating a complete conversion of A in the diffusion region. (b) The absorption rate of A is given by equation 1.19 with tanh = <£> . Thus aS * 1.21 ki bl®a & - 'k + 1 ^L_ which shows a dependency on the parameter a S Two extreme cases arise. (1) When the specific interfacial area is high so that c. L/a k.BT A. » L i or the overall rate BLt Ai- L 46 which is the homogeneous kinetic rate when the liquid reaction phase is in equilibrium with the interface. (2) As the specific interfacial area is decreased, resulting in the increase of L/aS , the de nominator on the right hand side of equation 1.21 becomes progressively greater than unity, with a subsequent decrease of the specific absorption rate N . In the limit, the denominator may be A equated to so that a 8 t 1 A. i or and This constitutes a mathematically elegant derivation of a result assumed by many authors in published literature. In physical interpretation, when 47 reaction rate is low relative to diffusion rate ( < 0.5) and the specific interfacial area is low (^L/a8 1), the overall absorption rate of the gas is diffusion controlled, and is expressed by the equation The conversion of A (and B) occurs in the diffusion region, and in the bulk liquid region, A = 0, as J-j shown in Figure 1.3b. As the specific interfacial area is increased, which can be achieved in practice by increased gas load or agitations the absorption rate increases. In the limit, the absorption rate is controlled by the kinetic rate and is given by k, Br A. 6t 1 L i L It can be seen therefore that the controlling absorption regime in the slow chemical reaction is governed by the relative maximum diffusion rate and the maximum kinetic rate. When the maximum diffusion rate is greater than the 48 maximum kinetic rate, a A. > k B A. 6 1 1 L L the absorption rate is kinetic reaction controlled . Conversely, when the maximum diffusion rate is less than the maximum kinetic rate, a A. <1 k B A.6 l 1 L l L the absorption rate is diffusion controlled. iii) When the diffusion parameter assumes a value intermediate between the extreme values above o.5 < (f) < 2.0 simplified and exact absorption rate equations cannot be derived. Chemical reaction between A and B occurs neither completely in the diffusion region or bulk liquid region, and a rather diffuse reaction zone may be visualized to exist in which the processes of diffusion and reaction occur. No regime can be defined since the diffusion and re action are both important. In terface 49 Figure 1 .4 . T ypical Concentration P rofile of A and Infinitely Fast Chemical Reaction. 50 1.6.4 Infinitely Fast Reactions The basic differential equations that describe the simultaneous processes of mass transfer and chemical reaction cannot be solved by simple mathematical manipulations for the second order reactions without the simplifying assumptions of a pseudo first order reaction. In the case of an infinitely rapid reaction, however, the concentration profiles of A and B assume a simplified form and absorption rates can be derived for a second order reaction of such a nature. Figure 1.4 illustrates a general case for rapid second order reactions. Because of the extreme rapidity of reaction, A and B cannot co-exist at any space within the reaction region. Reaction in fact occurs at a plane that is situated intermediate between the extremes of the diffusion region, reactants A and B being fed to the reaction plane by the process of diffusion. The exact position of the plane is dependent on various physico chemical parameters. 31 By simple mass balance, Hatta first derived the absorption rate of the gaseous component A followed by the infinitely rapid second-order reaction A + b B + products 51 as <2> A A 1.21 <5 where = distance of reaction plane from the interface, (shown in Figure 1.4) 22 Kramers derived the conditions for the validity of the absorption rate given by equation 1.21 as b A. 1.6.5 Chemical Acceleration Factor The chemical acceleration factor F is the quantitative measure of the increase in absorption of a gaseous component by a liquid owing to a chemical reaction. If the fractional liquid hold-up is assumed to be unity, the absorption rate of a gaseous solute A followed by a pseudo first order reaction is given by tanh NA = AJkl hSA 52 whereas the physical absorption rate is NA = k°LAVAL ) or for a maximum physical absorption rate with A = 0, JLj A. 1 The chemical acceleration factor is then defined as the ratio of the chemical absorption rate to the maximum physical absorption rate of A, hence F = (Jkl hSA tanh t ] / kLA for a pseudo first order reaction in A. (a) When reaction is rapid with $ > 2.0, the chemical acceleration factor becomes F = (b) For an infinitely fast second order reaction 53 Hence Van Krevelen solved by an approximate method the differential equation 1.14 for a second order reaction and from the solution showed the variation of the chemical acceleration factor with the parameters r and 1.6.6 Phase Utilization Factor The phase utilization factor CT may be defined as the ratio of the overall diffusion rate of A into the liquid reaction phase to the maximum conversion rate of A in the same phase. From equation 1.19, the absorption rate of A is <£+ tanh (f> A. 1.19 l - l^tanh^> + 1 54 while the maximum conversion rate of A occurs when the reaction phase is in equilibrium with the interface, that is A Conversion rate is therefore k1! BLT A.^Ti L Hence, the phase utilization factor is by definition (*L - l) + tanh Three cases of the factor can be distinguished depending on the diffusion parameter <|> . i) For the slow chemical reaction with cj>< 0.5, tanh -1 - ijf2 + i] 1.24 ((■ 55 The phase utilization factor will approach its optimum value of 1.0 for any value of when —is minimum. p ao Hence, to achieve a maximum utilization of the liquid reaction phase, the specific interfacial area should be increased. ii) For the fast chemical reaction with (f> ^ 2.0,tanh __1_ acT f eL It is evident that has the maximum value of 1.0 while The phase utilization factor may be used as a qualitative measure of the capacity of a reactor. An efficient utilization of the reactor liquid phase is indicated by a high value of the phase utilization factor. Generally, a high specific interfacial area leads to an increased phase utilization factor. 57 CHAPTER TWO 2.1 Gas-liquid Contact Systems Gas-liquid contact has far and wide applications in several aspects of chemical engineering, whether it is for gas-washing, gas recovery or the reaction of a gas with liquid in preparative chemistry. Reaction systems are designed with characteristics according to the needs of the system and many typical reactors have emerged. Thus packed towers and plate columns are ideally suited for gas absorption by virtue of their extensive interfacial areas whereas the stirred reactor would be preferred for reactions, especially those that involve great heat changes. Packed towers may not be suitable because of possible extreme local temperature variations. From time to time, reactors of specific description have appeared in literature. Although such reactors are not aimed at industrial applications, their value lie in the known hydrodynamic conditions prevailing and specific interfacial area which lead to a possible evaluation of mass transfer coefficients. Among these are included the disc column, laminar jet absorber and wetted wall columns. Packed columns are however also useful reactors for absorption studies because of the known interfacial areas from geometric considerations. 58 The agitated gas-liquid tank contactor has been the subject of research, often with the object of understanding the characteristics pertinent to design and scale up. Of late, the unagitated gas-bubble column has also come under extensive study with its increasing adoption in industry. However, the studies of agitated contactors appear to have been confined to determination of interfacial areas# power requirements, mass transfer coefficients in relation to stirrer speeds and geometry as well as the hydrodynamic variations with vessel size and geometry. Bubble column studies on the other hand centre on the mechanism of bubble formation and the effects of operating factors on the holdup, interfacial area, and gas-liquid mixing. Relatively little literature has been published on the application of these reactors to important preparative processes, although no doubt a great amount of information about this lies buried in proprietary process files. In the investigation of agitated reactors and bubble contactors, the capacity of the reactor system which will determine its efficacy is governed by two main factors - the hydrodynamic conditions and the specific interfacial area in the system. Hydrodynamic conditions are again affected by the operating characteristics of the system, including gas and liquid flow rates, reactor volume and geometry, as well as the type and position of stirrers used and speed of stirring. Interfacial area in the 59 reactor is in fact affected by the same factors. The un certainty about the relative importance of each of these characteristics makes the optimum design and scale up of gas-liquid contactors very difficult. Several techniques relying on physical or chemical methods have been reported which enabled the interfacial area in a gas-liquid contactor to be estimated. Physical measure ment techniques employ an instantaneous means of estimation, and are often localized. These include the techniques of light 33 34 35 transmission reported by Vermeulen , and Calderbank ' , 36 3 7—4 0 photography of bubbles and stroboscopic techniques. 41 Westerterp et al proposed a chemical means of measurement of the interfacial area from a knowledge of mass transfer and kinetic data. The same technique was extended by Dillon and Harris to the bubble column reactor. A chemical means of estimation yields an overall interfacial area but has to make the assumption that the area is identical in both chemical and physical gas absorption. Generally, in the studies of the gas liquid contact systems, relatively simple systems of well known kinetics have been employed. They include the air/oxygen-sodium sulphite 43 44 45 46 systems, # air-water systems ' and carbon dioxide- 47 water systems. 60 2.1.1 Characteristics of the Gas Bubble Column The gas bubble column, also called the sparged gas contactor or bubble column is assuming greater importance and application in gas-liquid contact operations. It offers the great advantage of simplicity in design and operation. Nevertheless it has a drawback in having a low specific inter facial area. Design is in fact very simple; to overdesign is not expensive, hence there is no incentive to proper sizing of components and design. Nevertheless, many studies have been undertaken of the column with the objective of the maximum utility of the contactor, especially in the application to industrial fermentation reactions. Some published literature on the bubble column is summarised in Table 2.1; characteristics of the column contactor are described below. 61 Table 2.1 Summary of Some Published Literature on Bubble Columns Author/ s Reference Gas U sed Liquid Used Remarks Abdel-Aal, H.K., 36 air water, glycerine Interfacial area correlated to dimensionless groups, gas et al hold-up increased linearly as gas velocity Benzing, R.J0, 37 air, carbon dioxide water, water-ethanol, Dimensional analysis of bubble mechanism et al hydrogen aqueous sugar Hayes, W0B. 38 air glycerine, isopropanel Bubble formation correlated to parameters by Newtons Laws et al of Motion Van Krevelen, D.W., 39 air water, glycerol Bubble formation, bubbles size, interfacial area, bubble Hoftyzer, P.J. ascent velocity investigated Dillon, GoB. 42 carbon dioxide water, aqueous Interfacial area and liquid phase mass transfer coefficient Harris, J.J. sodium hydroxide resolved from kinetic and diffusion data Zieminsky, S.T., 46 air water with additives Effect of additives on bubble size, mass transfer, hold up et al and interfacial area studied Shulman, H.L. 47 carbon dioxide water Extensive investigation of operation variables on mass Molstad, M.C. hydrogen transfer Liebson, I., 52 air water, aqueous Identified three regimes of bubble formation, bubble size et al butanol correlated to Reynolds Number Houghton, G. 55, 56 nitrogen, oxygen, water, various organic Mass transfer, bubble behaviour and hold up investigated et al carbon-dioxide, carbon liquids d ioxid e/hyd rogen mixture Towell, G.D., 57 air water Bubble size, hold up, mass transfer, interfacial area et al investigated Yoshida, F., 69 air, oxygen aqueous sodium Mass transfer coefficient correlated to various parameters Akita, K. sulphite with cupric ion catalyst Braulick, W.J. 70 air aqueous sodium Mass transfer coefficient correlated to various parameters sulphite 62 (a) Gas Dispersion Gas fed into a liquid column through a sparger will not flow as a continuous stream. Instead, the gas is dispersed by the effects of the sparger and liquid turbulence into an array of bubbles. Much work has been undertaken on bubble formation and mechanisms. Two excellent reviews are given by Jackson48'49 and Calderbank5.0 Since external agitation is absent, dispersion is affected by the forces of the gas velocity and the turbulent field created by the gas dispersion. Although many conflicting effects from liquid viscosity and other physical properties were reported, gas dispersion and hydrodynamic history are predominantly affected by gas flow rates and to a lesser extent by the gas inlet arrangements. Based on an orifice Reynolds Number,four regimes of bubble formation and dispersion can be distinguished. At a low gas rate and with an orifice Reynolds Number 51 54 of less than 200 ' a low turbulence field exists in the system. This regime is termed the laminar bubble formation, separate bubble formation or quiescent regime. Without the disturbing forces of a dynamic turbulent field, bubble formation at the inlet is affected only by static forces. A gas bubble forming at an orifice is acted on by a surface tension force at the orifice which tends to retain the bubble,while a counteracting buoyancy 63 force, increasing as bubble diameter increases, tends to dis lodge the bubble. Assuming a spherical configuration of the bubble, and a complete wetting of the orifice, the bubble diameter at the instant when it is dislodged is obtained by equating the two forces, giving 1/3 V.D Du = 1.82 i 2.1 b (Pl7&) Deviation from the confetant of 1.82 and the exponent 39 of 1/3 was indicated by Van Krevelen in the correlation of experimental work by previous authors. The general reason for the deviations is the a spherical nature of the bubbles and other effects due to liquid properties, and column diameters. Bubble formation within this regime is characterised by a constant bubble diameter, governed by the diameter of the orifice and is independent of gas flow rate. Frequency of bubble formation increases as gas flow rate is increased. A dislodged bubble ascends in a somewhat spiral path, there being no recirculation or coalescence of bubbles; evidence of a low turbulence field in the liquid. Within this regime, a fine orifice or porous plate gas inlet produces a finer bubble size with an increased interfacial area, a fact which may be exploited with advantage. Too fine a bubble size, however, may result in the decrease of internal circulation in the bubbles. 64 leading to a decreased mass transfer rate. As gas rate is increased, a critical rate is achieved at the onset of which, the bubbles do not rise separately, but begin to interact mutually as bubbles form at a high frequency. Bubble size and frequency will increase with the gas rate, while bubble configuration varies from a smooth ellipsoid to an increasingly elongated shape as gas rate rises. Vertical co alescence and bubble break-up will occur with greater frequency; the bubbles rising in a spiral path. An orifice Reynolds Number of 1000 to ZlOO^1 prevails in this regime. The turbulent regime commences with an orifice Reynolds Number in excess of 2100^ Transition is not marked as the phenomenon of bubble break-up and recoalescence which predominates in this regime also occurs, although to a lesser extent at lower Reynolds Numbers. An important factor in the turbulent regime appears to be the preponderance of spherical cap and torroidal bubbles formed at the orifice. Large bubbles have a high ascent velocity which creates a highly turbulent field in their wake. Subsequent bubbles are drawn into this field and are acted on by a shear force which tends to cause bubble break-up. The same field, however, serves to bring about the recoalescence of smaller bubbles. A violent and random contacting action exists, with poor bubble definition. Backmix 65 conditions may be assumed to be developed to a high extent. 52 Liebson et al characterised a further regime with a Reynolds Number in excess of 10,000. Turbulence is fully developed, the gas stream enters as a jet, and disintegrates into a multitude of coarse and fine bubbles near the orifice. 53 Rennie and Evans indicated, however, that even with an orifice Reynolds Number in excess of 40, 000 formation and break up of bubbles still occur; the bubbles assume a torroidal or irregular configuration. $3>) Bubble Size Distribution Bubble size distribution in a gas dispersion process will depend primarily on the disperser design but also on the secondary effects of the turbulent liquid phase, with the latter effects predominating with increasing turbulence. In the laminar regime, a reasonably uniform distribution is observed. Distribution in the turbulent regime, however, broadens into a multiplicity of bubble dimensions and configurations. Bubble size and con figuration determines the interfacial area in a contactor while the specific mass transfer rate is also influenced to a certain extent. Large bubbles which oscillate in configuration have a good gas circulation which enhances mass transfer. Small bubbles on the other hand are relatively quiescent internally, with poor mass transfer as a consequence. 66 54 The Sauter Mean diameter defined as the diameter of that spherical bubble whose surface area to volume ratio corresponds to that of the whole bubble population is a term often used to describe bubble size distribution. In the laminar 55 56 regime Houghton et al 7 observed a preponderance of bubble size in the range 1/8 - 1/4 inchr for several systems 57 and gas sparger designs. Towell obtained a mean Sauter diameter of 0.20 - 0.25 inch for a two-fluid sparger in a 16-inch diameter column. 52 Liebson et al using a photographic technique obtained an expression of D =0.71 (Re) s for bubble distribution in a highly developed turbulent regime (Re = 2100 - 10,000), observing a sharp fall in bubble size over the regime. The equation was confirmed approximately by Rennie and Evans. (c) Dynamic Gas Hold-up The volume of a liquid phase in a column increases with the dispersion of the gas in the liquid, a characteristic which 67 may be important in the reactor geometry. Interfacial area and gas residence time are also determinable from the gas hold-up. If is the clear liquid height without gas flow and the expanded liquid height, then the fractional gas hold-up is given by V The mean residence time of a gas in the column may then be obtained from the intergral However, where hold-up may be assumed to be invariant over the height of the column, a condition that is obeyed to a great extent in the laminar regime, t G ( Vf>/vG 68 Empirical relationships having a theoretical basis have been developed for estimation of the dynamic gas hold-up. From experiments, indications are that the fractional gas hold up increases as a function of the superficial gas velocity up to a critical gas velocity beyond which the gas hold-up approaches a constant value . Sparger types were not u t , rr . , . , 39,47,56,57 observed to affect hold-up. * In the quiescent regime, a semi-theoretical approach yields an equation relating the gas hold-up to the gas superficial velocity and a free rise bubble velocity, with the incorporation of a constant to take into account the manner in which the wall affects the bubble rise velocity. Wall effects tend to increase gas hold-up so that a small diameter column gives a greater gas 57 hold-up over a large diameter column. A similar approach towards gas hold-up in the turbulent regime is not easy owing to 5 8 the incomplete knowledge of bubble dispersion. Hughmark suggests the use of the term (62.4/ p + 72 /y ) instead of in correlations of gas hold-up against superficial velocity to account for liquid physical properties. The validity of the modification is yet to be verified. (d) Gas and Liquid Mixing The gas and liquid mixing and flow pattern in a reactor need to be established for conversion in a chemical reaction and 69 performance to be evaluated. At low gas rates within the quiescent regime, the gas stream progressively ascends through out the height of the column, albeit a few bubbles will swirl and recirculate. Plug flow may thus be attributed to the gas. At increased gas velocities, the secondary turbulence in the liquid creates downcurrents which can entrain significant amounts of gas. Partial backmixing of the gas in the turbulent regime is therefore observed. In contrast, liquid backmixing is established even at low gas rates, increasing with increasing gas rates. Axial mixing is however less predominant for small 47 than for large diameter columns. A dispersion model has also been used to characterise the liquid mixing in column contactors 59 00 01 by Tadaki and Maeda , Ichikawa and Argo and Cova 47 Shulman and Molstad however assumed plug flow for gas and liquid streams in a column contactor to deduce mass transfer data. 2.1.2 Mass Transfer Characteristics of the Gas Bubble Column The rate of absorption of a significant gaseous component (or the desorption of the same in a desorption process) is the most important single factor in the assessment of the efficacy of a contactor. Mass transfer rate takes into account the variables which characterise the dispersion and absorption process and hence 70 is often the overall index used in evaluating the absorption process. Correlations of the mass transfer rate have been made in terms of the inlet and outlet composition of the gas 55 56 62 stream, 7 ' overall liquid phase height of a transfer unit 47 (H.T.U.) and the liquid phase volumetric mass transfer co- 43 5 7 efficient. ' The last means of correlation appear to have the wider adoption although the three means are inter-related. In terms of a mass transfer coefficient, the overall rate of absorption is given by R = kLa W Overall rate of mass transfer is therefore a function of three variables; the mass transfer coefficient, interfacial area and a concentration driving force. The first two variables are however not easily resolved. Empirical correlations are therefore often made in terms of a volumetric mass transfer coefficient, k° a. In as much as the hydrodynamics are affected by the geometry of the vessel, liquid properties and other operational variables, the same variables similarly govern the mass transfer rate. Semi-empirical correlations have been developed from work on solid-liquid mass transfer systems and liquid drop/air stream evaporations which may be applied to a system involving gas dispersed in a liquid, although application is limited to the 71 laminar region. Hydrodynamic conditions are accounted for by the Reynolds Number while the Schmidt Number correlates the liquid properties. In the laminar regime, the process of gas-liquid mass transfer is amenable to a semi-theoretical ( analysis. A general equation is derived from Boussinesq's work as 1/3 i (Re)2 C1 + C2(S0)L There is evidence to suggest that is a function of the Grashof Number, a dimensionless group that describes the convective conditions existing in a bubble. For most cases however forced convection overshadows natural convection within a bubble so that C is reported to have a value of 2.0. 64 1 Thus Rowe et al obtains over a range of Reynolds Number of 30 - 2000 the equations 1 I /Q Air (Sh) = 2.0 + 0.69 (Re)2 (Sc) ' i ] /r> Water (Sh) = 2.0+0.79 (Re)2 (Sc) x for an air-water system. Other forms of correlation have also 65,66 appeared. Thus for an absorption with the gas-liquid interface 72 moving rapidly with respect to the main liquid stream, Ward 6 6 et al obtained Sh = 1.08 (Re)1 ^(Sc) for Re.Sc < 1000 and for the completely mobile bubble 1. _i Sh = 0.61 (Re)2 (Sc)2 for Re.Sc > 1000 Within the quiescent regime, mass transfer is generally 63 67 68 correlated by the relatively simple expression ' 7 Sh = 2.0 The mass transfer process at fully developed liquid turbulence does not yield to systematic theoretical analysis; correlations therefore have to be made only with experimental findings. With increasing turbulence, the gas rate begins to predominate over other operational variables in its influence on overall mass transfer rate. Correlations are generally made using the volumetric mass transfer coefficient, k° a, owing to difficulty in the separate assessment of the two terms, and to their dependency on the gas flow rate. When the liquid film 73 mass transfer coefficient was able to be ascertained ex perimentally, a linear dependency of the coefficient on gas rate was noted by several investigators. ^ Graphical correlations moreover showed k° a to increase as a function of Towell et al employed a photographic technique to obtain estimates of the interfacial area, and thus evaluate k° Jj and the interfacial area 'a' individually in the desorption of carbon dioxide from water. They concluded that the overall increase of k° a with gas rate was attributed in no small measure to the .Li increases in the interfacial area. 47 Shulman and Molstad from extensive absorption and desorption studies showed that the liquid phase height of a transfer unit (HTU) decreased as a function of the gas rate in the la minar regime. A sudden transition was observed in the change from laminar to the turbulent regime and in the latter, the (HTU) became independent of the gas rate. 43 Dillon and Harris ' investigated the absorption of carbon dioxide by sodium hydroxide and by water, and were able to evaluate the interfacial area. The volumetric mass transfer coefficient k° a was observed to increase as a function of gas Li rate but to decrease as the liquid seal height increased. The latter observation was explained by a decrease of the interfacial 74 area. An empirical relation between k° a and the variables L investigated gave 0 S4 0.58(0 . OOIVq 0.55) 4.72 (0.001VJ (3 while the liquid film mass transfer coefficient was estimated by = 0.0142 (0.001 )°*31 Zf°*22 where V and have units of on/min and cm. G respectively. Marked temperature changes can vary the hydrodynamic conditions in a system and thereby affect the mass transfer rate. 47 Shulman and Molstad observed the overall mass transfer height unit (HTU) to decrease in the laminar regime with temperature on a log-log relationship, but the trend was reversed in the turbulent regime. From a study of the absorption of carbon dioxide by 55 56 water, Houghton * observed an increase of absorption rate with increase in temperature on a log-log scale. However, gas and liquid rates did not affect the relationship. 75 2.2 The Agitated Tank Reactor In a gas bubble column, a gas stream is fed through a series of orifices, distributors, perforated or sintered plates into a column of liquid. Subdivision and dispersion of the gas phase occur as a result of the pressure energy in the gas. Agitation of the liquid and dispersion of the gas phase, on which specific interfacial area depends is therefore governed by the flow rate applicable to the column. When low gas rates, viscous liquids or slurries are encountered, the agitation and dispersion may prove inadequate. Agitation serves to increase the residence time of a bubble in the system, a factor which may be of significance in chemical reactions. Pockets of dead space, which lowers the capacity of a reactor, may also be reduced significantly by agitation. When a larger specific area and agitation is desired independently of the gas flow rate, an external mechanical agitation is applied, and in its most widely adopted form as the mechanically rotated impeller. The resultant contactor is usually termed an agitated tank or stirred tank reactor. Investigations in such a reactor appear to have polarized into two well defined fields. On one hand, workers have looked into the mechanisms of bubble break-up, mass transfer, gas hold-up and interfacial areas, effects of impeller design and geometry, power requirements etc. Relatively simple and well studied reactions such as the 76 cupric ion-catalysed absorption of oxygen by sodium sulphite, carbon dioxide absorption in sodium hydroxide, and the like have been utilized. On the other hand, the stirred tank reactor when operated with continuous fluid flow approaches in practice the idealized backmix reactor or continuous stirred tank reactor (CSTR). This reactor offers a great advantage in kinetic studies in that kinetic expressions can be obtained in a simplified form in terms of the concentrations and flow rates of fluids with the attainment of a time and space independent steady-state with respect to species concentration. In the study of complex reactions particularly, the simplifications lead to better understanding of the kinetics, a point outlined by 71 72 73 Denbigh ' and Stead et al . Heterogeneous gas-liquid kinetic studies in such reactors, however, do not keep pace with the homogeneous studies already developed or with the mathematics of heterogeneous kinetics. Of the few heterogeneous studies published, one disappointing feature has been the reluctance in the application of mathematical theory. Kinetic data have been presented without a kinetic controlled regime being specifically established. 