Salt effect of KBr on the liquid-liquid equilibrium of the water/ethanol/1-pentanol system

SALT EFFECT OF KBr ON THE LIQUID-LIQUID EQUILIBRIUM OF THE WATER/ETHANOL/1-PENTANOL SYSTEM

G.R. Santos, S.G. d’Ávila and M. Aznar

Departamento de Processos Químicos, (FEQ) UNICAMP, Universidade Estadual de Campinas,

C. P. 6066, CEP 13081-970, Campinas - SP, Brazil

[e-mail]

(Received: November 11, 1999 ; Accepted: April 6, 2000)

Abstract - Liquid-liquid equilibrium data for the water/ethanol/1-pentanol/potassium bromide systems were experimentally determined at 25°C and 40ºC. The experimental data were correlated through the NRTL and UNIFAC-Dortmund models for the activity coefficient, with the estimation of new binary interaction parameters for both models, corresponding to the salt-solvent and solvent-solvent interactions for the NRTL model and the ion-ion and solvent-ion interactions for the UNIFAC-Dortmund model. The results obtained have shown that the NRTL model was more able to represent equilibrium data for the studied systems.

Keywords: Experimental, liquid-liquid equilibrium, electrolytes, group contribution.

INTRODUCTION

Aqueous solutions containing non-volatile electrolytes, specifically salts, are of increasing importance and influence on separation processes in chemical engineering. The electrolyte influence must be considered both in process design and operation, because it can affect dramatically the thermodynamic equilibrium of the system. Liquid-liquid equilibrium is the result of intermolecular forces, mainly of hydrogen-bonding type. Addition of a salt to such systems introduces ionic forces that affect the equilibrium. When the ions are solvated, part of the water molecules become unavailable for the solution, and they are "salted out" from the aqueous phase. This salt effect can be used for removing organic compounds from water. In the other hand, when a polar solvent is added to an aqueous salt solution, it captures the water molecules that were solvated the ions, in a "salting in" effect. This effect may be used for recover salts from concentrated aqueous solutions. These effects of the addition of a salt on the thermodynamic equilibrium can be seen in two ways: graphically, by the variation in the size of the two-phases region and by changes in the slope of the tie-lines; and quantitatively, by the variation in the solute distribution coefficient and by changes in the solvents selectivity.

Electrolyte liquid-liquid equilibrium is often related to extraction processes. For instance, the ethyl acetate recovery from its mixture with ethanol involves an aqueous extraction step, in order to remove the ethanol. In this case, it is important to decrease the mutual solubilities of water and ester, improving the separation and yielding a dryer ester. This can be achieved by adding a salt. In this particular case, Pai and Rao (1966) have studied the addition of sodium or potassium acetate for the ternary system water/ethanol/ethyl acetate.

Aznar et al. (1998a) determined experimental data for six quaternary systems of the water/ethanol/alcohol/salt type. The alcohols used were 1-butanol and 3-methyl-1-butanol, and the salts used were sodium chloride, sodium acetate and calcium chloride. In this work, some experimental data of liquid-liquid equilibrium in water/ethanol/1-pentanol/potassium bromide system are determined. Experimental tie-lines for the quaternary system was determined, using a constant composition of 10% weight of salt, at 25°C and 40°C. Next, the experimental data are used for the estimation of new binary interaction parameters for both models, corresponding to the salt-solvent and solvent-solvent interactions for the NRTL model and to the ion-ion and solvent-ion interactions for the UNIFAC-Dortmund model. UNIFAC-Dortmund parameters for the interactions between solvent groups are taken from Gmehling et al. (1993). The effect of the salts potassium chloride and potassium sulfate in the water/ethanol/1-pentanol system was studied in two previous works [Santos et al. (1998, 1999)]. The interaction parameters for these systems, adjusted for both NRTL and UNIFAC-Dortmund models, were presented by Santos (1999); parameters for interaction between solvents group and chloride ion in the model UNIFAC-Dortmund was taken from Aznar et al. (1998a).

EXPERIMENTAL

In order to determine experimental liquid-liquid equilibrium data, a mixture with partial miscibility must be prepared. The mixture is placed inside an equilibrium cell, where it is agitated in order to allow an intimate contact between the phases, and the thermodynamic equilibrium is finally achieved by letting the mixture rest for 24 hours. The complete process is carried out at constant temperature, by using a thermostatic bath. When the thermodynamic equilibrium is achieved, samples of both liquid phases are collected and analyzed by gas chromatography. The chromatograph is a Varian CX 3400 Star, with a packed column of Porapak-Q and a thermal conductivity detector; ultra-pure hydrogen is used as carrier gas, with a mean flow of 30 cm³/min. The equilibrium cell used have been improved in several works [Bueno, 1990; Andrade, 1991; Vianna, 1991; Stragevitch, 1992, 1997].

