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Solubility of Flue Gas Components in Naoh Based Scrubber Solutions

Solubility of Flue Gas Components in Naoh Based Scrubber Solutions

ABO AKADEMI

KEMISK-TEKNISKA FACULTY OF FAKULTETEN CHEMICAL ENGINEERING

Forbranningskemiska Combustion Chemistry forskargruppen Research Group

REPORT 97-2

Solubility of Flue Components in NaOH Based Scrubber

Kristoffer Sandelin, Rainer Backman

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Lemminkainengatan 14-18 B FIN-20520 Abo, Finland Internet: http://rost.abo.fi/ccrg/ ISSN 0785-5052 ISBN 952-12-0003-0 Abo Akademis tryckeri Abo, Finland, 1997 DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document Preface

There is a growing interest for the chemical and the power generation industry to effectively recover possible harmful from their effluent streams. It is therefore of interest to predict the of gases into aqueous solutions. The purpose of this study was to develop a general thermodynamic model for calculating the solubility of flue gas components in sodium based scrubber solutions. Simultaneous of gaseous SO2, H2SO4 , CO2,

and NH3 was of special interest but N20, NO, and H2S were also studied.

The work presented here is part of the energy and environmental technology research programme, SIHTI 2. The Finnish Technology Development Centre (Tekes) is gratefully acknowledged for the funding of this work.

The authors want to thank TkL Bengt Skrifvars for valuable discussions and comments on the manuscript. Mr. Sture Bostrom is acknowledged for his help with the software.

Abo, May 6, 1997

Kristoffer Sandelin Rainer Backman Abstract

The work reported here is a thermodynamic study on the solubility of flue gas components in aqueous solutions containing sodium salts. The result of the work is an equilibrium model, based on the expressions developed by Pitzer and co-workers. The model developed here is based on a previous study by Sandelin (1996), where the effect on the solubility of S02, NH3, CO2, H2S, HCN, N2, 02, N20, and NO was investigated. The model presented here includes and sodium salts that makes it possible to study simultaneous absorption of flue gas components in alkaline scrubber solutions. The model is in this report applied on the absorption of a flue gas into a NaOH scrubber . The calculations show that it is possible to simultaneously absorb sulfur dioxide, sulfuric acid, and without co-absorption. The calculations also show that gaseous NO and N20 cannot be scrubbed unless they are oxidized to or reduced to ammonia.

Key words: alkaline, absorption, equilibrium, gases, Pitzer, scrubber, sodium hydroxide solubility, thermodynamic Contents

Preface Abstract Contents Introduction 1 Thermodynamic background 2 Method 5 Metastable equilibrium 7

Solubility data for nitrous and nitric oxide 8 Results 12 Application of the model 15 Discussion 19 Conclusions 20 Literature 21 Introduction

There is a growing interest for the chemical and the power generation industry to effectively recover possible harmful gases from their effluent streams. Flue-gas cleaning by using aqueous solutions to remove sulfur dioxide is in power plants already established technology, but since the 80’s development has also focused on nitrogen compounds. Special interest of the nitrogen compounds have arisen in the krafr recovery cycle. It has been shown that nitrogen compounds may be released from the krafr recovery process and could be a source of harmful nitrogen emissions. The recovery of weak electrolytes from the effluent streams in the industries is also of great importance. It is towards that end important to study the vapor- equilibrium of gases in aqueous solutions.

Dalton showed in 1801 that the solubility of a gas in a of gases is proportional to the partial of the individual gas, and that the solubility of each gas is nearly independent of the presence of an other gas. The solubility of gases in is however affected by the addition of other solutes, particularly electrolytes. With an increasing , the gas solubility is nearly always decreasing (Wiesenberger and Schumpe, 1996). The extent of the “salting out” effect varies with different salts, but with a given salt, the relative decrease in the solubility of a gas is nearly the same. Thermodynamic studies on vapor-liquid equilibria, in multi-component aqueous solutions has previously been done by many authors. The work by Edwards et al. (1978) gives an extensive and detailed description on the calculation of vapor- liquid equilibrium in aqueous solutions containing one or more volatile electrolytes: ammonia, carbon dioxide, sulfide, sulfur dioxide, and . An essentially identical model has been presented by Bautier and Renon (1978). This model in contrast to the model developed by Edwards et al. (1978) also includes ternary data (two-solute systems). Results on simultaneous absorption of ammonia and carbon dioxide in sodium salt solutions has more recently been reported by Kurz et al (1996a ), Kurz et al. (1996b), and Bieling et al. (1995). Practical studies on the chemical equilibria in flue-gas cleaning systems has been reported in Hudson and Rochelle (1982). A study on the topic has also been carried out by Luckas et al. (1994). Buzek and Jaschik (1995) have studied the of sulfur dioxide over aqueous sodium -bisulfite, -sulfite and - solutions. In their work they give a semi empirical formula for calculating this system. The absorption of SO2 into NazSC^ and

H2SO4 solutions has also been studied thoroughly by Hunger et al. (1990). There has also arisen an interest in predicting absorption of hydrogen sulfide in aqueous multi-component solutions. A study on the absorption of H2S in aqueous solutions including organic basis (, metyldiethanolamine, and monoethanolamine) has previously been reported in Li and Mather (1996).