2.2.1 Characteristics of the Agitated Tank A gas fed towards an impeller experiences two regions of shear forces which tend to break the stream into finer bubbles: Expected page number is not in original print copy 78 at the centre of the impeller bubbles are rapidly accelerated to the liquid velocity, and at the periphery the bubbles are equally rapidly decelerated by a highly turbulent environment. For the same power input, a smaller impeller develops a higher peripheral turbulence which results in a higher bubble breakup. However, there is a minimum limiting size of impeller, below which the increased peripheral velocity only serves to generate increasing turbulence without materially increasing bubble break-up. From a theoretical consideration of the dynamic and 7 static forces acting on a globule in a mobile fluid phase, Hinze derived three groups which govern the stability or break-up of the globule; the groups being the Weber Number, the Reynolds Number and the Viscosity Group. Bubble break-up occurs when the Weber Number exceeds a critical value, and from this con sideration, neglecting the occurrence of bubble coalescence, 74 Hinze was able to establish the maximum bubble diameter, which can be stable without break-up. The assumption of non coalescence does not appear in practice to be a serious source of error. On the other hand, when coalescence is taken into 75 consideration, Shinna and Church derived the minimum bubble diameter which will not coalesce as a consequence of the tur bulence field. Actual measurement of coalescence frequency in a stirred tank is highly complicated; an investigation by 79 Madden and Damerell indicated the bubble coalescence frequency to vary as the 2.4th power of the impeller speed and as the square root of the dispersed phase volume. 2.2.2 Mass Transfer and Interfacial Area in Agitated Tanks As in any gas-liquid reactor, the ultimate factor which usually determines the efficacy of the reactor is the mass transfer rate achieved under the operating conditions in the reactor. Mass transfer rate will depend on the liquid film mass transfer co efficient k° and on the specific interfacial area a. A great deal of effort had been devoted to mass transfer studies in a stirred gas-liquid contactor; correlations having been made between the volumetric mass transfer coefficient k° a when k° L o and a could not be separately evaluated (or between k and .Li a in cases when they could be determined) and the gas load or gas rate Vq , the speed of impeller n and the energy con sumption of the impeller P/ v* A summary of the work and correlations is made by 77 Westerte-p et al. General conclusions from this work show that the volumetric mass transfer coefficient k°a is influenced to a Li greater extent than a, indicating an affect of turbulence on the liquid phase mass transfer coefficient k° The coefficient k°a J_i varied as the gas load raised to an exponent of 0 to 1.0, as the impeller speed raised to an exponent of 1.26 to 3.00 and as the 80 impeller energy consumption raised to an exponent of 0.17 to 1.00. Many other factors also influence the mass transfer rate and interfacial area. Some of these are discussed below: (a) Overall Tank Construction Most investigators have utilized a tank with a liquid height approximating the tank diameter, a relationship also widely used in practice. Although the liquid height may be increased beyond this without deterioration in performance, 7 8 Westerterp and Kramers do not advise a liquid height greater than two tank diameters. A quiescent upper zone exists in such a tank in which bubble coalescence occurs with a decrease in the overall specific area. If larger ratios must be used in tank construction, multiple stirrers spaced vertically will give improved 79 performance over a single impeller. Gas inlet design does not appear to affect the overall absorption efficiency if the gas is fed into the eye of the impeller. Bubble formation and break-up depends so markedly on the effects of the impeller that any effect of the gas inlet is usually masked. Baffles are incorporated into contactors to prevent the formation of a vortex. They also increase liquid mixing. While the presence of baffles increases power requirements in the generation of turbulence it also increases the incidence of bubble 81 coalescent. Calderbank suggested that the vortexing , if developed so as to touch the impeller caused a surface aeration that represented a more efficient means of impeller power utilization than a sparger. However, it has been pointed 81 out by Blakebrough et al that the impeller speed required for surface aeration is high, particularly in viscous liquids. Partial elimination of baffles nonetheless does aid in the improvement of the contactor. (b) Stirrer Requirements A variety of impellers are available for industrial application. Little work has, however, been undertaken towards elucidating the effects of blade design and geometry on the surface area produced. The choice of a suitable impeller is quite often arbitrary. Insufficient data are available to estimate the effect of the number of blades on the specific area generated, although blade shape does have an influence in this respect. Power requirements of a stirrer are generally correlated 82. by the power number. For a single phase liquid system Rushton et al showed that for a baffled arrangement, the power number was a function of the Reynolds Number, being constant for Reyndlds Number in excess of 10,000. In unbaffled systems, the power number was lower and involved the Froude Number also. 82 Power consumption of an impeller decreases sharply as gas load increases up to a point termed the flooding point. Beyond the flooding point, power consumption decreases but 41 less markedly. Westerterp et al concluded from their work on the oxygen-sodium sulphite and carbon dioxide-sodium hydroxide system that two regions of agitation could be designated. At an agitation speed below a minimum rate, interfacial area was not affected by the stirring, and was dependent only on the gas rate and gas inlet. Above the minimum agitation rate, however, the interfacial area became independent of the gas load but increased linearly as the agitation rate. (c) Gas Hold-up Gas hold-up determines the interfacial area which will prevail. Bubble residence time also depends on the gas hold-up. Impellers can increase the residence time of a bubble in the dispersed liquid, during which time a gaseous solute may become so depleted that the extended residence time is of no consequence. However, in chemical reactions where gas reactant is incompletely absorbed, such an increase can be of considerable significance. In general, gas hold-up increases as the gas rate is increased, the former varying as the latter raised to an exponent of less than one in most cases. That specific area does not 83 increase at the same rate as gas hold-up (generally varying as the gas rate raised to a power of about 0.4), indicates that there is an increase in bubble size as gas rate increases. This point is further supported by the increasing bubble co alescence. At high power dissipation, the hold-up also depends on the impeller power consumption varying as the 84 latter raised to an exponent of 0.4 to 0.5. (d) Gas Mixing Gas mixing in a gas-liquid reactor is of importance because of its relation to the gas hold-up and to the conversion of the gas in a reaction. Plug flow of the gas had to be assumed 80 by several past atithors to correlate results. Calderbank however assumed homogeneity of the gas to correlate his results. 84 Hanhart et al relied on a residence-time-distribution method to study gas mixing in a stirred reactor. In the region where agitation increased interfacial area, and above, provided that the liquid height- to-vessel-diameter ratio was close to unity, the reactor behaved 84 as one well-mixed reactor. The results of Hanhart et al 85 were confirmed by Gal-Or and Resnick. 84 C HAPTER TH REE 3.1 Experimental Programme and Equipment Design It was suggested that the equipment design, in so far as it would not conflict with the primary objective should allow of the possibility of a subsequent new line of research related to cyclic processes, the primary objective being the investigation with an end towards kinetics of the reaction, kinetic and mass transfer data, including evaluation of the effect of diffusion on the selectivity of the intermediate products. Mass transfer and mixing characteristics were intended to be investigated under the natural agitation inherent with the intro duction of gas bubbles. Accordingly, the reactor was designed as a gas bubble column, with a bottom inlet for dispersing chlorine. At the gas rates utilized, this proved an effective means of agitation, and maintenance of liquid homogenity. Batch experimental runs were also made using an agitated batch reactor, in which the speed of agitation provided by a magnetic stirrer unit could be varied. Data obtained with these runs were compared with the same of the bubble column reactor. Key elements of the complete equipment lay-out are described in detail, while the arrangement is illustrated in 85 ammonia cylinder E quipm ent. Experimental of Layout o G en eral r\j J 3 .1 . o ? Figure chlorine cylinder Plate I. General Lay-out of Equipment 87 Figure 3.1. A photographic reproduction is also shown in Plate I. 3.1.1 Chlorine Supply and Measurement Chlorine gas is required in a continuous stream during any one experimental investigation. A most convenient source of supply is obtained from a cylinder of compressed and partly liquified chlorine proceeded from ICIANZ of Sydney, a 150 pound cylinder proving adequate for the requirements. Control and measurement of chlorine flow was achieved by means of an industrial water chlorination unit assembled from the following items supplied by Candy Filter Company Limited (London): (i) a cylinder attachment valve for flow control from chlorine cylinder (ii) a chlorine filter based on tWG discs of asbestos cloth (iii) a flow control valve of similar description to (i) but is intended for fine control of gas rate (iv) a needle valve gas pressure regulator (v) a manometric capillary orifice device for flow rate measurement utilizing concentrated sulphuric acid (S.G. 1.84) as manometric liquid, calibrated for chlorine flow rates of 0 to 1.0 lb/hr. (vi) a calcium chloride moisture trap which serves to maintain a low water vapour pressure in the whole unit as a pre caution against corrosion. Plate II Chlorine Meter and Control Panel 89 All the parts of the assembly except (i) were mounted on a panel, with copper pipes joining each item. Material of construction for the unit itself are either monel metal, rubber or glass. Although the chlorine gas was used without further treatment, a new cylinder was subjected to a ten minute purge to remove any alien gases. Flow rate was checked by a volumetric iodide/thiosulphate titration. Calibration showed that the indicated readings on the meter, particularly in the higher ranges (because of scale expansion) did not differ by more than 5% from the measured gas rate. Initially, a wash bottle of concentrated sulphuric acid was used to further dry the chlorine before reaction. This posed a problem because of a suck back of acid. The proposition was abandoned after a freak accident arising out of its use. A Quickfit wash bottle MF 29/3/500 was placed between the chlorine control panel and the reactor gas feed to prevent organic liquid suckback. The chlorine metering and control panel is shown in Plate II. 3.1.2 Toluene Supply and Purification Toluene of laboratory reagent grade was supplied by Ajax Chemicals Pty. Ltd of Sydney in steel drums. Although the assay excludes the presence of metallic ions, a distillation of the compounds was made to eliminate absorbed water and any 90 traces of metals. An all glass still with an unpacked column (to reduce the entrainment of toluene in the distillate) was utilized. The first few drops of toluene distillate were 'milky' showing the definite presence of water, and accordingly were discarded with the first two percent of distillate. The clear distillate was kept in clean dried all glass reagent bottles and was utilized within a week of the distillation. The toluene distilled at a temperature range of 109 - 112°C and had a refractive index of n = 1.4902 at 30°C. Further, when anhydrous copper sulphate was added to the toluene, no blue colouration was observed, indicating an absence of water. 3.1.3 Reactor Design (a) Bubble Column Reactor The column reactor was built around a cylindrical Pyrex glass tube of 4.6 cm. diameter. Gas and liquid feed were designed to be introduced co-currently through the base during continuous runs, or alternately, the liquid inlet would be closed in a batch run. A B29 socket with hooks, Quickfit SHB29 formed the bottom end of the reactor while a B29 socket, Quickfit SB29 on the same vertical axis formed the top end. A Quickfit cone/screw thread adaptor ST54/28 carried the Jumo contact thermometer 91 which was accommodated by the top B29 socket. The thermo meter was therefore situated on the vertical axis of the reactor, and its depth of immersion would be adjusted with ease by loosening the screw cap of item ST54/28. A water jacket of length about 6 inches surrounded the central portion of the reactor, with an annular space of about ■§■ inch between the jacket and reactor wall. An outlet arm carried a B19 socket to fit a Quickfit condenser C5/12, through which all effluent gases passed. A BIO horizontal arm, intended for liquid effluent was closed by a BIO stopper in batch runs. A sampling port, inclined at 45° to the vertical axis was closed by a Suba: seal (number 22) rubber septum, through which a syringe needle was conveniently inserted to sample the liquid in a batch run. The fluid feed inlet to the reactor was formed from a B29 cone, Quickfit CHB29, and carried an orifice for the gas-feed. Parallel to the gas-feed was the liquid feed arm. The gas-feed orifice, formed by drawing the glass tube had a diameter of about 0.1 Cm. Terminating the feed inlets were two BIO sockets into which two L-shaped glass tubes could be fitted as inlets from the gas or liquid sources. Conical joints proved superior to spherical joints with respect to gas leakage. A drainage Teflon stop-cock completed the feed assembly. 92 B29 Thermometer Gas Exit Inlet Liquid ) Sampling °/ flow Port ~bTcT^” Ga s Feed Tube Reactor Gas Inlet Assembly Annular 4.6 crp I.D Jacket Inlet Orifice k B29 BIO ) BIO Gas Teflon Stopcock Inlet -V Socket Figure 3.2. Sketch of Bubble Column Reactor 93 Figure 3.2 shows a sketch of the reactor, a photo graphic reproduction of the same is seen in Plates III to VI. The complete reactor carried a liquid volume of 308 ml when filled to overflowing with a liquid seal height of 7\ inch (19 cm) from the gas inlet orifice to the surface of liquid. * (b) Agitated Batch Reactor The agitated reactor was fabricated largely from Quickfit parts. A cylindrical reactor body, with an internal diameter of about 7.5 cm and a height of 8 cm was constructed from a Quickfit 75 mm flange joint (FG 75)the reactor thus having a capacity in excess of 300 ml. A Quickfit multiple socket/flat flange adapter with a 75 mm flange (MAF 1/75) formed the head of the reator and was secured to the reactor body by steel clips. A Jumo contact thermometer (MS 121) which was fitted through a rubber bung was carried by the central B19 socket on the reactor head; attack by chlorine gas on the rubber bung was reduced by wrapping the bung with Teflon tape. The gas feed inlet was made from a Quickfit part MF 15/2, which has a B19 cone with a stem and a reduced shank. A glass orifice joined to the shank completed the gas feed inlet. The feed inlet was carried by an inclined B19 socket of the reactor head; the orifice of the feed inlet being about 1 cm from the reactor bottom. Of the remaining two B19 sockets on the reactor head, one carried the gas exit condenser 94 (Quickfit C5/22), while the other was closed by a Subaseal (number 22) rubber septum through which a syringe needle could be inserted during sampling. The last socket, a B14 socket was closed with a B14 stopper. An annular water jacket surrounded the reactor body. Through this, cold or hot water used in the temperature control system flowed. Agitation of the reactor was provided by a magnetic stirrer system. An MS16B Toyo Kagakusangyo magnetic stirrer unit was used in conjunction with a 1 inch Teflon coated magnetic stirrer bar. Speed control provided in the magnetic stirrer unit was however unfavourable in respect of reproducibility and range. The problem was overcome by setting the unit's speed control to its maximum, and connecting the unit to the output of a variable voltage transformer (0-280V), speed control being achieved by varying the voltage of the electricity supplied to the stirrer unit. The speed of the magnetic bar when used in con junction with this adapted system could be varied with close reproducibility over a wide range of less than 100 to more than 2500 revolutions per minute. A stroboscope was utilized to measure the rotary speed of the magnetic stirrer bar. An illu str ation of the agitated batch reactor is shown in Figure 3.3 75 mm Flange 8 cm depth -I.D. 7.5 cm Annular Jacket Figure 3.3. Sketch of Stirred Batch Reactor 96 3.1.4 Light Irradiation Although the spectral energy of the illumination source was not intended for study, the light source of blue light used by Harring and Knol^ was adopted. This consisted of two 20 watt Philips TL 18 fluorescent light tubes mounted side by side, vertically parallel to the axis of the reactor. Calculations of g Ratcliffe show that a source of 0.05 watt was sufficient for photochemical chlorination, and with the intensity of the light source used, the distance of the reactor away from the light did not materially affect the reaction rate. The Philips LT18 has an energy maximum at 3,700 A°. 3.1.5 Reaction Temperature Control The photochemical chlorination of the toluene side- chain is exothermic. Dependent on the temperature of reaction desired, thermal energy would have to be removed from the system for low reaction temperature or supplied for higher reaction temperatures. A constant reaction temperature may be maintained if there is present a constant liquid composition with at least one g volatile component. Ratcliffe conducted a photo chlorination of the toluene side-chain at a temperature of 111°C at which temperature, the latent heat of evaporation absorbed by boiling toluene maintained the temperature. Disadvantages of the method is the inability of temperature variation while homogeneous vapour phase chlorination of toluene may occur. A further possible dis- To Jumo C o n tact Thermometer Figure 240 AC 'Hot' 3.4. V valve Solenoid 1 A LU Temperature neon indicator Control 0-=- Cold Circuit Two - vale 1 Electrical Solenoid way Breaker 97 Circuit 98 advantage is the variation in boiling point as liquid composi tion in the reactor is altered by reaction conditions. A hot/cold water temperature control described below was used and found to work admirably without supervision. The basis of the system was the alternative circulation of hot or cold water through an external jacket of the reactor when the reaction liquid temperature varied from a set temperature. A thermal sensor, consisting of a Jumo mercury contact thermometer dipped into the reactor fluid. This may be adjusted to any temperature in the range of 0-100°C. Contact of a mercury thread in the thermometer and two fine hair wires is made when the thermometer reads the set temperature. The hair wires are connected electrically to the solenoid of a Jumo solenoid mercury float switch, T15 (with a capacity of 15 AMPS), and the current carried by this switch operates a single pole, two way relay circuit-breaker. Two solenoid valves to control the flow of hot and cold water respectively were connected to the breaker. A complete electrical circuit is drawn in Figure 3.4. When the reactor fluid is below a set temperature, the electrical circuit in the thermometer is broken, deactivating the solenoids in the Jumo float switch. In this arrangement, the hot water solenoid valve is activated, circulating 99 hot water through the reactor jacket. As the reactor fluid approaches its set temperature, the reverse occurs, with cold water circulating through the jacket. Hot water was kept in a two litre beaker and was both heated and circulated by a Braun thermomix. Heating by this unit alone was inadequate and a commercial 1 kilo-watt electrical immersion heater was added to boost the heating capacity. Cold water came direct from tap. Both hot and cold water flowed into the hot water reservoir after leaving the reactor. An over flow from the beaker maintained the level of water. In practice* the arrangement allowed a temperature control within + 1 C degree. A maximum of 80°C and a minimum of 45°C could be maintained quite well. 3.1.6 Effluent Gas Treatment Reaction between chlorine and toluene or any of the intermediates produces hydrogen chloride gas, while in the later stages of chlorination, chlorine gas is incompletely absorbed by the reaction system. The gases constitute a very obnoxious product that has to be neutralized before discharge. Since both gases are acidic, ammonia gas is a convenient means of continuous neutralization, producing relatively harmless ammonium chloride. Effluent gas from the reactor was drawn by a main jet 100 pump and discharged into a 5 litre respirator bottle. An air leak device was incorporated in the suction line so that pressure in the reactor was maintained constant at atmospheric pressure. Ammonia gas from a cylinder was fed into the respirator where it neutralized the gases both in the wash water and the vapour space in the bottle. The residual air in the bottle, under a slight positive pressure, was led to atmosphere. 3„2 Analytical Techniques 3.2.1. Organic Liquid Analysis Four key organic liquids, toluene, benzyl, benzal and benzo-trichlorides had to be determined qualitatively and quantitatively during the experiments. The gas-liquid chromato graph appeared to be the most elegant and rapid means of analysis. No precise description of a chromatographic column to separate the above four liquid components has been found in the literature surveyed. Several available columns were therefore tried, using mixtures of the four components prepared from pure samples. All columns showed a good resolution of the four components not except that benzal and benzo-trichloride could/be resolved com pletely. Although the defect could be overcome by the use of a longer column and with temperature programming, the retention time is increased without greatly increasing the accuracy of analysis. 101 A column of 8 ft x 1/8 in. I.D. aluminium tube packed with an 8% di-nonyl phthalate on Anachrom A.D.S. of 90 - 100 mesh gave a satisfactory resolution with respect to retention time, tailing characteristics and chromatogram symmetry under the following conditions: Helium carrier gas rate : 20 cc/min. Column temperature : 135 - 142°C Column inlet temperature : 135 - 142°C Sample size : 0.5 yu^litre The operating temperature was actually affected by the ambient room temperature, but the variation did not affect the chromatogram. The chromatograms showed peak height which decreased considerably as the boiling point of the components fell. This is shown by the following data for chromatograms of the pure organic compounds. Peak Height Peak Height Attenuation Compound of on Unit Chromatogram Attenuation Toluene 5.70 inch 25 x 142.0 Benzyl Chloride 8.55 5 x 42.7 Benzal Chloride 4.00 5 x 20.0 Benzo- trichloride 3.00 5 x 15.0 102 -a•r-H O r—H JZ O Figure 3.5 Typical Gas-Liquid Chromatogram of Toluene, Benzyl, Benzal and Benzo-tri Chlorides. 103 (a) Theory of Gas-Liquid Chromatograph Calibration. A typical chromatogram of the four components obtained from the chromatograph operated under the conditions described is shown in Figure 3.5. The chromatogram obtained however was a varying function of the age of the column. Peak heights shown above for pure samples of each component were those obtained when the chromatographic column was new. As the column aged, the peak heights increased while retention time decreased. A deterioration in the separation of benzal and benzo trichloride ensued. The peak area, which is the area under the triangular chromatogram of each component, is the quantity most often used to assess quantitatively a mixture. In Figure 3.5, if the areas under the chromatogram are respectively A^ = area under toluene chromatogram A^ = area under benzyl chloride chromatogram A = area under benzal chloride chromatogram O A^ = area under benzo-trichloride chromatogram the sum of the areas under the chromatograms is A, + A„ + A„ + A 104 The composition of the mixture, in weight faction is then approximated by x. 3.1 1 which is rigorously true if the response factor of each chromato graphed compound is identical for the particular detector used. However, the more general case is that the mass fraction is a function of the area fraction multiplied by a correction factor, as A. __i_ 3.2 xi An internal area normalization calibration may be employed by taking a standard component j as the basis. Then 3.3 F is termed the relative response factor with respect to i/j component j. 105 The use of areas in the chromatograms does not appear to be the best procedure. Determination of the peak area is time consuming without the aid of integrators, while the calcula tion of areas by the product of base and height leads to increased error because two quantities are measured. Use of the peak height overcomes the disadvantages of the peak area method but introduces its own limitations. Thus particular operating conditions must be maintained from run to run while the chroma tograph column has to be calibrated carefully over the range of compositions expected. Nevertheless, peak height was chosen as the basis of correlation chiefly because of its speed in evaluation. Returning to equation 3.3 where b = base of the triangled chromatogram h = peak height of triangled chromatogram or, in mole fractions, m. h. 1 l 3.4 m i#j h. j 106 The conversion constant for weight fraction ratio to the mole fraction ratio and the ratio of triangle bases b. / 1 are included into the relative response factor F b. i/J J Equation 3.4 formed the basis of calibration. Toluene will be taken as the reference component, j. If mi is plotted against ^i equation 3.4 shows that a m. h. J J linear relationship will ensue, with a gradient equal to the relative response factor, f/\. (b) Qualitative and Quantitative Evaluations Pure samples of toluene, benzyl, benzal and benzo- trichlorides were obtained as B.D.H.AR quality reagents. The latter three compounds however were distilled under reduced pressure and kept in dark bottles with magnesium sulphate (anhydrous) prior to use. Samples of ortho-, meta- and para- chlorotoluenes were also available should a need for identification arise. Standard mixtures of toluene, benzyl, benzal and benzo- trichlorides were prepared in various ratios designed to represent the whole spectrum of possible ratios in an actual investigation. The mixtures were eluted in the chromatograph, and from the 107 chromatograms, the heights of each component were determined. A plot of the mole fraction ratios to the peak height ratios was drawn for equation 3.4, employing toluene as the standard. A linear function passing through the origin adequately correlated the relationship between the mole fraction ratios and the peak height ratios. Figure 3.6 represents the quantitative calibration / of the chromatograph. The gradients, representing F i/j are as follows: Component Gradient, F. . i/J Benzyl chloride 3.40 Benzal chloride 7.55 Benzo-trichlorid e 11.40 Quantitative analysis of an unknown chromatogram containing any of the four components may thus be made. The computer programme is appended, (Appendix I). Qualitative analysis was made by comparison of the unknown chromatogram with chromatograms of a known mixture. Within this restricted range of compounds, similar components will have similar retention times. Throughout the whole experimental investigations only toluene and the three side-chain substituted chlorides were Karra ot Chromatogram Peak H eig h ts/ R elativ eto T oluene Figure Ratio 3 . of 6 „ Molecular Calibration Fractions, of Chromatographic Relative to A X O - - - Toluene Column Component Benzal Benzyl Benzo-tri Chloride LEGEND Chloride Chloride 1UU 109 detected. Regular calibrations at intervals of one week were conducted as peak heights increased and retention times decreased with the age of the column. Figure 3.6 however did not require correction during the investigation. (c) Ring Substituted Compounds Ring substitution in toluene occurs as an undesirable parallel reaction to the side-chain chlorination. Ortho-, meta- and para- chloro toluenes may be detected quantitatively and qualitatively using the gas-liquid chromatogram, but these compounds did not appear. Poly-chloro nuclear substituted toluenes cannot be determined qualitatively or quantitatively with ease. Harring and Knol^ obtained a high boiling residue from reduced pressure separations which they assumed to be poly- chloro nuclear substituted toluenes, but the exact nature cannot be ascertained. In view of these difficulties, the presence (if any) of these products was ignored. Chlorination about 50°C also minimized the possibility of these undesired reactions. Calculations therefore are based on the absence of nuclear reaction, 3.2.2 Free Chlorine Determination Free chlorine in the organic liquid phase increased from an imperceptible level (no colouration with potassium iodide) to a distinct yellow-green cdoured liquid. Quantitative determina tion of the free chlorine was based on the methods of chlorine 8 7 determination suggested by Vogel. 