An Algebraic Description of the Absorption Equilibrium for the Solvay

Article pubs.acs.org/jced

An Algebraic Description of the Absorption Equilibrium for the Solvay Soda System Małgorzata Czernuszewicz, Eugeniusz Cydzik, and Zdzisław Jaworski* West Pomeranian University of Technology, Szczecin, Aleja Piastów 42, 70-065 Szczecin, Poland S Supporting Information *

ABSTRACT: Simplified relationships for the equilibrium partial pressure of the gas phase components were presented for the crystallization conditions of sodium bicarbonate in the NaCl−NH3−CO2−H2O system. Based on the partial pressures computed from the validated mixed-solvent-electrolyte (MSE) model, the regression equation coefficients were derived for explicitly correlating the partial pressures with the liquid phase concentrations and temperature in the range of (308.15 to 338.15) K. A good agreement was found between pressures calculated from the algebraic equations and compared with corresponding values computed from the MSE model. The obtained exponential equations can be directly used for the estimation of the equilibrium partial pressures in the process conditions of carbonation columns. experimental counterparts.2 In the second stage the MSE model equilibrium data of composition and temperature were computed for regular points at the NaHCO3 (sodium bicarbonate) crystallization surface. In parallel, the corresponding partial pressures of the gaseous components over those saturated solutions were also derived.3 The aim of the present study is deriving algebraic functions which describe relations between the partial pressures of the gaseous species and the ion concentrations in the liquid phase for the ranges of temperature and pressure occurring in carbonation columns employed in the Solvay technology. A capability of determination of the partial pressures for the three components of the gas phase from explicit algebraic equations enables one to simple calculations of the concentration differences for absorption of CO2 and desorption of NH3 along the carbonation column. To obtain the targets of the third stage, correlation equations were developed for the equilibrium values of the partial gas pressures as functions of temperature and concentrations of the liquid phase. Using the MSE computed data of the second stage, the accuracy of the algebraic correlations was tested in the final stage of this study.

1. INTRODUCTION A deep understanding of the equilibrium factors in the system of sodium chloride−ammonia−carbon dioxide−water is crucial in running and designing the industrial processes of the Solvay soda technology. Knowledge of the equilibrium data such as concentrations in the gas and liquid phases enables one to determine the absorption driving force in carbonation columns. When using the computational fluid dynamics (CFD) techniques to numerical predictions of the transport processes in the columns, information on the equilibrium conditions is crucial in establishing mass transfer conditions in such a reactor.1 Experimental data published in the literature for the equilibrium pressures as functions of the composition and temperature of the liquid phase in their range met in carbonation columns are rather scarce and fragmentary. Nevertheless, the existing data were used in this study for successful validation of the thermodynamic model known as mixed-solvent-electrolyte (MSE) that is available in the commercial software OLI Analyzer Studio issued by OLI System Inc. The applied methodology of deriving a simplified algebraic description of the equilibrium partial pressures in the soda system comprised three stages. Initially, at the first stage, a validation procedure of the MSE model was carried out by comparing model predictions of the equilibrium conditions for the NaCl−NH3−CO2−H2O system with their literature © 2014 American Chemical Society

Received: June 10, 2014 Accepted: August 11, 2014 Published: August 19, 2014 2901

dx.doi.org/10.1021/je500310u | J. Chem. Eng. Data 2014, 59, 2901−2908

Journal of Chemical & Engineering Data

Article

Figure 1. Partial pressures of the NaCl−NH3−CO2−H2O system computed from the MSE model (PMSE) compared with the experimental data8 (Pexp); (a) T = 313 K; (b) T = 353 K. ○, total pressure; ▲, pressure of carbon dioxide; ◇, pressure of ammonia; ×, pressure of water.

Table 1. Validation Data for the MSE Model vs Experiments8 for the System NaCl−NH3−CO2−H2Oa mi/mol·kg−1

Pi/MPa

AAD(P)/%

T/K

P/MPa

CO2

NH3

NaCl

CO2

NH3

N/pcs

CO2

NH3

H2O

no.

