Amine Extraction of Hydroxycarboxylic Acids. 3. Effect of Modifiers on

This method uses the FORTRAN procedure BSOLVE (Kuester and Mize, 1973), ... Finally, overloading, Z > 1, at higher acid concentrations indicates forma...
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Ind. Eng. Chem. Res. 1997, 36, 2799-2807

2799

Amine Extraction of Hydroxycarboxylic Acids. 3. Effect of Modifiers on Citric Acid Extraction Jaroslav Procha´ zka,* Alesˇ Heyberger, and Eva Volaufova´ Institute of Chemical Process Fundamentals, Academy of Sciences of Czech Republic, Rozvojova´ 135, 16502 Praha 6, Suchdol, Czech Republic

The extraction equilibrium in the systems aqueous solution of a hydroxycarboxylic acid-solution of trialkylamine in an organic diluent can be largely modified by the nature of the diluent. Binary diluents composed of a neutral paraffinic solvent and an active modifier can be used to adjust the desired equilibrium behavior of a particular system. In the present work the equilibria in the systems aqueous solutions of citric acid-solutions of trialkylamine in binary diluents have been measured. Chloroform or methyl isobutyl ketone has been used as modifiers and n-heptane as neutral diluent. Besides these two data systems earlier data for the system with 1-octanol as modifier are also considered. Different mathematical models for correlating these data are proposed comprising specific effects of formation of various acid-amine complexes and nonspecific effects of interactions among the components of the organic phase. The optimum parameter values of the individual models are presented, and the goodness of fit of models applied to a particular system is compared. When comparing the three modifiers investigated, are found a striking difference between octanol and chloroform on one side and MIBK on the other side. Whereas the systems with the former modifiers do not show a tendency to overloading of amine, the latter system exhibits strong overloading at higher aqueous acid concentrations. Introduction Because of their hydrophilic nature the hydroxycarboxylic acids are poorly extractable by common organic solvents. Therefore, for their recovery from aqueous solutions reactive extraction has been considered. Trialkylamines with 7 to 12 carbon atoms in the alkyl chains, dissolved in various diluents, have been proposed as suitable extractants for carboxylic and hydroxycarboxylic acids (Vanˇura and Kucˇa, 1976; Wennersten, 1983). Various active, polar, and proton- or electron-donating solvents enhance the extraction. At the same time, they make the reextraction of free acid into water difficult. Paraffinic, inert diluents, on the other hand, limit the solvent capacity by the third-phase formation at higher acid concentrations in organic phase. Binary diluents composed of a paraffinic solvent and an active modifier can be used to overcome these difficulties. Between the extraction and reextraction steps the composition of the diluent can be changed to promote the efficiencies of both steps (Tamada and King, 1990). In the preceding papers of this series (Bı´zek et al., 1992; Procha´zka et al., 1994) extraction equilibria in the systems aqueous solution of hydroxycarboxylic acidsolution of trialkylamines (TAA) in 1-octanol/n-heptane was investigated. Systems with lactic, malic, and citric acids were studied. The effects of temperature and of solvent composition on the equilibrium were examined in a fair range of aqueous phase acid concentrations. A mathematical model incorporating specific interactions (formation of acid-amine complexes in organic phase) and nonspecific interactions in aqueous and organic phases, as well as the effect of temperature, was developed. However, different complexes had to be considered for the individual acids to obtain a good fit of experimental data. Thus for lactic and malic acids * Author to whom correspondence should be addressed. Tel.: 0421 2 24311498. Fax: 0421 2 342073. E-mail: [email protected]. S0888-5885(96)00710-5 CCC: $14.00

the acid-amine complexes (1,1), (2,1), and (2,2) and for citric acid the complexes (1,1), (1,2), and (2,3) were included. Recently, mathematical models of extraction equilibria incorporating both chemical and physical interactions in aqueous and organic phases have been developed by Ziegenfuβ and Maurer (1994) and by Kirsch and Maurer (1994). These models, which involve also specific interactions of water and solvent molecules, have been used for correlating distribution data for acetic and oxalic acids between water and solutions of tri-n-octylamine in organic solvents. In the present work equilibria have been measured in the systems aqueous solution of citric acid-solutions of TAA in the binary diluents containing chloroform or methyl isobutyl ketone (MIBK) as modifiers and nheptane as the inert component. Chloroform has been proposed as the modifier for extraction of succinic acid by Tamada and King (1990) and King (1992). The equilibria in extraction of lactic, malonic, maleic, fumaric, and succinic acids with L-Alamine 336 in pure MIBK as diluent have been studied by Tamada et al. (1990); those of citric acid with TAA in chloroform and MIBK have been investigated by Bı´zek et al. (1993). The experimental results obtained in the present work have been correlated using similar models, as in the previous paper, and the effects of 1-octanol, CHCl3, and MIBK have been mutually compared. Specific interactions of the modifier, as well as coextraction of water, have been neglected. Experimental Section The trialkylamine used was a Russian commercial product, a mixture of tertiary, straight-chain aliphatic amines with seven to nine carbon atoms (2.75 mol/kg of amine molecules, M ) 363.3 g/mol). Before used it was extracted with aqueous hydrochloric acid, aqueous sodium hydroxide, and water. Citric acid monohydrate (Lachema Co.) and other reagents used were of analytical grade purity. Chloroform (Lachema Co.) was of the © 1997 American Chemical Society

