- Email: [email protected]
Modelling of liquid–liquid equilibria of mixed solvent electrolyte systems using the extended electrolyte NRTL
Fluid Phase Equilibria 171 Ž2000. 45–58 www.elsevier.nlrlocaterfluid
Modelling of liquid–liquid equilibria of mixed solvent electrolyte systems using the extended electrolyte NRTL Gerard H. van Bochove a , Gerard J.P. Krooshof b , Theo W. de Loos a, ) a
Laboratory for Applied Thermodynamics and Phase Equilibria, Delft UniÕersity of Technology, Julianalaan 136, 2628 BL Delft, Netherlands b DSM Research, R&D Department Base Chemicals and Technology, P.O. Box 18, 6160 MD Geleen, Netherlands Received 7 December 1999; accepted 17 March 2000
Abstract Liquid–liquid equilibria of mixed solvent electrolyte systems were correlated using an extended electrolyte NRTL model. The electrolyte NRTL expression for the activity coefficients has been modified by taking into account the derivatives to the solvent composition of the physical properties and by a new Brønsted–Guggenheim ŽBG. expression. In addition to some ternary mixed solvent electrolyte systems, the model has been applied to the quaternary systems that are of importance in the extraction process of ´-caprolactam: water q ´caprolactamq solventq ammonium sulfate ŽAS.. The liquid–liquid equilibria of the ternary and quaternary systems involved and the mean activity coefficients of the salt q water systems were used simultaneously to obtain the adjustable parameters. The results are compared to the original electrolyte NRTL of Chen. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Model; Liquid–liquid equilibria; Mixed solvent electrolyte solutions; Electrolyte NRTL; Caprolactam; Activity coefficient
1. Introduction In chemical engineering, liquid extraction plays an important role as a separation process. Simulation and design of extraction processes require a model that is able to describe the liquid–liquid equilibria involved. Several thermodynamic models have been developed to meet this requirement. However, the modelling becomes more complicated when electrolytes are present in the system. The charged species introduce a large deviation from ideality and have a large influence on the )
Corresponding author. Tel.: q31-15-278-8478; fax: q31-15-278-8047. E-mail address: [email protected] ŽT.W. de Loos..
0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 0 0 . 0 0 3 4 7 - 2
46
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
thermodynamic equilibrium. An example of an extraction process involving an electrolyte is the extraction of ´-caprolactam, the monomer of Nylon-6 w1x. In this process, liquid mixtures with water, ´-caprolactam, organic solvent and ammonium sulfate ŽAS. are present and liquid phase splitting occurs. The goal of this work is to find an appropriate model to describe this liquid demixing. Although several models for electrolyte solutions have been developed in the last years, most of these models are not able to give an accurate description of liquid–liquid equilibria of mixed solvent electrolyte systems. Since its publication in 1982, the electrolyte NRTL proposed by Chen et al. w2x based on the NRTL model of Renon and Prausnitz w3x, has been used successfully to represent thermodynamic properties of aqueous electrolyte solutions. The model has been extended for the description of multicomponent electrolyte solutions w4x and is able to give a reasonable representation of liquid–liquid equilibria of electrolyte solutions at low salt concentrations. Liu and Watanasiri w5x proposed the addition of a Brønsted–Guggenheim Ž BG. contribution to improve the performance of the electrolyte NRTL for liquid–liquid equilibria. Recently, two new modifications were published taking into account hydration and dissociation w6x and concentration dependency of the salt–water parameters w7x. Liu and Watanasiri w5x used their extended electrolyte NRTL for the correlation of four water q alcoholq salt systems measured by de Santis et al. w8x. However, we did not succeed in reproducing their results. Besides this, it appeared impossible to obtain a satisfactory correlation of systems without liquid demixing in one of the binary subsystems, like the water q caprolactam subsystem or the water q 1-propanol subsystem. Fig. 1 shows the result of our attempts to perform calculations with the model and parameters of Liu and Watanasiri w5x near the ternary critical point. It is remarkable that the NRTL parameters of Liu and Watanasiri w5x for the binary system waterq 1propanol do not predict a phase split in this binary. However, as soon as a very small amount of electrolyte is added, a very broad liquid–liquid region is calculated. We also had some problems correlating both liquid–liquid equilibria and mean ionic activity coefficients using the same solvent– Ž DH. parameter A, salt parameters. Liu and Watanasiri w5x used a fixed value for the Debye–Huckel ¨ which means that a constant dielectric constant is assumed over the full concentration range. This may be the reason that we found the model is unable to give a satisfactory description near a critical point.
Fig. 1. Liquid–liquid equilibrium for the system waterq1-propanolqNaCl at 258C. Data are in mass fractions. Experimental data w8x are represented by markers and solid lines. Dashed lines represent calculations with the extended electrolyte NRTL of Liu and Watanasiri w5x.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
47
However, if a mixing rule based on solvent fractions is used for the solution dielectric constant, this has to be accounted for in the derivation of the solvent activity coefficients. This is usually neglected. In this paper, we will study the effect on the representation of liquid–liquid equilibria by taking into account the derivatives of the solution properties with respect to the solvent mole fractions. Data sets of liquid–liquid equilibria of electrolyte and nonelectrolyte systems were used simultaneously in the regression to obtain a set of binary parameters that can be used for all the systems studied. In addition to this, mean ionic activity coefficients were correlated using the same set of parameters. Special attention was paid to the system waterq caprolactamq solventq AS.