313.15 353.15 313.15 353.15

(0.012 to 0.679) (0.085 to 0.566) 0.014 0.248

(0.3 to 4.0) (0.2 to 3.0) 2.13 2.40

4.1 3.9 4.1 3.9

4.0 4.0 4.0 4.0

(0 to 0.673) (0 to 0.523) 0.006 0.201

(0.019 to 0) (0.072 to 0.005) 0.003 0.010

14 10 1 1

5.17 4.23 0.29 3.15

8.55 7.99 0.44 0.10

4.82 1.31 0.07 0.52

(2 or 3) (2 or 3) 3 3

a

mi = concentration in liquid phase, P = total pressure, Pi = partial pressure, N = number of measurement points, AAD(P) = mean relative deviation, and no. = number of phases.

those of the published experiments,8 Pexp, is shown in Figure 1 for two temperature levels. The quantitative comparison of the model and experimental data for partial pressures of carbon dioxide, ammonia, and water resulted in the mean relative deviations, AAD(P) (eq 1), respectively of 5.17 %, 8.55 %, and 4.82 % at the temperature of 313.15 K and 4.23 %, 7.99 %, and 1.31 % for 353.15 K. The total pressure of the gas phase ranged from (0.012 to 0.679) MPa for 313.15 K and from (0.010 to 0.567) MPa for 353.15 K.

2. COMPUTATIONAL METHODS 2.1. Thermodynamic Model and Its Validation. One of the new and versatile thermodynamic models published in the subject literature, well-designed for saturated electrolyte solutions, is the mixed−solvent electrolyte (MSE) proposed by Wang et al. (2002).4 The model incorporates elements of both the electrolyte expanded UNIQUAC5 and the virial Pitzer models. The MSE model has the full spectrum of applications, starting from the infinitely diluted up to saturated solutions of dissociating salts.4 The MSE model equations incorporated in the commercial OLI Analyzer Studio software were used in this work to compute partial pressures corresponding to the literature concentrations of the liquid phase. The pressures and concentrations define coordinates of the absorption surfaces in the considered soda system. All data used for validating the MSE model in the version 2.1 software were generated for both the NaCl−NH3−H2O and NaCl−NH3−CO2−H2O systems. The computations were carried out in the “bubble point pressure” mode, and their results were compared with available experimental data.6−8 Results of the comparison for the soda system at (313.15 and 353.15) K were already published in Jaworski et al. (2011)2 where the quality of predictions of four thermodynamic models was assessed. The MSE model delivered superior results to those obtained from the aqueous, Pitzer, and extended UNIQUAC models. Therefore, the MSE model was chosen in this present study for reproducing the actual state of the thermodynamic equilibria in the soda system. Additional validation test was carried out for the MSE model using version 3.0 of the OLI software and identical procedure as in the version 2.1 for deriving the equilibrium partial pressures of NH3, CO2, and H2O in the Solvay soda system of NaCl−NH3−CO2−H2O at (313.15 and 353.15) K. A graphical representation of the MSE model partial pressures, PMSE, with

AAD(P)% =

100 N

N

∑ i

|Pexp − PMSE| Pexp

(1)

A selected set of important data of the validation conditions for the studied four-component system is collected in Table 1. The last two rows of Table 1 contain data for the equilibrium conditions of presence of solid NaHCO3 also with relative deviations of the model vs experiment. The relative average difference (eq 1) for the total pressure of 0.014 MPa and temperature of 313.15 K was close to 0.3 % for CO2, 0.4 % for NH3, and 0.1 % for H2O, while at 353.15 K and 0.248 MPa the MSE model pressures differed from the experimental ones by about 3.2 % for CO2, 0.1 % for NH3, and 0.5 % for H2O. Such differences are close to the usual experimental errors, and this allowed us to assume that the MSE model satisfactorily describes the gas−liquid−solid equilibrium conditions for the Solvay soda system.