2800 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

same purity and was not stabilized. To prevent the changes of solvent composition caused by gradual decomposition of chloroform and development of hydrochloric acid, fresh solvent was prepared for each block of experiments. The compositions of both coexisting phases were analyzed. The acid concentration was determined by potenciometric titration with sodium methanolate solution in a 3:1 methanol/dimethylformamide mixture. TAA in organic phase was titrated with perchloric acid in acetic acid. The water content in organic phase was determined using the Carl Fischer method. The desired ratio of diluents was prepared by weighing them up. The solubility of the diluents and TAA in aqueous phase was neglected. The acid content in aqueous phase was expressed in molalities and the content of acid, TAA, and water in organic phase in mole per kilogram of binary diluent. The data on coextraction of water were used only for expressing the molalities in organic phase on a waterfree basis. All equilibrium measurements were done at 25 °C in the same way as described in Procha´zka et al. (1994). From that paper also the equilibrium data on the system with citric acid and 1-octanol have been taken over. Theoretical Section Mathematical Model. To the systems investigated, the correlation procedure developed in the preceding paper (Procha´zka et al., 1994) has been adopted. As no effect of the dissociation and nonideality in aqueous phase on the goodness of fit were observed, these effects have been excluded from the model. The experiments in the system containing MIBK as the modifier have shown strong tendency to overloading. Accordingly, for this system the assumption of complexes (1,1), (2,1), and (3,1) has been used as the starting point. For the systems with chloroform and 1-octanol, which do not show a distinct tendency to overloading, the (1,1), (1,2), and (2,3) complexes have been considered. Measurements of physical distribution of the acid between water and pure modifiers have given values of distribution coefficients: 0.057-0.085 for 1-octanol, 1.5 × 10-4 for chloroform and 9.6 × 10-3-2.9 × 10-2 for MIBK. In what follows this effect has been neglected. The error thus caused will be highest for MIBK at high aqueous phase acid molalities and low amine and high modifier content in organic phase, amounting to less than 10%. The balances of acid and amine are as follows: K

m ja)

∑ ik(mj ij)k

(1)

k)1

m je)m j 0e /(1 + β′11ma + β′21m2a + β′31m3a)

For the complexes (1,1), (1,2), and (2,3) one obtains

m j a ) β′11mam j e + β′12mam j 2e + 2β′23m2am j 3e

)

∑ jk(mj ij)k + mj e k)1

In contrast to eq 4 the last equation is implicit in m je and has to be solved by an iterative method. The conditioned equilibrium constant of complex (i,j), β′ij, is related to the overall thermodynamic extraction equilibrium constant, βij, by the formula

βij ) m j ijγ j ij/mia m j je γ j je ) β′ijγ j ij/γ j je

(7)

where γ denotes the activity coefficient. Here the nonideality effects in aqueous phase have been neglected. The ratio of activity coefficients in eq 7 has been expressed as an exponential of linear function of solvent composition

j 0e + Bijxj + Cijm j a) β′ij ) βij exp(Aijm

(8)

where xj is the mass fraction of the modifier in the diluent and βij, Aij, Bij, and Cij are the model parameters. The last term in eq 8 represents the nonidealities due to various acid-amine complexes present in organic phase. This effect has not been taken into account previously. In the present work it has been found necessary to include it with respect to the wide range of organic phase acid molalities measured. Model Solution and Correlation Procedure. As in the present work three complexes in the organic phase have been considered; the mathematical model contains up to 12 parameters. Given the acid molality in aqueous phase, the solvent composition, and the parameter values, the equilibrium acid molality in organic phase can be calculated using the model equations (eqs 3 and 4 or 5 and 6 and 8). Even this simulation procedure, however, must be iterative, since, with respect to eq 8, the model is implicit in m j a. For correlation of experimental data and estimation of the model parameters an optimization procedure has been developed. This method uses the FORTRAN procedure BSOLVE (Kuester and Mize, 1973), on the basis of the Marquardt method (Marquardt, 1963). The weighted sum of squares of relative differences of experimental and calculated acid molalities in aqueous and organic phases has been used as an objective function: N

(2)

S)

Wk[(1 - ma(cal)/ma(exp))2 + ∑ k)1 N

Here m is the molality, the subscripts a and e refer to the acid and amine molecules, respectively, and the overbar denotes the organic phase. m j 0e is the total molality of TAA, (m j ij)k is the molality of the kth complex, and K is the number of complexes taken into account; ik, jk and the subscripts i and j are the number of acid and amine molecules in the kth complex, respectively. For the complexes (1,1), (2,1), and (3,1) the balances take the form

je m j a ) (β′11ma + 2β′21m2a + 3β′31m3a)m

(5)

m j 0e ) m j e + β′11mam j e + 2β′12mam j 2e + 3β′23m2am j 3e (6)

K

m j 0e

(4)

(3)