2. Model description The extended electrolyte NRTL model for the excess Gibbs energy G E is built up from four contributions: a local composition NRTL contribution Ž NRTL. , a Pitzer–Debye–Huckel contribution ¨ ŽPDH., a Born contribution and a modified BG contribution. G E s G E ,NRTL q G E ,PDH q G E ,Born q G E ,BG
Ž1.
The local composition contribution of the electrolyte NRTL has been used without modifications. The extended DH equation proposed by Pitzer w9x and generalised to mixed solvents is used for the long-range contribution to the activity coefficients: G E ,PDH sy RT
žÝx /
4 A x Ix
n
r
n
( /
ln 1 q r I x
ž
Ž2.
where n refers to any component and: Ix s
1 2
Axs
Ý x i z i2
1 3
)
1000 Ms
Ž3.
(2p N d A
3r2
e2
ž /
Ž4.
´ kT
where i refers to ions. Ms is the mixed solvent molecular weight. For the solvent activity coefficient, a different equation was derived, including an additional contribution from the solvent composition dependence of the solution properties. This contribution is usually ignored in electrolyte thermodynamics, but must be included in a proper derivation of the solvent activity coefficient if a solvent composition-dependent dielectric constant is used in the model. If the model is used to describe liquid–liquid equilibria of water q organic solventq salt systems, the difference in the dielectric constants of the solvents will be large and a physically correct description will require the use of a solvent composition-dependent dielectric constant. lng jPDH s
2 A x Ix
(
1 q r Ix
q
4 nI x A x
r
( /
ln 1 q r I x
ž
1 2 Ms
M j y Ms
Ý nk k
3 E´
1 Ed y
q 2 d En j
2 ´ En j
Ž5.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
48
Fig. 2. PDH and Born contributions to the solvent activity coefficients in a mixture with equal mass fractions of water Ž1. and 1-propanol Ž2. at 258C Ž asg 2Born Žmodified., bsg 1PDH Žmodified., csg 1PDH sg 2PDH Žoriginal., dsg 1Born sg 2Born Žoriginal. s1, esg 2PDH Žmodified., f sg 2Born Žmodified...
where j and k refer to any solvent. For the Born contribution to the solvent activity coefficient, the same applies as for the PDH contribution: if the solvent composition dependence of the dielectric constant is correctly taken into account in the derivation, a contribution will appear with the derivatives of the dielectric constant to the solvent composition: G E ,Born
e2 s
RT
ž
1
2 kT ´
lng jBorn s y
e2
1 y
/Ý
´w
i
ri
n i z i2
1 E´
2 kT ´ 2 En j
x i z i2
Ý
ri
Ž6.
Ž7.
where j is a solvent and i refers to ions. In Fig. 2, the influence of the additional terms on the activity coefficients of the solvents is shown for the system water q 1-propanolq NaCl at 258C for a 1:1 mixture of water and 1-propanol. Liu and Watanasiri w5x added a BG contribution to the electrolyte NRTL for the modelling of liquid–liquid equilibria to account for inadequacies in the Born term and the PDH term: G E ,BG RT
s 100 Ý x k Mk
bca
k
T
xa xc .
Ž8.
In this work, initially, the BG contribution as used by Christensen et al. w10x was used: G E ,BG
1000
bca
Ý x k Mk
T
s RT
k
xa xc .
Ž9.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
49
Since it was found that the results for systems with a ternary critical point are improved using a different definition of this term, the contribution was changed and a solvent composition-dependent BG interaction parameter is proposed, using a Margules-like equation:
bca s b jk ,ca x j x k .
Ž 10.
The generalised equation for the excess Gibbs energy is now: G E ,BG
Ý Ý b jk ,ca x j x k
1000
j
s RT
Ý x k Mk
k)j
T
xa xc .
Ž 11.
k
Although it is recognised that the Born model and the PDH model are derived in the McMillan– Mayer ensemble and therefore have to be converted to the Lewis–Randall ensemble if used in combination with a Lewis–Randall model like the NRTL model, the conversion Ž as described by Friedman w11x. has not been used due to the complexity and the lack of knowledge on the effect of salt concentrations on the molar volumes of the solvents.
3. Modelling The flash calculation routine was obtained from Koak w12x and uses the Rachford–Rice procedure w13x with the Newton–Raphson method for the mole balances and the successive substitution method for the liquid–liquid equilibrium calculations. The NRTL parameters were regressed using a Levenberg–Marquardt routine with the following objective function: nd
FOBJ s Ý
nc
2
2
calc exp calc Ý Ž wnexp k y wn k . I q Ž wn k y wn k . II
k
.
Ž 12.
n
Mass fractions were used in the objective function instead of mole fractions since this was found to give better results. The Born radii in the model were taken from Rashin and Honig w14x. The PDH closest approach parameter was fixed at 14.9, as used by Chen et al. w2,4x. The solution dielectric constant is calculated from the pure solvent dielectric constants using a mass fraction based mixing rule:
´ s Ý wjX ´ j
Ž 13.
j
where wjX is the salt-free mass fraction of solvent j. The pure solvent dielectric constants were obtained from Lide w15x. The solution density is calculated from the pure solvent densities assuming ideal mixing:
Ý x j Mj ds
j
Ý x k Mkrd k k
.
Ž 14.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
50
Table 1 Average deviations in mole fractions Ž D x . and mass fractions Ž Dw . of the representation of some liquid–liquid equilibria of ternary mixed solvent electrolyte systems at 258C Presented model Waterq1-propanolqNaCl Waterq2-propanolqNaCl Waterq1-butanolqNaCl Waterq2-butanolqNaCl Waterq1-pentanolqNaCl Waterq1-propanolq1-butanol Waterqbutanone q NaCl Waterq1-butanolqKBr WaterqbutanoneqKBr Waterq1-butanolqKCl WaterqbutanoneqKCl
Chen’s model
Source
D x Ž%.