The gas chromatography technique can not be applied directly to salt-containing systems, because salt can damage the chromatographic column or the thermal conductivity detector. Therefore, it is necessary eliminate the salt in the gas stream. In order to achieve this, an empty column section is placed before the main column. The salt is deposed on the walls, and the length of the column is a determinant factor. Vianna (1991) and Vianna et al. (1992) obtained good results in determining liquid-liquid equilibrium data of mixtures containing sodium acetate, using an empty column of 30 cm. After the salt is eliminated, the concentrations of the non-electrolyte components can be determined by traditional gas chromatography, while the salt concentrations in each phase can be calculated by gravimetric analysis. This empty column section must be cleaned by washing it with distillated water and acetone, and further drying at 120°C for 2 hours.

In the gravimetric analysis, samples of both phases are collected and weighted in an analytic balance. Next, these samples are evaporated and dried at 120°C for 24 hours, and weighted until constant mass. In this way, the masses of the salt and the solution are determined, and the mass fraction of salt can be calculated. This mass fraction can be converted to mole fraction, because the normal chromatographic analysis yields the composition of the free-salt solution.

EXPERIMENTAL RESULTS

Experimental tie-lines for the ternary system water/ethanol/1-pentanol/potassium bromide at 20, 25.5°C and 40ºC were determined and compared with those previously reported by Othmer (1941) at 25.5°C and by Galan et al. (1989) at 20°C. It is important to point out that the experimental data by Othmer (1941) and Galan et al. (1989) were not analyzed by chromatography, but by titration. This can explain the apparent systematic error in the aqueous phase points. These results are shown in Figures 1 and 2 as mole fractions, and appear in Tables 1, 2 and 3.

Figure 3 shows the representation of the effect of the addition of the salt on the water/ethanol/1-pentanol system at 25ºC and 40ºC, through a pseudoternary diagram. Figure 4 shows the Cruickshank projections, where the effect of the addition of the salt is observed on the other conjugated phase. The experimental data of the quaternary systems with addition of the salt potassium bromide appear in Tables 4-7.

It can be seen from Figures 3 and 4 that there is an increase in the area of immiscibility on addition of potassium bromide. The slope of the experimental tie-lines is also changed due to the decrease of the amount of ethanol in the aqueous phase and increase in the organic phase.

In order to analyze the salt effect, the distribution curve of ethanol between the water and the 1-pentanol (Fig. 5) and the distribution curve of the salt between the water and the 1-pentanol (Fig. 6) have been represented. These distribution curve follow the behavior described by Treybal (1963) for systems of the type 1. The distribution (K_i) and the selectivity (b_ij) coefficient are defined as

(1)

(2)

where x_ij is the mole fraction of the component i in the phase rich in the component j, and W = water, P = 1-pentanol, E = ethanol e S = salt.

In Figures 5 and 6, points corresponding to the tie-lines obtained in the liquid-liquid region for the quaternary system water/ethanol/1-pentanol/KBr have been plotted. The distribution of ethanol in the organic phase increase with addition of bromide potassium. This effect can be quantitatively verified through the mean distribution coefficient of the ethanol presented in the Table 8. In this table, it is observed that the addition of salt increase significantly the capacity of separate the ethanol of the systems. In particular, the distribution coefficient of the ethanol in the experiments accomplished with 10% in weight of KBr increased on the average 55% in the experiments to 25ºC and on the average 72% in the experiments accomplished to 40ºC.

PARAMETER ESTIMATION AND CORRELATION

These experimental liquid-liquid equilibrium data were used for estimation of new liquid-liquid molecular parameters for the NRTL model [Renon and Prausnitz, 1968] and group interaction parameters for the UNIFAC-Dortmund model [Weidlich and Gmehling, 1987; Gmehling et al., 1993]. Aznar et al. (1997, 1998b) showed that the UNIFAC-Dortmund model is inferior to the original UNIFAC [Fredenslund et al., 1977] for liquid-liquid equilibrium calculations with special parameters by Magnussen et al. (1981). However, the UNIFAC-Dortmund model was chosen because there is work in progress on a complete review of this model. The estimated parameters through the models NRTL and UNIFAC-Dortmund are presented below