110 A syringe of 5 ml capacity with a stainless steel needle was inserted through the rubber septum on the reactor into the organic liquid, A few quick flushes were made, followed by a slow withdrawal of the syringe plunger, so that free chlorine will not escape from the liquid, as would happen if the plunger was too rapidly withdrawn. The liquid contents in the syringe were transferred to a weighed flask containing 20 ml. of 10% aqueous potassium iodide, which reacts with all the chlorine immediately and thus quenches the reaction. Contents of the flask were weighed again to determine the weight of chlorine- containing liquid introduced. The iodine was determined by titra tion with 0.1 N sodium thiosulphate. During titration, the organic liquid layer acted as its own indicator. Iodine has a greater solubility in the organic layer which varied from a deep violet to a pale pink colouration as titration progressed. The end point was indicated by a total discolouration of the organic layer. 3.3 Experimental Procedure At the start of each investigation, toluene was charged into the reactor till it overflowed from the liquid effluent arm. The total toluene volume was thus 308 ml. The Jumo thermometer was then set to the required temperature. This resulted in the circulation of warm water through the reactor jacket. As the toluene temperature approached the set temperature, chlorine was fed into the reactor. The reaction which ensued at the end of a short induction period rapidly raised the whole liquid to the required temperature. Ill For analysis, a sample of liquid was withdrawn with a syringe. Any chlorine and acid gases were flushed out by a brief purge with instrument air. Sodium bi-carbonate was added to neutralize any residual hydrogen chloride, followed by anhydrous magnesium sulphate to remove water. Elimination of these two compounds is of importance as both are damaging to the chromato graph column while the latter may hydrolyse the side-chain chlorides. All samples were marked for identification and kept overnight. On the following day, an accurate amount of 0.5 yulitre of each sample was taken with a Hamilton 7101 micro syringe, which was then eluted in the chromatograph. Free chlorine determination was made when the organic liquid acquired a yellow green colouration, samples for which were taken simultaneously with those for chromatographic analysis. Withdrawal of the syringe plunger had to be slow as otherwise chlorine gas left the liquid phase under the reduced pressure in the syringe. A rapid flushing of the syringe with the organic liquid was also deemed advisable to reduce contamination. At the end of an investigation, the liquid was drained off from the bottom stop cock. Chlorine was then turned off. This procedure was necessary to prevent sucking back of organic liquid into the chlorine feed line. A similar procedure was adopted in the experimental runs with the stirred batch reactor. 112 CHAPTER FOUR Introduction Theoretical equations for absorption of a gas in heterogeneous gas-liquid reactions are centred around a first order reaction with respect to the gaseous reactant and for an infinitely fast second order reaction. Comparable equations and development for a heterogeneous reaction which is of first order with respect to the liquid reactant are lacking. Van de 8 8 Vusse has solved the equations pertaining to such a mechanism for both the unsteady and steady start absorption theories, while Asai and Hikita 89 have treated the general case for a mth, nth order bimolecular reaction. However, in both cases, inter pretation and development of the basic absorption rate equations are found wanting. A mathematical analysis of a heterogeneous gas-liquid reaction of a first order rate with respect to the liquid reactant will be developed in this chapter and the parameters which affect the absorption rate and hence conversion rate will be discussed. Mathematical analysis will also be extended to cover the heterogeneous gas-liquid consecutive reaction of similar kinetics, with a description of the various parameters which affect the selectivity of an intermediate. Absorption rate equations developed will then be applied to the chlorination of toluene, in which the kinetic rate from benzal chloride to benzo- 113 trichloride is found to be first order with respect to benzal chloride and independent of chlorine. The mechanism is assumed to be the same for the preceding two reaction stages. 4.1 On a Gas Liquid Absorption Followed by a First Order Reaction in the Liquid Reactant Consider a gas containing a gaseous component A absorbing into a liquid containing a component B. A chemical reaction between A and B occurs after absorption with zero-order reaction kinetics in A and first order with respect to B. Thus the reaction is represented as A + B C with kiB Product C may arbitrarily react further but this will be the subject of the next section. The basic equations for the components A and B that describe the process of diffusion with chemical reaction is 114 & A kiB and dB + kiB dt For the steady-state absorption film theory dA dB = 0 . dt dt Therefore S) 4.1 A kiB 4.2 B kiB which have the boundary conditions for A and B as -v A A dB X — nU f A — — Un Ai dx X = S , A = B = B al L dA _a SA 6 - a dx klBL ^ L § ) 115 dB / The condition that 'dx - 0 at x - 0 explicitly states that B will be non-volatile in the gas stream, while at x = & the absorption rate of A is equated to the bulk region reaction rate of A given by dA - a a dx (6 S) Equation 4.2 may be solved for the boundary conditions 4.3, yielding B L B = cosh X 4.4 cosh where * -45 On substituting the value of B in equation 4.4 into equation 4.1, and rearranging cosh • x 4.6 cosh Applying a Laplace Transform to the second order differential equation 4.6 -A (o) - p A(o) + p2 A (p) 4.7 <£> cosh where p = Laplace parameter of x in the differential equation A (o) = A. A (p) = Laplace transform of A as a function of x. Now A (o) will be unknown at this stage, but for a specific act of hydrodynamics and kinetics, the function A"(o) = (~~~) v dx / x=0 will be a constant, independent of x. Thus rearranging equation 4.7, B. B A (p) JO cosh P - k. B. cosh <^> A A. _ / l + + 4 117 from which £ B. B cosh X - 54 COS h + + A (o) x 4.8 Differentiating equation 4.8 and setting x to S , £) B sinh X + A (o) cosh £) > <£> f 2 B and hence £, B tanh 6 + A (o) A -J T> From equation 4.3b, klBL (eL'aS) 6 ©, hence £ B A (o) B^ tanh ^ £) c© A n B ( £ - a <5 ) klBL 4.9 118 and substituting A (o) in equation 4.8, B, Sb B cosh x - 1 cosh V a & B Sb. klBL (Vai)X ‘ B tanh ^ . x - 4.10 Sb Sb A A B The specific absorption rates of A into the reaction phase and into the bulk region respectively may be obtained from equation 4.10 above by differentiation and setting to the relevant boundary conditions, or equations 4.9 and 4.3b may be utilized, yielding (na) ^ • tanh j> x=0 + ( 3 £ ) klBL 4.11 a and (6l~ ) 4.12 klBL a Equations 4.10, 4.11 and 4.12 may now be utilized to define absorption characteristics and the controlling parameters 119 on conversion in the heterogeneous system. In passing, however, it may be noted that the gradient, A* (o), assumed previously to be constant is in fact so as is independent of x. x=0 A/(o) could also have been equated to the total conversion in the diffusion and bulk regions with the same results. Interpretation of the mathematical expressions for kinetics of first order with respect to the liquid phase reactant is not as straight forward as that with kinetics of first order with respect to the gaseous reactant. The cause lies in the fact that factors describing the reaction of B and hence of A occur even when the concentration of A is negligible. Mathematically this is rigorous because the kinetic expression is independent of A, but physically, because the reaction is bimolecular, reaction of B does not occur in the absence of A. Intuitive assumptions will therefore have to be made at times. The criteria of reaction rate to diffusion rate ratio is borne in the dimensionless diffusion parameter (j> . The square of the parameter may be defined as ki *L* t Sb B which is the ratio of the maximum rate of conversion of B (and A) 120 in the hypothetical diffusion region to the maximum diffusion rate of B into the same, on a unit specific area basis. For a value of greater than 2.0 a higher conversion rate than the diffusion rate is indicated, implying a rapid re action. Conversely, when 4.1.1 Controlling Parameters on Absorption and Conversion Rate The rate of diffusion of A into the liquid reaction phase is derived from the preceding section as tanh^> 4.11 klBL x=0 The first term on the right hand side of equation 4.11 indicates the conversion of A and B in the diffusion region while the second indicates the conversion of the same in the liquid bulk region. Diffusion and conversion of A into the bulk region is also expressed by 121 4.12 ki bl A second expression for the diffusion of A into the reaction phase is obtained by rearranging equation 4.10, with x =$ . Thus Si cosh - 1 + B. 4.13 (A.-Al) C cosh ) x=o 5 t The effect of chemical reaction rate in relation to the diffusion rate on the absorption and conversion rate of A may now be discussed. The important parameters which affect over all absorption rate are the dimensionless diffusion parameter (p and the specific interfacial area 'a'. (i) When reaction rate is low, the diffusion parameter, <£> <. 0.5, tanh p ~ 4.14 x= 0 <5 - acf and & + k B (—------) 4.15 klBL° + k 1 L >• a s x=0 122 For slow reactions the concentration of B in the diffusion region becomes everywhere equal to that in the bulk region (equation 4.15). Two subcases of absorption rates arise. Expressing equations 4.14 and 4.15 as overall rates, RA = k° a (A. -A ) 4.14a A. and ^ R = kB ad + kB (£ - a S) 4.15a -L J_ i JL _L_i J_ i (a) When reaction rate in the liquid reaction phase is relatively high, A may become very low or approximately l-i zero. This occurs when the maximum reaction rate is higher than the maximum diffusion rate of A, k B £ > k° a A. for A = 0. 1 L L ^ l L Since A^ = 0 in the bulk region, the bulk chemical reaction rate equalszero in equation 4.15a. The diffusion rate is therefore the rate controlling process. The absorption rate of A, and hence the conversion rates of A and B is given by equating A to zero in equations4.14 and 4.14a. J-j 123 4.16 or A. 4.16a 1 Conversion of A and B is effected entirely in the diffusion region. The overall absorption rate is expressed by equation 4.16a above. (b) Conversely, when reaction in the reaction phase is relatively very low, i.e. the maximum reaction rate is less than the maximum diffusion rate of A k, B_€ < k°a A, ILL La 1 a build up of free chlorine occurs in the bulk. Absorption rate is then controlled by a pseudo homogeneous kinetic rate and is given by substituting tanh (j) = (t> in equation 4.11, yielding, kn B + 1 L Vi/ or 4.17 ki bl 124 Governing the relative maximum conversion rate and diffusion rate, the parameter governing the controlling mechanism in slow reactions is the specific interfacial area, a. When 'a' is small, so that the maximum diffusion rate is less than the maximum kinetic rate, k° a A. < k. Bt £ _ La i ILL diffusion is rate controlling, and overall absorption rate is given by equation 4.16a 4.16a As 'a' increases beyond that in equation 4.16a the rate of absorption increases as it is dependent on the specific area. In the limiting case, when the maximum diffusion rate becomes greater than the maximum reaction rate, k° a A. > k B 6 J-j, 1 -i -Li -Li xx the absorption rate is maximum, given by the pseudo-homogeneous kinetic rate of equation 4.17. The absorption rate becomes in dependent of interfacial area and is expressed by the overall rate of 4.17a klBL£L 125 Slow R egion, Interfacial at P rofiles Reaction. Chemical Concentration 4 .1 a . Figure 126 o •-* C O O' CD CX co -'o—i CO +J CO w O J O r—< UH O s-< R eactio n . Oh c o •rH 4-J CO c C hem ical CD o c o o Slow a> WPh O' •rH Cm 127 For a heterogeneous absorption of a gas into a liquid with a slow reaction whose rate is first order with respect to the liquid phase reactant* mathematical treatment shows that maximum absorption and conversion rate, and hence the maximum capacity of the reactor is obtained when absorption proceeds at a pseudo-homogeneous kinetic rate. When the absorption rate is diffusion controlled* increase of the interfacial area, by stirring for example will increase the absorption rate. In the limiting case* absorption no longer becomes diffusion controlled, but proceeds at the pseudo-homogeneous kinetic reaction rate. The two cases are illustrated in Figures 4.1a and 4.1b.Kinetic controlled absorption is therefore the maximum rate of absorption and conversion in slow reactions. (ii) For the fast reaction relative to diffusion rate, diffusion parameter <^>2.0 and tanh ^ » 1.0. With a fast reaction, conversion of A in the diffusion region will be complete so that A is zero. Reaction therefore predominates in the diffusion region, J-j with both A and B falling in concentration as they diffuse and react along the diffusion path. The concentration of B along x from x = 0 to x = & is obtainable from equation 4.4. 4.4 128 in equation 4.11, with the term describing the bulk reaction equal to zero since A is zero in the bulk region, i.e. L = o ki h (^) Hence, 4.18 or 4.18a BLa This rate of absorption represents the maximum rate when reaction is fast and conversion of A is complete in the diffusion region.' The absorption rate given by equation 4.18 is dependent on the interfacial area, thus indicating an increase in absorption when interfacial area is increased. Examining equation 4.13 4.13 the second term on the right is non-zero as long as cosh ^ > 1. Further in the case of (f> > 2.0, A = 0, so that .Li 3 2)B cosh ^ - 1 A. + B, 4.13a 1 (- cosh ■) t 129 Region Interfacial at Reaction. P ro files Chemical Fast Concentration 4 .2 a . Figure 130 Region Interfacial at Reaction. P rofiles Chemical Fast Concentration 4 .2 b . Figure 131 Comparison with equation 4.20 derived in the next section shows that equation 4.2 0 is a limiting case of 4.13a. 'A' therefore falls to a zero value within the dimension of the film thickness, and a chemical mass transfer coefficient may be defined by / where & is the film distance at which A = 0 (see Figure 4.2b). Absorption and conversion rate is mass transfer controlled, given by the chemical mass transfer rate N = k A 4.19 A LA 1 or, overall rate R. = k_ a A. 4.19a A La i The two cases for cosh = 1.0 and cosh ^ > 1 are illustrated in Figures 4.2a and 4.2b. Absorption rate of A is thus a mass transfer controlled absorption. Comparison of equation 4.19 and 4.13a shows that k is defined by LA o /, cosh - 1 \ kL ” La k + £a Ai C0Sh ^ / 132 An increase of reaction rate increases 2.0, cosh <£ ), indicating an increase of k . Therefore, as reaction rate increases, the distance _/ o decreases in Figure 4.2b. In the limit when ^ ^ 2.0, the case of the infinitely rapid reaction arises. (iii) Infinitely Rapid Reactions The effect of chemical reaction in increasing the absorption of A is readily seen from equation 4.13. a s cosh - (A-Al) + B, 4.13 ( cosh For slow reactions with <^< 0.5, cosh kf (A.-AT) 4.14 X (AfAL> \ 1 L However, when the diffusion parameter y) increases above 2.0, cosh (j> approaches ji . The second term on the right hand side of equation 4.13 becomes non-zero, and absorption rate of A increases accordingly. In the extreme case of an infinitely 133 R egion. Interfacial R eaction. at Chem ical P ro files Fast Infinitely Concentration 4 .3 . Figure 134 rapid reaction cosh - 1 Absorption rate is given by a sb A. + B, 4.20 1 x-0 since, for the rapid chemical reaction A = 0. The absorption J-i rate given by equation 4.20 is illustrated in Figure 4.3 where A and B become mutually exclusive. Conversion occurs on a reaction plane situated within the diffusion region. By a mass balance from Figure 4.3 SB K) —— A B. x=0 S. 1 ( $ / 1 (na) x=0 and hence 2J B B___ L (Na) x=0 $ - (na) n x=0 135 Therefore (na) * - = s B BL x=0 \\ . B ^ K) c A. + ^ B 4.20 x=0 Sid L which is equation 4.20 The absorption rate of A in the infinitely fast reaction is again a mass transfer controlled absorption and is dependent on the specific interfacial area. From equation 4.20, a chemical mass transfer coefficient may be defined such that 4.20a Comparison with equation 4.20 will show that Mathematical analysis of a heterogeneous gas-liquid reaction with a chemical reaction of first order with respect to the liquid reactant shows that the important parameters controlling the absorption rate of the gas reactant are the dimensionless diffusion parameter and the interfacial area. Two limiting 136 cases of absorption are distinguished. (i) A diffusion controlled absorption regime is defined when (a) Reaction between A and B is very rapid or rapid. A chemical mass transfer coefficient may be defined such that NA kLA Ai where B, o <2ta ) for (j)^ 2. kL = kL ^ + W * "a" la la ^A Ai o r ^B ___BL_ , cosh^ - Li and p for (p> 2.0 \ l *A ' Ai cosh^ J (b) Reaction between A and B is low relative to diffusion ( ^><0.5) and with a low interfacial area so that the maximum diffusion rate is less than the maximum kinetic rate. klBL€ L Absorption rate is given by A. i 137 where k° = physical mass transfer coefficient LA In all cases of diffusion controlled absorption the overall rate of absorption will be dependent on the interfacial area. (ii) A kinetic regime will be defined when the reaction rate is low relative to the diffusion rate, so that the maximum kinetic rate is less than the maximum diffusion rate, or k° a A. > k B £ L 1 ILL The absorption rate will become independent of the interfacial area and is expressed by R A L Between these extreme distinct regimes will occur the regime where mass transfer and kinetic rate are each of importance. No simple mathematical expressions may however be defined. 4.1.2 Chemical Acceleration Factor The effect of chemical reaction on the increase of 138 absorption rate of A is described quantitatively by the chemical acceleration factor, F. The general rate of absorption of A is given by . cosh4> - 1. 4.13 V4?+ L* cosh<£ and the maximum physical absorption rate of A is given by 4.21 *■ Hencef in general, the chemical acceleration factor is expressed as (A.-A) + k° B . ( .1) cosh k° A- la 1 aB ,-COSh^- 1 . W + £> 1 cosh Equation 4.22 may be further simplified for the following well defined cases. (i) For the fast reaction, the liquid gas content A = 0, while for F 1 + *-1 4.23 t When reaction rate increases relative to the diffusion rate so that (j£$>2.0, the factor | ^ ^ ^ | approaches 1.0, and in the limit, for the infinitely fast chemical reaction, F = 1 + 4.23a »A (ii) For the slow chemical reaction, two subcases will arise, dependent on the rate controlling mechanism. (a) In the diffusion regime, with < 0.5 and k° aA, < k B £ / the bulk liquid gas content i1 JL J_j = 0. Further, cosh (j> = 1.0 so that equation 4.22 yields A. i 1.0 4.24 Otherwise stated, a slow chemical reaction in a diffusion controlled absorption does not result in an accelerated absorption over the maximum rate. (b) In the kinetic regime, with (j>> 0.5 and k° a A.:> k B £ , the bulk liquid gas content A is\ppreciable. 1 J_j Hence equation 4.22 gives F = 1 - 4.24a A. l 140 which in fact shows a fall in the factor. The reason is that in the slow chemical reaction, absorption rate may be given by a physical mass transfer rate. For a steady state absorption with no gas accumulation Ra = KLa a(A. - Al) which is less than the maximum diffusion rate of k° a A. la 1 The enhancement factor will reach the maximum of 1.0 when 0. Theoretical equations derived show that in the fast chemical reaction the chemical acceleration factor is a function of and the diffusion parameter (f> (equation 4,23). A. As o o Factor Acceleration Chemical on C-< CD 4-> o CD £ r-H s-.V r3 Dh Parameter C! 0 •rH CO zs «+h uh -rH Q Diffusion of Effect c 4a c 4 Figure o o o o rH CO LO •j /jo;ogj uoT}PJ8f0DOY ieoxiu0L[3 142 Factor Acceleration C hem ical on T B of E ffect 4 .4 b . Figure uoi;ej0i0oov ieojuieqo 143 factor are illustrated graphically in Figures 4.4a and 4.4b plotted from the theoretical equation of 4.22, but with the assumptions that = 3^ and A^ = 0 4.22a 4.1.3 Phase Utilization Factor, The factor has already been defined in Chapter One and its use in the evaluation of a reactor's efficiency was described. For the heterogeneous gas-liquid reaction of first order in the liquid reactant, the overall rate of absorption of A is described by the equation R = /k1 J& . EL tanh 6. a + k B ( £T -a 4.25 Generally, the phase utilization factor is therefore obtained by division of equation 4.13a by equation 4.25 or The effect of chemical reaction on the phase utilization factor is described again by the diffusion parameter . Two main cases arise: (i) For the slow chemical reaction, dependent on the inter facial area, two subcases are defined. (a) when cr tanht 4.27 Increase of the specific interfacial 'a' would therefore increase liquid phase spreads out to a film of thickness & , a & = 6 r Jj in which case, the phase utilization factor reaches the limiting optimum value of 1.0. Of course, increase in the area results in increase of the diffusion rate, and at 145 some point, k a A. > k B £ may be reached l_j^ 1 1 l_i earlier than the area required for a 6 = £ . Absorption L will revert to kinetic control, and as will be seen, the phase utilization factor equals one. Generally, however, when conversion is under diffusion control, increase of the gas-liquid interfacial area will increase the reactor capacity. (b) In the other extreme, if ^<0.5 and the interfacial area is high so that k_ a A. > ki bl L la 1 the absorption of A is under kinetic control. Since bulk reaction is present, equation 4.26 yields, for tanh <£ = a & or Therefore, under kinetic controlled absorption, the reactor capacity is optimum, and is in no way improved by increasing the interfacial area. 146 (ii) When chemical reaction is fast, diffusion parameter For tanh (j> = 1 when (j>> 2.0, equation 4.26 reduces to 0- - -SLjkl. kn BT£T or 4.28 The phase utilization factor is now dependent on two parameters, being dependent on the interfacial area 'a', and inversely proportional to the diffusion parameter 4.2 Effect of Diffusion on Selectivity in Heterogeneous Consecutive Reactions 90 Wheeler has shown mathematically that in a gas-solid heterogeneous consecutive reaction, diffusion limitations lead to a fall in the selectivity of an intermediate product. The same 29 treatment was applied by Van de Vusse to gas-liquid reactions. He showed that conditions governing a fall in selectivity differ slightly from that of gas-solid systems. In the present study, evaluation of the kinetics of the toluene side-chain chlorination showed that the reaction of benzal chloride to benzo-trichloride was zero order with respect to chlorine, and first order with respect to the organic reactant. If a similar mechanism is assumed to apply for the preceding stages of chemical reaction, then the consecutive reaction from toluene to benzo-trichloride is a first order reaction at each stage with respect to the organic molecule: kl k2 k3 B ------* C ------L—* D ------► E A mathematical analysis of the effect of diffusion on the selectivity of intermediates in the consecutive reaction may be made. Solution will be made however, only up to the stage of benzal chloride and for simplicity, diffusion coefficients are 148 assumed equal. The differential equations which describe the process of diffusion and chemical reaction at each stage are, for the steady-state diffusion theory 8 4.29, for toluene 4.30, for benzal chloride k2c-kiB 8 k1B+k2C for chlorine Boundary conditions are x = 0 : A = , UB . / 'dx /dx 6 : B = B, C = C, =AL 4.31 4.2.1 Qualitative Description Consider a heterogenous gas-liquid system with a consecutive reaction between the liquid component B and gas A: G as P h ase Liquid R eaction P hase 149 Figure 4 .5 . T ypical Concentration P rofile at Interfacial Region in a Heterogeneous Series R eaction, 150 A + B ------* C+A------—- D When C reaches a significant concentration, it reacts parallel to B to form D thus: The selectivity of C will therefore depend on its relative con centration to B in the reaction. If conditions exist so that C is greater than its homogeneous concentration relative to Bf a decrease in the selectivity of C results. For a more complete 91 description of the above mechanism, reference to Levenspiel is recommended. In a heterogeneous gas liquid reaction, con ditions which lead to a relative difference in the concentrations of B and C from their respective values in bulk can exist. Referring to Figure 4.5, B diffuses into the liquid film region where, by chemical reaction with A it produces C. In a parallel reaction to B, C reacts to yield D, and under a concentration driving force, C and D diffuse out of the diffusion region. The profile of D is not shown for simplicity while the exact profile of C cannot be defined. However, it is true that C > C for C to diffuse out of the film region. It can be L 151 > S elect on Reaction. D iffusion of Chemical Effect Slow 4 .6 . Figure 152 appreciated that from Figure 4.5, along the dimensions of the film, because of variations in the concentrations, of B and g C, B/c in the diffusion region is less than L/q . Con- sequently, conditions are established where the selectivity of C falls as a result of diffusion. It is also interesting to note that the concentrations of B, C and D are analogous to that of a gas reaction with gas diffusing into and out of a catalyst surface. Two conditions can exist for the gas-liquid reaction g where /~ in the diffusion region do not differ appreciably ^ g from the homogeneous bulk concentrations . For a slow chemical reaction, depicted in Figure 4.6 B is not rapidly depleted in the diffusion phase, and its con centration may be assumed to be constant at B , and assumption J-j which is in fact proved valid in equation 4.15. Although C will be higher than C , the low reaction rate ensures that C zs C . -Li Hence, relative concentrations of B and C are approximately equal both in the diffusion and bulk regions, with no resultant fall in the selectivity of C. The criteria for a slow reaction is (j> < 0.5 which results in no selectivity limitation. Overall absorption rate has been shown previously to be given by A. 4.16a i 153 S e le c ti on Reaction. D iffu sio n of Chemical E ffect Fast 4 .7 . Figure 154 e o “r—1 DU) <4-H M-l T5 >1 rQ >, C 4-J 0 3 CO -M 1 -/-I S e le c tiv i -4-> on *rH> 4-J o Reaction. 0 .—01 w 0 D iffusion +-* 0 r-H of a Chemical 6 o o Effect cT Fast OJ A 4 .8 . X! Figure 155 when a is small with kT aA. < k-B_ €_ 1 ILL and by 4.17a ra kl BL£'L when a is large with k a A. > k.B,. £ L i ILL Figure 4.7 refers to a fast chemical reaction, but with B^ high. The reaction with A in the film region therefore does not deplete B appreciably, and B may therefore be assumed L approximately constant in the diffusion region. C and C C CT L remains relatively low so that —— ~ -—=■... , with no resultant B B L L fall in the selectivity of C. The criteria for a fast reaction is $>>2.0, in which case, the overall absorption rate of A was shown to be ra = ■ bl 4-18a In the present case, B remains constant because of its relatively high concentration with respect to A^. However, if B decreases independently of A^, the situation where B » B^ throughout the film region no longer holds, but B falls in concentration as it reacts, as shown in Figure 4.8. An approximate value of B 4. 156 for which B shows an appreciable drop in concentration occurs when the diffusion rates of A and B equal approximately their complete conversion in the diffusion region, i.e. B = kL BL lb l ©. Taking k 76 then i B, ki bl with i + -SJ £ Such an observation was in fact made by Van de Vusse , who chlorinated n- decane under extreme diffusion resistance by passing chlorine gas over the surface of a still pool of n-decane. No change in selectivity over a homogeneous product distribution was observed. However, on dilution of n-decane with di-chloro benzene so that is satisfied, he observed a fall in L/n ~ f selectivity. i 157 S elect on Reaction. D iffu sio n of Chemical Fast E ffect 4 .9 . Figure 158 B When B continues to decrease so that J-i A. ^ $ the condition occurs when B completely reacts in the diffusion region, and falls to a zero concentration short of the gas-liquid interface, depicted in Figure 4.9. Between the planes x = 0 and x = A similar situation arises when <^^2.0 in infinitely rapid reactions. A and B become mutually exclusive, reacting at a film plane at 0 4.2.2 Mathematical Analys is An exact mathematical solution of the differential equations 4.29 and 4.30 for the boundary conditions of 4.31 can be achieved by application of a Laplace Transform. Solution in Appendix IIB gives the concentration profiles of B and C in the distribution phase as In terface 159 In fin itely fa s treactio nbetw een A and B, cosh 4.32 cosh ♦ a and ‘2 kl BL ■•X C = C. cosh x - cosh x - cosh 1 3b 3d O^-k^cosh ^ 3b 4.33 where k^ (cosh (f> ^ - cosh ^ ) i cosh 2 (k^-k^) cosh ^ cosh^>2 4.34 Differentiating equation 4.33 with respect to x and equating x to £ , k2 kl (^) CL tanh^2 + k,-k„ B„L tanh^^ dx & Sb 2) krk2 klBL tanh ^ i 4.36 £> and similarly tanh (j) 4.37 x= Dividing equation 4.36 by equation 4.37 and multiplying by -1, tanh rf)r tanh (p k2 kl B. tanh cp_ kl ^kl"k2^ k. 4.38 (krk2) Now ®CdB/dx) x= g describes the flux of C into the bulk liquid region against the flux of B into the diffusion region. It therefore gives the rate of accumulation of C in the bulk liquid region against the con version rate of B as a consequence of the diffusion and reaction process in the diffusion region. It describes the instantaneous yield of C in the series reaction. For a batch or plug flow reactor equation 4.3 must be integrated to give the overall yield. 