Dw Ž%.
D x Ž%.
Dw Ž%.
0.7 0.3 2.2 4.7 1.2 2.5 2.1 1.7 1.3 2.2 1.7
1.2 0.4 1.3 3.1 0.5 3.3 0.9 1.1 0.7 1.3 0.8
1.6 1.7 2.9 4.8 1.1 2.2 2.1 1.5 1.4 2.2 1.7
2.2 2.3 1.6 3.0 0.5 3.3 1.6 1.2 0.7 1.3 0.8
w8x w8x w8x w8x w19x w20x w21x w21x w21x w21x w21x
The pure solvent densities were taken from Perry w16x. All nonrandomness factors in the NRTL local composition model were fixed and not adjusted during the regressions. Best results were obtained when the nonrandomness factors were set at values of 0.10 Ž waterq salt., 0.20 Žsolvent or water q solvent. or 0.30 Žsolventq salt.. The accuracy of the results is represented by average deviations, as defined by Sørensen and Arlt w17x:
D xs
)
2
2
exp calc Ý Ý ½ Ž x kexpn y x kcalc n . I q Ž x k n y x k n . II 5
k
n
. Ž 15 . 2nc.nd Although this would have largely improved the results, tie-lines near the plait point were not excluded from the regressions to derive a more consistent and generally applicable set of parameters. 4. Results The model described in the previous section has been tested by correlating liquid–liquid equilibria and of some water q alcoholq salt systems and mean ionic activity coefficients of the water q salt Table 2 Mean ionic activity coefficients at 258C of some waterqsalt systems. Results were obtained by simultaneous regressions with the LLE presented in Table 1. Experimental data are from Robinson and Stokes w18x
WaterqNaCl WaterqKBr WaterqKCl WaterqŽNH 4 . 2 SO4
Presented model
Chen’s model
Dg Ž%.
Dg Ž%.
6.0 1.4 0.7 4.2
10.0 3.4 0.8 5.2
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
51
Table 3 Parameters for the systems in Table 1 and 2. NRTL nonrandomness factors were fixed at values of 0.10 Žwaterqsalt., 0.20 Žsolvent or waterqsolvent. or 0.30 Žsolventqsalt. Component 1 Water Water Water Water Water Water Water Water Water 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol Butanone 1-Propanol 1-Butanol Butanone 1-Butanol Butanone
Component 2 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol Butanone NaCl KCl KBr NaCl NaCl NaCl NaCl NaCl NaCl 1-Butanol KBr KBr KCl KCl
Presented model
Chen’s model
t 12
t 21
b 12
t 12
t 21
1.591 1.859 4.688 3.751 5.736 2.773 y11.12 y14.94 y11.07 y9.676 y11.59 y4.559 y4.501 y7.691 y5.719 y4.519 y7.608 y4.422 y10.86 y3.854
0.375 0.018 y0.763 y0.669 y0.522 0.250 y1.092 26.98 y0.552 30.00 10.37 1.418 3.059 1.401 0.626 3.088 28.19 y0.989 29.98 1.632
589.5 2008.5
1.250 0.585 4.897 3.845 5.562 2.777 y13.00 y14.43 y14.87 y7.875 y5.353 y8.202 y5.797 y10.70 y5.962 y4.716 y5.396 y4.248 y8.939 y4.019
0.489 0.595 y0.904 y0.758 y0.565 0.257 y1.971 23.07 y0.686 0.193 2.290 0.356 2.454 6.803 1.795 1.444 2.159 y0.226 6.719 1.937
systems involved. The mean ionic activity coefficients were obtained from Robinson and Stokes w18x and converted from molal to molar activity coefficients. If the model was found to give a good representation of the experimental data without a BG contribution, this parameter was fixed at zero. The presented model is compared to the original multicomponent electrolyte NRTL of Chen and Evans w4x. The results for this model have been obtained following the same procedure and with the
Fig. 3. Liquid–liquid equilibrium for the system waterq1-propanolqNaCl at 258C. Data are in mass fractions. Experimental data w8x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
52
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
Fig. 4. Liquid–liquid equilibrium for the system waterq1-propanolqNaCl at 258C. Data are in mass fractions. Experimental data w8x are represented by markers and solid lines. Dashed lines represent calculations with the electrolyte NRTL of Chen and Evans w4x.
Fig. 5. Liquid–liquid equilibrium for the system waterqbutanoneqKBr at 258C. Data are in mass fractions. Experimental data w21x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
Fig. 6. Liquid–liquid equilibrium for the system waterq1-butanolqKCl at 258C. Data are in mass fractions. Experimental data w21x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
53
Table 4 Liquid–liquid equilibria of ternary and quaternary systems with water, caprolactam, solvent and AS. Parameters were obtained by regression on the data sets measured by de Haan and Niemann w22x and Wijtkamp et al. w23x T Ž8C.
System Waterqbenzeneqcaprolactam
Waterq1-heptanolqcaprolactam
WaterqcaprolactamqAS
WaterqcaprolactamqbenzeneqAS
Waterqcaprolactamq1-heptanolqAS
20 40 60 20 40 60 20 20 20 30 40 40 50 20 40 60 20 40 60
Presented model
Chen’s model
D x Ž%.
Dw Ž%.
D x Ž%.
Dw Ž%.