The focus of this study is to develop a general thermodynamic model that describes the solubility of flue gas components in sodium based scrubber solutions. Chemical equilibrium

1 has in this study been calculated based on the non stoichiometric formulation (Smith and Missen, 1982). The benefit of the non stoichiometric approach is, in contrast to the stoichiometric approach, that no constants for the specific chemical reactions are needed.

Thermodynamic background

Chemical equilibrium in a system is given by the minimum of the total . For a pure species, the free energy, is dependent on the pressure and the temperature. It is usually determined from standard (AFFWk), (S°298°k ) and the heat capacity (C° p or C°v) as a function of the temperature and/or pressure. The total Gibbs free energy is the sum of Gibbs energies for all species in the system. The minimization of Gibbs free energy is therefore done for all species in all phases. The minimization problem may be written as:

Minimize G = (1) / where ju, is the of species i and n, is the number of moles of species i. In order to carry out the minimization one must have an expression for the chemical potential. The expression for the chemical potential is given as:

A =ju° +RTln(ai) (2) where //° is the standard chemical potential for species i. R is the and T is the absolute temperature, a, is the activity of species i. The activity of a single species is affected by the relative amount (concentration) and the composition (other solutes) due to interactions between the species of the system. For aqueous solutions the activity of a species is expressed as the product of the activity coefficient, y, and an the , m .

4 = (3)

There are many models for predicting the activity coefficients in aqueous solutions. The cornerstone for the more resent models: Bromley ’s- (1973) Chen’s- (1982), Davie ’s- (1938 and 1962), Guggenheim’s- (1935 and 1955), Meissner’s- (1972), Pitzer’s- (1973), and Sander ’s (1984) equations is the Debye-Huckel equation (Debye and Htickel 1923a and 1923b). A model based on the equations by Pitzer (1973) as referred to by Harvie et al. (1984) have been used in this study.

Consequently, the total Gibbs free energy is not only dependent on the temperature and pressure but also on the chemical composition. Determination of the composition of a multiphase multi-component system is practically done with an computer program using a

2 suitable algorithm for the minimizing process (Eriksson, 1975). The computer program ChemSage (Eriksson and Elack, 1990) was used in this study.

Gibbs free energy for a species can be calculated from the enthalpy and the entropy at a given temperature and pressure. At a constant pressure Gibbs free energy is given by:

7%; (4) where H°T is the enthalpy and S°T the entropy at the temperature T. Enthalpy and entropy values are in thermodynamic handbooks and databases given as standard and at 298K and 1 bar pressure. In order to calculate the enthalpy and entropy at an other temperature than 298K we need to know the heat capacity function, since the enthalpy and entropy is calculated from:

+ (5)

$t = ^298 + J (6) 298 *

The simplest method for calculating thermodynamic properties at other than 298K is to assume constant heat capacity. The heat capacity for aqueous species is however not found in most thermodynamic handbooks even at 298K (25°C). The heat capacity can however be calculated from the entropy. In 1964, Criss and Cobble proposed the principle of such a method (Criss and Cobble, 1964a and 1964b). The method has been successful in predicting the standard molal heat capacities for many aqueous species when experimental data is not available. The model gives however a rather poor fit for many experimental . In addition the Criss and Cobble method does not consider the temperature dependency of uncharged aqueous species. The heat capacity of aqueous species can also be predicted by the Helgeson-Kirkham-Flowers model, HKF-model (Helgeson et al., 1981). This semi-empirical model uses parameters from calorimetric or volumetric measurements and predicts the partial molal properties of aqueous solutions with a very good accuracy. This requires of course that the parameters for the model are known. The HKF-model have been simplified by Sippola (1992) by leaving out the pressure dependency in the equation. This simplified HKF-model can describe the thermodynamic properties of aqueous species with a good accuracy and is in agreement with the original HKF-model up to 170°C (Hamalainen et al., 1991). Sippola (1996) have used the simplified HKF-model to calculate the heat capacity for many aqueous species. The heat capacity in Sippola (1996) is given as a heat capacity function in the form:

3 cxn=/4+^xr+cxr+^- (7)

where A, B, C, and D are fitted constants. In figure 1 the constants from Sippola (1996) have been used to calculate the partial molal heat capacity for 7 univalent ions. The heat capacities for 5 solvated un protolyzed molecules and 3 bivalent ions are shown in appendix I.