162 Letting S = Vv , the selectivity factor, k2 S___ + 4.38 S-l The effect of reaction rate will now be apparent. (i) For a slow chemical reaction relative to diffusion <^ < 0.5. The diffusion parameter (p incidentally has an equivalent ' 92 factor termed the Thiele Modulus in gas-solid reactions. N ow tanh (f> ~ (p for (p < 0.5 Thus, from equation 4.38 _d,___CTL _ 1 __ . __CTL _ 1 4.39 dB S B JLi i-i Comparison with equation 3 in Appendix IIC dC _ -j _ _1_ _C_ 3 dB SB 163 shows that the product distribution in this case in idential to that of a homogeneous reaction, proving the qualitative conclusion that selectivity is not limited by diffusion for slow reactions. Integration of equation 4.39 by the integrating factor, for S > 1 exp ( - ^ In gives, for the limits B_ = O to B L o 4.40 (ii) When B undergoes a fast reaction with A so that -< for <£>>2.0 * and for (j> ^ 2.0 the selectivity of C falls. 164 For cj>^2.0, tanh <£ ~ 1.0. Hence from equation 4.38 Integration of equation 4.41 with the integrating factor for S>1 exp ( - 1/j-g • In Bl ) yields for B_ = O to B * L o for S > 1 4.42 Comparing equations 4.39 and 4.41 4.39 <£<0.5 and 165 is _ rr 4.41 Js + 1 J s bl 1 + Js and (b) -g- < 1, hence, J-^~ > for S>1 CL Hence for any value of ------the rate of accumulation of C with respect to B given by equation 4.39 is always greater than the same rate given by equation 4.41. In other words, selectivity in the case of equation 4.42 is limited by diffusion and falls below that given by equation 4.40 which is also identical to that given by a homogeneous reaction. Mathematical analysis of a heterogenous gas liquid reaction shows that the process of diffusion can limit the selectivity of an intermediate in a consecutive reaction. In conjunction with a qualitative analysis, the following cases may be distinguished: (i) Selectivity will not be diffusion limited when reaction rate is slow such that the diffusion parameter is less 166 than 0.5. (ii) For the fast chemical reaction, such that the diffusion parameter is greater than 2.0, selectivity decreases and is diffusion limited, provided that °L < 1 for and B ^ A for (iii) Under no selectivity limitation, the selectivity of C may be derived from the equation for when (p ^2.0, the selectivity of C may be derived from Is Js+1 4.41 167 Equations 4.39 and 4.41 describe the extremes of (^<0.5 and (£>^2.0. For an intermediate reaction rate such that 0.5 < (p < 2.0, the selectivity will decrease below that expressed by equation 4.39, and continue to decrease as increases above 0.5. The limiting case is reached when > 2.0 and selectivity is given by equation 4.41. A further discussion on the selectivity in heterogenous consecutive reactions will be made in Chapter Five, where the case of S = 1 will be dealt with also. 168 4.3 Unsteady-state Chlorination of Toluene in a Laboratory Bubble Column Reactor The bubble column reactor was operated as an unsteady- state, i.e. batch reactor to obtain information on kinetics, mass transfer characteristics and selectivity. Initially, experimental investigation was confined to three chlorine flow rates at 0.4, 0.6 and 0.8 lb/hr and at the temperature of 70°C. The results summarised in Tables Ai to A3 of Appendix VII are utilized to test for the controlling mechanisms in the photochemical chlorina tion of toluene. Subsequently, experiments were conducted at temperatures of 45 to 80°C in increment intervals of 5 C degrees with chlorine loads of 0.4 to 0.95 lb/hr. A judicious experimental plan yield much valuable data. The experimental results are summarised in Tables Al to A15 in Appendix VII. A disappointing feature of the investigation was the in consistency of gas hold-up measurements in the reactor. An unstable liquid surface contributed largely to the difficulty in assessment, while the rapid evolution of hydrogen chloride gas did not enable a true chlorine gas hold-up measurement. Results of gas hold-up measurements are not included. Nevertheless, a liquid hold-up of 1.0 will be assumed in the subsequent evaluations. Free chlorine determinations were made when the liquid acquired a greenish yellow colouration. Although chlorine could be detected even at low degrees of chlorination, its level 169 was quantitatively very low. A straw yellow colouration was obtained when a drop of the organic reactant was added to aqueous potassium iodide. Quantitative volumetric titration was not feasible as a drop of 0.1N sodium thiosulphate discharged the iodine colouration. A laboratory size stirred batch reactor was further utilized to investigate the effects of agitation on kinetic and mass transfer data evaluated from the bubble column reactor. A reaction temperature of 70°C and a chlorine flow rate of 0.6 Ib/hr was utilized, with the agitation rate of the magnetic stirrer varied from 500 rpm to 2000 rpm. The experimental results with the batch reactor are summarized in Tables A1 6 to A20 of Appendix VII. 4.4 Bubble Behaviour in Chlorination of Toluene A systematic and quantitative study of bubble behaviour and mixing in the heterogeneous chlorination of toluene will be beyond the scope of the present study. Nevertheless, without the use of auxiliary equipment, qualitative observations and deductions may be made. Photographic reproductions of the bubble swarms are illustrated in Plates III - VI with their respective chlorine flow rates indicated. When chlorine is initially passed into toluene, the gas does not leave the inlet nozzle as a swarm of separate bubble. 170 Plate III. Bubble Column Reactor with Chlorine Flow Rate at 0.4 lb/hr. 171 Plate IV. Bubble Column Reactor with Chlorine Flow Rate at 0.6 lb/hr. 172 Plate V. Bubble Column Reactor with Chlorine Flow Rate at 0.8 lb/hr. 173 Plate VI. Bubble Column Reactor with Chlorine Flow Rate at 1.0 lb/hr. 5783 174 Instead, a jet of the gas appears to emerge into the liquid, but this disappears at a height of 1 to 2 cm. above the inlet, since the chlorine dissolves very rapidly. Only one or two bubbles are formed but these also dissolve after traversing only a small vertical distance. The colour of the organic liquid begins to assume a deep yellow-green colour. As time progresses bubbles begin to appear both from the chlorine gas jet entering the liquid as well as from the bulk of the liquid. The frequency of this bubble formation increases rapidly in time, until the whole liquid appears to boil with a rapid and spontaneous evolution of gas. The observations thus far must be an induction period, caused probably by the present of air, an inhibitor, in the toluene. End of this period is marked by the rapid evolution of hydrogen chloride formed as a result of the reaction of the dissolved chlorine. After the induction period, the reaction subsides to a smooth and rapid reaction. Bubble formation is studied at this period. Chlorine entering the reactor shows a marked entrance effect, the gas leaving the inlet as a jet of finely divided bubbles. This extends for a height of about 2 cm., within which height, the surrounding liquid does not contain many bubbles. Above this region, however, the liquid appears to be in fully developed turbulence. Gas bubbles coalesce to yield larger bubbles 175 while large bubbles are subdivided by the turbulent field to yield smaller bubbles. Recoalescence of smaller bubbles is also highly frequent. Recirculation of bubbles is quite pre dominant, particularly at elevated gas flowrates. Backmix conditions may therefore be assumed to prevail in the reactor, this being particularly true in the higher gas flow rates. Plate III illustrates the bubbles observed at a gas flow rate of 0.4 lb/hr. It can be seen that the bubbles rise upwards in a spiral path. The entrance effect is also observable clearly, with the liquid above the gas jet consisting of more or less uniformly distributed bubbles. At a higher chlorine flow rate the entrance effect appears to be diminished with a denser bubble swarm as evidenced by Plate VIf for a chlorine flow rate of 1.0 lb/hr. Frothing on the liquid surface is evident, the pheno mena being more pronounced for a higher gas flow rate. It should be indicated at this juncture that the exact nature of the gas bubbles is in doubt. Measurements of the chlorine flow rate against that consumed by chemical reaction show a complete reaction of chlorine in the initial (diffusion regime) stage of reaction. It is more probable therefore that the bubbles observed in the diffusion regime are hydrogen chloride bubbles released from the liquid reaction phase. When reaction does not completely consume the chlorine fed with kinetic regime, chlorine 176 gas would constitute part of the bubble swarm. Bubble distribution phenomena will hence appear to be primarily a result of gas inlet dispersion with the secondary effect of hydrogen chloride evolution as a result of the chemical reaction. Although it is not very clear from the photographic reproduction, bubble size at the higher gas rates appear more uniform than those at lower rates, as well as being more homo geneously distributed. Nevertheless, an average bubble size of \ to \ cm. prevailed. Qualitatively, hydrodynamic conditions in the reactor would be prevalently turbulent from observations made thus far. A measurement of temperature along the vertical axis of the reactor was made during several runs, the results showing an absence of any localized temperature variation, which could be indicative of an extensive liquid mixing. A series of experiments were performed to examine the liquid mixing phenomena. In these, a dye was introduced to the surface of the liquid, where upon the turbulent forces dispersed the dye into the liquid. Within a short time, the dye became uniformly distributed through out the liquid, with no localized pockets of dye observable visually. Mixing of the dye appeared largely to be convective, while lateral mixing was also quite extensive. Dispersion time 177 was measured in each case, thrice for each gas rate and an average of the times was evaluated. A toluene soluble dye used in commercial felt pen s was utilized, being quite intense in colour and stable towards chlorine, a property which is absent in other dyes tried. Rather unfortunately, conditions were not optimum for photographic reproduction of the mixing phenomena, lighting and poor contrast, as well as the presence of extensive bubble swarms were major factors. Dispersion times for five gas flow rates are summarized in Table 4.1. An expected trend of decreasing dispersion time with increase of gas flow rate is indicated. It must be emphasized that the results are largely qualitative as the assessment of complete dispersion is subjective. The nature of the liquid turbulence was further evaluated by application of the orifice Reynolds Number, a necessary if not sufficient criteria in identifying a bubble regime. The orifice diameter, measured at 0.1 cm., was used as the significant length in the Reynolds Number. A sample calculation of the orifice Reynolds Number is shown in Appendix VED. The orifice Reynolds Number evaluated at 70°C (Table 4.1) indicated that at the gas flow rates of 0.4 to 1.0 lb/hr utilized experimentally the bubble formation was well within the turbulent regime (Re > 2100). At the elevated gas rates, bubble formation regime 52 approaches the gas-jetting regime described by Liebon et al 178 Table 4.1 Summary of Dye Dispersion Time and Orifice Reynolds Number for Bubble Column at 70°C Gas F Low Rate Dispersion Time Orifice Reynolds lb/hr. of Dye, sec. Number 0.2 6 2,000 0.4 4 4,000 0 o 6 3 6,000 00 o 3 8, 000 1.0 2 10,000 179 at Re > 10,000. Quantitative criteria and qualitative observations are indicative of a fully developed turbulence in the liquid phase at all the gas flow rates used in these experiments. Prevalently turbulent conditions justify the assumption of backmixing conditions. The absence of localized concentration thereby enables kinetic data to be evaluated on the basis of micro kinetics in subsequent treatment. 180 4.5 Kinetics and Evaluation of Kinetic Data The absorption rate of a gas into a liquid followed by a chemical reaction of the form A + B * products has been shown to reduce to four limiting rates of absorption by a mathematical analysis for two rate expressions (except case (i) below) of r (pseudo first order in A) klABL and r k B (first order in B ) (i) For infinitely fast reactions, for the kinetic expression r = kj A B (second order reaction) and r kiB 181 (ii) For fast reactions with 2.0, the limiting absorption rate is given by N = Ik. Bt X) .A. A N 1 L a l r = k B A for ■I J_i and N = / k S A ^ 1 B for r = k2B (iii) For the slow reaction, (p ^ 0.5 and with the kinetic rate greater than the diffusion rate, Na = A. for both first order rate expressions with respect to A or B (iv) For the slow reaction, (f)< 0.5 and with the kinetic rate less than the diffusion rate Na = k Bt £ / A 1 L L/a for r k1B 182 and N = K K bt e A 1 L L ^L/a for r Absorption rates expressed by the rates in cases (i) to (iii) will be dependent on the rate of feed of the gaseous component A, and on the interfacial area of the reactor. Kinetic rates cannot be determined from the absorption rates. Although a kinetic constant is incorporated in the rate equations of case (ii), the constant cannot be determined for three reasons: (a) The specific interfacial area cannot be determined with a great degree of accuracy. (b) The order of reaction cannot be determined directly. (c) The value of <£> cannot be established without a priori knowledge of k^ . From case (iv), the absorption rate of A is determined by a pseudo-homogeneous kinetic rate that is independent of 'a' when an overall rate is taken. Actual kinetic data can therefore be obtained if the absorption rate is controlled by the pseudo- homogeneous kinetic rate, and if the kinetic regime is established to be prevailing in a heterogeneous reaction system. The important working criteria of the dependence of the absorption rate on 183 specific interfacial area in the first three cases and the independence of kinetic rate on specific interfacial area will be utilized in the analysis of kinetic rates for the present reaction. In the initial runs with results in Tables A1 to A3 (Appendix VII) the following qualitative and quantitative observa tions were made: (i) Initially, reaction was rapid with no accumulation of free chlorine, as indicated by visual observation of the clear colourless bulk liquid and a negative test with potassium iodide. By a mass balance with the stiochiometric equations represented by Ph. CH3 + Cl2 ------* Ph.CH2Cl + HC1 one molecule of chlorine leaves an atom of combined chlorine in the liquid phase with one atom evolved as hydrogen chloride. An analysis of product mole fractions can therefore enable a factor called the degree of chlorination to be evaluated. By definition, the degree of chlorination is the moles of chlorine reacted per mole of initial toluene, hence, X = bxO.O + cxl.O + d x 2,0 + ex 3.0 184 Tim e. a g a in st Chlorination of m inutes - D egree of Time Plot 4 .1 1 . Figure o o o O CO CM o X 'uopeuijoxtio JO 00J60Q 185 o o CO Tim e. O LD A g ain st C/3 CD T oluene 4-> O P c •I—t £ i F raction CD £ H-f-H o M ole CO of Plot o 03 4 .1 2 . Figure O r-H o eiouy m 'ouanioj, uoTipejj aio^i 186 A graphical representation of the degree of chlorina tion against time is made for the results of Tables A1 to A3. For each chlorine flow rate, an initial linear relationship was obtained, shown in Figure 4.11. The bulk chlorine concentra tion is negligible in this linear region, hence the linear rate indicates the total rate of chlorine absorption by the organic liquid. The gradients of the linear portions also showed an increase with chlorine flow rate, and were measured quantita tively as: Gradient m°ie/mole min. Chlorine Rate lb/hr 1.48 x 10"2 0.4 2.13 x 10'2 0.6 3.3 x 10'2 0.8 A plot of the mole fraction toluene against time is shown in Figure 4.12. Again, the initial rate of conversion of toluene is a linear function of time, implying a constant rate of toluene reaction with respect to time, but dependent on the flow rate of chlorine as shown below: 187 Rate of toluene reaction Chlorine feed mole/ rate lb/hr /mole mm. -2 -3.2 x 10 0.8 -2 -2.0x10 0.6 -2 -1.43 x 10 0.4 Comparison of the reaction rates of toluene and the absorption rates of chlorine reveal that the reaction rate is dependent and controlled by the feed rate of chlorine. If absorption and reaction of chlorine are kinetic controlled, the kinetic rate is zero order with respect to both chlorine and toluene. However, conclusions are indicative of a dependency of absorption rate on the chlorine flow rate, which nullifies the probability of a kinetic regime. (ii) As reaction progresses, the absorption rate of chlorine decreases as the rate deviates from linearity (see Figure 4.11). Free chlorine also begins to accumulate. Harring and Knot1'*’ assumed that reaction is kinetic controlled when free chlorine appears. Accordingly, they plotted a mole concentration product distribution curve with respect to time, and at and beyond the vicinity of the peak concentration of benzal chloride, the authors assumed kinetic control. Assuming further a kinetic rate 188 of the form . . m r = k3 AL where m = unknown constant, they derived _dl_ = _ dD = k Am D dt dt 3 L L By measuring ^E/dt at they obtained a pseudo first order kinetic constant k A™ . On a characteristic O J—i curve for a series reactions the following relationship is shown in Appendix IIIC. At the peak concentrations of benzal chloride (D) and benzyl chloride (C), 4.43 and 4.44 189 In such a relationship, A1!1 would be cancelled J-j as a common factor. Having obtained a relative value of k vJ therefore enabled and k^ to be evaluated accordingly. There appear to be two flaws in the authors' arguments. In the first instance the authors have not established any con trolling regime, albeit the chlorine concentration is appreciable, proof of kinetic controlled absorption is insufficient. Second the correct order of the reaction had not been established. A most confirmatory test of chemical kinetic controlled absorption is to vary the chlorine flow rate, whereupon absorption rate should remain approximately constant in a kinetic controlled absorption. Variations are due to the change in the fractional liquid hold-up if any, as gas rate varies. Such a test will now be applied to the kinetic evaluation technique employed by Harring and Knol^? Figure 4.13 shows the time product distribution of the reaction up to the point where benzal chloride passes its maximum concentration. Conditions are a temperature of 70 C' and chlorine rate of 0.6 lb/hr (Table A2). The slope of the benzo-tri-chloride curve at the maximum for benzal chloride is drawn, which gives the rate of formation of benzo-tri-chloride, dE, /dt. A similar procedure is repeated for the results from Tables 190 o to r"H o "c < 00 cr o CM Plot w O CD 4-> o 3 G ->-i e Distribution i M 0 Time-Product o 4 .1 3 . Figure o cd o • • • • o o o o 191 A1 and A3. Results of this evaluation are listed below: Gradient Benzal Apparent Chlorine dE, Chloride Max. Feed Rate i a m at D_, mole/ k3A Max- mole -1 lb/hr mole/mole sec sec. 1.84 x 10”4 0.71 2.60 x 10"4 0.8 1.48 x 10"4 0.71 2.09 x 10"4 0.6 1.0 x 10”4 0.71 1.41 x 10~4 0.4 The values of k A evaluated increases as a function of the chlorine flow rate. Hence, it is conclusive that the absorption rate is not kinetic controlled. With a view of obtaining a true kinetic rate expression chlorination was conducted to beyond the maximum concentration of benzal chloride, when the probability of kinetic control is greatest. Flow rate of chlorine was varied to check the consistency of kg. A determination of free chlorine concentration has been described in the third chapter, while the units of calculation are appended in Appendix V. 192 From the results in Table A4 to A6, two kinetic models are tested, both first and second order, for the reaction k A + D ------♦ E + HC1 chlorine benzal benzo- chloride tri- chloride If reaction is second order, the kinetic expression k3 \ DL ^ L However, €. is assumed to be 1.0 without J-j appreciable error as gas hold-up is low. (a) The relationship between D and A is not easily Li -Lj analysed so that the second order kinetic equation cannot be integrated. The less accurate and more cumbersome analytical method is therefore applied. Results are however negative and do not indicate second order kinetic. (b) A priori inspection eliminates the possibility of first order kinetics in chlorine. The kinetic rate for this case is dA dt k3AL 193 However as the absorption and hence reaction rate of chlorine decreases, the chlorine concentration A increases, Jj thus necessitating a negative value in k^. (c) If the kinetics of reaction is first order with respect to the liquid reactant, the kinetic expression is dD dt k3°L which may be integrated with the initial condition of t = 0 , D D o Thus ln A t Hence, a graphical plot of In D/dq against the time of reaction would yield a linear relationship, with a gradient of k . The O exact commencement of a kinetic controlled absorption is not well defined. Generally, however, the experimental data of Tables A4 to A15 for the bubble column reactor, at degrees of chlorination in excess of 2.0, fitted the relationship t In 194 o CO o 'sT A gainst O CM r-H C hloride) B enzal o o In itial C/3 c B o 00 I CD (F raction B H log o of CO Plot o 4 .1 4 . Figure o CM o I (0piJOjiiO IOZU0Q uojioeij) 195 4.5.1 Variation of Against Flow Rate of Chlorine Figure 4.14 is the graphical representation of In D/60 at 70°C with chlorine flow rates of 0.4 lb/hr to 0.95 lb/hr (Tables A4 to A8). A linear function is seen and this does not show any appreciable or systematic change with chlorine flow rate. A kinetic controlled absorption regime is therefore established. The pseudo-homogeneous first order kinetic constant k^ is determined from the gradient. Its value is tabulated in Table 4.2 for a common temperature of 70°C. An average of the constant from the five evaluations gave -4 -1 k 2.54 x 10 sec 3 196 Table 4.2 Specific Kinetic Constant, k at 70°C O Temperature Chlorine Flow Kinetic Constant k -1 Rate lb/hr. k3 sec. °C 70 0.95 2.82 x 10~4 70 0.80 2.84 x 10~4 70 0.60 2.46 x 10"4 70 0.50 2.14 x 10”4 70 0.40 2.46 x 10"4 197 o Tim e, o CO a g a in st C hloride) o o I—I B enzal o . In itial 00 m in s - f r a c tio n Time o CO log of Plot o 0 4 .1 5 o Figure CO (spuomo xszuag iei}iui uoi:peijj fioj 198 4.5.2 Variation of with Temperature The unsteady state experiments summarized in Tables A9 to A15 were conducted at 0.6 lb/hr chlorine flow rate with temperatures ranging from 45°C to 80°C. These results can be analysed to obtain k^ within these experimental temperatures. Similar plots of In against time for these results were made. Figure 4.15 showing a plot involving three temperatures. As expected, the trend shows a decrease of the rate constant k with a decrease in temperature. The O magnitude of k^ evaluated by the graphical method are listed in Table 4.3. 199 Table 4.3 Specific Kinetic Constant, k 3 Temperature Chlorine k3 d -1 °c Flow Rate lb/hr. sec. 45 0.6 1.04 x 10"4 co o 50 • 1.23 x 10”4 I r-H r CO LO o — X 55 0.6 H 60 0.6 1.84 x 10”4 65 0.6 2.18 x 10"4 70 0.6 2.46 x 10”4 75 0.6 2.82 x 10”4 80 0.6 3.18 x 10”4 200 4.5.3 Evaluation of and In the first section of this chapter, the effects of mass transfer on the selectivity of a consecutive reaction have been developed. If it is assumed that diffusion does not affect the selectivity of the consecutive reaction, the product distribution will assume that of a homogeneous reaction, although diffusion may control the rate of conversion. If the chemical reaction of toluene to benzyl chloride and of benzyl chloride to benzal chloride have similar kinetic mechanisms to that of chlorination of benzal chloride, then A + B C + HC1 dB dt and k 1 A + C D + HC1 dC dt In Appendix IIIC , the derivation of the relationships 201 o o CXI o 00 I—I o CO o XT' P lo t. o CM CO CD +-> Distribution aP o •r-i o B i CD B H■i—i o Time-Product 00 4 .1 6 . o CO Figure o XT' O CM O 0JOUI/0XOUI 'UOTIOUJJ 0IOIAI 202 4.44 and 4.45 at the peak concentrations of benzyl chloride (C) and benzal chloride (D) are shown. Equations 4.44 and 4.45 may be conveniently used in conjunction with a product distribution graph to estimate and k^ from a knowledge of k^. A typical product distribution characteristics curve plotted with concentration units of mo*e/mole and time in minutes is shown in Figure 4.16 for a temperature of 60°C and a chlorine flow rate of 0.6 lb/hr (results from Table A12). Table 4.4 summarises the values of k^f k^ and k^ for the temperatures of 45°C to 80°C. An average value of k = 2.54 -4 o ^ x 10 is used at 70 C. 203 Table 4.4 Specific Kinetic Constants k^, k^ -1 . -1 Temp. (D/C) k3 sec'1 k2 sec k^ sec (C/B) max. max. 45 6.80 8.00 1.04x10_4 8.32xl0"4 5.65x10~3 50 6.75 7.90 1.23 9.72 6.55 55 6.75 7.80 1.56 1.22x10~3 8.24 60 6.75 7.80 1.84 1.43 9.65 65 6.75 7.50 2.18 1.58 1.06xl0”2 70 6.65 7.00 2.54 1.78 1.19 75 6.50 7.00 2.82 1.97 1.28 80 6.30 6.90 3.18 2.20 1.39 204 The constants k^ and k^ are obtained from a simple calculation. Thus x k Cc4)max 2 x k (%)max 'J In the evaluation of k^ and k^ from a characteristic curve, one very important assumption has been made, the validity of which is shown in section 4.8. The effect of mass transfer on selectivity has been developed in section 4.2 of this chapter. Under conditions when mass transfer limits selectivity, the ratios of B and C are expressed as 4 B, Bn 4.42 S-l V B B where B for conditions (f>> 2.0 % v and (j>^>2.0, B^ 205 For non-selectivity limitation, B and C vary according to the equation for 0.5 Differentiating equation 4.42 with respect to C L B L and at the maximum concentration of C, Similarly, from equation 4.40 max 206 Hence for a diffusion limited heterogeneous reaction, with conditions prevailing which depress the yield of an intermediate product, C, the maximum yield is given by the equation (_V) . V bl j is + 1 max which is less than the same for a non-selectivity product dis tribution expressed by equation 4.40. Therefore in the evaluation of and the important assumption was that the product distribution was non-selectivity limited with and similarly Two methods are employed to check the assumptions made. The first is to ascertain the selectivity-controlling regime; 207 equivalent to determining the value of 4.5.4 Variation of k^, and k^ with Temperature The kinetic constants for the photochemical chlorination of the toluene side-chain have been evaluated. Generally rate equations for photochemical reactions can be very complex, well exemplified by the hydrogen/bromine photochemical reaction^ which has a rate expression of the form kl 1K Kl1 ^ [HBrj / | k2 + [Br2l which is a compounded rate arising from several elementary rates. However, one elementary rate may control the overall rate, provided of course the rate is not initially diffusion controlled. As a result, reaction rates can be in many instances of a simple form. While k was evaluated, two simple reaction rates were O tried for data fitting. The reaction rate which is of first order with respect to the organic reactant and zero order with respect to chlorine responded positively to analysis. A reaction rate of the form dD D dt L 208 was taken. Since it is known that the reaction is bimolecular, a term containing chlorine must have been masked and compounded into k^ because it is constant. Two possible cases of a constant value of A arises: (a) Chlorine concentration is at the value of its interfacial concentration A., so that reaction rate becomes 1 dD A. D dt 1 L This case will not be likely to be true, otherwise the liquid must be saturated with chlorine during a pseudo-homogeneous reaction in the kinetic regime. Contrary to this, the ab sorption rate of chlorine was kinetic controlled for a value of A that was increasing in time. (b) Chlorine concentration remains at a low but constant concen tration. A more correct statement is rather that the active chlorine concentration remains constant. This possibility may be explained by reducing the reaction equation to itfe elementary equations: h v — 2 Cl- C12 (1) Cl- + Ph.CHCl2 — HC1 + PhCCl2 (2 ) PhCCl^ + Cl2 — PhCCl3 + Cl- (3) etc. 209 Step (2) in the series of reactions may be the rate determining reaction, so that H PhCHCld The active concentration [jCl'J '*'s ^orme<^ from active light dissociation of