1.4 1.8 2.3 2.4 1.6 2.7 0.9 1.0 0.5 0.2 0.8 0.6 1.8 1.7 1.1 1.6 1.7 1.8 1.8
1.9 2.2 2.0 3.8 2.8 4.3 2.6 2.7 1.6 0.7 1.6 1.0 2.8 1.8 1.0 2.0 2.1 1.3 1.5
1.0 1.5 2.0 2.2 1.9 3.1 1.6 1.7 1.2 0.4 0.9 0.8 1.6 2.1 1.2 1.7 1.8 1.7 1.7
1.7 2.0 1.5 3.8 3.1 4.4 4.8 4.8 3.2 1.0 2.7 1.7 2.6 2.8 1.4 2.2 2.5 1.5 1.7
Source w22x w22x w22x w23x w23x w23x w22x w24x w25x w26x w22x w27x w26x w22x w22x w22x w23x w23x w23x
same physical properties and the same regression and flash routine as the results for the modified model. Results for the water q alcoholq salt systems are given in Tables 1 and 2; the parameters obtained from the regressions are tabulated in Table 3. Some representative results have been plotted in Figs. 3–6. When the model was found to be able to represent the waterq alcoholq salt systems, the model was applied to the ternary and quaternary systems with and without salt of the system
Table 5 NRTL binary interaction parameters for the systems in Table 4. All nonrandomness factors Ž a . are fixed at 0.20, except those for solventqcaprolactam, which were fixed at 0.30 Component 1
Component 2
Water Water Water Benzene 1-Heptanol Water Benzene 1-Heptanol Caprolactam
Benzene 1-Heptanol Caprolactam Caprolactam Caprolactam ŽNH 4 . 2 SO4 ŽNH 4 . 2 SO4 ŽNH 4 . 2 SO4 ŽNH 4 . 2 SO4
Presented model
Chen’s model
A12
A 21
1383.5 1876.7 1171.0 y296.5 953.8 2888.4 4074.0 1620.9 576.0
696.3 y39.8 y649.4 153.5 y734.6 y1369.4 3232.9 4819.1 3598.2
b 12
29.65
A12
A 21
1596.8 2060.0 1155.9 y570.9 3794.3 2974.7 4048.4 1622.2 798.5
829.8 y55.6 y712.7 402.6 y803.7 y1400.4 4382.2 2363.8 3373.2
54
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
Fig. 7. Distribution curve Žin mass fractions. for caprolactam in the system waterqbenzeneqcaprolactam at 208C, 408C and 608C. Markers represent experimental values w22x, lines represent calculations using the NRTL model.
water q ´-caprolactamq solventq AS at 208C, 408C and 608C. For these systems, the built-in temperature dependence of the binary interaction parameters was used and the parameters were used as the difference in the binary interaction energies, divided by the universal gas constant: gi j y g j j Ai j ti j s s . Ž 16. RT T It was not possible to obtain a reasonable fit using the same values for the nonrandomness factors as described above. Therefore, all the nonrandomness factors were fixed at 0.20, except for the solventq caprolactam pairs, which were fixed at 0.30.
Fig. 8. Liquid–liquid equilibrium for the system waterqcaprolactamqAS at 408C. Data are in mass fractions. Experimental data w22x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
55
Fig. 9. Liquid–liquid equilibrium for the system waterqcaprolactamqAS at 408C. Data are in mass fractions. Experimental data w22x are represented by markers and solid lines. Dashed lines represent calculations with the electrolyte NRTL of Chen and Evans w4x.
The results for the systems with water q caprolactamq solventq AS are given in Table 4; the parameters used are given in Table 5. Fig. 7 gives the results for the salt-free system waterq benzene q caprolactam at 208C, 408C and 608C to show the ability of simultaneous fitting of electrolyte and nonelectrolyte systems. Figs. 8 and 9 give the ternary phase diagrams of the system water q caprolactamq AS at 408C, calculated with the model presented here and with the model of Chen and Evans w4x. These figures illustrate the performance of these models near the plait point. Calculated distribution curves for the system of water q caprolactamq benzene or 1-heptanolq AS at 408C are given in Figs. 10 and 11. It can be seen that the model performs well for the systems with benzene as the solvent, but somewhat less for these systems with 1-heptanol as the solvent.
Fig. 10. Distribution curve for caprolactam in the system waterqbenzeneqcaprolactamqAS at 408C at weight fractions of 0, 0.05, 0.10, 0.15 and 0.30 of AS in the aqueous phase. Markers represent experimental data w22x, lines represent calculations. Data are in mass fractions.
56
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
Fig. 11. Distribution curve for caprolactam in the system waterq1-heptanolqcaprolactamqAS at 408C at weight fractions of 0, 0.05, 0.10, 0.15 and 0.30 of AS in the aqueous phase. Markers represent experimental data w23x, lines represent calculations. Data are in mass fractions.
Attempts to get close to the ternary critical point in the calculations were successful for the modified extended electrolyte NRTL as discussed in this paper, but not for the electrolyte NRTL w4x of the electrolyte systems studied. This probably has to be accounted to the use of the correct derivatives or the use of the BG contribution in the modification of the extended electrolyte NRTL presented here. Chen et al. w6x suggested that the results could be improved by assuming partial dissociation. However, we found no significant improvement by assuming partial dissociation, despite the additional adjustable parameters required.