100 Temperature [°C]

Figure 1 Calculated partial molal heat capacities for 7 univalent ions

4 Method

The purpose of this study was to develop a general equilibrium model that describes the solubility of gases relevant to scrubber applications. The gases of interest were sulfur dioxide, ammonia, carbon dioxide, hydrogen sulfide, hydrogen cyanide, nitrogen, , , and nitric oxide. Main focus of the work was to extract data from the literature and databases, and to evaluate thermodynamic constants (AH°298k, S°29sk and C°P (T)) that describe the solubility of the gaseous species mentioned above. The reliability of the model was of special interest and calculated solubilities was for this reason tested against empirical solubility data. The testing was done graphically by comparing empirical solubilities with calculated results (Sandelin, 1996). During the testing the constants were selected from the literature, adjusted when needed, or calculated from solubility data. The temperature dependency of the solubility for the gases mentioned above was of special interest. The temperature dependency of the heat capacity was taken from Sippola (1996) who has calculated the heat capacities for many aqueous species with a simplified Helgeson-Kirkham-Flowers model developed earlier (Sippola, 1992). The evaluation of the thermodynamic data resulted in a chemical model including 14 gases and 27 aqueous species and 16 phases. Table 1 shows the gaseous and aqueous species and table 2 the solid phases in the model.

Table 1 The source of the thermodynamic constants (AH°f2 98K, S°2 9SKcmd C°P(T)) for the gaseous and aqueous species used in the model developed within this work

Species Source S03(g), H2S(g), HCN(g), CO(g), H2S04(g) Barin (1989)1 (Mg), C02(g), SO](g), COS(g) Barm (l 993)1 NH3(g) Barmetal ., (1977)1 H2(g), N2(g), H20(aq) C hase etal . (1985)1 H2S04 (aq), HS'*, CO(aq) Bailey etal . (1982)' NH2COO , e" SANDELM (1995) N20(aq), NO(aq) Sandelin (1996) N20(g), NO(g) SGTE-94 PS Na +, fT, OH", H2(aq), 02(aq), S02(aq), HS03", S032", Sippola (1996) HS04 ", S04 2", C02(aq), HC03 , C032", NH3(aq), W, CN", N2(aq) H2S(aq)*, S2", HCN(aq) Stumm and Morgan (1981) Heat capacity from Sippola (1996), ‘As referred to by Koine (1994)

5 Table 2 The source of the thermodynamic constants (AH°f298K, S°29sicand C°p (T)) for solid phases used in the model

Solid Source NaHC0 3, Na 20 Barin (1989)1

Na 2S03 BARIN (1993)1

(NH4) 2S04 Barin etal . (1977)1

Na 2S04 *7H20 Kubashewski etal . (1993)1

Na 2S04 , Na 2C03, NaOH, Na 2S Knacke et al . (1991)1

Na 2C03 *2Na 2S04 , NaHS, NaHS0 4 , NaHS0 3 This study

Na 2C03*2Na 2S04 Harvie etal . (1984)

Na 2C03*H20, Na 2C03*7H20, Na 2CO3*10H2O WEAST ETAL. (1986) ‘As referred to by Rome (1994)

Simultaneous absorption of gases

The model developed within this study utilizes the expressions developed by Pitzer (1973) for calculating the activity coefficients in the aqueous phase. The expressions in Harvie et at (1984) are parameterized with constants from the literature (Harvie et at (1984), Edwards et at (1978), Rosenblatt (1981), Heinonen (1995), and Pitzer (1991)). Pitzer’s expression for the Gibbs excess energy is divided into tree parts. The first part, a Debye-Huckel term, describes the long-range electrostatic while the second term takes into account binary interactions. The third part take into account ternary interactions. Third virial coefficients are small and can according to Pitzer (1980) often be omitted at moderate i.e. up to around 2 molal. The frame for the interaction parameters in our model was taken from the work by Harvie, Moller and Weare (1984). Parameters in Harvie et al. (1984) are based on experimental data at around room temperature and their model is developed for 25°C. It has shown to be a reliable model and is in excellent agreement with many experimental systems. The parameters in Edwards et al (1978) are mostly estimates and it only includes binary parameters. In their work, it is concluded, that there is much uncertainty in the parameters. It is therefore important to keep in mind that the values of the parameters are only estimates, often based on weak experimental evidence. They conclude that more reliable binary data are needed to determine the parameters with confidence. The parameters in Edwards et al. (1978) are said to be valid within the temperature interval 0-170°C. The /^-parameter by Edwards et al. (1978) for taking into account interactions between SO2-SO2 molecules was excluded from our model since this parameter has shown to be inconsistent with the data used here (Sandelin,

6 1995b). Parameters for interactions that already have been taken into account by parameters from the work by Harvie et al. (1984) were also excluded from our model. The interactions between Na-HSOg and Na-SOs has been estimated by Rosenblatt (1981) and we use his parameters for these interactions. The parameters are based on sound approximations and are valid in the temperature interval 25-55°C (Rosenblatt,

1981). Parameters for the interactions between NTL, and S04 was taken from Pitzer (1991) were he give an extensive list of carefully evaluated parameters at 25°C.

Heinonen (1995) have evaluated interaction parameters for the system Na 2S-Na 2S04 - H20 were he fitted the parameters by least squares to solubility data in Linke (1965). The parameters are valid for 25°C and were used as such in our model. Table 3 gives the binary parameters for ions of opposite sign used in our model though also interactions between molecules and ternary mixing parameters were used.