(1 - m j a(cal)/m j a(exp))2]kN/

∑ Wk

(9)

k)1

where N is the number of experimental points and Wk are the respective weights. The expression 9 corresponds to the case when both the aqueous and organic phase acid concentrations are considered to be subject to experimental error and are optimized for each experimental point during the process of parameter estimation. Comparison of Models. The sets of complexes proposed for the individual modifiers in the preceding

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2801

paragraph have been used as starting assumptions. In what follows other combinations are also considered and the respective model variants are mutually compared. To indicate the goodness of fit of a particular correlation, the relative standard deviation of the measured and calculated acid concentrations is used. Here n is the sr )

x

1

N

∑[(1 - m 2N - n

a(cal)/ma(exp))

2

+ (1 - m j a(cal)/m j a(exp))2]k

k)1

(10)

number of model parameters. For comparison of the model variants the F-test has been selected. In this test the ratio of variances F12 ) s2r1/s2r2 is compared with the respective 5% confidence limit F0.05. Results and Discussion Experimental Results. Results of equilibrium measurements in systems with CHCl3 and MIBK are depicted in Figures 1-6. The data cover a broad range of acid concentrations (ma ∈ (1 × 10-3,6.0)) and of solvent compositions (m j 0e ∈ (0.3,2.0); xj ∈ (0.4,1.0)). The acid concentrations in organic phase are expressed in terms of loadings of the extractant, Z ) m j a/m j 0e , which in the case of chloroform ranges up to 0.9 (m j a(max) ≈ 1.8) and in the case of MIBK up to 2.96 for m j 0e ) 0.3 and 1.28 for m j 0e ) 2.0 (m j a(max) ≈ 2.6). Qualitative Analysis of Data. The analysis of the sets of loading curves at varying solvent compositions allows one to indicate the main chemical species present in the organic phase. As was pointed out in Tamada et al. (1990), there is no specific effect of total amine concentration on loading, if only (i,1) complexes are present. If the loading at low acid concentration in aqueous phase increases with growing amine concentration, (i,j) complexes with j > 1 should occur; a drop of loading indicates formation of complexes specifically bonding the modifier. Formation of aggregates of simpler complexes should lead to a steeper ascent of the loading curve at a critical acid concentration. Finally, overloading, Z > 1, at higher acid concentrations indicates formation of complexes with i > j. If the overall extraction constants of the complexes forming differ significantly in magnitude, plateaux may appear on the loading curve, corresponding to the acid/amine ratios in the individual complexes. The above reasoning concerns specific effects only. Systems with CHCl3. In Figures 1 to 3 one can observe a moderate increase of the major part of the loading curves with increasing TAA molality. Thus presence of complexes with j > 1 can be expected. A contrary effect appears at the low-concentration end of the curves. This phenomenon may be caused by a simultaneous decrease of the mole fractions of the modifier with increasing TAA molality at constant xj. The mole fraction of the modifier or its molar concentration, based on the total amount of organic phase, would be a more appropriate measure of modifier activity. Similar reasoning applies to the use of molality related to the amount of diluent for expressing the influence of TAA activity. The units used here have been chosen for simplifying the calculations. Table 1 shows the values of mole fractions of the solvent components, moles of component/moles of amine + modifier + inert diluent, corresponding to the respective molality or mass

Figure 1. System with CHCl3, m j 0e ) 0.3. Points ) experiments; lines ) calculated with model I. 0, s (xj ) 0.4); 9, - - - (xj ) 0.7); 2, - - - (xj ) 1.0).

Figure 2. System with CHCl3, m j 0e ) 1.0. Points ) experiments; lines ) calculated with model I. 0, s (xj ) 0.4); 9, - - - (xj ) 0.7); 2, - - - (xj ) 1.0).

fraction levels used. The sharp drop of mole fraction values of the modifier with increasing m j 0e at constant xj is apparent. Specific interactions among the acid, amine, and modifier molecules may also take place in the system. They, too, would cause a drop of effective modifier concentration available for solvating the amine salt molecules. In the present work specific interactions of the modifier have not been considered. In Figures 1 and 2 the end points of the curves for xj ) 0.4 correspond to the appearance of the third phase. In Figure 3, the measurements for xj ) 0.4 could not be done as the third phase formed, even at low acid concentrations. Accordingly, third-phase formation is promoted by increasing TAA concentration and its loading. An increase of chloroform concentration prevents its formation by stabilizing simple acid/amine complexes. The curves for m j 0e ) 1.0 and 2.0 show a stepwise increase of Z to the level of Z ) 0.5, which indicates formation of the (1,2) complex or its associates, e.g., (2,4). With some dicarboxylic acids formation of the

2802 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Figure 3. System with CHCl3, m j 0e ) 2.0. Points ) experiments; lines ) calculated with model I. 0, s (xj ) 0.7); 9, - - - (xj ) 1.0). Table 1. Conversion of m j 0e and x j to Mole Fractions of Solvent (Mole of Component/Mole of Solvent): Mole Fraction of Amine/Mole Fraction of Modifier

Figure 4. System with MIBK, m j 0e ) 0.3. Points ) experiments; lines ) calculated with model II. 0, s (xj ) 0.4); 9, - - - (xj ) 0.7); 2, - - - (xj ) 1.0).