chlorine and regeneration by chain propagation. Statistically, however, the concentration may be assumed constant, and remains so in spite of temperature variation; since the primary and more important source of chlorine atom generation is external to the reaction system, in the form of light irradiation. This fact can be verified in the following observation. If the light irradiation source was switched off during chlorination, excess free chlorine built up immediately and reaction slowed down. Without light, the reaction system cannot sustain a high enough active chlorine concentration by a chain propagation. Most of the active chlorine must therefore be derived from the primary source of light activation. Accepting the second case as true, the kinetic constants k^, k^, k^ may be assumed to be absolute constant; any active chlorine concentrations will be temperature independent. For absolute constants, Arrehnius equation gives the relationship between k and the absolute temperature as 210 k 4.46 or £ 4.46 logiok 2.303 RT log 10•, n k plotted against / therefore yields a linear relationship with a gradient of - The intercept at ~- = 0 £'/2.303R. gives log10kO. Kinetic constants k^, k^, k^ in the temperature range 45°C to 80°C are applied to the equation 4.46. Relevant values are summarized in Table 4.5 and the plots of log^Q k against ^7 are shown in Figure 4.17. Gradients obtained and the evaluated figures of c and k are tabulated in Table 4.16 . The values of k° are however not evaluated by extrapolation as a value of -— = 0 would extend significantly. Instead, the values of k and T are substituted into equation 4.46 with £, evaluated graphically. A sample calculation is appended in Appendix VIA. The kinetic equations are summarized for reference: A n aly sis of S p ecific K inetic C o n sta n V t ariation w ith Temperature i r-H r-H --- I 1 — — o O O 1 I i 1 r-H 1 -V r 1 r-H M 1 H W — o O O' CO CD o o O' o> CO CD o CO CD O 1 H r-H CO i o 1 o CO 1 o CO 1 CO — — — H -- 1 1 1 1 1 £?COCOCOCOOOC^O 2 ^ 2 ^ 1-0 X X 45 318 3.14 x 10“3 1.04 x lo "4 -3 .9 9 3 -3 .0 8 9 -2 .2 4 8 ^ ^ CT) 50 323 3.10 1.23 -3 .9 1 0 -3 .0 1 2 -2 .1 8 4 00 CO r-H ° i — 3.05 X -2 .0 8 4 1.56 1 55 328 -3 .8 0 7 -2 .9 1 4 i — (X) 3.00 CO 1 60 333 1.84 -3 .7 3 5 -2 .8 4 5 -2 .0 1 5 r l ° O x — — H Ir-Hi -1 .9 7 5 65 338 2.95 2.18 -3 .6 6 1 -2 .8 0 1 i — > — -1 .9 2 5 1 1 70 343 2.92 2.54 -3 .5 9 5 -2 .7 5 0 -1 .8 9 3 i — — CO 1 )r -2 .7 0 5 75 348 2.88 2.82 -3 .5 4 9 -1 .8 5 7 — CO CN1 1 -3 .4 9 8 80 353 2.83 3.18 -2 .6 5 8 211 212 o 00 k and k # k of Plot CO I X Equation o A rrhenius 4 .1 7 . Figure e^oi6oj- 213 Table 4.6 Thermodynamic Constants of Reaction Activation Frequency Reaction Energy Factor -1 kcal/gm.mole C sec Toluene benzyl 4.57 8.9 chloride Benzyl benzal 6.73 36.4 chloride chloride Benzal benzo tri 7.75 21.8 chloride chloride 214 For the toluene reaction, k = 8.9 exp (—4.57, ) sec XRT For the benzyl chloride reaction, 1 or /l ,-6.73, v -1 k2 = 36.4 exp ( /rt ) sec For the benzal chloride reaction, , oio ,-7.75/ » -1 k^ = 31.8 exp ( /Rt ) sec with activation energies in kcal/gm mole. 4.6 Controlling Regime in Chlorine Absorption It has been shown in the preceding sections that the initial rate of chlorine absorption is independent of time, but varies as a function of the chlorine flow rate. Inspection of the degree of chlorination against time plots show that the linear portion exists up to a degree of chlorination of about 1.5, beyond which the rate of chlorination decreases. This is shown in Figure 4.18 for various chlorine flow rates and temperatures. At the maximum concentration of benzal chloride, with a degree of chlorination of about 2.0, the formation rate of benzo-tri- 215 o CO o o o o CM L inearit rH From Rate o o CO0) +J 3 c A bsorption -I-H o s 00 I CD L inear £ -r-f H of o to D ev iatio n o ■nT 4 ,1 8 . Figure o CM o X 'uoiiGuiJOxqo jo 00.160 q 216 chloride is still dependent on the flow rate of chlorine. However, beyond this point, the absorption rate from which k O was evaluated, of chlorine becomes kinetic controlled. The initial dependency of chlorine absorption rate on the chlorine flow rate can be explained by three absorption equations. In each case, diffusion is the controlling mechanism, so that increased gas loads increase the absorption rates. (i) The absorption of chlorine is followed by a slow chemical reaction, with the diffusion parameter <£ < 0.5. Further the maximum diffusion rate is less than the maximum kinetic rate, i.e. A. < 1 klBLe L In the consecutive reaction however the kinetic rate would be more appropriately expressed as the sum of the kinetic rate of each component present, thus kinetic rate = (k^ + k^C^ + k^D^) The absorption rate of chlorine is thus expressed as 217 with the physical mass transfer coefficient k° un- affected by chemical reaction. (ii) The absorption of chlorine is followed by a rapid chemical reaction, with the diffusion parameter 0 > 2.0. The absorption rate has been shown to be expressed by NA = BL 4‘18 or, a chemical mass transfer coefficient, k , may be defined such that 4.19 with B • l L % , cosh (p- 1 . . k (1 + 3 ©A cosh (p (iii) The absorption of chlorine is followed by a n infinitely fast reaction, with the diffusion parameter, (p 2.0. The absorption rate may be expressed by A. 4.20a i 218 where the chemical mass transfer coefficient is defined as r B ' 1 + . £) In each of the three cases above, the important parameter, the diffusion parameter (j) , is the necessary if not sufficient condition to determine the controlling mechanism. Practical evaluation of (p is limited by the uncertainty in knowledge of S , the film thickness. It must be borne in mind that S is a hypothetical quantity in an idealized hydro- dynamic concept. Thus it cannot be assessed experimentally. A conservative estimate in Appendix ECIB show that (p , is at all times less than 0.5, and since $ ^ > > the value of The value of (jp being less than 0.5 therefore indicates a slow reaction in the consecutive reaction, and the linear rate of chlorine absorption would be a diffusion controlled absorption expressed by the maximum physical mass transfer rate of 4.16 or k!? a A. 4.16a la 1 219 Beyond the maximum of benzal chloride, the absorption rate is kinetic controlled, with a chlorine absorption rate given by k3°L Va or k3DL€L Between the two regions is probably an indeterminate region where the absorption rate may be expressed by Difficulty in the assessment of bulk chlorine con centrations however did not enable quantitative determinations to be made. The end of the diffusion regime may be estimated graphically as the degree of chlorination at which the rate of chlorine absorption deviates from linearity. This is, however, very unsatisfactory as the accuracy is dependent on graphical intrapolation. Similarly, the commencement of the kinetic regime is ill-defined. The rather diffuse transition from a dif fusion regime to a kinetic regime may of course be explained by 220 the existence of the intermediate regime in which diffusion and kinetic rates are of approximate order. In Chapter Five, a method is suggested which allows the transition from the diffusion regime to kinetic regime to be sharply defined. 4.7 Evaluation of Volumetric Mass Transfer Coefficients Mass transfer data can be deducible in the two chlorine absorption regimes defined in section 4.6. The mass transfer coefficient k° , however, cannot be determined separately from the speciinc interfacial area, a. The two terms are there fore assessed together as the volumetric mass transfer coefficient k° a. A diffusion regime volumetric mass transfer coefficient ancl a kinetic regime volumetric mass transfer coefficient can be evaluated,and as the results show, they differ in value. 4.7.1 Evaluation of Diffusion Regime Volumetric Mass Transfer Coefficient The diffusion regime exists for a degree of chlorination of generally less than 1.5. The chlorine absorption rate is expressed by the maximum physical diffusion rate of R. k° a A. 4.16a A La or, more precisely, to define the volumetric mass transfer 221 coefficient. (k° a A. 1 LA On rearrangement of the above equation (k° a) = 4.16b LA D Ai Of the two factors on the right hand side of equation 4.16bf the chlorine absorption rate may be evaluated experimentally. The interfacial chlorine concentration A,., is a very difficult quantity to assess, although a semi-empirical method is avail- 94 able for its evaluation. The treatment of the succeeding section nevertheless, allowed of an evaluation of A,., the values of which will be applied here. When the degree of chlorination in the diffusion regime is plotted against the time of reaction, a linear relationship is obtained; the end of the diffusion regime being marked by the deviation of the graph from linearity. Hence, R may be evaluated from the linear portion of the graph since , _ Total moles of chlorine absorbed "A Total time of reaction is the gradient of the linear portion. 222 Regim e. D iffusion in Time a g a in st Chlorination i of of Plot 4 .1 9 . Figure X 'UOiq.BUTJOXl{0 jo 03J60Q 223 o CD o in GOO o o o o 03 LO LO O to co Time o x < O o Against C/3 G -.-H e i o CD CO e Chlorination -r-t H of Regime. o Degree co of Plot Diffusion o •sr 4.20. Figure o 03 o co <>» uox;suijaxqo jo eoifioQ 224 The results from Tables A4 to A8 and of Tables A9 to A15 are utilized to obtain the values of R for chlorine flow rates of 0.4 to 0.95 lb/hr at 70 C, and for a chlorine flow rate of 0.6 lb/hr for temperatures from 45°C to 80°C. Figure 4.19 shows the graphical representation of selected results from Tables A4 to A8, while Figure 420 shows the same for Tables A9 to A15. An interesting observation from the results is the fact that chlorine is completely absorbed in the diffusion regime. The molar chlorine flow rate, defined as the moles of chlorine flow per unit time per mole of initial toluene is calculated in Appendix IV. In Table 4.7, the values of the molar chlorine flow rate are included, and comparison with those of R at the chlorine flow rates indicated a complete absorption of chlorine. For the same reason, the results of Tables A9 to A15 are represented by the common -4 rate of 3.66 x 10 mole/mole sec. as all experimental points lie close to the line representing that value. Table 4.7 summarises the values of (k° a) evaluated. A sample calculation is appended in Appendix VIB. 4.7.2 Evaluation of Kinetic Regime Volumetric Mass Transfer Coefficient In the terminal stage of the chlorination of toluene, the reaction of benzal chloride to benzo-tri chloride becomes the 225 Table 4.7 Evaluation of Diffusion Regime Chlorine Physical Volumetric Mass Transfer Coefficient Chlorine Flow Rate Absorption A. Diffusion Temp- l Rate R^ Regime erature mole / lb/hr mole/ V.M.T.C.* mo*e/mole sec mole mole sec °c (k° a) sec-1 lA 0.95 5.80 x 10”4 5.80 x 10~4 70 0.101 5.74 x 10~3 0.80 4.88 4.88 70 0.101 4.83 0.60 3.66 3.66 70 0.101 3.62 0.50 3.05 3.05 70 0.101 3.02 0.40 2.44 2.44 70 0.101 2.42 0.60 3.66 3.66 45 0.118 3.10 0.60 3.66 3.66 50 0.113 3.24 0.60 3.66 3.66 55 0.111 3.30 0.60 3.66 3.66 60 0.110 3.32 0.60 3.66 3.66 65 0.107 3.42 0.60 3.66 3.66 75 0.091 4.02 0.60 3.66 3.66 80 0.089 4.11 *V. M. T. C Volumetric Mass Transfer Coefficient 226 rate controlling process, as the reaction rate progressively decreases. When the chemical reaction rate is low, the mass transfer coefficient is independent of the chemical reaction rate/ hence k = k° , the physical mass -LiA -j. LiA transfer coefficient. The rate of chlorine absorption by the liquid phase may be expressed by k a (A. - A ) LA 1 L In the steady state, the chlorine absorbed will be consumed by chemical reaction. However, in the unsteady state, an accumulation of free chlorine in the liquid phase requires an accu mulation term, so that, in an instantaneous mass balance. / Rate of feed of jRate of disappearance ^ \ chlorine } \ by reaction / j Rate of free chlorine 1 \ accumulation J or, expressed mathematically, 4.47 :T a (A - A ) .. LA 1 L -(*)reaction *(£)accumulation 227 At the beginning of the reaction in the diffusion regime, chlorine is being reacted faster than it could be transported to the reaction phase. Expressed mathematically. Consequently, the bulk chlorine concentration was initially almost zero, as shown by the nearly colourless reaction mixture. As the reaction became slower, chlorine began to accumulate, although, as was shown in the earlier section on kinetics, the absorption rate of chlorine at that stage was not reaction rate controlled. When the chlorine concentration becomes appreciable, the accumulation term for free chlorine begins to assume a non-zero value and equation 4.47 becomes valid. Returning to equation 4.47, since chlorine reacts with the organic reactants according to the stiochiometry Cl2 + Ph.CH3 ♦ Ph.CH2Cl + HC1 Cl2 + Ph.CH2Cl ♦ Ph.CHCl2 + HC1 Cl2 + Ph.CHCl2------» Ph.CCl3 + HC1 the rate of reaction of chlorine must be equal to the total rate of reaction of the organic reactants, i.e. hlorine C ypical T . 1 .2 4 Figure urve C ulation ccum A -» i B D B c CD a> w 4 -rH -r-l H O o o 03 o o CO o CO O O 03 O o oo 03 03 228 or 229 Rate of reaction = k-^B^ + + k^D^ assuming ^ = 1.0. This quantity is calculated as the .Lj kinetic rate in Tables A4 to A15. The accumulation rate of free chlorine has to be evaluated graphically. Figure 4.21 shows a plot of free chlorine against the time of reaction for the results of Table A13. The rate of accumulation at any time is then equal to the graphical gradient estimated at that point. If, in equation 4.47, ^ _ (rate of reaction of chlorine) + (rate of accumulation of free chlorine) R = k° a A. - k° a AT La l la l Hence, equation 4.47 is a linear equation of R in A . If R is plotted against A , a straight line will result, with a gradient J-j of - k a. The intercept at A =0 is k a A., from which A. JLi J_i J"J/\ ^ ^ may be obtained. Alternately, when R = 0, A^ = A^ also. Table 4.8 summarizes the values of the kinetic rate and accumulation rate of chlorine for the results of Table A13, the free chlorine accumulation rate being derived from Figure 4.21. The quantity R is then plotted against A in Figure 4.22. A L 230 Table 4.8 Evaluation of Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficient o Temperature = 65 C Chlorine Flow Rate = 0.6 lb/hr. Time of Free Chlorine Accumulation Kinetic Rate Total Rate Reaction Content, mole, min. Rate, dAL mole/moie sec mole/mole /mole sec mo*e/mole sec 115 0.042 2.0 x 10”5 1.57 x 10~4 1.75 x 10"4 130 0.059 1.9 1.09 1.28 145 0.072 1.5 8.52 x l(f5 1.02 160 0.077 1.2 6.84 8.04 x 10”5 175 0.083 1.2 5.71 6.00 190 0.088 4 x 10'6 4.55 4.95 205 0.090 3 4.18 4.48 220 0.093 2 3.37 3.57 235 0.095 2 2.92 3.12 Total C hlorine A bsorption Rate, m ole/m ole s e c . 0.04 Figure Temperature Chlorine 4.22. LEGEND Molar 0.06 Rate Graphical Physical = Free = 65 0.6 Chlorine C 0.07 Volumetric Evaluation lb/hr Gradient Content, 0.08 2.73 Mass of x Kinetic 10 mole/mole Transfer 0.09 Regime Coefficient 0.10 Chlorine 231 232 linear relationship, as predicted is shown. From Figure 4.22, Q "I (k° a). = 2.73x10 sec L k and A = 0.107 mole/mole where (k° a) = kinetic regime volumetric mass transfer k coefficient Table 4.9 summarises the values of (k^ a)^ and A. evaluated from the results of Tables A4 to A15. Comparison of the diffusion and kinetic regime volumetric mass transfer coefficients will show that they differ considerably in value. In the evaluation of the volumetric mass transfer co efficients, it was assumed that the coefficients would remain constant within a regime. While the diffusion regime generally occurs for a degree of chlorination of less than 1.5, the kinetic regime occurs for a degree of chlorination in excess of 2.0. The liquid properties change as the chlorination proceeds, viscosity and density increases as the degree of chlorination increases. It is likely therefore that the diffusion coefficient decreases as reaction progresses, since S) decreases as viscosity increases. Similarly, the film thickness & increases as the viscosity and density increases. Thus, a decrease 233 Table 4.9 Summary of Evaluated Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficients and Chlorine Solubilities Chlorine Flow Temperature Kinetic Regime Chlorine Solubi Rate V.M.T.C.* lity A. °C lb/hr -1 sec mole/mole 0.95 70 3.98 x 10"3 0.100 0.80 70 3.45 0.102 0.60 70 2.60 0.102 0.50 70 2.15 0.100 0.40 70 1.83 0.101 0.60 45 1.85 0.118 0.60 50 2.22 0.113 0.60 55 2.25 0.111 0.60 60 2.35 0.110 0.60 65 2.73 0.107 0.60 75 2.80 0.091 0.60 80 2.92 0.089 Av. chlorine solubility at 70°C = 0.101 mole/mole *V.M.T.C. = Volumetric Mass Transfer Coefficient 234 of the mass transfer coefficient k° occurs. The change -Li of liquid properties may also lead to a different bubble formation mechanism that leads to a decreased gas-liquid interfacial area as reaction progresses. Hence, an overall gradual decrease of the volumetric mass transfer coefficient occurs. 4.7.3 Variation of Volumetric Mass Transfer Coefficient with Chlorine Flow Rate It can be observed from the results in Tables 4.7 and o 4.9 that the volumetric mass transfer coefficient, k a increases JLi as the chlorine flow rate, both in the diffusion and kinetic regimes. A similar trend had been reported by many authors. Generally the correlations are made in terms of a superficial gas velocity, which is defined as _ volume flow rate of gas s cross sectional area of reactor Of course, vg only remains constant for a constant cross sectional area. This quantity is therefore used only in uniform cross section reactors . The general relationship between k°a and v is given by s m k OC V s or a 235 Table 4.10 Comparison of Diffusion Regime and Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficients Chlorine Temperature Kinetic Regime Diffusion Regime Rate mole/ mole sec °c V. M. T. C.* sec 1 V.M.T.C.* sec"1 5.80 x 10-4 70.0 3.98 x lCf3 5.74 x 10"3 4.88 70.0 3.45 4.83 3.66 70.0 2.60 3.62 3.05 70.0 2.15 3.02 2.44 70.0 1.83 2.42 3.66 45.0 1.85 3.10 3.66 50.0 2.22 3.24 3.66 55.0 2.25 3.30 3.66 60.0 2.35 3.32 3.66 65.0 2.73 3.42 3.66 75.0 2.80 4.02 3.66 80.0 2.92 4.11 *V. M.T. C Volumetric Mass Transfer Coefficient 236 where M,m are constants. The value of the constant m has been reported to vary between the limits of 0 to 1.0 for various gas-liquid systems, with or without a chemical reaction. Generally, a value of m ss 0,8 is applicable, especially for systems involving a gas-liquid reaction. A value of m = 1.0 is not uncommon for relatively fast absorptions. The use of a superficial gas velocity, however, will not take into account the ratio of the gas flow rate to the weight or amount of liquid reactant in a reactor. For the present work, the more appropriate velocity to use will be the molar flow rate of chlorine which takes into account the amount to liquid reactant. The molar chlorine flow rate is defined as, moles chlorine flow per sec moles initial toluene Table 4.10 summarizes the values of (k° a^ and (k° a\ with the molar chlorine flow rfetes. The conversion of la weight flow rate to superficial velocity is given in Appendix III. Figure 4.23 is the graphical representation of Ck° a)j^ and (k°_ a) against v , the molar chlorine flow ra . L, K m 4 "A V lo o D iffusion Readme • 0IX 09 o S • / q.U0IOIJJ0OO o co • J0JSUUJX \ SSU]/\[ \ CO o \ \ OIJi0UiR7OA \ \ \ \ \ \ \ \ \ \ \ \ 237 \ o CO o CO o o o CO o o uo o t". o I M olar C hlorine Flow Rate - m o le/m o le.s e c .x 10 Figure 4 .2 3 . Plot of P h y sical V olum etric M ass T ran sfer Coefficient A gainst Molar Chlorine Flow Rate. 238 Inspection shows that within the range investigated, (k° a) and (k° a). varied linearly with v . The linear L D L k m relationship between (k a) and v must be expected since L D m a complete absorption of chlorine is indicated. Extrapolation beyond the experimental range must be done with caution, since a flow rate is attainable at which the absorption rate deviates from linearity, and m deviates from 1.0 accordingly. This is especially true of the relationship between (k° a), and v L k m Strictly speaking, the linear relationship between (k° a) and v does not extend to the origin. The reason is L m that at suppressed gas velocities, laminar hydrodynamic conditions prevail in the liquid and this gives rise to decreased values of the mass transfer coefficient and interfacial area. Studies could not be made for chlorine flow rates much lower than 0.3 lb/hr because of the contracted scale of the chlorine meter and also because of the uncertain mixing conditions in the reactor at low gas velocities. Nevertheless, a linear relationship between k° a and v is assumed up to the point of origin. Two empirical L m equations between the two quantities are thus obtainable: In the diffusion regime. 1.0 10.0 v 239 In the kinetic regime, 1.0 7.20 v 4.7.4 Effect of Temperature on Mass Transfer In the steady-state diffusion theory, the mass transfer coefficient is directly proportional to the diffusion coefficient, £) . Thus Empirical equations quoted previously correlate the diffusion coefficient <© in the Sherwood Group to the Reynolds Number and the Schmidt Number. Primarily, o£? varies as a function of temperature, and as shown in Appendix IIIA, Table 4.11 Variation of Chlorine Volumetric Mass Transfer Coefficient with Temperature Chlorine Flow Rate at 0.6 lb/hr. Tfe mperature Diffusion Regime Kinfetic Regime °c V.M.T.C.* sec "*■ V. T. M. C.* sec * 45 3.10 x 10~3 1.85 x 10~3 50 3.24 2.22 55 3.30 2.25 60 3.32 2.35 65 3.42 2.73 70 3.62 2.60 75 4.02 2.80 80 4.11 2.92 * V.M.T.C Volumetric Mass Transfer Coefficient Figure 4 . 24. Plot of D iffusion and K inetic Regime P h y sical Volum etric M ass T ran sfer Coefficient A gainst Temperature. 242 o correlated. He attributed the change of k a with temperature J-j to changes in the diffusion coefficient. Values of k°a evaluated in the constant chlorine J-i ^ rate runs are conveniently applicable to the correlation of k a against temperature. Table 4.11 lists the values of (k a ) J—/ and (k°a ) with temperature. The resultant representation of i-i ^ (k a ) with temperature in C does not suggest any non-linear relationship. Again extrapolations should not be greatly extended. Two empirical correlations are obtainable from Figure 4.24 for k°a against temperature. In the diffusion regime: (k°a)D = (kLa)45°C + (2-58 x 10_5)(&- 45) &°C In the kinetic regime: (k°a)k = (k° a)45oc + (3.14 x 10_5) ( 45) &°C The above equations can in principle be applied to calculate mass transfer rates in the appropriate regimes although the use at temperatures beyond 45-80°C should be limited to a first approximation in the absence of more data. 243 4.8 Effect of Mass Transfer on Selectivity The photochemical chlorination of the toluene side chain is a consecutive reaction which has been shown to obey a first order rate with respect to the organic reactant at each stage of reaction, if the reaction of benzal chloride to benzo- trichloride has a mechanism shared by its preceding reactions. In section 4.2 of this chapter, the qualitative and mathematical bases on which a reaction of this type can show a fall in the selectivity of an intermediate product as a result of the diffusion process has been developed. Considering the reaction only up to the stage of benzal chloride formation, then the yield of C under non-selectivity limitation is given by 4.40 B o while for a selectivity - limited product distribution. 4.42 244 In the evaluation of k and k , the product distribu- C d 1 ^ tion of — and of — had been assumed to be non-selectivity D U limited. The validity of the assumption will be shown in this section for the first reaction of B C by two quantitative methods. 1. The value of the diffusion parameter , determined in Appendix IIIB has a value of less than 0.5. In a selectivity limited series reaction, a necessary condition is for <£,>• 0.5. When the condition is obeyed, along with the requirement that g L % 1 the product C falls in selectivity, while for the A i 1 i T diffusion parameter 2.0, total selectivity limitation will occur, with the product distribution given by equation 4.42. Hence, the fact that 2. The ratio of specific kinetic constants Vk' and 2/j_ has been evaluated on the assumption that product O distribution is not selectivity limited. Substituting the value of ]<£ 1/jr into the theoretical equations for both selectivity and non- 245 selectivity limited equations, two theoretical product distribu tion equations of C against B are obtained. Experimental . r C values of should lie close to the theoretical curve for non-selectivity limitation if the original assumption is true, otherwise a wrong value of l/k had been assumed initially. This inductive proof was carried out with experimental data obtained. Experimental values of (c/b) shown in Table 4.4 show a regular decrease with temperature, suggesting that no irregular changes in the physico-chemical processes between temperature of 45°C to 80°C have occurred which could drastically cause a selectivity limited distribution. Results at the extreme temperatures of 45°C and 80°C are taken. Values of S = 6.80 and 6.30 are substituted into equations 4.40 and 4.42 for 45°C and 80°C respectively. A computer was employed in the evaluation of L/go f°r re9ular increases of f the data being shown in Tables 4.12 and 4.13. A graphical representation of the yield Q of the intermediate L/. , is made against the amount of B B /B° remaining, L/ = (1 - conversion), Figures 4.25 and 4.26 'Bnu o o showing the cases for 45 C and 80 C respectively. Graphical evidence shows that theoretical data and experimental data agree closely for a non-selectivity limited product distribution validating the inductive assumption made initially. A similar procedure in analysis was repeated for the 246 Table 4.12 Theoretical Selectivity of Benzyl Chloride Under Diffusion and non-Diffusion Limitation at 45 C S = 6.80 Toluene Concentration Benzyl Chloride Benzyl Chloride Yield Under Yield Under = ( 1-Toluene Con Diffusion Limitation Non-Diffusion verted) Limitation mole / mole mole/mole mole/mole 1.00 0.00 0.00 0.80 0.13 0.19 0.60 0.26 0.38 0.40 0.35 0.55 0.30 0.38 0.63 0.25 0.39 0.66 0.20 0.39 0.69 0.15 0.39 0.71 0.10 0.36 0.71 0.05 0.31 0.69 0.04 0.29 0.68 0.03 0.27 0.66 0.02 0.23 0.63 0.01 0.18 0.58 0.00 0.00 0.00 | 247 45 at C hloride Benzyl of Selectivity 4 .2 5 , Figure 248 Table 4.13 Theoretical Selectivity of Benzyl Chloride Under Diffusion and non-Diffusion Limitation at 80 C S = 6.30 Toluene Concentration Benzyl Chloride Yield Benzyl Chloride Yield Under Diffusion Under non-Diffusion = (1 - Toluene Con- Limitation Limitation . / verted) mole / mole mole / mole mole / mole 1.00 0.00 0.00 0.80 0.13 0.19 0.60 0.25 0.38 0.40 0.34 0.55 0.30 0.37 0.62 0.25 0.38 0.65 0.20 0.38 0.68 0.15 0.37 0.70 0.10 0.35 0.70 0.05 0.30 0.67 0.04 0.28 0.66 0.03 0.25 0.64 0.02 0.22 0.61 0.01 0.17 0.56 0.00 0.00 0.00 249 80 at C h lo rid e Benzyl of Selectivity 4 .2 6 . Figure 250 Table 4.14 Theoretical Selectivity of Renzyl Chloride Under Diffusion and non-Diffusion Limitation at 70 C S = 6.65 Toluene Concentration Benzyl Chloride Yield Benzyl Chloride Yield Under Diffusion Under non-Diffusion = (1 - Toluene Converted Limitation Limitation mole / mole mole / mole mole / mole 1.00 0.00 0.00 0.80 0.13 0.19 0.60 0.25 0.38 0.40 0.35 0.55 0.30 0.38 0.62 0.25 0.39 0.66 0.20 0.39 0.68 0.15 0.38 0.70 0.10 0.36 0.71 0.05 0.30 0.69 0.04 0.29 0.67 0.03 0.26 0.65 0.02 0.23 0.63 0.01 0.18 0.57 0.00 0.00 0.00 251 C 70 at C hloride Benzyl of Selectivity 4 .2 7 . Figure 252 results of Tables A4 to A8, for a temperature of 70°C/ but with chlorine flow rate varying from 0.4 to 0.95 lb/hr. Experimental data again lie close to the theoretical curve for non-selectivity limitation for S = 6.65 (Figure 4.27) . Returning to the dimensionless diffusion parameter Physico-chemical factors did not alter with temperature variations from 45°C to 80°C and gas flow rates from 0.4 lb/hr to 0.95 lb/hr, to affect the non-diffusion limitation mechanism. Principally, the increase of temperature increases k and S , while a i B decrease of gas flow rate decrease fluid turbulence with an increase of the film thickness <5 29 Van de Vusse in the photochemical chlorination of decane had to pass chlorine over a still pool of n-decane in order to achieve the hydrodynamic conditions conducive to a fall in selectivity. In view of the rather extreme conditions required for selectivity limited series reactions, it can be generalized that the conditions can only be present in such practical cases as 253 (i) Rapid reactions so that the rate constant k is high. For a first order reaction, k can be estimated to be at least of the order of 10 ^ sec. for selectivity limitation. Some very fast organic reactions and inorganic reactions will fulfill these requirements. (ii) A very viscous liquid reactant or solvent so that laminar conditions prevail. This favours a large film thickness S and hence (j) . In the absence of any influence of diffusion on the selectivity of consecutive reaction, the selectivity will only be a function of the kinetic constant of k , k and k . Since k 12 3 1* k^ and k^ have different activation energies, as determined in section 4.5, the selectivity will be a function of the temperature also. Rather unfortunately, the temperature range available for the study of this reaction without thereby changing the basic mechanism is narrow so that a critical analysis of the temperature ]<£ effects cannot be made. In Table 4.4, the values of__ 1_ and of k ko 2 are both decreasing functions of temperature, 2 showing ko 05 that selectivity will decrease as the temperature increases. This observation is illustrated in Figure 4.28 which shows the product distribution curve against the degree of chlorination for o o temperatures of 45 C and 80 C. Peak values of benzal and benzyl 254 P lo t. X Distribution To O O c: -i-io "fO c -l—i Product o - I—I .c O u-tO CD . CD Cni-4 (D Q Chlorination of D egree 4 .2 8 . Figure uoiipuij sioiAI 0JOUI 255 4-> 13 N r—H Chlorination. of D egree c o -I-) a g a in st fO X O O O a (O 00 •j-H o +- o o o rHX O VM o <3 > Distribution <1) CD i-, Co a) Q Product of Plot 4 .2 9 . Figure o o o o 0IOUJ/0IOLU 'uopoejj 0foi/\[ 256 chloride are higher at 45°C than the corresponding peaks at 80°C. The higher selectivity of benzyl chloride at 45°C however leads to a decrease in the higher chlorinated product of benzal chloride, between the degrees of chlorination of 0.8 to 1.8 , while similarly, the increased selectivity of benzal chloride between a degree of chlorination of 1.8 to 2.5 also leads to a decreased yield of benzo-trichloride. As diffusion does not affect the selectivity, variation of chlorine flow rate will not affect selectivity and product distribution. This fact is clearly shown in Figure 4.29 for the temperature of 70°C and chlorine flow rates from 0.4 to 0.95 lb/hr. A single product distribution curve represents all the experimental results at the different chlorine flow rates. 