5. Discussion It may be concluded from the results presented in the tables that the modification of the electrolyte NRTL, which correctly takes into account the influence of the solvent composition on the electrostatic contribution to the solvent activity coefficient, can be used successfully to model liquid–liquid equilibria of mixed solvent electrolyte systems. More important, it can be applied for the modelling and prediction of the liquid–liquid equilibria that exist in an industrial extraction process like the recovery of caprolactam. The modified extended electrolyte NRTL produces only slightly better results than the electrolyte NRTL of Chen and Evans w4x, despite the physically more correct derivation of the solvent activity coefficients. It is more successful than the model of Chen and Evans w4x in performing calculations near the ternary critical point. For systems with demixing in the binary solventq solvent subsystem, the use of the original BG contribution, together with the correct derivatives to the solvent fractions in the solution properties, may provide a better representation of experimental data. Further research is still necessary. Improvements must be found both in the Ž electrolyte NRTL. local composition contribution and in the electrostatic contribution. Regarding the first approach,
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
57
many efforts have been made, but they usually result in an increase of the number of adjustable parameters or they cannot be extended to multicomponent mixtures. The electrostatic contribution may also need improvement. It is well known that the DH model can only be applied to dilute electrolyte solutions. Although the PDH equation is applicable to a broader range of concentrations, its use is still limited to moderate electrolyte concentrations. In the last years, much research has been done into the Mean Spherical Approximation ŽMSA. model w28x. This model explicitly takes into account the influence of ion size on the ionic activity coefficient. It seems that a model based on primitive or nonprimitive MSA theory is worth developing. List of Ax Ai j d e FOBJ gi j GE Ix k M n nc nd NA R r Ti w x zi
symbols Debye–Huckel parameter ¨ NRTL binary parameter Ž Ky1 . Density Žkg my3 . Electronic charge Žs 1.602 = 10y19 . ŽC. Objective function Binary interaction energy ŽJ moly1 . Excess Gibbs energy ŽJ moly1 . Ionic strength at mole base Boltzmann constant Žs 1.381 = 10y23 . ŽJ Ky1 . Molar weight Žkg kmoly1 . Mole number Žmol. Number of components Number of datapoints Avagadro’s number Žs 6.022 = 10 23 . Žmoly1 . Universal gas constant Žs 8.314. Ž J moly1 Ky1 . Born radius Žm. Temperature ŽK. Mass fraction Mole fraction Ionic charge
Greek a b g D ´ r ti j
letters Nonrandomness factor Brønsted–Guggenheim interaction parameter Ž K kg moly1 . Activity coefficient Average deviation Dielectric constant Žs 4p 8.85 = 10y12 ´r . ŽC 2 Jy1 my1 . Closest approach parameter NRTL binary interaction parameter
Subscripts and superscripts BG Brønsted–Guggenheim contribution Born Born contribution
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
58
calc exp i I, II j, k n NRTL PDH
Calculated value Experimental value Ion number Phase number Solvent number Component number Local composition contribution Pitzer–Debye–Huckel contribution ¨
Acknowledgements A grant from DSM Research is gratefully acknowledged.
References w1x A.J.F. Simons, N.F. Haasen, in: T.C. Lo, M.H.I. Baird, C. Hanson ŽEds.., Handbook of Solvent Extraction, Krieger, Malabar, 1991, pp. 557–566. w2x C.C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, AIChE J. 28 Ž4. Ž1982. 588–596. w3x H. Renon, J.M. Prausnitz, AIChE J. 14 Ž1. Ž1968. 135–144. w4x C.C. Chen, L.B. Evans, AIChE J. 32 Ž1986. 444–454. w5x Y. Liu, S. Watanasiri, Fluid Phase Equilib. 116 Ž1996. 193–200. w6x C.C. Chen, P.M. Mathias, H. Orbey, AIChE J. 45 Ž7. Ž1999. 1576–1586. w7x Abovsky, V.Y. Liu, S. Watanasiri, Fluid Phase Equilib. 150–151 Ž1998. 277–286. w8x R. de Santis, L. de Marelli, P.N. Muscetta, Chem. Eng. J. 11 Ž1976. 207–214. w9x K.S. Pitzer, J. Am. Chem. Soc. 102 Ž9. Ž1980. 2902–2906. w10x C. Christensen, B. Sander, A. Fredenslund, P. Rasmussen, Fluid Phase Equilib. 13 Ž1983. 297–309. w11x H.L. Friedman, J. Sol. Chem. 1 Ž5. Ž1972. 387–417. w12x N. Koak, Some computational and experimental aspects of polymer solution phase behaviour, PhD thesis, Calgary, 1997. w13x S.M. Walas, Phase Equilibria in Chemical Engineering, 1984, Stoneham. w14x A.A. Rashin, B. Honig, J. Phys. Chem. 89 Ž26. Ž1985. 5588. w15x R. Lide ŽEd.., CRC Handbook of Chemistry and Physics, 76th edn., 1995, Boca Raton. w16x R. Perry ŽEd.., Perry’s Chemical Engineer’s Handbook, 7th edn., 1997, New York. w17x J.M. Sørensen, W. Arlt, Liquid–liquid data equilibrium collection, DECHEMA Ž1980. Frankfurt. w18x R.A. Robinson, R.H. Stokes, Electrolyte Solutions, 1959, London. w19x V. Gomis, F. Ruiz, N. Boluda, D. Saquete, J. Chem. Eng. Data 44 Ž1999. 918–920. w20x V. Gomis, F. Ruiz, M. Ramos-Nofuentes, M.J. Fernandez-Torres, Fluid Phase Equilib. 149 Ž1998. 139–145. ´ w21x Z. Li, Y. Tang, Y. Liu, Y. Li, Fluid Phase Equilib. 103 Ž1995. 143. w22x A.B. de Haan, S. Niemann, in: Proceedings International Solvent Extraction Conference ’99, 1999, Žin press.. w23x M. Wijtkamp, G.H. van Bochove, Th.W. de Loos, S. Niemann, Fluid Phase Equilib. 158–160 Ž1999. 939–947. w24x I.G. Shubtsova, N.I. Nikurashina, S.K. Rybalov, Russ. J. Phys. Chem. 49 Ž1. Ž1975. 35. w25x K. Tettimanti, M. Nogradi, Period. Polytech. 5 Ž1. Ž1960. 15. w26x S. Vecera, J. Sladky, Coll. Czech. Chem. Commun. 20 Ž1955. 557. w27x A.J. Gucwa, K. Makal, J. Azymczak, Przem. Chem. 55 Ž8. Ž1976. 420. w28x L. Blum, J.S. Hoye, J. Phys. Chem. 81 Ž13. Ž1977. 1311.