Table 3 Binary parameters for ions with opposite sign that were used in this study (Harvie et al (1984), Edwards et al. (1978), Pitzer (1991), Rosenblatt (1981), and Heinonen (1995))

H+ Na + nh4+ OH 0 Harvie et al. Edwards et al. HS03" Edwards et al. Rosenblatt Edwards et al. SO/' Edwards et al. Rosenblatt Edwards et al. HS" Edwards et al. Heinonen Edwards et al. S2 ' Edwards et al. 0 Edwards et al. HSOf Harvie et al. Harvie et al. 0 SO/ Harvie et al. Harvie et al. Pitzer

hco 3" 0 Harvie et al. Edwards et al. CO/ 0 Harvie et al. Edwards et al.

NH2COO" Edwards et al. 0 Edwards et al. CN" 0 0 0 * O-parameters are zero

Metastable equilibrium

Multi-component equilibrium calculations in real systems often requires the assumption of metastable equilibrium. A system is said to be in a metastable state if it has the “ability ” to undergo a spontaneous change but remains in an unchanged state. In this study, a metastable state is defined as a state with a long enough lifetime for it to be treated as an equilibrium system. A classical example of metastable equilibrium is a mixture of H2 and 02 at 25°C and 1 bar pressure. In equilibrium the mixture would

7 react and form water but in practice no change of the system can be observed. Another example of a metastable state is a supersaturated solution. A typical example in flue gas applications is the oxidation of sulfite to sulfate. Sulfate together with small amounts of sulfide are the thermodynamically stable forms of sulfur when sulfur dioxide is absorbed in water. The reactions are however so slow that they can be neglected (Sandelin 1995a and 1995b). An other example of a metastable state in scrubber applications is the absorption of NH3, NO, and/or N2O. Nitrogen with oxidation state 0 (i.e. N%) is thermodynamically stable (Pourbaix, 1974), but in practice metastable equilibrium is observed.

Though calculation of the chemical equilibrium with the Gibbs free energy minimization approach do not need to consider specific chemical reactions, metastable equilibrium can be taken into account. This is done by a proper formulation of the stoichiometric matrix. In the stoichiometric matrix, see figure 2., columns represent the system components and rows the species or compounds of the system. Usually chemical elements are chosen as system components. When system components consists of chemical elements, metastable state is taken into account by suppressing species from the mass balance. In other words, the formation of thermodynamically stable species is hindered. Another way of taking into account metastable equilibrium is to choose species as system components in the stoichiometric matrix. A third way, is to introduce different components of an element in the stoichiometric matrix, reactive elements and non reactive ones. The third approach is used in Luckas et al. (1994). The stoichiometric matrix for some species in the sulfur-water system is shown in figure 2.

Species \ Components H 0 S S04 e" H20 2 1 0 0 0 IT 1 0 0 0 -1 OH 1 1 0 0 1 HS04" 1 0 0 1 1 HSO/ 1 3 1 0 1

Figure 2 The stoichiometric matrix for some species in the sulfur-water system including HSO3 as a metastable species

Solubility data for nitrous oxide and nitric oxide

Standard thermodynamic data for the solubility of nitrous oxide and nitric oxide is not found in standard thermodynamic handbooks and databases. These data are however given in Brewer (1982). When we started this study Brewers work was unknown to us

8 and standard thermodynamic values was therefore calculated based on the work by Battino (1981a). Besides the compilation work for the solubilities of the gases in water, Battino (1981a) also calculates thermodynamic constants for the solubility of nitrous oxide and nitric oxide in water. Battino (1981a) gives however the constants in fraction units. Standard thermodynamic data for aqueous species is normally given in molal (mol/ kg H20) units. The constants by Battino can for this reason not be used together with other standard thermodynamic data from the literature. In this work we used the same method as Battino (1981a) to calculate the constants in molal units. These constants can then be used together with standard data from thermodynamic- handbooks or databases when calculating the solubility of N20 and NO in multi-component solutions.

Nitrous oxide and nitric oxide are in this study assumed to be absorbed into water as hypothetical hydrated molecules, N20(aq) and NO(aq). Solubility of the gases in water is described by the thermodynamic constants for these molecules. The method that was used for calculating the standard constants is outlined here. First the solubility, given in Battino (1981a), was calculated in molal units. The solubility of nitrous oxide and nitric oxide in 1 kg H20 at 1 bar partial pressure of the gas is described by equation 8. Values for the constants, A, B, and C are given in table 4.