m j 0e , mol/kg of diluent

xj, kg/kg of diluent

0.3

1.0

2.0

0.4 0.7 1.0

CHCl3 0.0311/0.348 0.0967/0.324 0.0328/0.640 0.101/0.595 0.0346/0.965 0.107/0.893

0.176/0.295 0.184/0.540 0.193/0.807

0.4 0.7 1.0

0.0292/0.389 0.0292/0.681 0.0292/0.973

MIBK 0.0911/0.364 0.0911/0.637 0.0911/0.910

0.167/0.334 0.167/0.584 0.167/0.834

Table 2. Model Variants variant no.

complexes

I II III IV V VI VII

(1,1); (1,2); (2,3) (1,1); (2,1); (3,1) (1,1); (1,2); (3,1) (1,1); (1,2); (2,4) (1,1); (2,2); (2,3) (1,1); (1,2); (2,2) (1,1); (1,2); (2,1)

(1,2) complex in 1-octanol, chloroform, and their mixtures was observed (Tamada et al., 1990; Tamada and King, 1990). The enhancement of this complex formation by proton-donating solvents has been ascribed to their ability to prevent intramolecular hydrogen bonding in these acids. The subsequent growth of Z with increasing ma reflects the transition of these complexes to the (1,1) salt. This process should be promoted by higher modifier concentrations. According to Tamada and King (1990) chloroform, as a proton-donating solvent, may stabilize the (1,1) complexes of higher carboxylic acids. Such solvents should also act against overloading of the amine by preventing formation of (i,1) complexes with i > 1. Indeed, the present system, as well as the system with 1-octanol studied earlier, does not exhibit marked tendency to overloading. At ma about 1 the curves for m j 0e ) 1.0 and 2.0 show a steeper slope. This indicates formation of aggregates, e.g., the complexes (2,2) or (2,3). System with MIBK. In contrast to the systems with 1-octanol and chloroform, this system shows a striking tendency to overloading of amine. At m j 0e ) 0.3 (Figure

Figure 5. System with MIBK, m j 0e ) 1.0. Points ) experiments; lines ) calculated with model II. 0, s (xj ) 0.4); 9, - - - (xj ) 0.7); 2, - - - (xj ) 1.0).

4) even values of Z approaching 3 have been reached. Hence, at high aqueous phase acid concentrations, a low amine content and a high concentration of modifier, formation of complexes (2,1) and (3,1) has been assumed. A positive effect of MIBK on overloading in extraction of succinic, malonic, fumaric, and maleic acids with TAA was observed by Tamada et al. (1990). With these dicarboxylic acids, however, the difference between MIBK and the proton-donating solvents was less conspicuous than here. In the range of ma ) 0.1-1.0, the curves at constant xj ) 0.7 and 1.0 asymptotically approach Z ) 1.0 and their course does not seem to be affected by the amine concentration. This indicates predominance of the (1,1) complex. However, the curves for xj ) 0.4 at low aqueous phase acid content, and the curves for xj ) 0.7 and 1.0, display a distinct shift to higher loadings with increasing amine molality. Moreover in Figures 5 and 6 one can detect a steeper ascent of these curves at their beginning and a tendency to form a plateau at Z ) 0.67. These findings are consistent with the assumption that at low aqueous phase acid concentrations even in the

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2803 Table 3. Parameter Values of Models for Complete Data Sets

(i,j)

βij, (kg/mol)(i+j-1)

Aij, kg of diluent/mol

Bij, kg of diluent/kg of modifier

Cij, kg of water/mol

System with 1-Octanol-Model I (1,1) (1,2) (2,3)

sr ) 4.32 × 10-2; N ) 93 -1.476 × 100 3.444 × 100 -1.474 × 100 4.981 × 100 2.659 × 10-1 -7.426 × 10-1

4.535 × 100 3.336 × 101 3.325 × 102

2.473 × 100 1.813 × 100 2.318 × 100

System with CHCl3-Model I (1,1) (1,2) (2,3)

sr ) 4.36 × 10-2; N ) 99 -9.710 × 10-1 3.093 × 100 -4.669 × 100 5.943 × 100 8.569 × 10-1 -4.380 × 10-1

1.214 × 100 1.493 × 101 2.319 × 102

4.694 × 100 1.077 × 101 2.201 × 100

System with MIBK-Model II

Figure 6. System with MIBK, m j 0e ) 2.0. Points ) experiments; lines ) calculated with model II. 0, s (xj ) 0.7); 9, - - - (xj ) 1.0).