4.9 An Evaluation of Specific Interfacial Area and Film Thickness The absorption rate of a gaseous reactant A followed by a chemical reaction of first order with respect to a liquid reactant B is shown to be given by 6 -a cT 4.11 x=0 JhQ h tanh<£ + 2 2) (A -A ) + -2- ( .=JL. ) 4.13 n V £ 1 cosh and 4.12 In the chlorination of toluene, the reaction rate is slow relative to the diffusion rate so that (j> is deduced to be less than 0.5. Further, bulk chlorine concentration is very low, and the assumption AT ^ O may be made. The right hand side JLi of equation 4.11 contains the terms which describe the reactions of A and B in the diffusion and bulk regions respectively. In the absence of an appreciable A , reaction in the bulk region J-j may be considered to be absent, so that O and hence 4C48 jh-Vl tanhf The last statement of equation 4.48 however cannot be completely correct as it is more probable that A is maintained at an im- L perceptibly low concentration because of a very rapid bulk liquid reaction. For discussion, however, the assumption of no bulk liquid reaction will be made, and all conversion of A and B 258 are deemed to occur in the diffusion region. The concentration of B remains constant at B Xj in the diffusion region in contrast to the case of a rapid reaction. Thus, for fA „ = klBL^ x=0 and ki A- x=0 la 1 from which \h 4.49 i ki bl For the assumption of complete reaction in the diffusion region, the initial stage of reaction when B^ = Bq would be the best approximation. Calculated on a molar basis, Bq=1.0 mole/mole initial toluene. Hence, 4.49a Equation 4.49a above shows that 6 would be dependent only- on physical and chemical constants, and independent of gas flow rates or other hydrodynamic variables. In the diffusion regime, it was shown earlier that all 259 chlorine fed to the reactor is reacted. Therefore* if v m is the molar flow rate of chlorine. v = R. = k° A. . a 4.50 m A L 1 and hence a 4.51 A Calculated values of a and o are tabulated in Table 4.15. A sample calculation for results at a temperature of 55°C and chlorine flow rate of 0.6 lb/hr is given in Appendix VIC. Evaluated data on & shown in Table 4.15 are much -2 , greater than the value of 10 cm assumed in the estimation of cp . C -2 In view of the fact that O = 1x10 is already a conservative estimate, the values of & must be vastly overestimated, and an error of 500-1000% will not be excessive. This gross over estimation arises from the assumption of the absence of bulk retion reaction, Even a small reaction in the bulk region is reflected as a large diffusion region reaction, because of the large ratio of bulk volume to film volume. The specific interfacial area and film thickness are related by equation 4.51, so that errors in 5 are also compounded in a. In view of the assumptions made, the value of S is not acceptable with confidence, and a 260 Table 4.15 Summary of Film Thickness and Specific Interfacial Area Chlorine Flow Rate Temperature 5 a -1 mole/ cm cm lb/hr mole sec. &°c 0.6 3.66 x 10"4 45 3.13 xl(f2 2.16 0.6 3.66 50 2.93 1.91 0.6 3.66 55 2.70 1.64 0.6 3.66 60 2.56 1.47 0.6 3.66 65 2.46 1.40 0.6 3.66 70 2.34 1.34 0.6 3.66 75 2.21 1.26 0.6 3.66 80 2.18 1.20 0.4 2.44 70 2.34 0.88 0.5 3.05 70 2.34 1.10 0.8 4.88 70 2.34 1.76 0.95 5.80 70 2.34 2.10 . 2(i 1 LEGEND Chlorine Flow Rate at 0.6 lb/hr 1.4 — Temperature C Figure 4.30. Plot of Specific Interfacial Area and Film Thickness Against Temperature 262 CD o A gainst 00 o T h ick n ess Film SO I and o 0 +J asCO Area £ o Rate pH CO 0 c -rH o Flow o Interfacial so O of Plot LO Chlorine o 4 .3 1 . o Figure CO o CM o uio 'eajv leioejjaiui cijicodg 263 value of o = 1x10 cm. is used in estimation of ^ . Since of value of Figure 4.30 shows the increase of both a and as temperature decreases, gas flow rate being constant at 0.6 lb/hr. The change in S can be expected because lowered temperatures increase viscosity in the liquid. Turbulence may be expected to decrease, hence & increases. Gas rate does not alter & but as shown in Figure 4.31, increasing gas rate increases the specific interfacial area linearly. In section 4.7.3, it is shown that the volumetric mass transfer coefficient increases as gas rate increases. From the present estimate, since & does not vary with gas flow rate, the increase of the interfacial area accounts for the increase of the volumetric mass transfer coefficient. Strictly speaking, 'a' and <3 should not be estimated to three significant figures, and because of the approxi mations, an average value should be taken. Thus, on averaging, 264 average film thickness = 2.5 x 10 cm average specific interfacial are = 1.5 cm 1 93 Kramers estimates the specific interfacial area for column reactors as follows: Bubble column reactors : 20 m ^ (0.2 cm Agitated bubble contactors : 2 00 m ^ (2 cm ^ ) The values of 'a' have therefore been overestimated, but nevertheless are of the correct order. 265 4.10 Chlorine Solubility Data - A Comparison of Experimental and Empirical Data 94 Prausnitz and Shair derived an empirical means to derive gas solubility data in non-polar liquids. The final equation is quoted below: exp 4.52 Two valid approximations are made: (1) The fugacity of pure gas is equal to its pressure at 1 atm i. e. f° = 1 atm (2) The solubility of gas in the liquid is low so that may be taken as 1.0. Taking P as the critical pressure of the gas, Prausnitz C L and Shair plotted a graphical representation of f /P against T/j-. c c for a gas where T is the gaseous critical temperature. C L Knowing T , P and T, the value of f can be estimated C C 95 graphically. Critical data for chlorine is obtained from Perry . 266 To solubility param eter s is calculated for 96 toluene from Hildebrand's empirical equation 4.53 and 2 = -2950 + 23.7 T,_ + 0.020 T 4.54 b b 298°k w here = enthalpy of vaporization at 298°K 298 Kf cal./gm mole. VJ = molar volume of liquid , c,c*/gm mole T, = boiling point of liquid at T°K The factor in equation 4.52 is an independent function of temperature. It is most conveniently calculated at 25°C = 298°K. Data given below are: o 94 8.9 (Cal/c.c. ) 25 C o s = 8.7 25 C from equations 2 4.53 and 4.54 267 =74.0 cc/gm mole94 R = 1.98 cals/ gm mole°C 1.0 v" (^i”s2)2 li2 Therefore 1.49 °C 1 Table 4.16 lists the data that lead to a value of y for 40 to 90°C . A graphical plot of the molar chlorine solubility against is presented in Figure 4.32 both for the empirical and experimental values. Examination of Table 4.17 and Figure 4.32 shows that the experimental value of A is always higher, but the experimental and empirical values are nevertheless of a similar order of 10 ^ mole/mole. It must be borne in mind that A^ had been calculated for chlorine in a benzal chloride/ benzo trichloride mixture, and not in toluene, although the empirical values are based on toluene owing to the unavailability of data for the other organic liquids. The chloro-organic compounds definitely are polar, contradicting the theoretical requirement of a non polar liquid. Approximations and limitations of the theory may however contribute substantially to the errors in a theoretical value. Without other reliable sources of comparison, it may be concluded that the solubility data of chlorine determined 268 Table 4.16 Evaluation of Empirical Chlorine Solubility o atm mole/ y mole/ T K V/T V exp T mole /mole 313 .00476 1.0048 10.17 10.22 0.098 323 .00461 1.0046 12.63 12.69 0.079 333 .00447 1.0045 15.20 15.27 0.066 343 .00434 1.0044 18.02 18.10 0.055 353 .00422 1.0042 21.40 21.49 0.047 363 .00410 1.0041 25.20 25.30 0.040 269 Table 4.17 Comparison of Experimental and Empirical Chlorine Solubility Data A. mole/ G°c T°K *4 V1 ymole/mole 1 mole x lO-3 40 313 3.20 0.098 - 45 318 3.14 - 0.118 50 323 3.10 0.079 0.113 55 328 3.05 - 0.111 60 333 3.00 0.066 0.110 65 338 2.96 - 0.107 70 343 2.92 0.055 0.101 75 348 2.88 - 0.091 80 353 2.83 0.047 0.089 90 363 2.75 0.040 C hlorine S o lu b ility in T oluene, 5 0.10 0.06 Fig. 4.32. Comparison Chlorine Solubility of Experimental 3.00 Data. Experimental Empirical and Empirical 270 271 experimentally are of a correct order and may be accepted and utilized with confidence. Ill 4.11 Experimental Investigation in the Agitated Batch Reactor The photochemical chlorination of toluene was further investigated in a laboratory scale stirred batch reactor. A constant chlorine flow rate of 0,6 lb/hr and a temperature of 70°C was used. The speed of agitation, provided by a laboratory magnetic stirrer unit was varied from 500 to 2000 revolutions per minute (rpm). A liquid volume of 308 ml was used so that the data could be compared with similar conditions in the bubble column reactor. Kinetic data and the volumetric mass transfer coefficients in the diffusion and kinetic regimes were evaluated in the same manner as those in the bubble column reactor. Generally, the chlorination of toluene in the stirred batch reactor closely paralleled the same reaction in the bubble column in respect of qualitative observation. An induction period of about two minutes always preceded the normal reaction. Agitation produced uniform bubble size which did not differ greatly from that generated in the bubble column reactor. Experimental results for the stirred batch reactor are summarized in Tables A16-A20 of Appendix VII, 4.11.1 Evaluation of Kinetic Constants k^, k^f k^ The first order specific rate constants k^, k^ and k^ were evaluated by first calculating k^ in the kinetic regime and 273 Chloride) R eactor B enzal Batch In itia l A gitated - (Fraction 0 Time log of Plot a g a in st 4 .3 3 , Figure 274 subsequently and k^ were determined from the product distribution curve, similar to the procedure for the bubble column reactor. Figure 4.33 is a plot of log against e o time for the stirred batch reactor investigations. Good reprodu cibility was indicated by the results, and a single linear relationship represented quite adequately the experimental values obtained for all stirrer speeds used. From the gradient of the linear correlation, the specific reaction rate constant k^ was determined as k = 2.50 x 10 ^ sec * 3 The good agreement of the kinetic constants determined over the range of agitation rates used adds further evidence to the regime being kinetic controlled. A common product distribution - degree of chlorination curve was found to represent all the experimental data of Tables A16 to A20. This was again expected as the product distribution with respect to the degree of chlorination was already shown previously to depend only on the reaction temperature and to be independent of a variation in the chlorine gas flow rate. The latter, with respect to hydrodynamic conditions is similar to a variation of the agitation rate. From the product distribution curve 275 o a! c o fO c •rH C> 3c O Mo—( 0 ti o Chlorination of D egree P ■8 a.u. 'sr CO a) mp. tr> -<-H Pm 0IOUJ/aToui 010^ 276 8fom / 'apuomo lAzuag jo PI^IA ' atoui 277 of Figure 4.34f the ratio of the reaction rate constants are -— = 6.65 and — = 7.00 z K3 from which k^ and were evaluated as k^ = 1.34 x 10 ^ sec ^ k^ = 1.75 x 10 ^ Sec * Comparison between the product distribution curve of Figure 4.34 with Figure 4.20 for the bubble column reactor showed a close similarity. By virtue of this similarity also, it was deduced that the process of diffusion did not limit the selectivities of benzyl and benzal chlorides in the consecutive reaction. This observation was also indicated by the yield-conversion plot of Figure 4.35 for a value of S = 6.65 in the reaction kl k2 B ------* C ------* D toluene benzyl benzal chloride chloride The experimental values obtained lie close to the theoretical equation for a non-diffusion limited selectivity (equation 4.40). Hence agitation did not affect the selectivity of the inter mediate. 278 2000 1500 Coefficient Regime Transfer r.p.m . Diffusion Mass of 1000 Rate, Volumetric Agitation of Agitation Physical Effect 500 4.36. Figure 00 s 1U0TOTJJ0OQ jsjsueij, ssej/M OTj;0iunxoA leoisAq^ 279 4.11.2 Volumetric Mass Transfer Coefficients In a gas liquid contactor, agitation increases the rate of mass transfer between the two phases. An increase of both the mass transfer coefficient (k ) and the specific J_i interfacial area ( a) have been reported previously in the literature review. The chlorination of toluene in the agitated batch reactor was observed to be distinguishable into two distinct regimes. At low degrees of chlorination, the absorption and conversion of chlorine was a diffusion controlled process. Further, as in the case of the same reaction in the column reactor, chlorine was completely absorbed in the diffusion regime. This observa tion led to the conclusion that the diffusion regime volumetric mass transfer coefficient was independent of rate of agitation, as shown in Figure 4.36. Utilizing a value of A^ = 0.101 mole/m02e, the diffusion regime volumetric mass transfer coefficient for the stirred batch reactor and the bubble column reactor at 70°C and a chlorine gas flow rate of 0.6 lb/hr were identical. Hence, in the diffusion regime where the absorption of chlorine is complete, even in the unagitated bubble column reactor, the application of agitation in a stirred reactor will not increase mass transfer rates. The kinetic regime volumetric mass transfer coefficient for the stirred batch reactor were again evaluated from the mass balance equation 280 Rate of absorption'' { Rate of chlorine reaction J 4 v of chlorine / Rate of free chlorine 1 accumulation} The rate of chlorine reaction will be equal to the rate evaluated with the kinetic constants of = 1.34 x 10 ^ sec k^ = 1.75 x 10 ^ sec * kg = 2.50x10 ^ sec for the stirred batch reactor. For the various agitation rates these are tabulated in Tables A16-A20 (Appendix VII). A summary of the volumetric mass transfer coefficients determined for each agitation rate is shown in Table 4.18. Figure 4.37 is the graphical representation of the results, from which the effect of agitation on mass transfer becomes evident. Agitation at 500 rpm in the batch reactor increased the kinetic regime mass transfer coefficient above that for the bubble column reactor. Increasing the agitation rate increased the co efficient, but above an agitation rate of 1000 rpm, the volumetric mass transfer coefficient became almost independent of the agitation rate. 281 2000 1500 Volumetric Physical Regime 1000 Kinetic r.p .m . on Coefficient. Rate- Agitation of Transfer Agitation Mass Effect 50 7. 4.3 Figure o o o O lO o uO • • o CO CM CO CM • oi x O0S 'lueTOijjeoQ J0JSU0JX sspjm 0ij;0iunjoA 282 Table 4.18 Effect of Agitation on Kinetic Regime Chlorine Physical Volumetric Mass Transfer Coefficient Temperature = 70°C Chlorine Flow Rate = 0.6 lb/hr Agitation Rate Kinetic Regime _ i r.p.m. V.M.T.C. sec -3 - (Bubble Column) 2.60 x 10 500 2.70 750 2.95 1000 3.05 1500 3.20 2000 3.18 283 Since the conversion rate of chlorine in the kinetic regime is kinetic controlled, the increased rate of chlorine diffusion resulted in an increase in the free chlorine concentra tion in the liquid phase. This was evident from an inspection of the free chlorine concentrations in Tables A16-A20. In Chapter Five the subject is further discussed. The experimental investigation in the stirred batch reactor confirmed the probability of the kinetic regime observed in experiments conducted with the bubble column reactor. Kinetic information was reproducible in the stirred reactor, and was in dependent of the agitation rate. Although the inference would have been obvious, the diffusion regime mass transfer coefficient did not increase with agitation since chlorine absorption was complete in this regime. On the other hand, the kinetic regime volumetric mass transfer coefficient increased with agitation, but became constant above a particular agitation rate. The results of these obse rvations on the stirred batch reactor will be utilized in the next chapter. 284 CHAPTER FIVE 5.1 Controlling Parameters on Conversion Rate The general theory developed in the preceding chapter for a gas-liquid heterogeneous reaction with kinetics of first order with respect to the liquid reactant showed that the absorption rate of the gaseous reactant A is dependent on the dimension less diffusion parameter j) . Three limiting cases of absorption rates are designated according to <^> . (i) When the chemical reaction is infinitely fast, <£ 2.0 and the absorption rate of A is given by a chemical diffusion rate where (ii) When the chemical reaction is fast, rate of A is given by the chemical diffusion rate N A A l A with k L JA 285 (iii) The third and perhaps most interesting case occurs when the chemical reaction rate is slow. Theoretical treatment shows that two sub-cases arise with a further controlling parameter: (a) When the reaction rate is low and the interfacial area is high, so that the maximum physical mass transfer rate is greater than the reaction rate. > k- bl* L the overall rate is chemical reaction controlled, with kl BL £ L (b) Conversely, when the reaction rate is low, and the inter facial area is low, so that the maximum physical mass transfer rate is less than the chemical reaction rate, a A. <• 1 ki bl6l the absorption rate becomes physical mass transfer controlled, and A. 1 286 The photochemical chlorination of toluene to benzo-trichloride was shown to be a slow chemical reaction relative to the diffusion rates of the components, i.e.^X.0.5. Also in the course of the chemical reaction, the absorption rate of chlorine was initially physical mass transfer controlled, but at some statje of the reaction, changed to a chemical reaction controlled rate. In other words, the criteria of k° a A i BL€L LA has changed to k° a A. > Z.k Bt fcT L„ 1 ILL where B is a general liquid reactant in the consecutive reaction. L Accordingly, the kinetics indpendent of mass transfer rate was determined, along with a volumetric mass transfer coefficient (physical) in both the kinetic and diffusion regimes. However, because of the existence of an undefined intermediate regime between the kinetic and diffusion regimes, transition from the diffusion to the kinetic regime was not sharply defined. The position is not aided by the fact that the deviation of the absorption curve from linearity in the diffusion regime, which would mark the end of a diffusion controlled absorption, cannot be defined because the deviation occurs gradually. The 287 commencement of the kinetic controlled absorption was similarly ill-defined, and was not established until the degree of chlorination exceeded 2.0. Obviously, such a treatment would leave much to be desired, particularly in relation to the design of a suitable reactor where the controlling regime and the absorption rate need to be defined. Dimensions and geometric design are of importance in a mass transfer controlled absorption* but the volume would be the only factor of importance in a kinetic controlled absorption. Application of the results from the preceding chapter will allow of a more precise determination of the transition point from the diffusion regime to the kinetic regime. 5.1.1 Effect of Chlorine Flow Rate on Conversion In the diffusion regime, the overall rate of chlorine absorption* and its conversion, since the chlorine absorbed is totally reacted* may be expressed by a linear time rate of dA , o _ rA “ dt “ (kLA a Ai Deviation from linearity in an unsteady state chlorina tion marks the end of the diffusion regime. In the kinetic regime the rate of conversion is indicated by the expression kinetic rate = k D £. 288 since reaction is largely the conversion of benzal chloride. The overall absorption rate of chlorine may be expressed by (k“ a), W which is greater than the kinetic rate because free chlorine accumulates in the reactor. Since the kinetic rate is the limiting rate for conversion, a transition from the diffusion absorption regime to the kinetic absorption regime may be determined if the intermediate regime is assumed not to exist. In figure 5.1, the kinetic rate is plotted against the degree of conversion for a temperature of 70°C. The kinetic rate for the consecutive reaction is the summation of the kinetic rates of each reacting species, so that kinetic rate = (k B + k C + k D ) £ 1 Ll Ca J_| O J_j i_| The kinetic rates are tabulated in Tables A4-A15 for the bubble column reactor, and are calculated on an assumption of 1.0 K in e tic R a te , ' m o le s e c . 5-80 x Temperature 1 Figure Q LEGEND ‘ 5.1. Maximum Diffusion at Determination 70 Degree C Kinetic overall Rates of . Chlorination Curve of Transition Points. 2813 290 Utilizing a semi-log plot, the kinetic rate is shown as a decreasing function of the degree of conversion. On the same plot are drawn the lines that represent the linear overall rates of absorption in the diffusion regimes for chlorine flow rates of 0.4, 0.5, 0.6, 0.8 and 0.95 lb/hr. respectively. At any chlorine flow rate, it can be observed that the overall maximum diffusion rate is less than the kinetic rate at the same degree of chlorination. Conversion rate is therefore limited by and equal to the linear physical mass transfer rate of chlorine. However, as conversion progresses, the overall diffusion rate remains constant but the kinetic rate falls. At a certain degree of conversion X-p, the kinetic rate equals the overall diffusion rate. This point is therefore the transition point which differentiates the diffusion and kinetic regimes; although it is probable that an intermediate regime actually exists around the point which marks the gradual advent of either the diffusion or kinetic regimes. The transition point is obtained by projecting the linear overall physical diffusion rate till it intercepts the kinetic curve, thus obtaining a very distinct transition point. Beyond the transition point, conversion follows the kinetic curve while excess chlorine accumulates. Two rates determine the transition point; at which point the maximum overall diffusion rate is equal to the kinetic rate 291 when the intermediate regime is excluded. The transition point is thus a function of the maximum overall diffusion rate and the kinetic rate, and hence is a function of the chlorine flow rate and the temperature. At a common temperature of 70°C/ the trend is well illustrated by Figure 5.1, which shows transition to occur at a lower degree of chlorination at the higher chlorine flow rates. By a similar treatment, at a common chlorine flow rate of 0.6 lb/hr. the transition occurs at a lower degree of chlorination for 45°C than for 80°C. Table 5.1 summarises the transition points obtained for these determinations. The transition from diffusion controlled conversion to kinetic controlled conversion is hence independent of the degree of chlorination. It will only depend on the relative rates of the maximum overall diffusion rate (k° a A.) and the bulk liquid kinetic _ 1 rate of k B £ . The transition point X , may, by this JL J_j i. reckoning, occur at any point from a degree of chlorination of 0 to 3.0 if the overall gas diffusion rate can be controlled to be equal to the kinetic rate predominating at that degree of chlorination. Returning to Figure 5.1, the product of the ordinate and abscissa has the dimensions of sec \ In fact the area under the curve bounded by the linear overall diffusion rate and the kinetic rate after the transition point is the graphical integration of the integral 292 Table 5.1 Summary of Transition Points From Diffusion Regime to Kinetic Regime Temperature Chlorine Maximum Diffusion Transition Flow Point, Xm °C Rate Rate'(k° a)D At T lb/hr. Mole/mole sec. 70 0.4 2.44 x 10"4 2.25 70 0.5 3.05 x 10”4 2.15 70 0.8 4.88 1.95 70 0.95 5.80 1.85 70 0.60 3.66 2.07 80 0.60 3.66 2.17 75 0.6 3.66 2.12 65 0.6 3.66 2.00 60 0.6 3.66 1.95 55 0.6 3.66 1.90 50 0.6 3.66 1.77 45 0.6 3.66 1.65 1 293 A=X=3.0 A=X=0.0 which gives the inverse of the total reaction time. At a higher chlorine flow rate (equal to the diffusion rate as all chlorine reacts) the area under the curve is larger, hence reaction time is less. Optimum operation of the reactor is thus obtained by using the maximum gas flow rate thfet equals the maximum conversion rate, which is the kinetic rate at any degree of chlorination. In other words, the conversion rate of the gas should be equal to the kinetic rate at all times. Reaction time is minimujn, hence reactor capacity is maximized as the area under the curve bounded by the kinetic curve is maximum. A similar conclusion may be arrived at by consideration of the phase utilization factor. By theoretical derivation, the phase utilization factor is expressed by equation 4.27 for a physical diffusion controlled conversion, with d><0.5 as To increase (T , 'a' should be increased. When gas absorption is incomplete, the interfacial area may be increased beyond that created through gas dispersion by agitation, whereupon 294 the increased gas residence time and increased specific area leads to increased gas absorption. For the chlorination of similar toluene (or other/^as liquid reactions) where a total absorption of gas is indicated in the diffusion regime, the only means to increase the specific area is to increase the gas flow rate. The phase utilization factor reaches an optimum of 1.0 when the gas flow rate to the system is such that the overall rate of gas diffusion equals the kinetic rate. Under kinetic controlled absorption, the phase utiliza tion factor was derived as The increase of specific area and thus overall gas diffusion rate to the system in the kinetic regime does not increase conversion, with the phase utilization factor remaining at 1.0. Conversion rate follows the kinetic rate which is not altered by variation of the chlorine flow rate. In fact, the increased chlorine flow rate in the kinetic regime results only in increased free chlorine content, a fact illustrated in Figure 5.2 for the reactions at 70°C and chlorine flow rate of 0.4, 0.6 and 0.95 lb/hr. An increasing free chlorine content at the same degree of chlorina tion is indicated for the higher chlorine flow rate. 295 o C o n ten t. C hlorine Free on x’ Rate c o ■i-H ra Flow c -rH o 2 o C hlorine o Q) of 5 .2 . Figure auijojqo eeij J0jo]/Nj 0JOUI ^ Z) u o CO Factor Acceleration X C hem ical G o on •rH 4-> fO G -rH Rate o r—•< LO rC OJ O Flow 0 O 0 CnS-. 0 C hlorine Q of Effect 5 .3 . Figure o OJ o o o •j 'jo:pej UOI1BJ0I3OOV leoiuieqo 296 A more quantitative measure is obtained by utilization of the chemical acceleration factor. For the slow chemical reaction, the chemical acceleration factor is derived in equation 4.24a as at F = 1.0 - VA i A plot of the chemical acceleration factor against the degree of chlorination is made for the results at 70°C, and chlorine flow rates of 0.4, 0.6 and 0.95 lb/hr. At the high conversions obtained, a lower chemical acceleration factor is shown by the chlorination as 0.95, 0.6 and 0.4 lb/hr. chlorine flow rate respectively in Figure 5.3. In the absence of free chlorine, the chemical acceleration factor is equal to 1.0 irrespective of chlorine flow rate. From the investigations of the chlorination of toluene in the stirred batch reactor, it was shown that the application of agitation in the diffusion regime did not increase the volumetric mass transfer coefficient, and hence did not increase the transfer rate of chlorine. This was expected because a complete absorption of chlorine occurred in the diffusion regime. In the kinetic regime, however, agitation provided by a magnetic stirrer increased the volumetric mass transfer coefficient. Similar to the effect of an increased gas load, the increase of agitation in the kinetic regime resulted in the increase of a free chlorine content in the 0.101 u /m ole s 1° m /oiom 0UTJO-[L[O 09JJ J0-[O]A[ 297 o M-l r Q O rC •rH X* — Di S-i F ig u re 5 . 