NRTL model

The NRTL model for the activity coefficient of multicomponent systems is expressed for:

(3)

(4)

(5)

(6)

with five adjustable parameters (t_oij, t_oji, t_1ij, t_1ji and a_ij) for each binary pair. The parameters Dg_ij and Dg_ji are related to the characteristic energy of interaction between the molecules of type i and j, while the parameter a_ij is related the nonrandomness of the mixture. In agreement with Stragevitch and d’Ávila (1997), the parameter t_ij is function of the temperature, as shown in equations 6. The objective function used in this model to fit the interaction parameters is:

(7)

where, i represents the components; j is the phases; k is the tie-lines and l is the group of data, while x_ijkl and represents the experimental and calculated mole fractions.

In this work, the NRTL model was used as a tool to predict the LLE data through the adjustment of the parameters of salt-solvent and solvent-solvent interactions. These binary interaction parameters were estimated using the program TML-LLE 2.0 developed by Stragevitch and d’Ávila (1997) and appear in Table 9. The interaction parameters between pairs salt-salt were not calculated because mixed-salt systems are not treated.

UNIFAC-Dortmund model

In the UNIFAC-Dortmund model, anions and cations are considered new functional groups. Aznar et al (1998a) estimated group interaction parameters for interactions between solvent groups and the ions Na⁺, Ca⁺², Cl^- and ACE^- (acetate ion), while Santos (1999) estimated group interaction parameters for interactions between solvent groups and the ions K⁺ and SO₄⁼. In this model, the activity coefficients are given by the sum of two contributions, combinatorial and residual:

(8)

The first part represents the contribution due to differences in size and shape of the molecules in the mixture. The second represents the effects of interaction between group pairs in the molecule. The combinatorial part is given by:

(9)

(10)

(11)

(12)

In these equations, q_i is the area fraction, while F_i’ and F_i are volume fractions. Pure component parameters r_i and q_i are, respectively, measures of molecular van der Waals volumes and areas, calculated as the sum of the group volume and area parameters R_k and Q_k:

(13)

(14)

The residual part is given by the solution-of-groups concept [Wilson and Deal, 1962]:

(15)

where G_k is the group residual activity coefficient of

group k in the solution and G_k⁽ⁱ⁾ is the group residual activity coefficient of the group k for a reference solution of pure i, and can be calculated by:

(16)

The group interaction parameter y_mn is given by:

(17)

These temperature-dependent energy parameters a_mn, b_mn and c_mn, have been fitted for solvent groups by Gmehling et al. (1993), using vapor-liquid equilibrium, infinite-dilution activity coefficients, heats of mixing and, sometimes, liquid-liquid equilibrium data. The objective function used by Gmehling et al. (1993) is:

(18)

where, for LLE data:

(19)

where k is for data point and i is for phases.

The group area and volume parameters R_k and Q_k are considered adjustable parameters for improve the quality of predictions. The R_k and Q_kfor the ions have been retrieved by Macedo et al. (1990). These parameters are shown in Table 10.

Group interaction parameters for pairs solvent-cation, solvent-anion and anion-cation appear in Table 11. Interactions parameters between pairs cation-cation and anion-anion were not calculated, because mixed-salt systems are not treated.

Estimation procedure

The parameter estimation of both models is carried out by minimization of the objective function, S, using the TML-LLE 2.0 program developed by Stragevitch and d’Ávila (1997).

(20)

where, D is the number of data sets, N_k and C_k are the number of points and compounds in data set k, and sT_jk, sx^I_ijk and sx^II_ijk are the observed standard deviations in the independent variables temperature and composition of both liquid phases.

With these estimated parameters, the experimental liquid-liquid equilibrium data were correlated, performing liquid-liquid flash calculations. The results, expressed as mean deviations between experimental and calculated compositions in both phases, appear in Table 12. This deviation is given by:

(21)

The Table 12 shows the superiority of the NRTL model. The predictions with this model are always superior to those made with UNIFAC-Dortmund. One of the reasons is that group contribution methods are necessarily approximate, because the contribution of a group in a molecule is not necessarily the same that in another; also, as mentioned by Aznar et al. (1998b), the parameters of group interaction fitting by Gmehling et al. (1993) are general parameters determined by simultaneous adjustment of VLE, h^E, g^¥ , and in some few cases, Cp^E and LLE data; in this way, one cannot expect these parameters are capable to represent all the LLE systems that can be formed.