3. RESULTS AND DISCUSSION 3.1. Computing of Equilibrium Data. The validated MSE model in OLI Analyzer Studio v. 3.0 was employed in computing the equilibrium concentrations both in the liquid and gas phases for six temperatures, T, with the 10 K increments in the range from (288.15 to 338.15) K and the total pressure, P, of either (0.101 or 0.304) MPa. In the 2902



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Figure 2. Absorption surfaces for CO2, NH3 and H2O obtained from the MSE model, (a) P = 0.1 MPa, T = 328 K and (b) P = 0.3 MPa, T = 308 K. ○, calculated data from the MSE model.

previous study3 it was found the total pressure has a minor effect on the solid−liquid equilibrium parameters of the studied system in the range from (0.1 to 0.3) MPa. Therefore, in this paper only two border levels of the system pressure are studied; however the temperature span is a little wider than typically met in a carbonation column of the Solvay method. Graphical forms of the phase diagrams in the case of two pairs of reciprocal salts are usually presented by using the diagram base coordinates as the anion and cation ratios. In the analyzed case, the dimensionless molar proportions of cationic ions, x, eq 2 and anionic ones, y, eq 3 were applied with a sum of those originating from carbon dioxide eq 4. nNH+4 x= nNH+4 + nNa+ (2) y=

shape and range of the absorption surfaces are closely related to the crystallization ranges of the four reciprocal salts, i.e., NaHCO3, NaCl, NH4HCO3, and NH4Cl. This implies separate mathematical descriptions of the absorption surfaces within the ranges of the {x, y} coordinates corresponding to crystallization of each salt. 3.2. Initial Tests of the Algebraic Model. The new model of mathematical description of the absorption equilibrium should be easily applicable and therefore appear in a simple form of explicit algebraic equations. To achieve the goal one has to identify and select functions describing the relationships between the partial pressure of the i-th component, Pi, and the independent variables such as the concentrations in the liquid phase, x and y, and temperature, T. A general form of the equations may be written in the form of eq 5.

n(CO2)− n(CO2)− + nCl−

n(CO2)− = nHCO−3 + 2nCO32− + nNH2COO−

Pi = f (x , y , T )

(3)

(5)

In the search for the particular function class to satisfactorily describe shapes of the absorption surfaces, the first step was associated with selecting one of the possible regression functions of independent variables, x and y, for a constant temperature. After deriving coefficients of the algebraic functions, by means of the least-square method, in the next step the coefficients were correlated against temperature. The absorption surface shapes for CO2, NH3, and H2O (Figure 2) differed significantly depending on the crystallizing salt. Since the study is focused on the soda technology, only the liquid−gas equilibria corresponding to the NaHCO3 crystallization conditions were considered. These conditions comprised the ammonium cation ratio, x, in the range from 0 to about 0.83 and the anionic ratio, y, almost in the whole range from 0 to 1. In the first step the correlation equations for absorption surfaces Pi = f(x, y) for i = CO2, NH3, and H2O in constant temperatures were reviewed. Initially, polynomial functions up to the fourth degree of the two independent

(4)

The applied software predicted essentially complete dissociation of the salts in the studied solutions. In computing the equilibrium concentrations of the gas and liquid phases in the presence of either single or double salts in the solid phase, the “Precipitation Point” mode was applied in the software, and water was the component added stepwise. Altogether, 26 × 26 = 676 points of the {x, y} coordinates evenly distributed over the diagram base were used in the simulations for constant pressure and temperature. The computing results allowed to calculate the predicted equilibrium composition of the gas and liquid phases and the type of solid phase(s) present. Examples of graphical presentation of the absorption surfaces for CO2, NH3, and H2O are shown for two cases of {P, T} values in Figure 2. An analysis of the graphs shown in Figure 2 compared with those for crystallization3 led to the conclusion that both the 2903



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Figure 3. Graphs of the carbon dioxide partial pressure vs the ion concentrations within the range of the sodium bicarbonate crystallization for the total pressure of 0.3 MPa and temperature of: (a) 288 K, (b) 308 K, and (c) 338 K. ○, calculated data from the MSE model.