Modelling of liquid–liquid equilibria of mixed solvent electrolyte systems using the extended electrolyte NRTL Gerard H. van Bochove a , Gerard J.P. Krooshof b , Theo W. de Loos a, ) a
Laboratory for Applied Thermodynamics and Phase Equilibria, Delft UniÕersity of Technology, Julianalaan 136, 2628 BL Delft, Netherlands b DSM Research, R&D Department Base Chemicals and Technology, P.O. Box 18, 6160 MD Geleen, Netherlands Received 7 December 1999; accepted 17 March 2000
Abstract Liquid–liquid equilibria of mixed solvent electrolyte systems were correlated using an extended electrolyte NRTL model. The electrolyte NRTL expression for the activity coefficients has been modified by taking into account the derivatives to the solvent composition of the physical properties and by a new Brønsted–Guggenheim ŽBG. expression. In addition to some ternary mixed solvent electrolyte systems, the model has been applied to the quaternary systems that are of importance in the extraction process of ´-caprolactam: water q ´caprolactamq solventq ammonium sulfate ŽAS.. The liquid–liquid equilibria of the ternary and quaternary systems involved and the mean activity coefficients of the salt q water systems were used simultaneously to obtain the adjustable parameters. The results are compared to the original electrolyte NRTL of Chen. q 2000 Elsevier Science B.V. All rights reserved. Keywords: Model; Liquid–liquid equilibria; Mixed solvent electrolyte solutions; Electrolyte NRTL; Caprolactam; Activity coefficient
1. Introduction In chemical engineering, liquid extraction plays an important role as a separation process. Simulation and design of extraction processes require a model that is able to describe the liquid–liquid equilibria involved. Several thermodynamic models have been developed to meet this requirement. However, the modelling becomes more complicated when electrolytes are present in the system. The charged species introduce a large deviation from ideality and have a large influence on the )
Corresponding author. Tel.: q31-15-278-8478; fax: q31-15-278-8047. E-mail address: [email protected] ŽT.W. de Loos..
0378-3812r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 Ž 0 0 . 0 0 3 4 7 - 2
46
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
thermodynamic equilibrium. An example of an extraction process involving an electrolyte is the extraction of ´-caprolactam, the monomer of Nylon-6 w1x. In this process, liquid mixtures with water, ´-caprolactam, organic solvent and ammonium sulfate ŽAS. are present and liquid phase splitting occurs. The goal of this work is to find an appropriate model to describe this liquid demixing. Although several models for electrolyte solutions have been developed in the last years, most of these models are not able to give an accurate description of liquid–liquid equilibria of mixed solvent electrolyte systems. Since its publication in 1982, the electrolyte NRTL proposed by Chen et al. w2x based on the NRTL model of Renon and Prausnitz w3x, has been used successfully to represent thermodynamic properties of aqueous electrolyte solutions. The model has been extended for the description of multicomponent electrolyte solutions w4x and is able to give a reasonable representation of liquid–liquid equilibria of electrolyte solutions at low salt concentrations. Liu and Watanasiri w5x proposed the addition of a Brønsted–Guggenheim Ž BG. contribution to improve the performance of the electrolyte NRTL for liquid–liquid equilibria. Recently, two new modifications were published taking into account hydration and dissociation w6x and concentration dependency of the salt–water parameters w7x. Liu and Watanasiri w5x used their extended electrolyte NRTL for the correlation of four water q alcoholq salt systems measured by de Santis et al. w8x. However, we did not succeed in reproducing their results. Besides this, it appeared impossible to obtain a satisfactory correlation of systems without liquid demixing in one of the binary subsystems, like the water q caprolactam subsystem or the water q 1-propanol subsystem. Fig. 1 shows the result of our attempts to perform calculations with the model and parameters of Liu and Watanasiri w5x near the ternary critical point. It is remarkable that the NRTL parameters of Liu and Watanasiri w5x for the binary system waterq 1propanol do not predict a phase split in this binary. However, as soon as a very small amount of electrolyte is added, a very broad liquid–liquid region is calculated. We also had some problems correlating both liquid–liquid equilibria and mean ionic activity coefficients using the same solvent– Ž DH. parameter A, salt parameters. Liu and Watanasiri w5x used a fixed value for the Debye–Huckel ¨ which means that a constant dielectric constant is assumed over the full concentration range. This may be the reason that we found the model is unable to give a satisfactory description near a critical point.
Fig. 1. Liquid–liquid equilibrium for the system waterq1-propanolqNaCl at 258C. Data are in mass fractions. Experimental data w8x are represented by markers and solid lines. Dashed lines represent calculations with the extended electrolyte NRTL of Liu and Watanasiri w5x.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
47
However, if a mixing rule based on solvent fractions is used for the solution dielectric constant, this has to be accounted for in the derivation of the solvent activity coefficients. This is usually neglected. In this paper, we will study the effect on the representation of liquid–liquid equilibria by taking into account the derivatives of the solution properties with respect to the solvent mole fractions. Data sets of liquid–liquid equilibria of electrolyte and nonelectrolyte systems were used simultaneously in the regression to obtain a set of binary parameters that can be used for all the systems studied. In addition to this, mean ionic activity coefficients were correlated using the same set of parameters. Special attention was paid to the system waterq caprolactamq solventq AS.