In m = A +------+ CTn(T/100K) (8) T/100K

Table 4 Constants in equation 8. describing the temperature dependency of the solubility of NfJ and NO in water. The solubility is in molal units

Coefficients/Species A B C Nitrous oxide, N20 -56.7724 88.89506 21.2716 Nitric oxide, NO -58.7941 82.34521 22.8164

The Gibbs free energy for a reaction can be calculated from the , K:

AGreaction= - RT In K (9)

9 For the absorption of a gas, the equilibrium constant is described by: (10) JS _ mGAS{aq) Pgas (S)

Since the partial pressure of the gas, Pgas ®, in our case is 1 bar, the equilibrium constant is equal to the molality of the hypothetically solvated gas molecule, mOAs. Equation 11. was used to calculate the Gibbs energy for this aqueous molecule:

AG. -RAT-100RB - RCT\n(—) (11) 100

When the Gibbs energy is known for the reaction the entropy can be calculated:

dG (12)

The relationship between the solubility and the entropy is given by equation 13.:

+ ac in(^) + ac (13)

The enthalpy for the reaction is then calculated from the relationship:

AG = AH - TAS -> AH = AG + TAS (14)

The relationship to the empirical formula (equation 8.) is:

A*^ = -iooag+acr (15)

Finally the heat capacity is calculated from the relationship:

^Cp.reacuon = ^ (16)

The heat capacity is described by the gas constant and the term C in the empirical formula:

AC,. reaction= RC (17)

10 Enthalpy, entropy and the heat capacity for the reactions were calculated according to the procedure described above in the temperature interval 0-120°C. The enthalpy and entropy values at 25°C were used in the thermodynamic model, since this temperature, by convention is used as the standard state for thermodynamic data in aqueous solutions. The enthalpy for the reactions at 25°C is -21.18 kJ mol"1 for nitrous oxide and -11.91 kJ mol"1 for nitric oxide. The entropy is -101.96 kJ mol"1 K"1 and -91.89 J mol"1 K"1 for the same reactions. The enthalpy, entropy, and heat capacity for the aqueous molecules was calculated from the relationship:

GAS{aq) ~ ^GAS(g) + reaction (18)

^GAS(aq) ^GAS(g) reaction (19) and

Vc°'P,GAS{aq ) ~— r°vP,G4S(g) ^j- P,reaction (20) where AH°GAS(aq) is the calculated standard enthalpy of formation for the aqueous molecule. AH°GAs(g) is standard enthalpy of formation for the gaseous species taken from the SGTE-94 database for pure substances. AHrea ction is the calculated enthalpy for the reaction as shown above. S°GAS(aq) is the calculated standard entropy for the aqueous molecule at 25°C. S°GAS(g) is the standard entropy at 25°C for the gaseous species taken from the SGTE-94 database for pure substances. ASreac tion is the calculated entropy for the reaction described above. The heat capacity for N20(aq) and NO(aq) was calculated in the same manner as the enthalpy and the entropy for the aqueous molecules. CP, GAs(aq) is the calculated heat capacity for the aqueous specie. Cp,GAS(g) is the heat capacity for the gas as given by the SGTE-94 database for pure substances. ACP,reaction is the calculated heat capacity for the reaction as shown above.

Table 5 gives the thermodynamic constants for the solvated molecules, N20(aq) and NO(aq). A, B, C and D are constants in the heat capacity function (equation 7).

Table 5 Thermodynamic constants: AH°2 98k > S°29sk and A, B, C, and D in the Cp- function for Nf)(aq) and NO(aq). The unit for Cp is J mol1 K1

Specie \ Constants AH°298K S°298K Tmax A B C D [kJ mol'1] [J mor’K'1] [K] N20(aq) 60.42 118.05 318 208.07 0.0383 -1.41xl0" 5 -2.46x10? NO(aq) 79.37 118.85 298 212.75 0.0155 -4.77x1 0"6 2.33x10? 343 0 0 0 0

11 Results

The result from this study is a consistent thermodynamic model predicting the solubility of nine gases in water. Consistent thermodynamic constants, enthalpy, entropy and constants for the heat capacity function combined with Pitzers method for calculating the activity coefficient results in a general thermodynamic model for calculating the solubility of SO2, NH3, CO2, H2S,

HCN, N2, O2, N2O, and NO in water. The model is pH dependent and as it includes sodium salts as well as sodium hydroxide it can be used in flue gas scrubber applications.

This section outlines the results from a comparison between calculated and empirical solubilities for a single component absorption at 1 bar partial pressure of the gas. The comparison between the calculated and empirical solubility is summarized by drawing some conclusions about accuracy of the solubility calculations for each gas.

SO?: Calculated and empirical solubilities was in good agreement with each other. Empirical solubilities by Battino (1981b) and Wilhelm et al. (1977) was in good agreement with the temperature dependent Henrys constant by Edwards et al. (1978) and the thermodynamic model developed within this study. The interactions between molecules in the solution can be taken into account by a interaction parameter, f}^ in the extended Pitzer model that was used in this study (Harvie et al., 1984). This parameter takes into account interactions between uncharged molecules. The -parameter by Edwards et al. (1978) for taking into account the interactions between the SO2 molecules was however excluded since this parameter have shown to be inconsistent with the model used here (Sandelin, 1995).

NH3: Ammonia is very soluble in water. A high concentration of NH3 leads to strong interactions between the aqueous species. Thermodynamic calculations on the solubility of ammonia in water must therefore already at low partial take into account the non­ ideality of the system. Calculated solubilities with a constant -value of 0.027 are in very good agreement with the empirical solubility by Wilhelm et al. (1977). Calculations with the model without this parameter is in good agreement with the temperature dependent Henys constant by Edwards et al. (1978).