Figure 4. Graphs of the carbon dioxide partial pressure vs the ion concentrations within the range of the sodium bicarbonate crystallization for the total pressure of 0.1 MPa and temperature of: (a) 288 K, (b) 298 K, and (c) 308 K. ○, calculated data from the MSE model.

type (1 − exp(−x)) growing to a maximum level of the CO2 partial pressure that is almost independent of both the x and y in a wide range of those concentrations, cf. Figures 3 and 4. However, the maximum CO2 pressure was attained for a higher temperature in the case of P/MPa = 0.3 than for 0.1 MPa, as shown in Figures 3 and 4. The varying character of absorption surfaces entailed a multioption method of correlation equations for the equilibrium pressure of carbon dioxide. An algorithm scheme presented in Figure 5 along with eqs 6 to 9 were proposed for calculating the complex relationship of the CO2 pressure on the ion relative concentrations and temperature.

variables, x, y, were tested by the analogy to a successful procedure for the crystallization surfaces reported by Cydzik and Jaworski, 2012.3 The commercial Sigma Plot v.12 software was used in the consecutive approximation attempts. Then, polynomial functions of the fourth, fifth, and sixth degree were also tested along with the logarithmic polynomial of the fifth degree. The correlating functions had from 15 up to 29 coefficients, which were nonlinearly dependent on temperature. This would imply the necessity of using three times higher number of coefficients for the quadratic dependence on temperature needed to describe each of the three partial pressures corresponding to the conditions of NaHCO 3 crystallization. Despite a reasonable accuracy of those polynomial correlations, that method was abandoned due to an excessive number of required coefficients. On the basis of the analysis of the broad initial investigations, the exponential functions were selected for the final correlations. A range of model parameters for the equilibrium model equations for the partial pressures, Pi*/MPa, of CO2, NH3, and H2O was computed for the conditions of NaHCO3 crystallization. Due to the varying character of the absorption surfaces of the gas phase components (Figure 2), choice of the correlating functions, Pi* = f(x, y, T), was additionally made dependent on the cation and anion concentrations and temperature in the range from (308.15 to 338.15) K. The next section is dedicated to detailed description of the derived equilibrium relationships describing the partial pressures of the gas phase components. 3.3. Correlation of the Partial Pressures. For the total pressure of 0.3 MPa and the lowest studied temperature of 288.15 K, the CO2 partial pressure grows exponentially with increase of the x concentration in its entire range. However, for the rising temperatures the CO2 absorption surface changes its character first into a logarithmic one for x > 0 or an exponential

* /MPa = ⎡⎣d0 + d4(1 − exp(−d 2y))(1 − exp(−d3x)) PCO 2 + d5(1 − exp(−d 2y)) + d 7(1 − exp(−d3x)) + d8x(1 − exp( −d 2y))⎤⎦·0.1013

ycr = 5.9583 − 0.2T /°C + 0.00167(T /°C)2

(6) (7)

* /MPa = [d1 + d6(1 − exp( −d 7x)) PCO 2 + d 9(1 − exp( −d10y))]·0.1013

xcr = 3.3375 − 0.1210T /°C + 0.0011(T /°C)2

(8) (9)

The factors of 0.1013 serve to convert the original correlation of P* in atm into MPa. When considering the surfaces of the equilibrium pressure for water vapors in the range of the liquid phase concentrations corresponding to crystallization of sodium bicarbonate once again one meets an exponential growth to a maximum with increasing concentration ratios of both the ammonium cation, x, and the carbonate anion, y. Two examples of water pressure graphs for P/MPa = 0.3 and the boundary temperatures of 2904



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for x < 0.35 PH*2O/MPa = [w1 + w6(1 − exp( −w7y))]·0.1013

(11)

The part of the ammonia absorption surface in the range of {x, y} concentrations corresponding to crystallization of sodium bicarbonate exhibits the exponential dependence on the concentrations (Figure 7b) for all studied temperatures. Only for the total pressure of 0.3 MPa and temperature of 288.15 K a nearly linear relationship of the NH3 pressure to the x concentration was noted (Figure 7a). For computing the equilibrium partial pressure of ammonia over saturated solutions characterized by the {x, y} composition, the derived correlationeq 12can be used. * /MPa = a0−1[a1 exp(a3y) exp(a4x) + a 2 exp(a3y) PNH 3 + a5 exp(a4x)]·0.1013

(12)

In the correlation equations from 6 through 12, the dimensionless cation and anion ratios, x and y, are defined in eqs 2 and 3, and the temperature, T, is used in °C. The regression coefficients, coeff = di, wi, or ai, (i = 0 to 10), that appear in eqs 6 to 12 were correlated against temperature by means of a quadratic polynomial 14 for all coefficients, with the exception of a0 correlated by means of an exponential function 13.