2. Model description The extended electrolyte NRTL model for the excess Gibbs energy G E is built up from four contributions: a local composition NRTL contribution Ž NRTL. , a Pitzer–Debye–Huckel contribution ¨ ŽPDH., a Born contribution and a modified BG contribution. G E s G E ,NRTL q G E ,PDH q G E ,Born q G E ,BG
Ž1.
The local composition contribution of the electrolyte NRTL has been used without modifications. The extended DH equation proposed by Pitzer w9x and generalised to mixed solvents is used for the long-range contribution to the activity coefficients: G E ,PDH sy RT
žÝx /
4 A x Ix
n
r
n
( /
ln 1 q r I x
ž
Ž2.
where n refers to any component and: Ix s
1 2
Axs
Ý x i z i2
1 3
)
1000 Ms
Ž3.
(2p N d A
3r2
e2
ž /
Ž4.
´ kT
where i refers to ions. Ms is the mixed solvent molecular weight. For the solvent activity coefficient, a different equation was derived, including an additional contribution from the solvent composition dependence of the solution properties. This contribution is usually ignored in electrolyte thermodynamics, but must be included in a proper derivation of the solvent activity coefficient if a solvent composition-dependent dielectric constant is used in the model. If the model is used to describe liquid–liquid equilibria of water q organic solventq salt systems, the difference in the dielectric constants of the solvents will be large and a physically correct description will require the use of a solvent composition-dependent dielectric constant. lng jPDH s
2 A x Ix
(
1 q r Ix
q
4 nI x A x
r
( /
ln 1 q r I x
ž
1 2 Ms
M j y Ms
Ý nk k
3 E´
1 Ed y
q 2 d En j
2 ´ En j
Ž5.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
48
Fig. 2. PDH and Born contributions to the solvent activity coefficients in a mixture with equal mass fractions of water Ž1. and 1-propanol Ž2. at 258C Ž asg 2Born Žmodified., bsg 1PDH Žmodified., csg 1PDH sg 2PDH Žoriginal., dsg 1Born sg 2Born Žoriginal. s1, esg 2PDH Žmodified., f sg 2Born Žmodified...
where j and k refer to any solvent. For the Born contribution to the solvent activity coefficient, the same applies as for the PDH contribution: if the solvent composition dependence of the dielectric constant is correctly taken into account in the derivation, a contribution will appear with the derivatives of the dielectric constant to the solvent composition: G E ,Born
e2 s
RT
ž
1
2 kT ´
lng jBorn s y
e2
1 y
/Ý
´w
i
ri
n i z i2
1 E´
2 kT ´ 2 En j
x i z i2
Ý
ri
Ž6.
Ž7.
where j is a solvent and i refers to ions. In Fig. 2, the influence of the additional terms on the activity coefficients of the solvents is shown for the system water q 1-propanolq NaCl at 258C for a 1:1 mixture of water and 1-propanol. Liu and Watanasiri w5x added a BG contribution to the electrolyte NRTL for the modelling of liquid–liquid equilibria to account for inadequacies in the Born term and the PDH term: G E ,BG RT
s 100 Ý x k Mk
bca
k
T
xa xc .
Ž8.
In this work, initially, the BG contribution as used by Christensen et al. w10x was used: G E ,BG
1000
bca
Ý x k Mk
T
s RT
k
xa xc .
Ž9.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
49
Since it was found that the results for systems with a ternary critical point are improved using a different definition of this term, the contribution was changed and a solvent composition-dependent BG interaction parameter is proposed, using a Margules-like equation:
bca s b jk ,ca x j x k .
Ž 10.
The generalised equation for the excess Gibbs energy is now: G E ,BG
Ý Ý b jk ,ca x j x k
1000
j
s RT
Ý x k Mk
k)j
T
xa xc .
Ž 11.
k
Although it is recognised that the Born model and the PDH model are derived in the McMillan– Mayer ensemble and therefore have to be converted to the Lewis–Randall ensemble if used in combination with a Lewis–Randall model like the NRTL model, the conversion Ž as described by Friedman w11x. has not been used due to the complexity and the lack of knowledge on the effect of salt concentrations on the molar volumes of the solvents.
3. Modelling The flash calculation routine was obtained from Koak w12x and uses the Rachford–Rice procedure w13x with the Newton–Raphson method for the mole balances and the successive substitution method for the liquid–liquid equilibrium calculations. The NRTL parameters were regressed using a Levenberg–Marquardt routine with the following objective function: nd
FOBJ s Ý
nc
2
2
calc exp calc Ý Ž wnexp k y wn k . I q Ž wn k y wn k . II
k
.
Ž 12.
n
Mass fractions were used in the objective function instead of mole fractions since this was found to give better results. The Born radii in the model were taken from Rashin and Honig w14x. The PDH closest approach parameter was fixed at 14.9, as used by Chen et al. w2,4x. The solution dielectric constant is calculated from the pure solvent dielectric constants using a mass fraction based mixing rule:
´ s Ý wjX ´ j
Ž 13.
j
where wjX is the salt-free mass fraction of solvent j. The pure solvent dielectric constants were obtained from Lide w15x. The solution density is calculated from the pure solvent densities assuming ideal mixing:
Ý x j Mj ds
j
Ý x k Mkrd k k
.