CO?: The solubility of carbon dioxide is lower than the solubility of ammonia and a model for taking into account the interactions between the aqueous species is not needed at low partial pressures of the gas (<1 bar). The predicted solubility was in very good agreement with the temperature dependent Henry ’s constant by Edwards et al. (1978) and the empirical solubilities by Wilhelm et al. (1977).

12 H?S: A review of the thermodynamic constants for the H2S-H2O system showed that data was inconsistent. The empirical solubilities for the system by Fogg (1988), Wilhelm et al. (1977), and the temperature dependent Henry’ s constant by Edwards et al. (1978) was however in good agreement with each other. The enthalpy and entropy values for the aqueous hydrogen sulfide species in the model is taken from Stumm and Morgan (1981). Constants for the Cp- function are from Sippola (1996). The data for the anion, HS' was taken from Bailey et al. (1982) as referred to by Roine (1994). The model developed within this study describes the empirical solubility of H2S by Fogg (1988) with an maximum error of 22% at 120°C.

HCN: The solubility of hydrogen cyanide could not be properly reviewed due to lack of empirical data. The calculated solubility was compared to solubilities calculated with the temperature dependent Henry ’s constant from Edwards et al. (1978). The thermodynamic model developed here agree with the solubilities calculated with the Henrys constant at temperatures over 40°C. The model is not in agreement with solubilities calculated with the Henrys constant at lower temperatures.

N?: The calculated solubilities of nitrogen gas, N2 agree well with the experimental and empirical data by Morrison and Billet (1952)', Bohr and Bock (1891)', Winkler (1891)' and Wilhelm et al. (1977).

O2. As for the solubility of N2 the calculated solubility of oxygen gas showed to be in agreement with the experimental solubilities by Bohr and Bock (1891)', Winkler (1891)' and Morrison and Billet (1952)'. The empirical values by Wilhelm et al. (1977) was also in good agreement with the model.

N?0: Thermodynamic constants for nitrous oxide was calculated from empirical solubility data by Battino (1981a). The calculated solubilities are in good agreement with the empirical data by Wilhelm et al. (1977) and Battino (1981a). Our model also agree with experimental solubility data from different sources as referred to by Battino (1981a). Figure 3 shows a comparison between experimental and calculated solubilities.

NO: The solubility of nitric oxide is predicted with thermodynamic constants calculated from the empirical solubility by Battino (1981a). In the report, he states, that he only used experimental values by Winkler (1901) in the smoothing equation. It is though worth pointing out that the solubilities by Battino (1981a) and Wilhelm (1977) differ from the values by Winkler (1901)' at higher temperatures. Figure 4 show a comparison between experimental and calculated solubilities. All broken lines, the solubilities by Wilhelm (1977), Battino (1981a) and the calculated one agree with each other. The solid line that is in agreement with the experimental values by Winkler (1901) is calculated with the heat capacity data in table 5.

1 As referred to by Linke, 1965

13 P(N,0)=Ibar

Experimental solubilities compiled by Battino (1981) - Battino (1981), smoothed experimental data, latm * Wilhelm et al. (1977), empirical formula, P=lbar -This study, calculated 3.3 1997 O 0.04

Temperature [°C|

Figure 3 Solubility of nitrous oxide in water at 1 bar partial pressure. Smoothed empirical data by Battino (1981a) and Wilhelm (1977), experimental solubilities from Battino (1981a) versus thermodynamic calculations

P(NO)=lbar

0 Winkler (1901), ref Linke (1965), P=760mm - * Battino (1981), smoothed experimental data, latm - - Wilhelm et al., (1977), empirical formula, P=latm “ * This study, calculated 3.3 1997 0.002 —“This study, calculated 3.3 1997, for T>298 Cp=0

3 0.001

0.000

Temperature [°C]

Figure 4 Solubility of nitric oxide in water at 1 bar partial pressure. Smoothed empirical data by Battino (198la) and Wilhelm (1977), experimental solubilities by Winkler (1901) versus thermodynamic calculations Application of the model

The general thermodynamic model that was developed within this study is here used to calculate the equilibrium composition of a multi-component system - the absorption of an exhaust gas from a typical diesel engine into a scrubber solution. The main components of the

exhaust gas was 5% water vapor, 6% carbon dioxide, 0.2% sulfur dioxide, 12% oxygen and

76.7% nitrogen. In addition, the gas also contained 10 ppmVoi. N2O, 1500 ppmvoi. NO, and 50 ppmVoi. NH3. The conditions were assumed to be: 60°C and 1 bar total pressure. It was assumed that 1 leg of the flue gas was in equilibrium with 5 kg of water (gas to liquid ratio was 5). Absorption of the exhaust gas, was calculated as a function of added sodium hydroxide to the system. Two different cases were calculated: 1.) the scrubbing solution contained no other compounds and 2.) the solution was enriched: containing 0.5 molal and 0.006 molal sulfate - a ca 36 fold enrichment of ammonia and total sulfur.