Figure 5. Calculation scheme for the equilibrium partial pressure of carbon dioxide, P*CO2/MPa, depending on the total pressure, P, and the x and y concentrations.

(288.15 and 338.15) K are shown in Figure 6 for the range of x, y concentrations corresponding to NaHCO3 crystallization range. The positive effect of the anion ratio, y, on the partial pressure is valid for its whole range, both for the pressure of 0.1 and 0.3 MPa. That increase of H2O vapor pressure practically reaches its maximum at low temperatures and below a critical cation ratio, xcr. Therefore, two correlations, eqs 10 and 11, were proposed with the critical value of the x ratio, xcr = 0.35, below which eq 11 should be used. However, the dependency of the wi coefficients on temperature was correlated in the next stage. For x > 0.35

a0 = t0 + t1 exp( −t 2T /°C)

(13)

coeff = t0 + t1(T /°C) + t 2(T /°C)2

(14)

In the initial tests of the algebraic model, temperature was varied between 288.15 K (15 °C) and 338.15 K (65 °C). However, it turned out that correlating the whole variability range of the equilibrium partial pressures was extremely difficult, if possible at all, due to the varying character of the absorption surfaces, cf. Figures 3 to 7. On the other hand, the temperature inside the carbonation column varies between 305.15 K (cooling part) and about 341.15 K (upper part).9 Therefore, to simplify the algebraic correlations, it was decided to exclude the MSE data the lowest temperatures of (288.15 and 298.15) K and compute the temperature coefficients, t0, t1, and t2, of eqs 13 and 14 only for the range of (308.15 to 338.15) K. All the regression coefficients appearing in eqs 6 to 14 are collected in Table S1; see Supporting Information (SI).

PH*2O/MPa = ⎡⎣w0 + w4(1 − exp(−w2y))(1 − exp(−w3x)) + w5(1 − exp( −w2y)) + w7(1 − exp( −w3x))⎤⎦·0.1013 (10)

Figure 6. Absorption surfaces of the water partial pressure for the total pressure of 0.3 MPa and two boundary temperatures of: (a) 288 K and (b) 338 K. ○, calculated data from the MSE model. 2905



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Figure 7. Absorption surfaces for ammonia at the total pressure of 0.3 MPa and temperature of: (a) 288 K and (b) 338 K. ○, calculated data from the MSE model.

Figure 8. Partial pressures of CO2, NH3, and H2O computed from the algebraic model compared with those from the MSE model: (a) P = 0.1 MPa, T = 323 K and (b) P = 0.3 MPa, T = 303 K. ×, pressure of carbon dioxide; ▲, pressure of ammonia; ●, pressure of water.

3.4. Evaluation of the Algebraic Model. Experimental data on the partial pressure of carbon dioxide, ammonia, and water vapor could not be found in the subject literature exactly for the chosen temperatures in the range of (288.15 to 338.15) K and the total pressure of (0.1 or 0.3) MPa. Therefore, the quality of the simplified, algebraic model, eqs 6 to 14, for estimating the equilibrium partial pressures was tested against the validated MSE model using two quantitative measures, the standard deviation and the average relative deviation. In the testing, the equilibrium partial pressures of CO2, NH3, and H2O over NaHCO3 saturated solutions for identical conditions of {T, P, x, y} were computed both from the MSE and algebraic models. Two examples of the graphical comparison of the equilibrium pressures of the i-th components computed from the algebraic model, Pi,MOD, with the corresponding data from the validated MSE model, Pi,MSE, are shown in Figure 8. Both pressure coordinates are presented in the logarithmic scale. Values of the standard deviation, SMSE|MOD, of the equilibrium pressure computed from regression equations, Pi,MOD, compared with that obtained from the MSE model, Pi,MSE, were calculated from eq 15 using data for N points at a constant temperature and total pressure.