Besides, it should be noted that the objective function minimized in UNIFAC-Dortmund (eqns. 18 and 19), as defined by Gmehling [Weidlich and Gmehling, 1987; Gmehling et al., 1993], is an implicit function, where the involved amounts are activities coefficients, that cannot be calculated from LLE experimental data. In this case, the activity coefficients are obtained by fitting temperature-dependent NRTL or UNIQUAC parameters to the experimental data.

The results of the correlation can be seen in Figs. 7-¹³ where the calculated and experimental data are plotted together, for all the studied systems. In Figures 7-9, the experimental points for the salt-free ternary system, water/ethanol/1-pentanol, at 20ºC, 25.5ºC and 40ºC are shown together with the points predicted by the NRTL model using the parameters predicted in this work. As the mean deviations in the compositions of the calculated phases by UNIFAC-Dortmund, presented in Table 12, were around 26%, the predicted points are not capable of represent this ternary system, and therefore they are not shown in these figures.

In ^{figures 10-13}, comparative results are shown between the experimental and calculated data of quaternary system, water/ethanol/1-pentanol/KBr, through projections of Cruickshank. This projection facilitates the visualization of the behavior of the phase equilibrium of quaternary systems.

These graphics show a superior performance of NRTL model. The mean quadratic deviations between experimental and calculated compositions in the salt-free system using the NRTL model was on the average 0.8% and using UNIFAC-Dortmund model was on the average 26%. The mean quadratic deviations between experimental and calculated compositions in the quaternary system using the NRTL model was on the average 0.9% and using UNIFAC-Dortmund model was on the average 11%. This means that the model UNIFAC-Dortmund is not capable to represent LLE of the ternary systems satisfactorily so much (salt-free) as the studied quaternary systems. The mean global deviation for the systems using the NRTL model was 0.95% and using UNIFAC-Dortmund model was 15.26%. These values show that the NRTL model was able to represent better the equilibrium data of the studied systems. Indeed, the UNIFAC-Dortmund model predicts total miscibility to some points in the water/ethanol/1-pentanol/KBr systems at 10% (25ºC) and 10% (40ºC).

CONCLUSIONS

Electrolyte liquid-liquid equilibrium data of quaternary water/ethanol/1-pentanol/KBr system at 25ºC and 40ºC were experimentally determined by chromatographic and gravimetric analysis. The effect of the salt addition on the original ternary system was observed by the increase of the two-phase region and the changes in the slopes of the experimental tie-lines. Experimental data for the ternary system without salt were also determined and compared with those published by Othmer (1941) and Galan et al. (1989).

The addition of bromide potassium improves ethanol extraction by means of 1-pentanol. This improvement results from the salt effect, which modifies the phase equilibrium of water/ethanol/1-pentanol system, increasing the distribution coefficient for ethanol and the selectivity of the solvent.

With these experimental data, new binary interaction parameters were estimated through the NRTL and UNIFAC-Dortmund models for the activity coefficient, corresponding to the salt-solvent and solvent-solvent interactions for the NRTL model and to the ion-ion and solvent-ion interactions for the UNIFAC-Dortmund model. In this model, anions and cations were considered as new independent functional groups.

With these estimated parameters, the data were correlated for both models, and the results were expressed as mean quadratic deviations between the experimental and calculated values of the compositions of the two phases in equilibrium. The results shown the superiority of the NRTL model for the prediction of LLE data of the studied systems.

ACKNOWLEDGEMENTS

G.R. Santos recognizes with thanks the financial support by National Council for Research, CNPq (Brazil). The financial aid by Teaching and Research Support Foundation, FAEP/UNICAMP (Brazil) is also acknowledged.

NOTATION

a, b, c group interaction parameters C number of components D number of data sets K_i distribution coefficient of the component i N number of points q molecular Van der Waals area Q group area parameter r molecular Van der Waals volume R group volume parameter S maximum likelihood objective function T temperature x molecule mole fraction x_ij molecule mole fraction of the component i in relation to component j X group mole fraction

Superscripts - Subscripts

C combinatorial I, II liquid phases in equilibrium i, j component j experimental point k, m, n group k data set m measured variable R residual

Greek Letters

_bij selectivity coefficient of the component i in relation to component j g activity coefficient F volume fraction q area fraction G residual activity coefficient s standard deviation y group energy interaction parameter n _k⁽ⁱ⁾ number of groups k in molecule i

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Publication Dates

• Publication in this collection
  16 Mar 2001
• Date of issue
  Dec 2000

History

• Received
  11 Nov 1999
• Accepted
  06 Apr 2000