Weidong Yanb, Magnus Topphoff
b. Department of Chemistry, Zhejiang University, Hangzhou 310027, P. R. China
Phase equilibria for mixed-solvent electrolyte systems are of significant interest for the different separation processes in chemical industry since the presence of salt in the liquid phase may substantially influence the phase equilibrium behavior of the systems. Even small amounts of salt can have an appreciable effect on the boiling points, the mutual solubility and the relative volatility of solvents. This salt effect is important for different industrial separation processes, such as salt distillation , crystallization processes, e.g. extractive crystallization of salts , and extraction processes. While powerful models (gE models, equations of state) are available for non-electrolyte systems the situation is worse for electrolyte systems. However, this information is required to describe the influence of the electrolytes (salting-in or salting-out effects) on vapor-liquid equilibria, liquid-liquid equilibria, gas solubilities, salt solubilities in order to be able to simulate separation processes. This has been the incentive for the development of a data base which now contains more than 3700 VLE data sets and 7500 salt solubility data sets for electrolyte systems and a software package with available thermodynamic models for the correlation and prediction of phase equilibria of electrolyte systems.
The correlation and prediction of the VLE behavior for electrolyte systems in mixed solvents has been examined by a number of investigators: Hala , Mock et al. , Sander et al. , Tan , Macedo et al. , Kikic et al. , Li et al. , Achard et al. , Zerres and Prausnitz , Kolker and de Pablo .
The first electrolyte model based on the group-contribution approachmethod was published by Kikic et al. ). This model combines a modified Debye-Hückel term (Macedo et al., ) accounting for the long-range electrostatic forces with the original UNIFAC group contribution method for the short range physical interactions (Fredenslund et al. ) with concentration independent group interaction parameters. Achard et al.  developed a model composed on the extended form of the Debye-Hückel law given by Pitzer , the modified UNIFAC group contribution method (Larsen et al. ) and solvation equations accounting for the hydration of ions. The combination of the solution of groups concept with a Debye-Hückel expression is very attractive since it allows to predict VLE for mixed–solvent electrolyte systems.
The model developed in this work consists of three terms for the excess Gibbs energy: (1) a Debye-Hückel term which represents the long-range interactions; (2) a virial term which accounts for the middle-range interactions caused by the ion-dipole effects; (3) a UNIFAC term (Fredenslund et al. ) which represents the short-range interactions.
This model is different from the other two models (Kikic et al.,  and Achard et al., ), focusing mainly on charge-dipole and charge-induced dipole interactions between solvent groups and ions. Therefore, a virial term is introduced into the expression for the excess Gibbs energy. In the UNIFAC term the ion-solvent and ion-ion interactions are not taken into account because these parameters show only a minor influence on the calculated activity coefficients of the solvents. In this way the new model has the advantage that only a relative small number of parameters have to be fitted, without diminishing the precision of the prediction. Only virial parameters for the middle-range term to be fitted. The required group-interaction parameters between solvent groups in the UNIFAC term are directly taken from the literature (Hansen et al. ).
A computerized data base was used to fit the model parameters for 9 solvents (water, methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, acetone, ethyl acetate and THF which correspond to seven solvent groups: H2O, CH2, OH, CH3OH, CH2CO, CCOO and CH2O); 13 cations (lithium, sodium, potassium, calcium, barium, magnesium, strontium, copper, nickel, zinc, cobalt, mercury and ammonium) and 7 anions (fluoride, chloride, bromide, iodide, nitrate, acetate, and thiocyanate). The maximum salt concentration considered was 20 mol kg-1 for 1:1 salts and 22 mol kg-1 for 2:1 salts. A computerized data base was used for fitting the model parameters. The VLE data types included are: Isobaric T-x-y,P-x-y, osmotic coefficients (x-Φ , isothermal) and mean activity coefficients (x-ϒ ± , isothermal).
During fitting the interaction parameters, it was found that the group interaction parameters aij between solvent groups and ions and between cations and anions in the UNIFAC equation are not very sensitive to the values of the objective function. This means that the quality of the estimations is not affected by changing the values of these parameters. In order to reduce the number of parameters to be fitted, the parameters aij between solvent groups and ions and between cations and anions were set equal to zero and only the middle-range interaction parameters bij and cij were fitted.. The current status of interaction parameters matrix is shown in Figure 1.
Fig. 1. Present Status of the Parameter Matrix of the Proposed Model
The predicted VLE results for the system methyl acetate + methanol + sodium thiocyanate at different constant salt concentrations at 101.3 kPa are shown in Figure 2.
Fig. 2. y–x Phase Diagram for the System Methyl Acetate + Methanol + Sodium Thiocyanate at 101.32 kPa. Mole fractions of salt:
0.01 (D); 0.03 (o); 0.05 (¡), experimental data from Iliuta and Thyrion . – – – – (0.01); –– –– –– (0.03); –– – –– – –– (0.05), prediction (this work).
The total mean absolute deviation of osmotic coefficients is 0.052. Figure 6 shows examples for the calculation of osmotic coefficients at moderate and high salt concentrations up to molalities of 20.
Fig. 3. Experimental and Predicted Osmotic Coefficients for Aqueous Electrolyte Solutions at 25 °C. Salt molalities 0.0-20 mol× kg-1, —–——, prediction (this work) , (Δ , O , +) experimental values from (A) Na(OOCCH3), Hamer and Wu ; CoCl2 Stokes ; (B) LiBr, Hamer and Wu ; CaCl2, Robinson and Stokes .
The results for the mean ion activity coefficients are even better than those for osmotic coefficients across the whole salt concentration range. In most cases the calculated results for the mean ion activity coefficients are in perfect agreement with the experimental ones for moderate and high salt concentration. Figure 4 shows some results in which the salt molalities vary from 0 to 20 and the values for the mean ion activity coefficients between from 0.2 to 500.
Fig. 4. Experimental and Predicted Mean Activity Coefficients for Aqueous Electrolyte Solutions at 25 °C. Salt molalities 0.0-20 mol× kg-1, g ± 0.2-500. —–——, prediction (this work) , (Δ , O , + ) experimental values from (A) Na(OOCCH3) and NaCl, Hamer and Wu ; Ca(NO3)2 and Sr(NO3)2 Stokes ; (B) LiBr and LiCl, Hamer and Wu ; CaCl2, Stokes .
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