The calculated standard deviation values, multiplied by 100, are shown in Table 2 for the three components of the gas phase Table 2. Values of the Standard Deviation for Pressures Computed from the MSE Model and Algebraic Correlationsa 102·SMSE|MOD/MPa 0.1 MPa

a

∑i = 1 (Pi ,MSE − Pi ,mod)2 N

CO2

NH3

H2O

CO2

NH3

H2O

308.15 318.15 328.15 338.15

0.259 0.034 0.043 0.262

0.003 0.003 0.014 0.140

0.006 0.013 0.029 0.036

0.364 0.316 0.292 0.143

0.001 0.001 0.003 0.015

0.005 0.011 0.023 0.046

SMSE|MOD = standard deviation

at four levels of temperature and two levels of the total pressure. The maximum standard deviation of pressures computed form the algebraic model against those from the MSE model was obtained for CO2 and was lower than 2.6 % and 1.2 % of the total pressures of (0.1 and 0.3) MPa, respectively. In addition, the absolute differences of the two partial pressure values standardized by the Pi,MSE value were averaged using eq 16 for N of about 600 pairs of the partial pressures for four constant temperatures and two total pressures.

N

SMSE|mod =

0.3 MPa

T/K

(15) 2906



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Table 3. Relative Pressure Deviations Computed from eq 16 Using the MSE and Algebraic Models for the CO2, NH3, and H2O Pressures and the Required Number of Model Coefficientsa AAD/%

number of model coefficients

T/K gas phase component

308.15

318.15

328.15

338.15

P/MPa

a0

di, ai, wi

for x, y

total no.

CO2

2.05 3.69

0.70 2.59 11.09 4.98 3.24 2.58

1.45 1.13 8.72 5.76 1.96 3.73

3.81

0.1 0.3 0.1 0.3 0.1 0.3

0 0 3 3 0 0

27 33 12 9 24 24

3 3 0 0 0 0

30 36 15 12 24 24

NH3 H2O a

coefficient type

5.64 1.36 6.98

13.84 2.72 8.06 2.16

AAD = mean relative deviation.

AAD% =

N |Pi ,MSE − Pi ,mod| 100 ·∑ N i Pi ,MSE

statistically analyzed to obtain a series of their correlations against the composition of the liquid phase in the equilibrium with solid NaHCO3 and temperature in the range from (308.15 to 338.15) K. A satisfactory degree of match for the exponential functions was achieved with the mean deviations in the partial pressures below 3.9 % for carbon dioxide, 13.9 % for ammonia, and 8.1 % for water. Those maximum deviations were obtained for the pressure of 0.1 MPa and temperature of 338.15 K. However, for the total pressure of 0.3 MPa the highest deviation of about 7 % was detected for water vapors at 308.15 K. The correlations of partial pressures can be used in practical estimations of the driving force of the absorption/desorption processes taking place in carbonation columns of the ammoniac soda technology both in quick process calculations and in noniterative determinations of the partial pressures in CFD calculations.

(16)

The calculated AAD% values are assembled in Table 3 along with the total number of all regression coefficients necessary to compute the model pressures, Pi,MOD. The maximum of 36 coefficients is necessary to calculate the partial pressure of carbon dioxide at the total pressure of 0.3 MPa. The number seems high; however, if we deal with a specific range of concentrations, e.g., for x > xcr, then the required number of empirical coefficients to derive the CO2 partial pressure at P/ MPa = 0.3 is only 21, according to the relevant eq 6. Examples of those calculations are presented in the Supporting Information part S.II for two data sets. Table 3 contains single vacancies of the AAD% data for CO2 and NH3, which result from the character of their absorption surfaces. In the case of CO2 at 338.15 K and P/MPa = 0.3, its partial pressure is practically constant; therefore the exponential function was not applicable. Moreover, high-pressure levels are met only in the cooling part of the carbonation column, where the temperature is up to 330.15 K.10 The vacant data for NH3 at 0.1 MPa and 308.15 K are also irrelevant to a carbonation column since the working parameters in its upper part comprise higher temperatures than 323.15 K.10 The standard deviation values of Table 2 and the relative pressure deviations of Table 3 are generally similar to those between the MSE model and experiments found at the validation stage (Table 1), and therefore the algebraic model can be regarded as a good approximation tool to calculate the equilibrium pressures in the Solvay soda system.