systems with MIBK citric acid tends to form (1,2) and/ or (2,3) complexes, similarly as in systems with the proton-donating modifiers. The end points of the curves for xj ) 0.4 again mark out the boundary of the threephase region. Correlation of Complete Data Sets. The above qualitative analysis of the experimental results has shown that in each of the systems formation of several complexes can be assumed. Thus in the system with chloroform the complexes (1,1), (1,2), and their associates (2,2), (2,3), and (2,4) can be expected to form. Similarly in the system with MIBK the complexes (1,1), (1,2), (2,1), (3,1) and some of their associates may occur. However, in the mathematical model described above, no more than three complexes can be included to preserve reasonable convergence properties of the optimization algorithm. Therefore a feasible mathematical model must be expected to correlate individual parts of the region investigated with varying levels of systematic error, as can be seen in Figures 1-6. The curves in Figures 1-3 have been calculated using the model with complexes (1,1), (1,2), and (2,3) (model I); those in Figures 4-6 are the result of simulation with complexes (1,1), (2,1), and (3,1) (model II). To assure low error of correlation for the prominent parts of the data sets, different weights have been ascribed to the respective experimental points. Thus the instrument of weighted mean squares has been employed for prompting the correlation procedure to reduce the systematic error at the data segments of major importance. Table 3 shows the parameter values obtained for the complete data sets of the individual liquid systems. The respective values of the standard deviation and of the number of points included are also shown. The values of the standard deviation compare reasonably with the average experimental error, which is about 4%. From these data, however, one cannot make conclusions about the importance of the individual complexes involved in a particular model for the final fit of correlation. For this purpose the contributions (m j a)k of the individual complexes, m j ij, to the total organic phase acid molality have to be compared across the range of variables investigated. According to eq 1

(m j a)k ) ik(m j ij)k;

k ) 1, ..., K

(11)

sr ) 7.41 × 10-2; N ) 113 5.628 × 10-1 4.074 × 100 1.457 × 10-2 3.209 × 10-1 5.595 × 10-1 -7.485 × 10-2 -1.778 × 100 1.023 × 101 1.610 × 100

(1,1) (2,1) (3,1)

1.403 × 100 1.767 × 10-1 1.617 × 10-4

(1,1) (1,2) (3,1)

sr ) 7.40 × 10-2; N ) 113; FII/III ) 1.00; F0.05 ) 1.47 5.804 × 10-1 3.963 × 100 -2.847 × 10-2 1.270 × 100 1.606 × 100 4.045 × 10-1 2.030 × 100 -2.734 × 10-2 5.287 × 10-5 4.309 × 10-3 1.167 × 101 6.267 × 10-2

System with MIBK-Model III

Table 4. Ranges of Contributions of Individual Complexes to Total Acid Concentration in Organic Phase System with 1-Octanol-Model I (m j a)12 (m j a)23 (m j a)11 1.1 × 10-2-1.5 × 100 2.4 × 10-2-5.0 × 10-1 1.7 × 10-5-3.9 × 10-1 System with CHCl3-Model I (m j a)12 (m j a)23 (m j a)11 5.4 × 10-3-1.7 × 100 1.9 × 10-2-2.1 × 100 9.3 × 10-9-3.1 × 10-1 System with MIBK-Model II (m j a)21 (m j a)31 (m j a)11 4.5 × 10-2-2.1 × 100 3.8 × 10-6-4.2 × 10-2 3.3 × 10-8-9.9 × 10-1 System with MIBK-Model III (m j a)21 (m j a)31 (m j a)11 -2 4.0 × 10 -2.1 × 100 1.3 × 10-6-1.6 × 10-1 4.5 × 10-8-1.0 × 100

Some information can be obtained by mutually comparing the ranges of these contributions, which are shown in Table 4. Whereas in systems with octanol and chloroform the ranges for the three concentrations partly overlap; in the system with MIBK the range of (m j a)21 lies entirely below that of (m j a)11. That means that although the (2,1) complex should be present in the system, the effects of overloading can be satisfactorily expressed by including the complex (3,1) alone. Therefore model III containing the complex (1,2) instead of (2,1) has been tried, which could provide for better correlation in the range of low acid and high amine concentrations. Although the variance thus obtained is not significantly lower according to the F-test on the 5% level, a better fit in the mentioned range has been observed. The values of the constants βij, Aij, Bij, and Cij in Table 3 vary considerably with the individual liquid systems, with the models selected, and with the particular complexes within the models. This fact testifies their empirical nature and mutual dependence. Nevertheless, some regularities can be observed: 1. The values of B11 for all modifiers investigated are positive and close to each other, which means that the modifiers exert a positive synergistic effect on the complex (1,1). This statement is also true for the constants B12 and B21, though the value of the latter one is about 1 order smaller. In contrast to it the values of B23 are negative in accord with the expectation that the modifiers should act against the aggregation of

2804 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997

Figure 7. System with CHCl3, m j 0e ) 0.3. Points ) experiments; lines ) calculated with model I for low-concentration range and with model VI for high-concentration range. 0, s (xj ) 0.4); 9, - - (xj ) 0.7); 2, - - - (xj ) 1.0).

Figure 9. System with CHCl3, m j 0e ) 2.0. Points ) experiments; lines ) calculated with model I for low-concentration range and with model VI for high-concentration range. 0, s (xj ) 0.7); 9, - - (xj ) 1.0).

Figure 8. System with CHCl3, m j 0e ) 1.0. Points ) experiments; lines ) calculated with model I for low-concentration range and with model VI for high-concentration range. 0, s (xj ) 0.4); 9, - - (xj ) 0.7); 2, - - - (xj ) 1.0).

