Prediction of electrolyte vapor-liquid equilibrium by UNIFAC-Dortmund

PREDICTION OF ELECTROLYTE VAPOR-LIQUID EQUILIBRIUM BY UNIFAC-DORTMUND

M.Aznar1^* and A.S.Telles2

¹Faculdade de Engenharia Química, Universidade Estadual de Campinas, C.P. 6166,

CEP 13081-970, Campinas - SP, Brazil

E-mail: [e-mail]

²Escola de Química, Universidade Federal do Rio de Janeiro, C.P. 68542,

CEP 21949-900, Rio de Janeiro - RJ, Brazil

(Received: October 10, 2000 ; Accepted: April 23, 2001)

Abstract - The modified UNIFAC-Dortmund group contribution model is used for the correlation and prediction of salt effects in binary solvent-salt and ternary mixed solvent-salt systems. The long-range electrostatic interaction contribution, usually represented by a Debye-Hückel term, was empirically dropped. Previously published parameters for interactions between solvent groups (CH₂, OH, CH₃OH, H₂O and CH₃CO) were used, and group interactions between ions (Li⁺, Na⁺, K⁺, Ca⁺², Cl^-, Br^-, NO₃^- and ACE^-) and between ions and solvent groups have been estimated. The data base includes 29 binary and 56 ternary systems, used in part for the calculation of group interactions and in part for the testing of predictions.

Keywords: thermodynamics, vapor-liquid equilibrium, electrolytes, prediction, UNIFAC.

INTRODUCTION

Prediction of vapor-liquid equilibrium in electrolyte systems is of particular importance in the design and operation of extractive or azeotropic distillation. In these processes, the addition of a strong, nonvolatile electrolyte, i.e., a salt, modifies the relative volatility of the components through the salt effect. There are several g^E models proposed in the literature for description and/or prediction of the salt effect. The basic idea is to combine a local composition g^E model for the activity coefficient, used for the representation of the short-range interactions between ions and solvents, with a Debye-Hückel term (Robinson and Stokes, 1970) for the long-range ion-ion electrostatic interactions. Chen et al. (1982) and Chen and Evans (1986) combined the NRTL model and the Pitzer-Debye-Hückel (Pitzer, 1980) model for solvent-salt mixtures. Haghtalab and Vera (1988) presented a similar approach, using the original Debye-Hückel term. Liu et al. (1989) combined a three-parameter Wilson equation (Renon and Prausnitz, 1969) with an extended Debye-Hückel term for solvent-salt mixtures. Sander et al. (1986) presented a model combining a modified UNIQUAC model with a Debye-Hückel term for description of the salt effect on the vapor-liquid equilibrium of water-solvent mixtures. Macedo et al. (1990) modified the Sander model by using a modified Debye-Hückel term. Kikic et al. (1991) extended the Sander model, replacing UNIQUAC with UNIFAC, generating a predictive model. In another approach, Dahl and Macedo (1992) neglected the Debye-Hückel term, at the suggestion of Mock et al. (1986) and Cardoso and O'Connell (1987). These authors showed that the Debye-Hückel term had no effect on vapor-liquid equilibrium behavior, although it could be essential in aqueous-phase ionic activity coefficient calculations. Aznar et al. (1994) followed the approach of Dahl and Macedo and tested the Wilson model (1964) in place of UNIFAC.

In this work, the modified UNIFAC-Dortmund model for short-range activity coefficients (Weidlich and Gmehling, 1987; Gmehling et al., 1993) is used for the correlation and prediction of experimental vapor-liquid equilibrium data in electrolyte systems without a Debye-Hückel long-range term. The data includes 29 binary solvent-salt and 56 ternary mixed solvent-salt systems. New group interaction parameters have been estimated for the ion-ion and ion-solvent group interactions.

THERMODYNAMIC MODEL

The UNIFAC-Dortmund model, as developed by Gmehling et al. (1993), is based upon empirical modifications of UNIFAC (Fredenslund et al., 1975, 1977). The basic idea stems from the expression of the activity coefficient as the sum of a combinatorial and a residual part.

For the representation of electrolyte systems, it is usual to include a Debye-Hückel term that accounts for the long-range electrostatic interactions. However, Mock et al. (1986) discovered that this long-range interaction contribution term, although essential in computing aqueous phase ionic activity coefficients, had little effect on phase equilibrium behavior. Therefore, only the local interactions were considered, and the long-range interaction contribution term was neglected. For phase equilibrium calculations it is convenient to consider the salt as a single molecule and not as charged ions distributed in the solution. Thus, the salt molecule is treated as all other substances and its mole fractions are calculated ignoring ionic dissociation. Of course, the functional groups that describe the salt are the corresponding ions.

The original UNIFAC combinatorial part is modified in the Dortmund version to the following expressions including a 3/4 exponent in the calculation of the volume fraction:

The residual part is given by the solution-of-groups concept, expressed by

In this equation, G_k is the group residual activity coefficient and G_k⁽ⁱ⁾ is the group residual activity coefficient for a reference solution of pure i, which can be calculated by

The residual part, therefore, remains unchanged comparing with to the original UNIFAC, except for the fact that the energy parameter, y_mn, is correlated by a more complex expression for the temperature dependence.