4 . E ffe c o t f A g ita tio on n F re eC h lo rin C e o n te n t 298 o Factor Acceleration X C hem ical c o on -1-1 CO c -r~l Rate o % O VMO 5 .5 . Figure j 'jotosj uoiq.ej0xsoov I^oiiLiaqo 299 liquid with increasing the conversion rate of benzal chloride and chlorine. Figure 5.4 shows that at a similar degree of chlorina tion, increasing agitation increases the free chlorine content. Similarly, in Figure 5.5, the chemical acceleration factor F decreases as the agitation rate increased from 500 rpm to 2000 rpm. Application of theory and data obtained experimentally thus show that the bubble column is well suited for the chlorina tion of toluene (or a similar reaction). When a chlorine flow rate less than the kinetic rate is used, total absorption and conversion of chlorine occurs. Maximum conversion rate is obtained when the maximum overall chlorine diffusion rate equals the kinetic rate. Increase of chlorine diffusion rate however can only be effected by increasing the chlorine gas load on the reactor, since total chlorine absorption occurs. Increased interfacial area in agitated reactors over the bubble column offer no advantages, except probably at very elevated gas loads when overall diffusion rate is greatly exceeded by the chlorine gas load. Further, maximum capacity of the reactor is obtained when conversion rate in an unsteady-state reaction is maintained at the kinetic rate, a fact shown by the minimum conversion time and the optimum phase utilization factor of 1.0. Increasing the overall chlorine diffusion rate by increased gas loads or by the use of 300 agitation again offers no advantage, and results only in an increased free chlorine concentration in the reactor without increasing the conversion rate. Moreover, this results in a decrease of the chemical acceleration factor at higher gas loads or at increased agitation rates. In the theoretical cases of the fast and infinitely fast reactions, the absorption rates are given by the chemical absorption rate where k and k L JA The phase utilization factor for the fast reaction is expressed by equation 4.28, 4.28 301 The optimum value of (f> = 1.0 cannot be attained, but for increasing reaction rate, ( (p increasing), an increase of the specific area will increase the utilization factor. If a complete absorption of the gas occurs ( a very likely case in fast reactions), the use of the gas bubble column will prove effective, since the increased agitation provided in the agitated reactor will not increase absorption rates or phase utilization. In contrast, when gas absorption is incomplete, the increased specific area and gas residence time provided by agitation will effect an increased gas absorption and phase utilization. 5.2 Effect of Diffusion on the Yield of the Intermediate in a Heterogeneous Consecutive Reaction In a homogeneous first order consecutive reaction kl k2 B ------►C ------* D the selectivity of C may be expressed by the equation the derivation of which is shown in Appendix IIC. The yield of C will be a maximum if C does not undergo any subsequent reaction. 302 i. e. 0, and equation 5.1 becomes dC = 1 5.2 dB On integration for the initial conditions of Cq = 0 when B = B . o C = B - B o or for B = 1 o ' C = 1 - B 5.3 Equation 5.3 is in fact the mass balance for where the yield of C is equal to the amount of B reacted. In the heterogeneous environment for the same reaction, the effect of diffusion on the selectivity of C was derived in chapter four as equation 4.38 k2 CL tanh S^2 ^2 ^1 tanh ^2 V.dB Jx=6 B tanh ^“^2 tanh(jb^ n -s kl L + 5.4 k 2 303 Equation 5.4 approximates to two limiting cases according to the rates of chemical reaction and diffusion. The discussion will be limited to the case where S = ^V 1.0. (i) (a) When chemical reaction is slow with respect to diffusion, which may be integrated to give the yield of C in a batch or plug-flow reactor: 1 5.5 \ (b) No change in selectivity from that of the homogeneous reaction may also be expected for the rapid reaction where (p ^ and (p ^ ^ 2.0, but 304 or for the infinitely rapid reaction and (p £ 2.0, but B ^ (ii) However for the fast chemical reaction with (j) ^ cj)^ > 2.0, equation 5.4 reduces to 1 Js 5.4b 6 Js+l B. which may be integrated to B. °L S 5.6 S-l B B. provided that < — . The case for (j) ^ > 2.0 but < 0.5 i will be discussed in the succeeding section. The yield and selectivity of in equation 5.6 was shown to be lower than that given by equation 5.5, the former being the yield and selectivity of C under complete diffusion limitation. A theoretical plot of equations 5.4, 5.5 and 5.6 is made in Figure 5.6. Equation 5.3 is the line joining C = 1.0 and B = 1.0, a graphical mass balance of the relationship C 1 - B Yield of intermediate Figure 5.6. B = Plot ( 1 of - 0.4 Intermediate conversion) 0.5 , Yield m LEGEND °^ e /mole against (1- conversion). 305 306 Curve I represents equation 5.5 for a value of S = 6.30 (the value obtained experimentally at 80°C) while Curve II represents equation 5.6 for the same value of S. The decrease of the yield of C as a result of a consecutive reaction to D compared to the yield of C as a result of a single reaction from B is thus obtained by comparison of curves I and II with the linear mass balance C = 1 - B Curve I will be the yield with respect to conversion in a homogeneous reaction or a heterogeneous reaction under non selectivity limitation. Curve II is the corresponding curve for the complete selectivity-limited heterogeneous reaction. Observa tion shows that initially when conversion of B is low, the yield and hence selectivity of C in both curves I and II lie close to the maximum yield of C. However, as the conversion of B is increased, the yield of C falls progressively below the maximum possible yield, which is more so in the case of the diffusion- limited selectivity. This observation may be derived mathematical ly. The selectivities of curves I and II are described by the equations and 307 Is 5.4b JS+1 B. In both equations, selectivity is a dB dC maximum when B. 1.0. As Bn decreases also decreases numerically. 5.2.1 Effect of the Ratio of Kinetic Constants on Yield and Selectivity in a Heterogeneous Consecutive reactions The effect of diffusion on the selectivity in a hetero geneous first order consecutive reaction is expressed by equation 5.4 tanh cp k^ tanh (p^ tanh (p k -kg tanh (f) + 5.4 (i) When (ii) However, when <£>^>2.0, (p may be less than 0.5 if k^ is much less than k . Hitherto, it has been assumed that when 308 tanh (j) tanh (j>, ki krk2 + 5.7 krk2 Now let cp ^ vary from less than 0.5 to greater than 2.0. (a) At Js 5.4b ■ " 4 S (b) However, as Cp 2 decreases, and in the limit when k^O, (p2 = 0. Equation 5.7 gives 1.0 which is identical to equation 5.2 for ^=0. The result may be expected from qualitative consideration; since in the single 309 reaction (k^O), diffusion only affects the rate of con version but does not alter the yield of the product. The selectivity of C given in equation 5.4b will be the minimum while the same indicated in equation 5.2 is maximum. Hence as In the general case when k^O the maximum selectivity of C is the non-diffusion-limited selectivity given as 1 - 5.4a which may be integrated to % B. for S => 1.0 S-l B At the maximum yield of C, 0. Whence, from equation 5.4a S B. 5.8 ^Max^ which on substitution into equation 5.5 yields S/l-S (Bt) _ = S for B =1.0 5.9 ij O o Max S/1-S/ Hence (C ) = S.S 5.10 MaX <^<0.5 For S = 1.0, equation 5.4a simplifies to from which the maximum yield of C is derived in Appendix IID as for S = 1.0 5.10a ^CMax^ (/>,< 0.5 L < 1 For selectivity limitation, provided that ——— ______h ~ Js 5.4b 1+JS B. By similar treatment as above, the maximum yield of C in the selectivity-limited heterogeneous reaction is 311 _ ^(1- JS) S s+ is ■ (C for S>1.0 Max 1+ is 1+ is' 5.11 For S = 1.0, equation 5.4b is shown in Appendix II D to yield (C ) for S = 1.0 5.11a Max7 $2 >2’° Dividing equation 5.11 by equation 5.10 above, (C., ) 1- Is MaX Similarly, dividing equation 5.11a by 5.10a gives ^CMax ^2>2 •0 1 for S = 1.0 5.13 S=1.0 (CMax> <^<0.5 The ratio o< compares the maximum yield of C in a selectivity limited heterogeneous reaction to that of the non-selectivity- 312 limited heterogeneous reaction. A second ratio jB may be defined. When selectivity of the series reaction is non diffusion limited, the selectivity is idential to that of the homogeneous reaction. Hence P 5.14 and is independent of the parameter S. The ratio cx may therefore be redefined as (CMax) .0 c< 4>2>2 CCMax) Horn. which is the ratio of the maximum yield of C in a selectivity limited heterogenous reaction to that in a homogeneous reaction. With the use of a computer, the value of o< is evaluated as a function of S given in equation 5.12. The linear function jB = 1.0 is also shown in the plot of Figure 5.7. The theoretical maximum yield of C under selectivity limitation relative to its yield when selectivity is not limited by diffusion may be studied from Figure 5.7. Parameter S will have a value of 1.0 when for which c< =0.5. 313 Yield Intermediate -lim ited 314 As S increases however (i.e. decreases relative to k^) will increase. In the limit when ^=0, C produced will not react at all and oc approaches 1.0 as k^ approached zero. In Figure 5.7 it is evident that o< approaches the limit of 1.0 as symptotically as S approaches infinity. The yield of C in other words will not be influenced by diffusion ir respective of the value of The yield and selectivity of C and the influence of the parameter S have already been discussed in literature for the 97 homogeneous reaction by Chermin and Van Krevelen. The maximum yield of C in the homogeneous reaction, and for the heterogeneous reaction with no selectivity limitation is given by equation 5.10. Again, with the use of a computer (C^x < q.5 is evaluated as a function of the parameter S# the graphical result is shown in Figure 5.8. When S = 1.0, ^Max^l^ 0.5 equals . Similar to Figure 5.7 C,. increases as k0 e Max 2 decreases relative to k^ (i.e. S increases). In the limit, when S approaches infinity, (Ch, ) reaches 1.0 Max <0.5 Theoretical treatment shows that the diffusion parameter influences the selectivity of the intermediate in a heterogeneous consecutive reaction. The selectivity and yield of the intermediate 315 on C o n sta n ts Rate R eaction of Ratio of Interm ediate. Effect 5 .8 . Figure 316 is moreover affected by the ratio of the reaction rate constants. (i) When the reaction rate is slow, with 0.5, the selectivity and yield of C will be identical to that of the homogeneous reaction. The yield of C is a maximum when k =0; the series reaction reduces to a single reaction. However, as k^ increases, the yield and selectivity of C decreases. In the limit when k^= k^, the maximum yield of C is (ii) When reaction rate is rapid, with ]_ (C Max) 2e 4>2>2.o As k^ decreases so that S increases, the yield of C increases. In the limit when k^ = 0, the series reaction reduces to a single reaction. The yield of C is then un affected by diffusion. 317 Theoretical considerations therefore show that C will be obtained in greater yield if reaction conditions are such that the selectivity is not limited by diffusion. This may be achieved by (i) slowing the reaction so that (j> < 0.5 (ii) controlling the concentrations so that B, B » A. if Moreover, the yield of C will be increased if the series reaction c ------k2 ** D is suppressed either by a selective catalyst or inhibition of the reaction. When the selectivity C will outweigh other considera tions, a low degree of conversion is indicated for maximum selectivity. 318 CHAPTER SIX 6.1 Summary and Conclusions Experimental equipment has been designed and used for experimental investigations in the chlorination of the toluene side chain. A laboratory column reactor was designed with a degree of flexibility incorporated so that it could operate as an unsteady-state reactor with allowance for adaptation for other purposes. Gas-liquid chromatography was shown to be a rapid and sufficiently accurate means of qualitative and quantita tive analysis of toluene and its reaction products. An initial induction period of about two minutes always preceded the reaction of toluene and chlorine. The initial stage of reaction, below a degree of chlorination of about 1.5, was shown to follow a diffusion controlled mechanism. Terminal stage of reaction from benzal chloride to benzo-tri chloride however showed the mechanism to be kinetic controlled. Bulk chlorine concentration increased from an imperceptible level to a con centration that imparted a yellow green colouration in the liquid, as the absorption changes from diffusion control to kinetic control. Kinetic data was determined in the kinetic regime, where the chlorination of benzal chloride was shown to have a rate expression of zero order with respect to chlorine and of first order with respect to benzal chloride. This allowed the kinetic constant k^ to be 319 evaluated directly, while the other kinetic constants k^ and k^ were evaluated indirectly with the assumption of similar kinetic mechanisms in the preceding series reactions. The process of simultaneous gas diffusion into a liquid with a chemical reaction having the above kinetic expression did not appear to have been well treated theoretically. According ly, the theoretical equations pertaining to such a process were solved. Parameters and the rate controlling mechanisms were identified. The diffusion parameter, the specific gas-liquid interfacial area and the diffusion rate of the gas relative to the kinetic rate were identified as the important parameters. Equations were developed to define the phase utilization factor and the chemical acceleration factor. The theoretical treatment was extended to consecutive reactions. Parameters and the conditions that would lead to a diffusion-limited selectivity of the intermediate were deduced. The effect of the ratio of kinetic constants on the 4 selectivity were also discussed. Applying the equations developed theoretically, a volumetric mass transfer coefficient was evaluated for the kinetic and diffusion regimes respectively. The volumetric mass transfer coefficients wero> correlated against the molar chlorine flow rates and temperature. In each case, the volumetric mass 320 transfer coefficient varied linearly as the first power of the chlorine flow rate and of temperature. The diffusion regime and kinetic regime volumetric mass transfer coefficients differed appreciably in value. Equations for non-selectivity and selectivity limited reactions were applied to the consecutive reaction of toluene to benzal chloride. Selectivity of benzyl chloride under the experimental conditions was not affected by the diffusion process because of the slow reaction rate relative to the diffusion process with a diffusion parameter of less than 0.5. Variations in temperature and chlorine flow rates did not affect the non selectivity limited mechanism. Determination of volumetric mass transfer coefficient in the kinetic regime also provided an opportunity for determination of an experimental chlorine interfacial solubility A . Its value was evaluated for temperatures of 45 to 80°C. Comparison with values calculated from empirical equations showed a comparable order. The chlorination of toluene was further carried out in a stirred batch reactor to investigate the effects of agitation. Agitation did not affect the kinetics or kinetic constant. The diffusion regime volumetric mass transfer coefficient did not change with agitation; the same in the kinetic regime increased 321 with agitation rate, but appears to become constant beyond a certain agitation rate. Free chlorine content in the liquid increased with agitation. With the assumption that an intermediate regime does not exist between the diffusion regime and kinetic regime, the transition point was determined from the experimental data calculated. Results show that the transition point is a function of the maximum diffusion rate and the kinetic rate, and not of the degree of chlorination. From theoretical considerations, the absorption rate of a gas and its conversion are defined by two limiting rates. For the infinitely fast, fast, and slow reaction in the diffusion regime, absorption of the gas is controlled by diffusion rate. The phase utilization factor for such an absorption is not optimum. Design of a reactor for such a reaction should allow for mechanical agitation to increase specific interfacial area if gas absorption is not complete. On the other hand, if gas absorption is complete, increased agitation does not increase absorption rates further. A greater gas load could therefore be used in such circumstances. Absorption rate is kinetic controlled when chemical reaction is slow, and less than the maximum diffusion rate. Reactor capacity is then optimum, and increased gas transfer rates by increased gas load or agitation only increases the liquid 322 gas solute level. The chemical acceleration factor then decreases. Generally, for a slow reaction, optimum reactor capacity is obtained if the conversion rate is maintained at the kinetic rate by control of the gas transfer rate to the reaction; conversion time for an unsteady-state process is minimum when this occurs. The gas bubble column is a suitable reactor for the chlorination of the toluene side chain. When the absorption rate is under diffusion control, complete absorption of chlorine occurs, indicating that a greater gas load may be applied. Agitation as provided in agitated tank reactors will not increase the conversion rate. In the diffusion regime, agitation again does not increase conversion rate, and provided that the liquid com position and temperature are maintained homogeneous by dispersive agitation the bubble column should perform adequately. 6.2 Suggestions for Further Research Difficulty in ascertaining gas hold-up in column reactors appears to be experienced by many other authors. Uncertainty in this determination arises in no small way from the instability of the liquid surface. If some surface active compounds which do not interfere with chemical reaction could be found, surface instability may perhaps be reduced with the subsequent ease in gas-hold up measurements. The use of 323 a silver wire gauze probe, for example, to dampen surface irregularity is also suggested. The reaction of chlorine with toluene is a consequence of the absorption of the gas by the liquid. Reaction produces hydrogen chloride, most of which leaves the liquid as gas bubbles. An investigation into the gas-liquid phase phenomena, the mechanism of gas eduction should prove an interesting area for further research. ooooooooonoooooo 250 240 230 220 210 200 -00 100 AFRN AFRNR(4) AFRNR AFRNR AFRNR{ WT WITH WITH T0TM0L=AFRN(1)+AFRN(2)+AFRN(3)+AFRN(4)DO AFRNR SUM1=AFRNR(1 GO PKHTR(I) DO GO TOTMOI. PKHTR DO FORMAT READ DIMENSION DEGCHL VOL TIME PEAKHT C0MP0NENT3 C0MP0NENT2 C0MP0NENT1 EVALUATE PKHTR COMPONENTS IF AFRN TO TO 300 240 - 220 (PEAKHT(1 = ( WEIGHT 200, = RESPECT RESPECT (3) (2) ( I)=AFRNR(I)/SUM1 1) 250 250 VOLUME = = - ( I » = 7F1 TIME - 1= ) 1=1 1=1 MOLECULAR RATIO RATIO - = = » = = TIME, MOLE DEGREE SUM PEAK 1,4 0,0) PEAKHT ,4 ,4 IA PKHTR(1)*1 PKHTR(4)*1 PKHTR(3)*7.55 PKHTR(2)*3.40 PEAKHT PEAKHT(I = = = = )+AFRNR(2)+AFRNR(3)+AFRNR(4) OF OF ) TOLUENE OF OF TO TO BENZOTRI BEN7A1. BEN7.YI. -0.1) HEIGHT FRACTIONS OF OF (PEAKHT Computer REACTION SAMPLE OF MOLE TOLUENE 0. TOLUENE (4), MOLECULAR ( CHROMATOGRAM FRACTION IN I CHLORINATION ) I/O.1 /PEAKHT PKHTR(4) Clil.OR CHLORIDE 1.40 .0 210,210,230 FRACTIONS SODIUM OF Fractions APPENDIX CHLORIDE ( III Programme H COMPONENT TITRATION ,1=1,4), IDE FRACTIONS (1 THIOSULPHATE , AFRNR(4) ) from I PEAK for VOL.WT Chromatogram CHROMATOGRAM Evaluation HEIGHTS , AFRN IN (4) of TITRATION Molar o o o o o o o 800 750 650 600 550 450 400 700 500 1 1 1 1 1 1 WTCHL FORMAT FORMAT FORMAT FORMAT WTCHL WTX FORMAT PRINT PRINT PRINT PRINT FORMAT/ AX WTX-47T-WT NORMALITY AX PRINT PRINT FORMAT/ FORMAT 4X, DEGCHL=AFRN(2)*1 PRINT PRINT FORMAT(1H0// PRINT CHLMCN SUM2=AFRN(1 CHLMOL CHLMOL=VOL*( EVALUATE CHLMCN 4HM0LE 7X.8HCHLOR 1 7X,8HCHL0RIDE,9X +AFRN(4)*1 3HM0LE = » 1 = Ml WTX/SUM2 MOLES “ 750, WEIGHT 800 700 650 600 550, 500 450 400 VOL*( = PEAK (1 (1HO,13X,F5.3.10X,F5.3,10X,F5.3,10X,F5.3,7X.F5.3)(1H ,1 (1 1 = - = (1H (1 1 HO, H WEIGHT H HO///, HO///, X, FRACTION,2X, HOLES FREE CHLORINE CHLMOL/AX CHI. (AFRN( OF (PEANUT .11 ,26X,6H[3EN7YL,9X.6HBENZAL,RX,9HBENZ0 HEIGHT,4X,1 1 95.477 ORGANIC , 1 25.00*3.5671*35.457)/(26.35*35.67*1000.0) , I )*92.142+AFRN(2)*126.587+AFRN(3)*161.032 3HC0NCENTRATI DE.6X,5HM0I.ES 28X, 0X.F7.2.6X.F7, 1 25.00*3.56711/(26.35*2000.0*35.67) ////////.1 2X X,7HTOLUENE OF THIOSULPHATE CHLORINE 1 1 OF FREE 3X,6HDEGREE,9X,6HVOLUME 7HT0I.UENE, 6ll OX, ORGANIC 11,1=1 .0 ( 4IIMINS MOLE BENZYL, FREE I 1 4AFRN(3)*2.0+AFRN(4)*3 COMPONENT ),1=1,4) 3HM0LE CHLORINE 1 3HM0I.E OX,1 1HPEAK 4),T0TM0L CONCENTRATION CHLORINE CONCENTRATION COMPONENT 1 ON) 9X, 7X,8HCHL0RIDE,7X,8HCHL0RIDE ) 8X, 2,1 = 1HPEAK FRACTION, .TIME 6HBENZAL, (25.00*3.5671 8HCHL0RI FRACTION,4X.5HTOTAL) HE 0X.F7.2.7X.F7. IN IN IGHT,7X.4HTIME) SAMPLE SAMPLE IN HEIGHT IN SAMPLE 2X, DE 7X.9H SAMPLE 1 , , 9X,6HWEIGHT,6X 7X, 3HM0I.E 4X, ) BENZ 0 /(26. 8HCHL0R 2, 1 1HPEAK 8X.F7. 0 FRACTION,2X, TR 35*35.67) TRI) I I ) DE, HEIGHT, 1) , , 325 326 PR I NT 8S0 850 F0RMATOH ,1r>X,2HOF,13X,2HOF,13X,2HOF.1!;X,4HFREF) PRINT OOO 900 FORMAT (1H , 1 OX, 1 2HCHI.0R I NAT I ON, 3X, 1 2HTH I OSUI.PHATE, 1 6X.6HSAMPI.E.11X.8HCHI.0RI HE) PR I NT 930 DEGCHI.. VOI. ,V/T, CHI.MCN 950 F0RMATOH0,10X.F7.3,10X.F5.2,7X.F10.4, 7X.F10.31 GO TO 100 END UI X PEAK HEIGHT PEAK HEIGHT PEAK HEIGHT PEAK HEIGHT IB BENZYL BEHZAL BEHZO TRI OO X x Typical TOLUENE CHLORIDE CHLORIDE CHLORIDE 00 0 k 0 0 O O 0 O O O O O • • • • • Result 0 J- < X H- UJ < t-O'C O ■y 01 ------UJ 1- < h X 0 u. 400 O O _ I (4ZO < 0 0 0 0 U l4 O — — ■;r < | — _ O UJ U 04 — l 1 1 MOLE r-J u IT UJ N < CO > CO U m JO CO Z JC ------— UJ J from UJ ! UJ CO 2: 0 X 04 UJ UJ 0 X — — — O or Ui X O 4 — X X J X C 1 ! C \D CT\ CT\ CT\ C<\ cr. t/\ O r O O O'. CM O O Computer — • • • • • • < H- 0 X lucre t 04 UI 0 0 X 0 X U O UI h- -5- -J O X X ILL > — O X u- UI > U* zc- — X X ’ Ui UJ u O Lu C U ___ UJ — X 0 x 04 «y UJ X 1 O 00 u H- UJ 00 X X J < < O- < — X H- — 0 X 04 0 X c X — 1 -4 O -4- - -4- LO c -4- CT. N rr\ r-. 4 - m 327 328 APPENDIX II A. Gas-liquid Heterogeneous Reaction - Solution of Differential Equations The process of diffusion and simultaneous chemical reaction in a gas-liquid absorption with the pseudo first order reaction, represented by the kinetic equation r = - k B A (B = constant) JL JLj JL for the reaction A + B ------* products gas liquid is (1) ki bla (2) ki bla with the boundary conditions x = 0 ; A = A. ; = 0 (a) x=<5; A = Al; -a^ (^)x= (3) 329 The general solution of equation (1) is „, mx ,, -mx Me + M2G where Mj * M2 constants ki bl and £> Substitution of the boundary conditions give -mx A = 2M, sinh mx + A.e (4) 1 i and -0 A^ = 2M^ sinh<|> + A^e (5) where S' k1' B L oD Differentiating equation (4) with respect to x, — my 2 M, m cosh mx - m A.e (6) 1 l and at x = S , in boundary condition (3b) # a ^ m (2M^ cosh (f> - A^e ^ ) = 330 on substituting the value of A from equation (5), jj - a 2) m (2M coshp - A e ) -4> = kg (2M sinhd) + A.i ) ( eL- a£ ) 1 L 1 r i which on rearrangement gives t1 - + Substitution of M into equation (4) gives on rearrangement ( ''acf ~ 1)4+ tanh ~ - \ —------sinh^)- ^ ' ( L/^ - 1 ) (f) tanh which is equation 1.17 of Chapter One. Equation (9) describes the concentration of the gas solute A along its diffusion path into the liquid phase x. A = A. for x = 0 l And A = A for x >cf L 331 B. Selectivity in a Heterogeneous Series Reaction - Solution of Differential Equations For a series reaction with the first order reactions represented by A + B ------C gas liquid liquid k2 A + C ------D gas liquid liquid with -ki bl ~k2 CL+ klBL* the process of diffusion and simultaneous reaction is described by the equations d2A Z> k^B + k2C for A (1) d B for B (2) kiB JP) k2 C - k B for C (3) , 2 dx 332 in the steady-state absorption (film) theory. For the sake of mathematical simplicity, diffusion coefficients are not differentiated. Boundary conditions are x = 0 : A = A. x = & : A = A ; B = B , C = C J-i L L -a £( = kl\+ k2CL dx Integration of equation (2) gives B_ B cosh m^x cosh <£> ki where N X) pr and h = 6 Substitution of B into equation (3) gives B. d2C 1 C - cosh m^x (4) dx" 2) ~ X) C°Sh Using a Laplace Transform, equation (4) becomes B. P -C '(o) - pC(o) + p2 C (p) - m2 C (p) = -m2 -g*-^ 2 2 P -m 333 where c'(o) = CdC/dx) x=0 C (o) = C at x = 0 P = Laplace Parameter C (p) = Laplace function of x 2) Hence 2 2 , - 2 \ (p m2 ) C (p) C.p m1 cosha>' 2 2 T1 d - m. which on rearrangement gives CiP r P P C (p) (kl Y ^ • , 2 2. / cosh Whence klBL C, cosh m0 x - tt —:—:------:—t— (cosh m.x - cosh m^x i 2 (k 1~k2) cosh <±> 1 1 At x = & , C = C is substituted into (5) ki bl CL = cosh p ^ rk2) cosh f ~ {cOSh * 1 -COSh and thus CL kl BL C. 1 cosh ^ ^ + (k1~k2) cosh ^ cosh ^ ^ ^COSh ^ 1 COsh^2^ (6) The concentration profiles of B and C in the diffusion region ( 0 < x < &) are described by equations (4) and (5) respectively B cosh (4) cosh <} and C C. cosh i ( klBL lcosh - cosh x (5) (k1~k2)cosh <^1 A where CL klBL C. i cosh ^2 + (k^-k2) cosh (6) The effects of chemical reaction and diffusion on the selectivity C are described by the parameters (£ ^ and and Section 5.2 of Chapter Five. The assumption of equal diffusion coefficients, ^ for chlorine, toluene and benzyl chloride is made to simplify the equations derived. Diffusion coefficients are difficult to ascertain experimentally but empirical correlations derive a general value of —5 2 Sb ^ 5x10 cm /sec for most solutes in liquids. Relative diffusion coefficients of solutes in liquids therefore do not differ appreciably from unity. 336 C0 Selectivity in a Homogeneous Series Reaction In a homogeneous series reaction of first order similar to the one described in the preceding section A + B ------—* C k A + C ------—•* D where A# B and C occur in a common phase. The reaction rates of B and C are respectively klB (1) dC k2c - klB (2) dt Division of equation (2) by (1) gives dC = _ ___ C__ (3) dB kx ‘ B which describes the selectivity of C with respect to B in a batch or plug-flow reactor. Equation (3) is similar to the selectivity of an intermediate in a heterogeneous reaction which is not selectivity limited (Equation 4.39 of Chapter Four). 337 From equation (3), C is a maximum when = 0 Hence 1 - B ('— B /i) dB _0 By assuming that B = 0 when D is appreciable, it can also be shown that dC in a third stage of the series reaction A + D products. Equations (4) and (5) may be used to ascertain the values of the relative specific reaction rate constants of __ 1 and from a time-production distribution or degree of chlorination- product distribution curve. 338 D. Maximum Yield of Intermediate in a Heterogenous Series Reaction for S = 1.0. In the heterogenous series reaction, kl A + B ------C k2 A + C ------* D the selectivity of C when diffusion does not limit selectivity is given by 4.39 Under diffusion limitation, the selectivity of C is Js 4.41 ~ 1+JS For S >1.0, equations 4 .39 and 4.41 may be integrated to yield respectively 4.40 B o 4.42 339 When S =1.0 however, the indeterminate quantity of S appears in both equations 4.41 and 4.42. Equations 0 4.39 and 4.40 must therefore be integrated specially for the case of s =1.0. For s =1.0, 4.39a for selectivity not under diffusion limitation, and 4.41a Eh for selectivity under diffusion limitation. Equations 4.39a and 4.41a may be integrated by multiplication with the integrating factor —— , from which they yield hL In BL and In BL B. When CT is maximum, ~r~ 0. Hence, in equation 4.39a L dB, ^CL ^ Max 340 (q \ on substitution of ^ Max into e<3uati°n W / - In B Therefore L' ( = 0.368 ) Max when diffusion is not under diffusion limitation. Similarly, from equations 4.41a and (2) when selectivity is under diffusion limitation. ( = 0.184) (CT) 2e Max APPENDIX III A. Evaluation of Diffusion Coefficients Data for diffusion coefficients are rare in literature. Good empirical equations which enable the coefficients to be 98 evaluated do exist however, Reid and Sherwood recommend the use of Wilkie and Chang's equation for organic solvents. The equation is expressed below: 7.4x10 8 (X m) 2 T r r0.6 where diffusion coefficient of solute (1) 2 in solvent (2) cm /sec. molecular weight of solvent o temperature, K viscosity of solution, centipoise molal volume of solute at normal boiling 3 point, cm /gm.mole 'association' parameter of solvent 99 100 Data used for calculation are obtained from Perry. 342 Now M = 92.06 for toluene X= 1.0 for toluene, assuming no association 3 100 V = 48.4 cm /gm mole for chlorine . Equation (1) then simplifies to _ o _L T 2 , 7.4 x 10 x (92.06)2 x —”— cm /sec. (48.4)0*6 D12 = 6«94 x 10 8 x T/^ The data used for a temperature of 45°C to 80°C are listed in Table 1. 