Figure 10. System with MIBK, m j 0e ) 0.3. Points ) experiments; lines ) calculated with model I for low-concentration range and with model II for high-concentration range. 0, s (xj ) 0.4); 9, - - (xj ) 0.7); 2, - - - (xj ) 1.0).

complexes. The values of B31 in models II and III for the system with MIBK are similar, large and positive, thus manifesting the strong enhancement of overloading by this modifier. 2. The meaning of the values of the parameters Aij and Cij is less unequivocal. An obvious reason for it is that the respective species are the reactants, whose main effects are expressed by the stoichiometry. These constants then express only the nonspecific effects of the complexes and of free amine on β′ij. Nevertheless, most of the corresponding values of Aij, Bij, and Cij for the systems with octanol and chloroform as modifiers are close to each other. 3. The values of the extraction equilibrium constants, βij, for the system with octanol are higher than those for the system with chloroform, thus indicating a higher synergistic effect of the former modifier. The β11 values for models II and III and MIBK as the modifier do not differ very much from the value for the same complex

for the system with chloroform. Physically the equilibrium constants βij represent the values of conditioned constants β′ij at infinite dilution. Their values may be subject to extrapolation error, since the lower limits of amine and modifier concentrations used have been kept far from zero for practical reasons. Correlation of Subsets of Data. The above qualitative analysis of data has indicated that in both systems studied the individual complexes can be expected to be of significance mainly in some parts of the whole concentration range. These subranges can be delimitated in terms of aqueous phase acid molality, as well as of solvent composition. Hence mathematical models including particular selections of three complexes, when applied to suitably selected subranges, could correlate the respective subsets of data with a better fit and yield parameter values better suited for interpretation. The overlapping limits of ma have been set to 0.3 and 0.1 for the system with chloroform and to 0.5 and 0.3 for the system with MIBK.

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2805 Table 5. Parameter Values of Models for Subsets of DatasCHCl3 (i,j)

βij, (kg/mol)(i+j-1)

Aij, kg of diluent/mol

Bij, kg of diluent/kg of modifier

Cij, kg of water/mol

Low-Concentration Range-Model I (1,1) (1,2) (2,3)

1.310 × 100 1.269 × 101 4.261 × 102

sr ) 4.348 × 10-2; N ) 62; Fc/s ) 1.01; F0.05 ) 1.56 -1.031 × 100 3.473 × 100 -4.930 × 100 6.316 × 100 7.486 × 10-1 -6.985 × 10-1

3.936 × 100 1.053 × 101 2.201 × 100

Low-Concentration Range-Model IV (1,1) (1,2) (2,4)

1.520 × 100 2.085 × 101 5.987 × 102

sr ) 5.267 × 10-2; N ) 62; FIV/I ) 1.47; F0.05 ) 1.61 -9.327 × 10-1 3.252 × 100 -4.790 × 100 5.854 × 100 8.062 × 10-1 -6.074 × 10-1

1.720 × 100 2.526 × 101 2.166 × 10-4

sr ) 3.253 × 10-2; N ) 52; Fc/s ) 1.80; F0.05 ) 1.62 2.527 × 100 1.565 × 100 2.861 × 100 2.615 × 100 7.207 × 10-1 -2.508 × 10-1

3.632 × 100 9.877 × 100 1.018 × 100

High-Concentration Range-Model VI (1,1) (1,2) (2,2)

-7.585 × 10-1 -6.037 × 10-1 -2.225 × 10-1

High-Concentration Range-Model VII (1,1) (1,2) (2,1)

2.510 × 100 6.597 × 101 3.084 × 10-4

sr ) 3.435 × 10-2; N ) 52; FVII/VI ) 1.12; F0.05 ) 1.69 2.333 × 100 1.146 × 100 2.554 × 100 1.516 × 100 5.105 × 100 -2.750 × 100

-6.341 × 10-1 -4.123 × 10-1 -1.132 × 10-1

Figure 11. System with MIBK, m j 0e ) 1.0. Points ) experiments; lines ) calculated with model I for low-concentration range and with model II for high-concentration range. 0, s (xj ) 0.4); 9, - - (xj ) 0.7); 2, - - - (xj ) 1.0).

Figure 12. System with MIBK, m j 0e ) 2.0. Points ) experiments; lines ) calculated with model I for low-concentration range and with model II for high-concentration range. 0, s (xj ) 0.7); 9, - - (xj ) 1.0).

To each of the data subsets, particular model variants have been applied. Thus for the system with chloroform these variants include the complexes (1,1), (1,2), and (2,3) or (2,4) for the low-concentration range and (1,1), (2,2), and (2,3) for the high-concentration range. For the system with MIBK at low acid concentrations the complexes (1,1), (1,2), and (2,3) and at high concentrations the complexes (1,1), (2,1), and (3,1) have been chosen. The summary of all model variants used is presented in Table 2. The simulated curves for the individual subranges and for the model variants exhibiting the lowest correlation error are shown in Figures 7-12. The results of the correlation of these subsets are shown in Tables 5 and 6. Here the symbol Fc/s designates the variance ratio for the complete data set from Table 3 and the respective subset. If two models have been used for correlating the complete data, the lower variance value has been taken into account. As has been expected, most of the subset correlations show a better fit than

the corresponding results for the complete sets. However, for low-concentration ranges in either system, the improvement is below the 5% significance level. For the system with chloroform alternative models have been examined in both the low- and highconcentration ranges and their variances have been compared. In Table 5 the respective F values, Fp/q, are given, where p and q represent the model numbers. For the low-concentration range the model I shows a better fit, but with the F value slightly below the 5% significance level. The model IV, however, is successful in describing the steep parts of the equilibrium curves at very low acid and higher amine concentrations, as has been expected. In the high-concentration range the difference between the models VI and VII is insignificant, but both models correlate this subset significantly better than the model I does in correlating the complete data set. Apparently, including the complexes (2,2) or (2,1) helps to describe the turning points and the ascending slopes of the equilibrium curves in this