Diesel exhaust gases contain several metals (vanadium, cobalt, copper etc.) that might catalyze the oxidation of sulfur with the oxidation state four, S(IV) to the oxidation state six, S(VI). This oxidation can take place in both the gas and the aqueous phase. In the gas phase, vanadium is known to be a good catalyst, efficient in temperatures over 450°C (Backman, 1983). This would in practice lead to an oxidation of sulfur dioxide already in the gas phase. In the calculations here, we therefore assume two cases a) sulfur is absorbed as S(IV) i.e. sulfite and no oxidation takes place, b) 20% of the sulfur forms S(VI) while 80 % remains as S(IV).

The equilibrium calculations show that S(IV), S(VI) and ammonia can be absorbed in an simultaneously without carbon dioxide co-absorption. This happens in a pH interval between 5 and 7 depending on the components that are of most interest. Hydrogen sulfide is not absorbed efficiently without carbon dioxide co-absorption since the dissociation

of H2S requires a higher pH. The results from the calculations are shown in figure 5 and 6. Figure 5 shows the absorption of carbon dioxide, ammonia, and total sulfur as a function of added sodium hydroxide to a scrubbing solution that not yet have been enriched on sulfur or ammonia. The solid line represent the absorption when sulfur not have been oxidized. When no sodium hydroxide have been added to the system 20.5% of the total sulfur is absorbed. The pH of the solution is buffered at 2.7 and the ionic strength is low (0.002). Ammonia is at this point absorbed to almost 100% and only very small amounts carbon dioxide are absorbed. As sodium hydroxide is added, the absorption of sulfur dioxide is increasing and is reaching 99.9% when 0.08 moles of sodium hydroxide have been added. At this point the absorption of ammonia starts to decrease and co-absorption of carbon dioxide begins. The pH of the solution is 6.3. The broken line represents the case when 20% of the S(IV) have been oxidized. If no sodium hydroxide have been added, 30% of the total sulfur is absorbed.

15 9 No sulfur oxidation 20% sulfur oxidation

100 T

70 -

40 --

mol NaOH /kg flue gas

Figure 5 Absorption of carbon dioxide, ammonia, and total sulfur in a scrubber solution as a function of added sodium hydroxide. pH versus added NaOH is shown in the upper graph while the percentage of the absorbed gas species are shown in the lower graph

16 Ammonia is absorbed to almost 100% and only negligible amounts of carbon dioxide is co­ absorbed. As sodium hydroxide is added to the system, the absorption of sulfur increases. The absorption of total sulfur is reaching 99.9% at pH 6.2 and 0.09 moles NaOH added. After this point co-absorption of carbon dioxide begins and absorption of ammonia starts to decrease. Figure 5 shows that an oxidation of sulfur dioxide in the gas or aqueous phase greatly affects the consumption of sodium hydroxide in a scrubber. Oxidation of S(IV) to S(VI) gives a lower pH and is in other words inactivating the pH raising effect of sodium hydroxide in the scrubbing solution.

Figure 6 shows absorption of total sulfur, ammonia and carbon dioxide when the scrubbing solution have been enriched in sodium sulfate and (containing 0.5 molal

Na 2S04 and 0.006 molal (NH^SCXt). The solid lines represent absorption in case a.), when no oxidation has occurred. The solution is buffered at pH 3.3 when no NaOH is added. At this point 65% of the sulfur is absorbed. Ammonia is absorbed to almost 100% and only 0.15% of carbon dioxide is co-absorbed. As Sodium hydroxide is added to the system, absorption of sulfur dioxide increases and reaches 99.9% at 0.09 mol added sodium hydroxide. Absorption of ammonia is at this point still high, 94.3 % and only 0.42 % carbon dioxide is co-absorbed. pH is 6.0 at this point. After this, the absorption of ammonia is decreased and absorption of carbon dioxide starts to play an important role. The decrease in the ammonia absorption is first “slow” and is increased as pH increases. There will even be an desorption of ammonia when

0.23 mol sodium hydroxide has been added. The broken line in figure 6 describes the absorption in the enriched solution when 20% of S(IV) has been oxidized. The absorption of gases shows a pattern, very much like the absorption of only S(IV). The pH when no sodium hydroxide is added is a little lower, 3.2 since the oxidation “inactivates ” the pH raising effect of sodium hydroxide. One therefore has to add more sodium hydroxide (0.1 mol) to the solution to achieve 99.9% absorption of sulfur. The desorption of ammonia also starts “later ”.

As a result of these calculation we draw the conclusions that H2S04 (g), S02(g) and NH3(g) can be absorbed simultaneously without carbon dioxide co-absorption. The absorption is sensitive to pH that is adjusted by additions of salts into the aqueous solution. In the example calculated here, absorption of nitric oxide and nitrous oxide showed to be very low and these species can not be absorbed unless they are oxidized or reduced. “No sulfur oxidation “ 20% sulfur oxidation

ro : ' /

mol NaOH /kg flue gas

Figure 6 Absorption of carbon dioxide, ammonia, and total sulfur in an enriched scrubber solution as a function of added sodium hydroxide. pHversus added NaOH is shown in the upper graph while the percentage of the absorbed gas species are shown in the lower graph

18 Discussion

The thermodynamic constants (AH°298k, S°29sk and C°? (T)) that were used in this study are believed to be the best available today. The consistency is believed to be good for all species except for the aqueous sulfide and cyanide species.