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ASSOCIATED CONTENT

S Supporting Information *

Section S.I: regression coefficients for CO2, NH3, and H2O. Section S.II: Determination of the equilibrium partial pressures−sample calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. Tel.: +48-91449-4020. Funding

The authors are grateful for the financial support from the National Centre for Research and Development in Poland, West Pomeranian University of Technology, Szczecin and the European Social Fund of the European Commission in the frame of the Operational Programme Human Capital 20072013 with cofinancing by the State Budget of Poland.

4. CONCLUDING REMARKS On the basis of the mixed-solvent electrolyte (MSE) model available in the commercial OLI Analyzer Studio code, a simplified model of gas−liquid equilibrium for the Solvay soda system was prepared. The MSE model was first validated using the literature experimental data for the NaCl−CO2−NH3− H2O system, and a satisfactory agreement was ascertained. In the three-phase equilibrium points where the solid NaHCO3 was present, the discrepancies in the partial pressures between those from the MSE model and experiments were lower than 3.2 %, and a maximum relative deviation of 8.6 % for the partial pressures was found for ammonia at 313.15 K. With the proven MSE model a number of values for the equilibrium partial pressure of CO2, NH3, and H2O over the saturated electrolyte solutions was derived for temperatures in the range from (288.15 to 338.15) K and two levels of pressure at (0.1 and 0.3) MPa. The computed pressure values were then

Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Jaworski Z.; Cydzik E. Customization of thermodynamic models of electrolytes for incorporation in CFD codes. 18th International Conference Process Engineering and Chemical Plant Design, Sept 19−23, 2011, Berlin; pp 59−66. (2) Jaworski, Z.; Czernuszewicz, M.; Gralla, Ł. A comparative study of thermodynamic electrolyte models applied to the Solvay soda system. Chem. Proc. Eng. 2011, 32, 135−154.

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(3) Cydzik, E.; Jaworski, Z. A simplified description of crystallization equilibrium in the NaCl−NH3−CO2−H2O system. Przem. Chem. 2012, 91, 1283−1287 (in Polish). (4) Wang, P.; Anderko, A.; Young, R. D. A Speciation-Based Model for Mixed−Solvent Electrolyte System. Fluid Phase Equilib. 2002, 203, 141−176. (5) Rafal, M.; Berthold, J. W.; Scrivner, N. C.; Grise, S. L. In Models for electrolyte solutions; Sandler, S. I., Ed.; Marcel-Dekker: New York, NY, 1994; Models for Thermodynamic and Phase Equilibria Calculations, Chapter 7, pp 601−670. (6) Stephen, H.; Stephen, T. Solubilities of inorganic and organic compounds; Pergamon Press: New York, 1963. (7) Sing, R.; Rumpf, B.; Maurer, G. Solubility of ammonia in aqueous solutions of single electrolytes sodium chloride, sodium nitrate, sodium acetate, and sodium hydroxide. Ind. Eng. Chem. Res. 1999, 38, 2098−2109. (8) Kurz, F.; Rumpf, B.; Sing, R.; Maurer, G. Vapor−Liquid and Vapor− Liquid−Solid Equilibria in the System Ammonia−Carbon Dioxide−Sodium Chloride−Water at Temperatures from 313 to 393 K and Pressures up to 3 MPa. Ind. Eng. Chem. Res. 1996, 35, 3795− 3802. (9) Shokin, I. N.; Krashennikov, S. A. Soda technology; Khimia: Moscow, 1975 (in Russian). (10) Niederliński, A.; Bukowski, A.; Koneczny, H. Soda and associated products: Guidance for engineers and technicians; WNT: Warsaw, 1978 (in Polish).

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An Algebraic Description of the Absorption Equilibrium for the Solvay

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