343 Table l Diffusion Coefficients from Wilkie and Chang's Equation __ cm 2// a°c T°K Centipoise sec (toluene vis- 99 cosity ) 45.0 318.2 0.47 4.70 x 10‘5 55.0 323.2 0.45 4.97 55.0 328.2 0.42 5.41 60.0 333.2 0.40 5.76 65.0 338.2 0.39 6.01 70.0 343.2 0.37 6.43 75.0 348.2 0.35 6.90 80.0 353.2 0.33 7.42 344 o 00 LO r-x o fx. Temperature. a g a in st LO CO O Coefficient o o CO i CD (0 i-, D iffusion CD Cu of LO B LO CD H Plot . A 1 o LO Figure LO •^r OX x 00s XU0IOIJJ0OO UOISnXJTQ 345 -5 2 The values of D^ are of the order of 5x10 cm /sec, which is in close agreement with the values normally obtained for solutes in liquids. With a scarcity of viscosity and t>ther data for benzyl, benzal and benzo-tri chlorides, the value of Df2 will be assumed to apply for all the compounds. Figure A1 shows the variation of against &. It shows that D ^ can be assumed approximately to be a linear function of &. B. Estimation of the diffusion Parameter The diffusion parameter is by definition, the square root of the ratio of the maximum reaction rate in the diffusion region of a heterogeneous reaction system to that rate of diffusion of a key reactant. In a pseudo first order reaction of the type A + B C dA where is constant, dt ki bl a klBL (1) 346 The definition of <£ in equation (1) is the relevant factor for quantitative and qualitative discussions in the present work. Accurate evaluation is limited since the quantity & is hypo- r -2 thetical and can only be approximate. A value of ^ = 10 cm. is a conservative estimate which has been used by at least one ., 101 author. In the series reaction of toluene to benzo-tri chloride, the reaction rate constant would be the largest in value. As estimated in Table 2 , <£ ^ estimated based on k is less than 0.5, so that it may be concluded that Table 2 Estimation of Diffusion Parameter , -1 *' Temperature sec — fib cm /sett; i °c 45 5.65 x l(f 3 4.70 x 10"5 0.29 60 9.65 x 10”3 5.76 0.24 80 1.39 x 10“2 7.46 0.23 348 In gas liquid heterogenous reactions, the diffusion parameter <£> is encountered generally as a hyperbolic function, tanh tanh (f> ~ (ft cosh (p ~ 1.0 However, for tanh (f> cr 1.0 cosh (j> For all values of (f> , sinh Various values of (p have been quoted by authors for the above approximations to hold. For the first approximation. (f>> 2.0, and (}> ^ 1.0 and for the second approximation (P< 0.3, and <^ In the present work, the value of of APPENDIX IV A. Evaluation of Molar Chlorine Flow Rate The molar chlorine flow rate is defined as the gram molecular flow rate of chlorine per gram molecule of toluene in the batch reactor. Evaluation of the quantity, based on 1.0 lb/hr. of chlorine flow rate employ the following data: Volume of toluene in reactor = 308 ml Density of toluene = 0.866 gm/ml Hence Weight of toluene ex reator = 2 67 gm. = 2.9 gm. mole _3 1 lb/hr. chlorine = 1.77 x 10 gm. mole/sec. Hence, molar chlorine flow rate = 6.1 x 10 m°le/mole sec. Calculation of the same quantity is therefore a simple procedure at other chlorine flow rates, and is summarised below for flow rates used experimentally. 351 Table 3 Molar Chlorine Flow Rates Chlorine Flow Rate Molar Chlorine Flow Rate lb/hr m°*e/mole sec. 0.40 2.44 x 10”4 0.50 3.05 x 10~4 0.60 3.66 x 10~4 0.80 4.88 x 10"4 0.95 5.80 x 10”4 352 B. Evaluation of Orifice Reynold Number The orifice was measured by a travelling microscope to have a diameter of 0.1 cm. Evaluation of the orifice Reynolds Number is again based on a chlorine flow rate of 1 lb/hr, at a temperature of 70°C. At 70OC, viscosity of chlorine, = 0.016 cpoise The mass flow rate of chlorine, G, at 1 lb/hr. through the orifice = 16 gms/sec cm2 Hence GD Re r at a chlorine flow rate of 1 lb/hr. 353 APPENDIX V Concentration Units in the Evaluation of Data The units in general use for concentration of liquid solutes are weight per unit volume or moles per unit volume; in kinetic studies, concentration units of moles per unit volume are more commonly used. For first order rate expressions, the mole fraction may be used in place of moles per unit volume. In a first order kinetic expression d(bVv) ki ( V ^ where y, concentration of b, in mole/unit volume, 1 the expression may be divided by the factor 2bi ■ — ■— = total mole/unit volume Hence, the rate expression becomes, __d V* f dt 1 Zb. but k^ will not be altered dimensionally. 354 b^ will now have the units of mole fraction, a unit which is used in the kinetic data for the present study. A similar simplification may be made in the mass transfer expressions. Thus, in the diffusion regime, if volumetric concentrations are used, the absorption rate of chlorine may be given by (. \ a^D Ai moles A/unit volume -1 The interfacial area 'a' will have the dimension of L where L denotes length. A suitable unit for A would be gm.mole/c.c. 2 -1 so that 'a' may have the units of cm /cm3 = cm . However, since expression (2) is first order with respect to A, mole fractions may be used. Thus, if expression (2) is divided by ^ i , the total liquid moles/c.c., A in the same expression will^have the unit of mole/mole liquid without affecting the units of (k° a) . LA In the reaction of toluene to benzyl, benzal and benzo- tri chlorides, the sum of the organic components always equal the initial amount of toluene. The mole fraction is hence con veniently equated to the m°le/mcqe initial toluene 9 which be expressed as mole/mole f°r simplicity. 355 APPENDIX VI c o A. Calculation of and k^ For the chemical reaction of chlorine toluene benzyl chloride the Arrhenius equation gives, to a first approximation, -E Vrt i o kl 6 or, on taking logarithms, e loglOkl = Iog10kl 2.303 RT In Figure 4.17, the plot of log^k a9ainst — is linear, 3 and has a gradient of -1.00 x 10. H ence e. -1.00 x 10' 2.303R Q or = 1.00 x 2.303 x 1.98 x 10 cals/gm.mole & = 4.57 kcal/bm.mole. 356 1 -3 In Figure 4.17, at / = 3.0x10 logioki -2.05 Substituting the values into equation (1), with £i 1.00 x 10' 2.303R -2.05 +(l.00 x 3.0) log10kl -2.05 +3.00 or = 0.95 log10k? o kl = 8.9 sec 357 B. Evaluation of Diffusion Regime Volumetric Mass Transfer Coefficient Figure 4.19 shows the linear absorption rate of chlorine in the diffusion regime. At 70°C/ for the chlorine flow rate of 0.4 lb/hr. the linear rate may be evaluated from the linear portion of Figure 4.19. The gradient of the linear portion is the overall absorption rate R . From Figure 4.19 R. = 2.44 x 10 ^ mole/ , A /mole sec. (which is equal to the molar flow rate of chlorine) Now where (k° a ) = diffusion regime volumetric mass transfer LA ^ coefficient. The value of A. at 70°C, is i Aj_ “ 0-101 mo^e/mole initial toluene Therefore (k° a.) =2.42 sec ^. La D ------358 C0 Evaluation of Gas/Liquid Interfacial Area and Film Thickness A sample calculation for a reaction temperature of 55°C and chlorine flow rate of 0.616/hr. is shown below. Molar chlorine flow rate 3.66 x 10 ^ mole/ . ' mole sec. from Appendix IVA At 55 C, = 5.41 x 10 ^ cmVsec A from Appendix IIIA k = 8.24 x l(f3 mole/ , 1 ' mole sec A. = 0.111 mole/mole 2 A1 Now £ = for B =1.0 o -5 5.41 x 10 x 0.111 Hence cm 4.49 8.24xi 0~'* _2 i 2.70 x 10 cm. From 4.51 <£) A A i 1.64 cm } 359 Table A1 Temperature of Reaction : 70°C Agitation Rate : — rpm Chlorine Flow Rate : 0.4 lb/hr Submergence : 19.0 cm Reactor : Bubble Column Dq (in kinetic regime);-md^mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Degree of Time, min. Benzyl Benzal Benzo-tri Chlorina Toluene Chloride Chloride Chloride tion t B C D E X 0.0 1.000 0.000 0.000 0.000 0.000 15.0 0.780 0.220 0.000 0.000 0.220 30.0 0.548 0.429 0.023 0.000 0.475 45.0 0.360 0.583 0.058 0.000 0.700 60.0 0.217 0.674 0.110 0.000 0.898 75.0 0.087 0.722 0.192 0.000 1.105 90.0 0.020 0.641 0.327 0.000 1.330 110.0 0.000 0.434 0.517 0.050 1.614 130.0 0.000 0.235 0.660 0.105 1.870 150.0 0.000 0.078 0.692 0.230 2.152 170.0 0.000 0.016 0.553 0.431 2.415 190.0 0.000 0.000 0.437 0.563 2.560 210.0 0.000 0.000 0.306 0.694 2.694 360 Table A2 Temperature of Reaction: 70°C Agitation Rate : - rpm Chlorine Flow Rate : 0.6 lb/hr Submergence : 19.0 cm Reactor : Bubble Column Dq (in kinetic regime): - mo^e/Jnoje Reaction \4ole Frn Mole Frn Mole Frn Mole Frn Degree of Benzyl Benzal Benzo-tri Chlorina Time, min. Toluene Chloride Chloride Chloride tion t B C D E X 0.0 1.000 0.000 0.000 0.000 0.000 10.0 0.800 0.200 0.000 0.000 0.200 20.0 0.635 0.339 0.026 0.000 0.390 30.0 0.386 0.562 0.051 0.000 0.665 45.0 0.155 0.691 0.153 0.000 0.998 60.0 0.027 0.649 0.324 0.000 1.300 75.0 0.001 0.431 0.538 0.000 1.597 90.0 0.000 0.204 0.678 0.119 1.915 105.0 0.000 0.054 0.690 0.255 2.200 120.0 0.000 0.008 0.565 0.427 2.418 361 Table A3 Temperature of Reaction : 70°C Agitation Rate : - rpm Chlorine Flow Rate : 0.8 lb/hr Submergence : 19.0 cm Reactor : Bubble Column Dq (in kinetic regime) t-mole/J^^g Reaction Mole Frn Mole Frn Mole Frn Mole Frn Degree of Time, min Benzyl Benzal Benzo-tri Chlorina Toluene Chloride Chloride Chloride tion t B C D E X 0.0 1.000 0.000 0.000 - 0.000 10.0 0.665 0.319 0.016 0.000 0.351 20.0 0.351 0.586 0.062 0.000 0.711 30.0 0.130 0.703 0.167 0.000 1.036 40.0 0.015 0.657 0.314 0.014 1.326 50.0 0.000 0.444 0.514 0.042 1.598 60.0 0.000 0.234 0.655 0.111 1.876 70.0 0.000 0.082 0.696 0.222 2.140 80.0 0.000 0.016 0.621 0.363 2.347 90.0 0.000 0.000 0.544 0.456 2.456 100.0 0.000 0.000 0.447 0.553 2.553 110.0 0.000 0.000 0.387 0.613 2.613 120.0 0.000 0.000 0.335 0.665 2.665 Table A4 Temperature of Reaction: 70°C Agitation Rate: — rpm Chlorine Flow Rate: 0.4 lb/hr. Submergence: 19 .0 cm, Reactor: Bubble Column D (in kinetic regime): 0.547 mole/mole ______o ___ Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic log D/ Time, min. Benzyl Benzal Benzo-tri Free Chlorination se 'D Rate Toluene o Chloride Chloride Chloride Chlorine t B X mole/mole. C D E \ sec. 2.0 0.952 0.048 0.000 0.000 - 0.048 - 1.14 x 10~2 22.0 0.666 0.324 0.010 0.000 - 0.344 - 1.50 x 10-3 32.0 0.548 0.430 0.021 0.000 - 0.472 - 7.29 50.0 0.356 0.582 0.062 0.000 - 0.706 - 5.29 62.0 0.215 0.684 0.101 0.000 - 0.886 - 3.80 0 0 o o o 0.150 0.700 0.150 0.000 - 1.000 - 3.07 i lOOoO 0.030 0.645 0.335 0.000 1.315 - 1.59 - - 120 o 0 0.000 0.431 0.520 0.048 1.615 9.01 x 10 4 140.0 0.000 0.230 0.660 0.100 - 1.870 - 4.68 160.0 0.000 0.080 0.691 0.229 - 2.149 - 3.18 180.0 0.000 0.022 0.547 0.433 - 2.415 0.00 1.78 200.0 0.000 0.000 0.436 0.564 0.040 2.564 -0.22 1.11 220.0 0.000 0.000 0.311 0.689 0.052 2.689 -0.57 7.89 x 10~5 240.0 0.000 0.000 0.220 0.780 0.068 2.780 -0.91 5.58 260.0 0.000 0.000 0.173 0.827 0.077 2.827 -1.17 4.39 280.0 0.000 0.000 0.132 0.868 0.080 2.868 -1.44 3.35 300.0 0.000 0.000 0.100 0.900 0.085 2.900 -1.70 2.54 320.0 0.000 0.000 0.068 0.932 0.090 2.932 -2.06 1.72 Table A5 Temperature of Reaction : 70°C Agitation Rate : - rpm Chlorine Flow Rate : 0.5 lb/hr0 Submergence : 19o0 cm. Reactor : Bubble Column D (in kinetic regime): 0.630 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Benzyl Benzal Benzo-tri Free Chlorination l0*e% Rate Toluene o Time, min. Chloride Chloride Chloride Chlorine mole/mole X t B C D E sec. al o o . 1.00 0.000 0.000 0.000 - 0.000 - 1.19 x 10-2 - - CO o o 8.33 x 10"3 o 0.647 0.353 0.000 0.000 0.353 30.0 0.481 0.489 0.030 0.000 - 0.549 - 6.60 45.0 0.278 0.641 0.081 0.000 - 0.803 - 4.48 60.0 0.093 0.701 0.207 0.000 - 1.116 - 2.41 75.0 0.011 0.630 0.349 0.010 - 1.358 - 1.34 90.0 0.000 0.392 0.550 0.058 - 1.666 - 8.37 x 10 110.0 0.000 0.154 0.689 0.157 - 2.003 - 4.49 130.0 0.000 0.042 0.630 0.328 - 2.286 0.00 2.34 150.0 0.000 0.000 0.488 0.512 0.039 2.512 -0.25 1.24 170.0 0.000 0.000 0.383 0.617 0.050 2.617 -0.50 9.72 x 10"5 190.0 0.000 0.000 0.304 0.696 0.062 2.696 -0.74 7.72 210.0 0.000 0.000 0.232 0.767 0.070 2.767 -1.00 5.91 230.0 0.000 0.000 0.180 0.820 0.078 2.820 -1.25 4.57 250.0 0.000 0.000 0.146 0.854 0.083 2.854 -1.43 3.72 270.0 0.000 0.000 0.112 0.888 0.087 2.888 -1.74 2.84 Table A6 Temperature of Reaction : 70°C Agitation Rate: - rpm Chlorine Flow Rate : 0.6 lb/hr. Submergence : 19,0 cm. Reactor : Bubble Column Dq (in kinetic regime): 0.647 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Time, min. Benzyl Benzai Benzo-tri Free Chlorina Rate Toluene °/D Chloride Chloride Chloride Chlorine tion o mole/mole t B C D E X sec. al 0,00 1.000 0.000 0.000 0.000 - 0.00 - 1.19 x 10"2 15,0 0.651 0.349 0.000 0.000 - 0.349 - 8.37 x 10~3 CO 00 - o o 0.480 0.461 0.059 0.000 0.579 - 6.55 42.0 0.189 0.680 0.131 0.000 - 0.942 - 3.49 48.0 0,125 0.699 0.176 0.000 - 1.051 - 2.78 50.0 0.070 0.701 0.229 0.000 - 1.159 - 2.14 65.0 0.012 0.590 0.378 0,020 - 1.406 - 1.29 75.0 0.000 0.431 0.530 0.039 - 1.608 - 9.02 x 10"4 80.0 0.000 0.291 0.658 0.051 - 1.760 - 6.85 90.0 0.000 0.200 0.691 0.109 - 1.909 - 5.31 102.0 0.000 0.062 0.680 0.258 - 2.196 - 2.83 110.0 0.000 0.040 0.647 0.310 - 2.247 0.00 2.34 120.0 0.000 0.011 0.608 0.381 0.026 2.370 -0.04 1.74 130.0 0.000 0.000 0.464 0.536 0.050 2.536 -0.33 1.18 140.0 0.000 0.000 0.417 0.583 0.056 2.583 -0.42 1.06 160.0 0.000 0.000 0.320 0.680 0.065 2.680 -0.69 8.12 x 10”5 200.0 0.000 0.000 0.161 0.839 0.083 2.839 -1.38 4.08 180.0 0,000 0.000 0.234 0.766 0.075 2.766 -1.02 5.94 Table A7 Temperature of Reaction : 70°C Agitation Rate : - rpm Chlorine Flow Rate : 0.8 Ib/hr. Submergence : 19o0 cm. Reactor : Bubble Column Dq (in kinetic regime): 0.651 mole/mole Reaction Mole Fm Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Benzyl Benzal Benzo-tri Free Chlorina Rate Time* min„ Toluene lo*e % Chloride Chloride Chloride Chlorine tion o mole/mole sec. t B C D E X 0.0 1.000 0.000 0.000 0.000 - 0.000 - 1.19 x 10'2 10.0 0.704 0.296 0.000 0.000 - 0.296 - 8.90 x 10~3 20 o 0 0.531 0.429 0.040 0.000 - 0.509 - 7.09 30.0 0.168 0.690 0.142 0.000 - 0.074 - 3.26 40.0 0.051 0.694 0.255 0.000 - 1.204 - 1.91 50.0 0.000 0.522 0.450 0.028 - 1.506 - 1.04 60o0 0.000 0.271 0.631 0.098 - 1.827 - 6.43 x 10"4 70.0 0.000 0.118 0.700 0.192 - 2.094 - 3.88 80.0 0.000 0.050 0.651 0.299 - 2.249 0.00 2.54 90.0 0.000 0.000 0.538 0.462 0.055 2.462 -0.18 1.37 100.0 0.000 0.000 0.465 0.532 0.061 2.535 -0.34 1.18 HOoO 0.000 0.000 0.394 0.606 0.068 2.606 -0.51 1.00 120 o 0 0.000 0.000 0.317 0.683 0.074 2.683 -0.70 8.05 x 10"5 130.0 0.000 0.000 0.271 0.729 0.077 2.729 -0.87 6.88 140.0 0.000 0.000 0.233 0.767 0.081 2.767 -1.04 5.91 160.0 0.000 0.000 0.170 0.830 0.084 2.830 -1.34 4.31 366 Table A8 Temperature of Reaction : 70°C Agitation Rate : - rpm Chlorine Flow Rate : 0.951b/hr Submergence : 19.0 cm. D (in kinetic regime): 0.592 mole/mole Reactor : Bubble Column o Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of F) Kinetic Benzyl Benzal Benzo-tri Free Chlorina i°g /_. Rate Time, min. Toluene e 'D Chloride Chloride Chloride Chlorine tion o mole/mole. t B C D E X sec. 0.0 1.000 0,000 0.000 0,000 - 0.000 - 1.19 x 10-2 5.0 0.842 0.158 0,000 0,000 - 0.158 - 1.03 15.0 0o559 0.421 0.020 0,000 - 0.461 - 7.40 x 10-3 25,0 0.273 0.638 0.089 0,000 - 0.816 - 4.41 30.0 0,182 0.691 0.127 0.000 - 0,945 - 3.43 35.0 0,059 0,690 0.240 0.011 - 1.203 - 1.90 o o - 9 0,031 0.652 0.298 0.019 - 1.305 1.61 45 o 0 0,000 0,512 0.450 0.038 - 1,526 - 1.03 57.0 0.000 0,270 0.648 0.082 - 1.812 - 6.45 x 10 66,0 0.000 0,081 0.700 0,219 0.01 2.138 - 3.22 78.0 0.000 0.016 0.592 0.319 0,045 2.365 0,00 1,89 90.0 0.000 0.000 0.481 0.519 0.065 2.519 -0,20 1.22 102,0 0.000 0.000 0.391 0.609 0.072 2.609 -0,41 1.00 114.0 0,000 0,000 0.302 0.698 0,078 2.698 -0.67 7,67 x 10~5 126,0 0.000 0.000 0.247 0.753 0.083 2.753 -0,85 6.27 138,0 0.000 0.000 0.224 0.776 0.084 2.776 -0.98 5.68 Table A9 Temperature of Reaction : 45°C Agitation Rate : - rpm Chlorine Flow Rate : 0. 6 lb/hr Submergence : 19.0cm. Reactor : Bubble Column D (in kinetic regime): 0.659 mole/mole o Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Time, min. Benzyl Benzal Benzo-tri Free Chlorina i°ga e D'D/C, Rate O Toluene Chloride Chloride Chloride Chlorine tion mole/mole t B C D E X sec. al 0.0 1.000 0.000 0.000 0.000 - 0.000 - 5.65 x 10~3 15.0 0.671 0.320 0.009 0.000 - 0.338 - 4.07 25.0 0.488 0.478 0.034 0.000 - 0.546 - 3.16 35.0 0.324 0.606 0.070 0.000 - 0.746 - 2.34 45.0 0.165 0.700 0.135 0.000 - 0.970 - 1.53 50.0 0.061 0.710 0.229 0.000 - 1.168 - 9.59 x 10"4 60.00 0.010 0.621 0.359 0.010 - 1.369 - 6.10 70.0 0.000 0.446 0.522 0.032 - 1.576 - 4.24 - - 00 o o o 0.000 0.304 0.631 0.065 1.761 3.19 90.0 0.000 0.177 0.690 -.133 - 1.956 - 2.19 100.0 0.000 0.091 0.720 0.189 0.020 2.098 - 1.51 110.0 0.000 0.040 0.720 0.240 0.030 2.200 - 1.08 120.0 0.000 0.021 0.659 0.320 0.064 2.349 0.00 8.60 x 10"5 130.0 0.000 0.100 0.602 0.388 0.075 2.378 -0.09 7.09 140.0 0.000 0.000 0.571 0.429 0.080 2.429 -0.14 5.93 150.0 0.000 0.000 0.526 0.474 0.085 2.474 -0.21 5.47 170.0 0.000 0.000 0.498 0.502 0.087 2.502 -0.27 5.17 190.0 0.000 0.000 0.461 0.539 0.088 2.539 -0.36 4.79 210.0 0.000 0.000 0.412 0.588 0.090 2.588 -0.47 4.28 Table A10 Temperature of Reaction : 50°C Agitation Rate : - rpm Chlorine Flow Rate : 0.6 lb/hr. Submergence : 19.0cm. Reactor : Bubble Column Dq (in kinetic regime): 0o657 mole/mole Reaction Mole Fm Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Time, min. Benzyl Benzal Benzo-tri Free Chlorina Rate Toluene Chloride Chloride Chloride Chlorine tion 1o%\o t mole/mole B C D E X sec. al o o . 1.000 0.000 0.000 0.000 - 0.000 - 6.55 x 10"3 o r LQ — e 1 0.742 0.248 0.010 0.000 - 0.268 - 5.10 25o0 0.531 0.448 0.030 0.000 - 0.508 - 3.92 30.0 0.366 0.581 0.053 0.000 - 0.687 - 3.03 40.0 0.219 0.700 0.081 0.000 - 0.862 - 2.12 45.0 0.144 0.711 0.145 0.000 - 1.001 - 1.64 50.0 0.082 0.720 0.198 0.000 - 1.116 - 1.26 60.0 0.024 0.656 0.320 0.000 - 1.296 - 8.34 x 10~4 70.0 0.001 0.522 0.458 0.019 - 1.495 - 5.70 00 o o 0 0.000 0.353 0.588 0.059 - 1.706 - 4.15 90.0 0.000 0.218 0.671 0.111 - 1.893 - 2.94 100.0 0.000 0.124 0.710 0.166 - 2.042 - 2 0 08 120.0 0.000 0.061 0.701 0.238 0.045 2.177 - 1.46 130.0 0.000 0.023 0.657 0.320 0.065 2.298 0.00 1.03 1 o o to 140.0 0.000 0.000 0.602 0.398 0.075 2.398 . 7.40 x 10-5 CD O i — 1 0 150.0 0.000 0.000 0.559 0.441 0.079 2.441 1 6.87 160.0 0.000 0.000 0.531 0.469 0.080 2.469 -0.21 6.53 170.0 0.000 0.000 0.477 0.523 0.082 2.523 -0.31 5.86 190.0 0.000 0.000 0.424 0.576 0.084 2.576 -0.45 5.21 210.0 0.000 0.000 0.390 0.610 0.086 2.610 -0.52 4.79 Table All o Temperature of Reaction : 55 C Agitation Rate : - rpm Chlorine Flow Rate : 0.6 lb/hr Submergence : 19.0 cm Reactor : Bubble Column D (in kinetic regime): 0.611 mole/mole o ! Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Benzyl Benzal Benzo-tri Free Chlorination Time, min. logeD/D Rate Toluene Chloride Chloride Chloride Chlorine o mole/mole t B C D E X \ sec. 0.0 1.000 0.000 0.000 3.000 - 0.000 - 8.24 x 10-3 10.0 0.737 0.263 0.000 C1.000 - 0.263 - 6.39 20.0 0.524 0.446 0.030 C .000 - 0.506 - 4.86 30.0 0.361 0.579 0.060 C .000 - 0.699 - 3.69 40.0 0.218 0.670 0.112 C .000 - 0.894 - 2.63 50 o 0 0.100 0.710 0.190 C1.000 - 1.090 - 1.72 60.0 0.021 0.639 0.332 C .008 - 1.327 - 1.00 70.0 0.000 0.514 0.457 C .028 - 1.515 - 6.98 x 10"4 80,0 0.000 0.329 0.591 C .080 - 1.751 - 4.94 90.0 0.000 0.191 0.670 0 .139 - 1.948 - 3.38 100.0 0.000 0.124 0.701 0 .175 - 2.051 - 2.61 110.0 0.000 0.060 0.671 0 .269 - 2.209 - 1.78 120.0 0.000 0.032 0.611 C .357 0.045 2.325 0.00 1.34 130.0 0.000 0.011 0.562 0 .427 0.065 2.416 -0.08 1.01 140.0 0.000 0.000 0.509 c .491 0.072 2.491 -0.17 7.94 x 10~5 150.0 0.000 0.000 0.455 c .545 0.078 2.545 -0.28 7.09 160.0 0.000 0.000 0.422 c .578 0.080 2.578 -0.37 6.58 180.0 0.000 0.000 0.350 0 .650 0.084 2.650 -0.55 5.46 200.0 0.000 0.000 0.292 c .708 0.086 2.708 -0.74 4.55 370 Table A12 Temperature of Reaction : 60°C Agitation Rate : - rpm Chlorine Flow Rate : 0o6 lb/hr Submergence : 19.0cm. Reactor : Bubble Column Dq (in kinetic regime): 0o668 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Time* min. Benzyl Benzal Ben zo-tri Free Chlorina Rate Toluene o Chloride Chloride Chloride Chlorine tion mole/mole sec. t B C D E X al 0.0 1.000 0.000 0.000 0.000 - 0.000 - 9.65 x10~3 10.0 0.747 0.253 0.000 0.000 - 0.253 - 7.57 20.0 0.541 0.430 0.029 0.000 - 0.488 - 5.84 30.0 0.357 0.581 0.059 0.000 - 0.699 - 4.29 40.0 0.204 0.677 0.119 0.000 - 0.915 - 2.96 50o0 0.090 0.709 0.201 0.000 - 1.111 - 1.92 60.0 0.021 0.635 0.343 0.000 - 1.321 - 1.17 70.0 0.009 0.482 0.480 0.029 - 1.529 - 8.64 x 10~4 80.0 0.000 0.322 0.608 0.070 - 1.748 - 5.72 90.0 0.000 0.200 0.677 0.123 - 1.923 - 4.10 100o0 0.000 0.087 0.698 0.213 - 2.122 - 2.53 110.0 0.000 0.042 0.668 0.290 0.050 2.248 0.00 1.83 120.0 0.000 0.000 0.591 0.418 0.073 2.406 -0.12 1.09 130.0 0.000 0.000 0.544 0.456 0.076 2.456 -0.21 1.00 140.0 0.000 0.000 0.462 0.538 0.081 2.538 -0.37 8.50 x 10”5 150.0 0.000 0.000 0.411 0.589 0.084 2.589 -0.49 7.56 160o0 0.000 0.000 0.375 0.625 0.086 2.625 -0.59 6.90 180.0 0.000 0.000 0.300 0.700 0.090 2.700 -0.80 5.52 200.0 0.000 0.000 0.254 0.746 0.095 2.746 -0.94 4.67 371 Table A13 Temperature of Reaction : 65°C Agitation Rate : - rpm Chlorine Flow Rate : 0.6 lb/hr Submergence ; 19.0cm. Reactor : Bubble Column Dq (in kinetic regime): 0.500 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Min. Time Benzyl Benzal Benzo-tri Free Chlorina log °/ Rate Toluene e D Chloride Chloride Chloride Chlorine tion o mole/mole t B C D E X sec. al 0.0 1.000 0.000 0.000 0.000 - 0.000 - 1.06 x 10"2 15.0 0.642 0.348 0.010 0.000 - 0.368 - 7.35 x 10"3 30.0 0.427 0.531 0.042 0.000 - 0.615 - 5.37 40.0 0.265 0.644 0.091 0.000 - 0.826 - 3.84 50.0 0.131 0.709 0.170 0.000 - 1.049 - 2.54 60.0 0.033 0.670 0.287 0.010 - 1.274 - 1.47 65.0 0.000 0.536 0.442 0.022 - 1.476 - 9.27 x 10~4 85.0 0.000 0.285 0.631 0.094 - 1.799 - 5.88 100.0 0.000 0.092 0.701 0.207 - 2.115 - 2.98 115.0 0.000 0.011 0.642 0.347 0.042 2.336 - 1.57 130.0 0.000 0.000 0.500 0.500 0.059 2.500 0.00 1.09 145.0 0.000 0.000 0.391 0.609 0.072 2.609 -0.24 8.52 x 10'5 160.0 0.000 0.000 0.314 0.686 0.077 2.686 -0.47 6.84 175.0 0.000 0.000 0.262 0.738 0.083 2.738 -0.65 5.71 190.0 0.000 0.000 0.209 0.791 0.088 2.791 -0.86 4.55 205.0 0.000 0.000 0.192 0.808 0.090 2.808 -0.96 4.18 220.0 0.000 0.000 0.155 0.845 0.093 2.845 -1.20 3.37 235.0 0.000 0.000 0.134 0.866 0.095 2.866 -1.34 2.92 372 Table A14 Temperature of Reaction : 75°C Agitation Rate : - rpm Chlorine Flow Rate : 0o6 lb/hr Submergence : 19.0 cm. Reactor : Bubble Column (in kinetic regime): 0.650 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Time, min. Benzyl Benzal Benzo-tri Free Chlorina Rate Toluene l0«eD/D Chloride Chloride Chloride Chlorine tion o mole/mole t B C D E X sec. al 0.0 1.00 0.000 0.000 0.000 - 0.000 - 1.28 x 10”2 10.0 0.736 0.264 0.000 0.000 - 0.264 - 9.94 x 10"3 20.0 0.511 0.489 0.000 0.000 - 0.489 - 7.44 30.0 0.408 0.561 0.031 0.000 - 0.623 - 6.08 40.0 0.212 0.670 0.055 0.000 ” 0.780 - 4.05 50o0 0.091 0.701 0.208 0.000 - 1.027 - 2.58 60.0 0.020 0.646 0.334 0.000 - 1.314 - 1.62 75.0 0.000 0.390 0.547 0.063 - 1.672 - 9.22 x 10-4 90.0 0.000 0.147 0.692 0.161 - 2.014 - 4.85 105o0 0.000 0.048 0.650 0.302 - 2.54 0.00 2.78 120.0 0.000 0.000 0.500 0.500 0.036 2.500 -0.26 1.41 135.0 0.000 0.000 0.388 0.612 0.048 2.612 -0.51 1.09 150.0 0.000 0.000 0.314 0.686 0.059 2.686 -0.74 8.85 x 10~5 165.0 0.000 0.000 0.233 0.767 0.065 2.767 -1.03 6.57 180.0 0.000 0.000 0.177 0.823 0.071 2.823 -1.28 4.99 195.0 0.000 0.000 0.154 0.846 0.073 2.846 -1.46 4.34 210.0 0.000 0.000 0.111 0.889 0.075 2.889 -1.77 3.13 373 Table A15 Temperature of Reaction : 80°C Agitation Rate : - rpm Chlorine Flow Rate : 0.6 Ib/hr Submergence : 19.0 cm. Reactor : Bubble Column D (in kinetic regime): 0o640 mole/mole o Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Time, min. Benzyl Benzal Benzo-tri Free Chlorina Rate Toluene l0geD/D Chloride Chloride Chloride Chlorine tion o t mole/mole B C D E A X sec. L 0.0 1.000 0.000 0.000 0.000 0.000 - 1,39 x 10"2 10.0 0.749 0.251 0.000 0.000 - 0.251 - 1.10 20 o 0 0.552 0.427 0.021 0.000 - 0.469 - 8.62 x 10"3 45.0 0.180 0.681 0.139 0.000 - 0.959 - 4.04 55o0 0.069 0.692 0.239 0.000 - 1.170 - 2.56 65 o 0 0.012 0.590 0.378 0.020 - 1.406 - 1.59 80.0 0.000 0.343 0.586 0.071 - 1.728 - 9.41 x 10-4 95.0 0.000 0.130 0.698 0.172 - 2.042 - 5.08 110.0 0.000 0.034 0.640 0.326 - 2.292 0.00 2.78 125 o0 0.000 0.000 0.491 0.509 0.033 2.509 -0.26 1.56 i O o — o i 0.000 0.000 0.357 0.643 0.046 2.643 -0.57 1.14 155.0 0.000 0.000 0.266 0.734 0.056 2.734 -0.86 8.45 x 10"5 170.0 0.000 0.000 0.204 0.796 0.065 2.796 -1.16 6.48 185.0 0.000 0.000 0.150 0.850 0.070 2.850 -1.45 4.77 200.0 0.000 0.000 0.121 0.879 0.072 2.879 -1.67 3.84 215.0 0.000 0.000 0.093 0.907 0.076 2.907 -1.96 2.95 230.0 0.000 0.000 0.064 0.936 0.080 2.936 -2.30 2.03 374 Table A16 Temperature of Reaction : 70°C Agitation Rate : 500 rpm Chlorine Flow Rate : 0.6 lb/hr Submergence : - cm Reactor : Agitated Batch Reactor D (in kinetic regime): 0.640 mole/mole o Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of log D/f) Kinetic Time, min. Benzyl Benzal Benzo-tri Free Chlorina e o Rate Toluene Chloride Chloride Chloride Chlorine tion mole/mole t B C D E X sec. al 0o0 1.000 0.000 0.000 0.000 - 0.000 - 1.34 x 10”4 10o0 0.704 0.296 0.000 0.000 - 0.296 - 9.95 x 10-3 20.0 0.547 0.423 0.030 0.000 - 0.483 - 8.08 30.0 0.351 0.590 0.059 0,000 - 0.708 - 5.75 40.0 0.198 0.681 0.121 0.000 - 0.923 - 3,87 50o0 0.081 0.701 0.218 0,000 - 1.137 - 2.37 60.0 0.020 0.604 0.345 0.031 - 1.387 - 1.41 70.0 0.000 0.417 0.520 0.063 - 1.646 - 8.59 x 10~4 80 o 0 0.000 0.282 0.631 0.087 - 1.805 - 6.51 90.0 0.000 0.154 0.687 0.159 - 2.005 - 4.41 100.0 0.000 0.080 0.690 1.230 - 2.150 - 3.12 110.0 0.000 0.039 0.640 0.311 - 2.633 0.00 2.27 120.0 0.000 0.016 0.551 0,433 0.030 2.417 -0.15 1.66 130.0 0.000 0.000 0.472 0.528 0.053 2.528 -0.30 1.18 140.0 0.000 0.000 0.410 0.590 0.061 2.590 -0.44 1.03 160.0 0.000 0.000 0.304 0.696 0.068 2.696 -0.75 7.60 x 10“5 180.0 0.000 0.000 0.217 0.783 0.078 2.783 -1.06 5.42 200.0 0.000 0.000 0.165 0.835 0.084 2.835 -1.32 4.12 375 Table A17 Temperature of Reaction : 70°C Agitation Rate: 750 rpm Molar Chlorine Flow Rate : 0.6 lb/hr Submergence : - cm Reactor: Agitated Batch Reactor Dq (in kinetic regime) : 0.629 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Benzyl Benzal Benzo-tri Free Chlorina Rate Time. min. Toluene loge % Chloride Chloride Chloride Chlorine tion o mole/mole sec t B C D E X al 0.0 1.000 0.000 0.000 0.000 - 0.000 - 1.34 x 10~2 10.0 0.695 0.305 0.000 0.000 - 0.305 - 9.84 x 10"3 20.0 0.542 0.427 0.031 0.000 - 0.489 - 8.02 30.0 0.348 0.590 0.062 0.000 - 0.714 - 5.71 40.0 0.190 0.681 0.129 0.000 - 0.939 - 3.77 50.0 0.098 0.702 0.200 0.000 - 1.102 - 2.59 60.0 0.033 0.617 0.350 0.000 - 1.317 - 1.61 70.0 0.000 0.422 0.539 0.040 - 1.623 - 8.73 x 10"4 80.0 0.000 0.257 0.631 0.112 - 1.855 - 6.07 90.0 0.000 0.143 0.690 0.167 - 2.024 - 4.23 100.0 0.000 0.072 0.681 0.247 - 2.175 - 2.97 110.0 0.000 0.038 0.629 0.333 - 2.295 0.00 2.24 120.0 0.000 0.020 0.544 0.436 0.035 2.416 -0.75 1.71 130.0 0.000 0.000 0.471 0.529 0.059 2.529 -0.29 1.17 140.0 0.000 0.000 0.404 0.596 0.062 2.596 -0.45 1.01 160.0 0.000 0.000 0.300 0.700 0.070 2.700 -0.74 7.50 x 10”5 180.0 0.000 0.000 0.216 0.784 0.079 2.784 -1.05 5.40 200.0 0.000 0.000 0.173 0.827 0.085 2.827 -1.30 4.32 376 Table A18 Temperature of Reaction : 70°C Agitation Rate : 1000 rpm Molar Chlorine Flow Rate: 0.6 lb/hr Submergence : - cm Reactor : Agitated Batch Reactor Dq (in kinetic regime): 0.602 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Time, min. Benzyl Benzal Ben zo-tri Free Chlorina log D/„ Rate Toluene e D Chloride Chloride Chloride Chlorine tion o mole/mole sec t C D E X B al 0.0 1.000 0.000 0.000 0.000 - 0.000 - 1.34 x 10-2 10.0 0.686 0.314 0.000 0.000 - 0.314 - 9.74 x l(f3 20.0 0.554 0.428 0.018 0.000 - 0.464 - 8.18 30.0 0.347 0.581 0.072 0.000 - 0.725 - 5.68 40.0 0.190 0.681 0.129 0.000 - 0.939 - 3.77 50.0 0.097 0.700 0.203 0.000 - 1.106 - 2.58 60.0 0.031 0.631 0.328 0.010 - 1.317 - 1.60 70.0 0.000 0.393 0.537 0.070 - 1.677 - 8.22 x 10~4 80.0 0.000 0.246 0.643 0.111 - 1.865 - 5.91 90.0 0.000 0.062 0.680 0.258 - 2.196 - 2.79 100.0 0.000 0.029 0.602 0.369 0.045 2.340 0.00 2.01 110.0 0.000 0.021 0.509 0.470 0.047 2.449 -0.16 1.64 120.0 0.000 0.000 0.442 0.558 0.059 2.558 -0.31 1.11 130.0 0.000 0.000 0.377 0.623 0.065 2.623 -0.45 9.42 x 10-5 150.0 0.000 0.000 0.281 0.719 0.075 2.719 -0.76 7.02 170.0 0.000 0.000 0.210 0.790 0.080 2.790 -1.04 5.25 190.0 0.000 0.000 0.158 0.842 0.086 2.842 -1.32 3.95 377 Table A19 Temperature of Reaction 70°C Ag tat ion Rate : 1500 rpm Molar Chlorine Flow Rate : 0.6 lb/hr Submergence : - cm. D (in kinetic regime) : 0.647 mole/mole Degree of Kinetic Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Benzyl Benzal Benzo-tri Free Chlorina Rate Time, min. Toluene Chloride Chlorine tion Chloride Chloride %o mole/^ole sec E X B C D al 0.000 - 0.000 - 1.34 x l(f2 0.0 1.000 0.000 0.000 _3 - 9.85 x 10 10.0 0.695 0.305 0.000 0.000 - 0.305 - 8.02 20.0 0.541 0.438 0.021 0.000 - 0.480 - 5.66 30.0 0.345 0.580 0.075 0.000 - 0.730 - 3.79 40.0 0.192 0.679 0.129 0.000 - 0.937 - - 2.61 50.0 0.100 0.699 0.201 0.000 1.101 - 1.50 0.021 0.650 0.318 0.011 - 1.319 60.0 -4 - 1.722 - 7.62 x 10 70.0 0.000 0.354 0.570 0.076 - 5.89 80.0 0.000 0.244 0.646 0.110 - 1.866 - 3.68 90.0 0.000 0.110 0.702 0.188 - 2.078 0.00 2.53 100.0 0.000 0.052 0.647 0.301 0.015 2.249 -0.14 1.75 110.0 0.000 0.020 0.561 0.419 0.041 2.399 -0.30 1.20 120.0 0.000 0.000 0.482 0.518 0.060 2.518 0.000 0.417 0.583 0.067 2.580 -0.43 1.04 130.0 0.000 r 150.0 0.000 0.000 0.300 0.700 0.075 2.700 -0.77 7.50 x 10 170.0 0.000 0.000 0.227 0.773 0.081 2.773 -1.03 5.67 190.0 0.000 0.000 0.168 0.832 0.085 2.832 -1.34 4.20 200.0 0.000 0.000 0.152 0.848 0.087 2.848 -1.46 3.80 378 Table A20 Temperature of Reaction : 70°C Agitation Rate : 2000 rpm Molar Chlorine Flow Rate : 0.6 lb/hr Submergence : -cm Reactor : Agitated Batch Reactor Dq (in kinetic regime): 0.657 mole/mole Reaction Mole Frn Mole Frn Mole Frn Mole Frn Mole Cone. Degree of Kinetic Benzo-tri Free Chlorina log D/ Rate Time, min. Toluene Benzyl Benzal e 'D Chloride Chloride Chloride Chlorine tion o mol^fanole sec t B C D E A X L 0.0 1.000 0.000 0.000 0.000 - 0.000 - 1.34 x 10"2 10.0 0.714 0.286 0.000 0.000 - 0.286 - 1.01 20.0 0.542 0.447 0.011 0.000 - 0.469 - 8.05 x 10 30.0 0.349 0.602 0.049 0.000 - 0.700 - 5.74 40 .0 0.194 0.687 0.119 0.000 - 0.925 - 3.83 50.0 0.087 0.701 0.212 0.000 - 1.125 - 2.45 60.0 0.020 0.652 0.318 0.010 - 1.318 - 1.49 70.0 0.000 0.325 0.591 0.084 - 1.759 - 7.17 x 10 80 .0 0.000 0.236 0.662 0.102 - 1.866 - 5.79 90.0 0.000 0.100 0.698 0.202 - 2.102 - 3.50 100.0 0.000 0.044 0.657 0.299 0.018 2.255 0.00 2.41 110.0 0.000 0.020 0.570 0.410 0.040 2.390 -0.14 1.78 130.0 0.000 0.000 0.423 0.577 0.066 2.577 -0.45 1.06 150.0 0.000 0.000 0.310 0.690 0.076 2.690 -0.75 7.75 x 10 170.0 0.000 0.000 0.233 0.767 0.080 2.767 -1.05 5.82 190.0 0.000 0.000 0.165 0.835 0.083 2.835 -1.35 4.12 200.0 0.000 0.000 0.152 0.848 0.086 2.848 -1.48 3.80 i 37 9 APPENDIX VII References 1. Eyring, H., J. Chem. 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