Parameters a_mn, b_mn and c_mn in the above expression have been fitted by Gmehling et al. (1993) using vapor-liquid equilibrium, infinite-dilution activity coefficients, heats of mixing, and sometimes, liquid-liquid equilibrium data.

Additionally the group contributions, R_k and Q_k, for the molecular van der Waals volumes and surface areas, respectively, which in the original UNIFAC were the values given by Bondi (1968) are adjustable parameters in the minimal deviation search process in the Dortmund version. In contrast, the values of R_k and Q_k for the ions are those presented by Macedo et al. (1990). For the anions, R_k and Q_k are based on the molecular sizes of the ions. However, the very small values of the ionic radii of the cations led to Q_k values on the order of 0.1-0.5. This reduces the fitting capabilities of the model, and therefore the R_k and Q_k for the cations are also adjustable parameters. These parameters are shown in Table 1.

RESULTS AND DISCUSSION

The group interaction parameters were estimated by using the maximum likelihood principle (Anderson et al., 1978; Niesen and Yesavage, 1989; Stragevitch and d'Ávila, 1997). The database employed is composed of 29 binary solvent-salt systems and 56 ternary mixed solvent-salt systems, shown in Tables 2 and 3. Of these, 9 binary and 15 ternary systems were used in the estimation of the parameters of the model; the remaining systems were used for testing the adequacy of the method.

Group interaction parameters for the solvent-cation, solvent-anion and cation-anion pairs were estimated. There are available parameters for cations Li⁺, Na⁺, K⁺ and Ca⁺² and anions Cl^-, Br^-, NO₃^- and ACE^-. The ACE^- anion, corresponding to acetate ion, must not be identified with the acetate solvent group, CH₃COO. The calculated parameters are shown in Table 4. The numbers in the columns labeled m and n refer to the group numbering employed in Table 1. Lack of experimental data has prevented the estimation of some parameters, marked in Table 4 as not available "na". Interactions between cation-cation and anion-anion can not be obtained from single salt data. In Table 4 they are marked "NC". It is suggested (Sander et al., 1986) that in calculations of mixed salt solutions these parameters be set equal to zero. The matrix of estimated parameters appears in Figure 1.

Prediction of vapor-liquid equilibrium, based upon the estimated parameters, was performed for all binary and ternary electrolyte systems in Tables 2 and 3. The results are shown in Tables 2 and 3, in the form of deviations in pressure and vapor-phase composition. These deviations are given by

For the binary solvent-salt systems reported in Table 2, the deviations in pressure were always below 0.06 atm, with a global mean value of 0.0111 atm. The deviations in vapor-phase compositions were always zero, since the vapor phase is the pure solvent. For the ternary mixed solvent-salt systems reported in Table 3, the deviations in pressure were below 0.27 atm with a global mean value of 0.0803 atm, while the deviations in vapor-phase composition were below 0.180 with a global mean value of 0.051. Representative results are shown in Figures 2, 3 and 4 for one binary and two ternary systems chosen from among those not used in the determination of the parameters.

Results obtained by Macedo et al. (1990) and Kikic et al. (1991) are compared with those of this work for the nine systems in common. This comparison appears in Table 5, where the first column identify the system according to Table 3. Deviations from experimental data, of both total pressure and vapor-phase composition, are of the same order of magnitude for the three methods. Macedo et al. (1990) employed UNIQUAC, a nonpredictive model, and represents a fitting of the experimental data, a fact that explains the smaller average deviations (DP = 0.0329 atm, Dy = 0.020). Kikic et al. (1991) used the original UNIFAC, modified by the Debye-Hückel term, and their results are equivalent to those of the present work.

CONCLUSION

In this work, vapor-liquid equilibrium data for 29 binary solvent-salt systems and 56 ternary mixed solvent-salt systems were predicted using the modified UNIFAC-Dortmund group contribution model for the activity coefficient. The long-range, electrostatic interaction contribution Debye-Hückel term was empirically dropped. New group interaction parameters were estimated for the interactions between eight ions and five solvent groups, by using a maximum likelihood principle-based minimization procedure. The results are shown in the form of deviations between experimental and predicted values of the pressure and the vapor phase composition. These results are very satisfactory, considering that UNIFAC-Dortmund is a group contribution predictive method and that the group interaction parameters are concentration independent. The deviations are compared with similar results obtained by Macedo et al. (1990) using the UNIQUAC model and by Kikic et al. (1991) using the original UNIFAC model.

ACKNOWLEDGMENT

The authors are very grateful to Dr. Luiz Stragevitch for his helpful advice. The authors express their thanks for the financial support of FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo), Brazil, under grant 96/6341-7.

NOMECLATURE

a, b, c group interaction parameters r molecular van der Waals volume R group volume parameter P pressure q molecular van der Waals area Q group area parameter x liquid mole fraction y vapor mole fraction Super and Subscripts C combinatorial calc calculated exp experimental i, j component k, m, n group R residual Greek Letters g activity coefficient F volume fraction q area fraction G residual activity coefficient y group energy interaction parameter nk⁽ⁱ⁾ number of groups k in molecule i D absolute deviation

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To whom correspondence should de addressed

Publication Dates

• Publication in this collection
  02 Aug 2001
• Date of issue
  June 2001

History

• Received
  10 Oct 2000
• Accepted
  23 Apr 2001