2806 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 6. Parameter Values of Models for Subsets of DatasMIBK (i,j)

βij, (kg/mol)(i+j-1)

Aij, kg of diluent/mol

Bij, kg of diluent/kg of modifier

Cij, kg of water/mol

Low-Concentration Range-Model I (1,1) (1,2) (2,3)

1.509 × 100 4.698 × 10-2 9.554 × 100

sr ) 6.345 × 10-2; N ) 61; Fc/s ) 1.36; F0.05 ) 1.54 4.949 × 10-1 3.346 × 100 1.616 × 100 2.540 × 100 -1.283 × 100 1.010 × 101

9.375 × 10-2 5.478 × 10-1 2.276 × 10-1

High-Concentration Range-Model II (1,1) (2,1) (3,1)

2.575 × 100 1.521 × 10-2 3.376 × 10-4

sr ) 4.071 × 10-2; N ) 58; Fc/s ) 3.31; F0.05 ) 1.58 7.898 × 10-1 1.693 × 100 1.625 × 100 2.101 × 100 9.848 × 10-2 8.157 × 100

-1.698 × 10-1 -4.219 × 10-1 -1.622 × 10-2

Figure 13. System with MIBK, high-concentration range. Contributions of individual complexes to overall loading of amine. m j 0e ) 0.3; xj ) 0.7. Lines calculated with model II. s (Z11); - - (Z21); - - - (Z31).

Figure 14. System with MIBK, high-concentration range. Contributions of individual complexes to overall loading of amine. m j 0e ) 0.3; xj ) 1.0. Lines calculated with model II. s (Z11); - - (Z21); - - - (Z31).

concentration range, mainly at high amine and modifier contents. For confirming the possible amine overloading, experiments at still higher acid concentrations would be necessary. Model I has proved suitable for correlating the lowconcentration data of the system with MIBK. When simulating the contributions of individual complexes, j a)ij/m j 0e , to the total loading, Z, the contribution Zij ) (m of complex (1,2) has been found significant only at low acid and high amine concentrations, where it amounts to over 10%. The complex (2,3), on the other hand, proved very important by contributing 30-50% of the total acid concentration, mainly at lower amine and higher MIBK contents. Apparently, this complex is effective in simulating the plateau at Z ) 0.67, indicated by the data points in Figures 5 and 6. High-concentration range data of the system with MIBK could be correlated with low error of correlation using model II. The fit of this subset is significantly better than that obtained with the same model for the complete data set. Here again the contribution of the complex (1,1) to the total organic phase acid concentration is dominant in a greater part of the range, but at the highest acid concentrations the contributions of the (1,1) and (3,1) complexes are comparable; in the range of low amine and higher MIBK contents the latter complex even predominates. The contribution of the complex (2,1) does not exceed the 10% level. The simulated curves of the contributions of individual

complexes to the total loading at m j 0e ) 0.3 and xj ) 0.7 and 1.0 are depicted in Figures 13 and 14. Conclusion 1. All the three modifiers investigated display a strong effect on the distribution of citric acid. Increasing their fraction in the binary diluent with n-heptane restricts the third-phase formation and enhances the acid distribution. With 1-octanol and chloroform, however, the latter effect decreases with growing loading of amine, since these systems do not show tendency to overloading. In contrast to them the systems with MIBK exhibit marked overloading at higher acid concentrations, lower amine molalities, and higher content of the modifier in the diluent. In these systems a particularly strong effect of modifier on distribution has been observed at high acid concentrations. The different behavior of octanol and chloroform in comparison with MIBK has been explained by the proton-donating character of the former modifiers and the electrondonating character of the latter ones. The proton donors are expected to stabilize the acid/amine complex (1,1); the proton acceptors may promote formation of (i,j) complexes with i > j. 2. Higher amine content in the solvent favors association of simple complexes into higher aggregates, e.g., (2,2), (2,3), or (2,4). At a sufficiently low content of modifier this process leads to the formation of the third phase at higher acid molalities.

Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2807

3. A general model describing the investigated equilibria has been developed comprising simultaneous formation of three acid/amine complexes. Nonspecific effects of solvent composition and of total acid molality in organic phase have also been included. An algorithm has been developed for data correlation and parameter evaluation, on the basis of the Marquardt optimization method. A satisfactory fit has been reached by correlating the whole data sets for the systems with octanol and chloroform using the model with complexes (1,1), (1,2), and (2,3) and for the system with MIBK using models with complexes (1,1), (2,1) or (1,2), and (3,1). 4. Since different complexes should predominate in different parts of the acid concentration range studied, the data for the systems with chloroform and MIBK have been divided into two overlapping subranges and different models have been applied to each of them. A significantly better fit of correlation has been obtained in some instances in comparison with correlating the whole data sets with a single model. In particular, the results indicate the importance of complexes (1,1), (1,2), and (2,3) in the low-concentration range for both modifiers. However, for the high-concentration range the model with complexes (1,1), (1,2), and (2,2) for chloroform and that with complexes (1,1), (2,1), and (3,1) for MIBK have been more successful. Acknowledgment This work was supported by Grant No. 104/93/2289 of the Grant Agency of Czech Republic. Nomenclature Aij ) constant in eq 8, kg of diluent/mol Bij ) constant in eq 8, kg of diluent/kg of modifier Cij ) constant in eq 8, kg of water/mol F ) s2r1/s2r2 ) ratio of variances in comparing model I with model II F0.05 ) value of 5% confidence limit of single-sided F-test Fc/s ) variance ratio for comparison of variances of complete data set and subset correlations Fp/q ) variance ratio for comparison of variances of correlations with models p and q, respectively K ) number of complexes in the model ma ) molality of acid in aqueous phase, mol/kg of water m j a ) total molality of acid in organic phase, mol/kg of diluent (m j a)k, (m j a)ij ) contribution of kth complex, or complex (i,j), to total acid molality in organic phase, mol/kg of diluent m j e ) molality of free amine in organic phase, mol/kg of diluent m j 0e ) total molality of amine in organic phase, mol/kg of diluent m j ij ) molality of (i,j) complex in organic phase, mol/kg of diluent (m j ij)k ) molality of kth complex in organic phase, mol/kg of diluent M ) effective molar mass of TAA, g/mol n ) number of model parameters N ) number of experimental points sr ) relative standard deviation, eq 10

S ) sum of squares of relative deviations, eq 9 TAA ) trialkylamine Wk ) weight of square of kth deviation xj ) mass fraction of modifier in binary diluent, kg of modifier/kg of diluent Z ) loading of extractant, mol of acid/mol of amine Zij ) contribution of complex (i,j) to total loading of extractant, mol of acid/mol of amine Greek Letters βij ) thermodynamic overall extraction equilibrium constant of (i,j) complex, (kg/mol)i+j-1 β′ij ) conditioned overall extraction equilibrium constant of (i,j) complex, (kg/mol)i+j-1 γ j e ) activity coefficient of free amine in organic phase γ j ij ) activity coefficient of (i,j) complex in organic phase Subscripts cal ) calculated values exp ) experimental values

Literature Cited Bı´zek, V.; Hora´cˇek, J.; R ˇ erˇicha, R.; Kousˇova´, M. Amine Extraction of Hydroxycarboxylic Acids. 1. Extraction of Citric Acid with 1-Octanol/n-Heptane Solutions of Trialkyl Amine. Ind. Eng. Chem. Res. 1992, 31, 1554-1562. Bı´zek, V.; Hora´cˇek, J.; Kousˇova´, M. Amine Extraction of Citric Acid: Effect of Diluent. Chem. Eng. Sci. 1993, 48, 1447-1457. King, C. J. Amine Based Systems for Carboxylic Acid Rrecovery. CHEMTECH 1992, 289-291. Kirsch, T.; Maurer, G. Distribution of Oxalic Acid between Water and Organic Solutions of Tri-n-octylamine. Ind. Eng. Chem. Res. 1996, 35, 1722-1736. Kuester, J. L.; Mize, J. H. Optimization Techniques with FORTRAN; McGraw-Hill: New York, 1973. Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11, 431441. Procha´zka, J.; Heyberger, A.; Bı´zek, V.; Kousˇova´, M.; Volaufova´, E. Amine Extraction of Hydroxycarboxylic Acids. 2. Comparison of Equilibria for Lactic, Malic, and Citric Acids. Ind. Eng. Chem. Res. 1994, 33, 1565-1573. Tamada, J. A.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 2. Chemical Interactions and Interpretation of Data. Ind. Eng. Chem. Res. 1990, 29, 1327-1333. Tamada, J. A.; Kertes, A. S.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 1. Equilibria and Law of Mass Action Modeling. Ind. Eng. Chem. Res. 1990, 29, 1319-1326. Vanˇura, P.; Kucˇa, L. Extraction of Citric Acid by the Toluene Solutions of Trilaurylamine. Collect. Czech. Chem. Commun. 1976, 41, 2857-2877. Wennersten, R. The Extraction of Citric Acid from Fermentation Broth Using a Solution of Tertiary Amines. J. Chem. Technol. Biotechnol. 1983, 33B, 85-94. Ziegenfuβ, H.; Maurer, G. Distribution of Acetic Acid Between Water and Organic Solutions of Tri-n-alkylamine. Fluid Phase Equilib. 1994, 102, 211-225.

Received for review November 12, 1996 Revised manuscript received April 15, 1997 Accepted April 21, 1997X IE9607107

X Abstract published in Advance ACS Abstracts, June 15, 1997.