Pitzer parameters that were used in this study were taken from earlier work in the field (Harvie et al. (1984), Edwards et al. (1978), Rosenblatt (1981), Heinonen (1995), and Pitzer (1991)). Much confidence is put in the parameters by Harvie, Mailer and Weare since their model have been widely used and has been tested on many experimental solubilities. The values by Rosenblatt and Pitzer are also believed to be of good accuracy. The values by Rosenblatt are based on sound approximations and the values by Pitzer has been carefully evaluated. Parameters by Heinonen (1995) has been evaluated from solubilities in Linke (1965) using the least square method. Though there are much inconsistency for aqueous sulfide species we use his parameters. It is hard to estimate the reliability of the parameters by Edwards et al. The parameters are estimates (except for molecule-molecule self interaction parameters) and because their model only have been tested on very few experimental systems (Maurer, 1980) the reliability of the parameters must be questioned. In addition we have no evidence for consistency of the parameters. The parameters from Edwards et al (1978) were however included in this model with only a few exception.

In the calculations, we assume that the absorption takes place at 60°C. The standard enthalpy, entropy and heat capacity for pure species can be calculated with good accuracy at this temperature but most of the parameters used in our model are evaluated at 25°C and we therefore “extrapolate ” them to 60°C. It is admitted that temperature has an effect on the interaction coefficients in the Pitzers expression but this effect is shown to be small. Effect of temperature on the values of parameters /3(0), /?(1) and Cw has been examined by Silvester and Pitzer (1978) (see also Pitzer (1991). The effect are small, about 0.001 and according to Rosenblatt (1981), no significant change is observed in the parameters within 25°C or so.

A robust test of the model is presented below. The absorption of sulfur dioxide into a concentrated sodium sulfate solution at 60°C is calculated and compared to experimental solubilities. The test is stated to be robust since all the interaction parameters for S(IV) in our model has been estimated and since our model do not take into account the interaction between S(IV) and S(VI). The experimental values by Hudson (1925), as referred to by Linke (1965), Wilhelm et al. (1977) and Battino (1981b) are compared to calculated solubilities. The calculated solubilities differ from the solubilities by Hudson (1925) but, the solubility in pure water by Hudson (1925) and the compiled solubilities in Wilhelm et al. (1977) and Battino (1981b) also differ from each other. The calculated solubility of SO2 in pure water is in good agreement with the values by Wilhelm et al. (1977) and Battino (1981) and since our model gives the right trend, compared to the solubilities by Hudson (1925) we state that our model passed the test surprisingly well. A graphical representation of the system Na 2S04 -S02-H20 at 60°C is given in appendix II where data by Hudson (1925), Wilhelm (1977), and Battino (1981b) are compared to calculated solubilities.

19 Conclusions

Thermodynamic calculations is a useful tool in predicting the solubility of gases in aqueous solutions. The non stoichiometric approach, based on Gibbs free energy minimization, is very powerful for calculating the equilibrium in multiphase multi-component systems, since, specific constants for the chemical reactions are not needed. A proper formulation of the stoichiometric matrix also makes it possible to take into account metastable states for the system. Calculations of chemical equilibrium in multi-component systems are however very sensitive to the numerical values of the constants. It is therefore important to use only correct and consistent data from the literature. In this study, a set of reliable and consistent constants have been used to investigate the temperature effect on the solubility of nine gases into water. The gases of interest were sulfur dioxide, ammonia, carbon dioxide, hydrogen sulfide, hydrogen cyanide, nitrogen, oxygen, nitrous oxide, and nitric oxide but the model also includes absorption of H2, CO, SO3, and H2SO4 . In addition, condensation of H20 is predicted. In this study, the temperature dependency on the thermodynamic constants and the interactions between solutes have been of special interest. Heat capacities, as calculated by a simplified Helgeson-Kirkham-Flowers model has therefore been used. Simultaneous absorption of gases into an aqueous solution, that is containing sodium salts, requires that interactions between solutes are considered. The essence of taking into account the interactions increases with increasing concentrations and are of special importance for aqueous ions. In this study, a model based on Pitzers equations have been used for predicting the non­ ideality of a real solution. Parameters for the model was taken as such from the literature and implemented in our model. Consistent thermodynamic constants and the interaction parameters makes it possible to calculate simultaneous absorption, of gases into aqueous sodium salt solutions. As an example of multi-component absorption the equilibrium between a diesel flue gas and a scrubber solution was calculated.

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25 Appendix I

350 --

300 --

250 -

200 --

150 -

100 Temperature [°C]

Figure Appendix la Calculated heat capacities for 5 solvated unprotolyzed molecules

l Appendix I

Temperature [°C]

Figure Apendix lb Calculated heat capacities for 3 bivalent ions mol SOz/kg H20 X X

60°C, 60°C, 60°C,

Battino Wilhelm Hudson

(1981) (1925)

etal.

(1977) molality

Na 2 S0

4

IX Appendix

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