Ž 14.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
50
Table 1 Average deviations in mole fractions Ž D x . and mass fractions Ž Dw . of the representation of some liquid–liquid equilibria of ternary mixed solvent electrolyte systems at 258C Presented model Waterq1-propanolqNaCl Waterq2-propanolqNaCl Waterq1-butanolqNaCl Waterq2-butanolqNaCl Waterq1-pentanolqNaCl Waterq1-propanolq1-butanol Waterqbutanone q NaCl Waterq1-butanolqKBr WaterqbutanoneqKBr Waterq1-butanolqKCl WaterqbutanoneqKCl
Chen’s model
Source
D x Ž%.
Dw Ž%.
D x Ž%.
Dw Ž%.
0.7 0.3 2.2 4.7 1.2 2.5 2.1 1.7 1.3 2.2 1.7
1.2 0.4 1.3 3.1 0.5 3.3 0.9 1.1 0.7 1.3 0.8
1.6 1.7 2.9 4.8 1.1 2.2 2.1 1.5 1.4 2.2 1.7
2.2 2.3 1.6 3.0 0.5 3.3 1.6 1.2 0.7 1.3 0.8
w8x w8x w8x w8x w19x w20x w21x w21x w21x w21x w21x
The pure solvent densities were taken from Perry w16x. All nonrandomness factors in the NRTL local composition model were fixed and not adjusted during the regressions. Best results were obtained when the nonrandomness factors were set at values of 0.10 Ž waterq salt., 0.20 Žsolvent or water q solvent. or 0.30 Žsolventq salt.. The accuracy of the results is represented by average deviations, as defined by Sørensen and Arlt w17x:
D xs
)
2
2
exp calc Ý Ý ½ Ž x kexpn y x kcalc n . I q Ž x k n y x k n . II 5
k
n
. Ž 15 . 2nc.nd Although this would have largely improved the results, tie-lines near the plait point were not excluded from the regressions to derive a more consistent and generally applicable set of parameters. 4. Results The model described in the previous section has been tested by correlating liquid–liquid equilibria and of some water q alcoholq salt systems and mean ionic activity coefficients of the water q salt Table 2 Mean ionic activity coefficients at 258C of some waterqsalt systems. Results were obtained by simultaneous regressions with the LLE presented in Table 1. Experimental data are from Robinson and Stokes w18x
WaterqNaCl WaterqKBr WaterqKCl WaterqŽNH 4 . 2 SO4
Presented model
Chen’s model
Dg Ž%.
Dg Ž%.
6.0 1.4 0.7 4.2
10.0 3.4 0.8 5.2
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
51
Table 3 Parameters for the systems in Table 1 and 2. NRTL nonrandomness factors were fixed at values of 0.10 Žwaterqsalt., 0.20 Žsolvent or waterqsolvent. or 0.30 Žsolventqsalt. Component 1 Water Water Water Water Water Water Water Water Water 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol Butanone 1-Propanol 1-Butanol Butanone 1-Butanol Butanone
Component 2 1-Propanol 2-Propanol 1-Butanol 2-Butanol 1-Pentanol Butanone NaCl KCl KBr NaCl NaCl NaCl NaCl NaCl NaCl 1-Butanol KBr KBr KCl KCl
Presented model
Chen’s model
t 12
t 21
b 12
t 12
t 21
1.591 1.859 4.688 3.751 5.736 2.773 y11.12 y14.94 y11.07 y9.676 y11.59 y4.559 y4.501 y7.691 y5.719 y4.519 y7.608 y4.422 y10.86 y3.854
0.375 0.018 y0.763 y0.669 y0.522 0.250 y1.092 26.98 y0.552 30.00 10.37 1.418 3.059 1.401 0.626 3.088 28.19 y0.989 29.98 1.632
589.5 2008.5
1.250 0.585 4.897 3.845 5.562 2.777 y13.00 y14.43 y14.87 y7.875 y5.353 y8.202 y5.797 y10.70 y5.962 y4.716 y5.396 y4.248 y8.939 y4.019
0.489 0.595 y0.904 y0.758 y0.565 0.257 y1.971 23.07 y0.686 0.193 2.290 0.356 2.454 6.803 1.795 1.444 2.159 y0.226 6.719 1.937
systems involved. The mean ionic activity coefficients were obtained from Robinson and Stokes w18x and converted from molal to molar activity coefficients. If the model was found to give a good representation of the experimental data without a BG contribution, this parameter was fixed at zero. The presented model is compared to the original multicomponent electrolyte NRTL of Chen and Evans w4x. The results for this model have been obtained following the same procedure and with the
Fig. 3. Liquid–liquid equilibrium for the system waterq1-propanolqNaCl at 258C. Data are in mass fractions. Experimental data w8x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
52
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
Fig. 4. Liquid–liquid equilibrium for the system waterq1-propanolqNaCl at 258C. Data are in mass fractions. Experimental data w8x are represented by markers and solid lines. Dashed lines represent calculations with the electrolyte NRTL of Chen and Evans w4x.
Fig. 5. Liquid–liquid equilibrium for the system waterqbutanoneqKBr at 258C. Data are in mass fractions. Experimental data w21x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
Fig. 6. Liquid–liquid equilibrium for the system waterq1-butanolqKCl at 258C. Data are in mass fractions. Experimental data w21x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
53
Table 4 Liquid–liquid equilibria of ternary and quaternary systems with water, caprolactam, solvent and AS. Parameters were obtained by regression on the data sets measured by de Haan and Niemann w22x and Wijtkamp et al. w23x T Ž8C.
System Waterqbenzeneqcaprolactam
Waterq1-heptanolqcaprolactam
WaterqcaprolactamqAS
WaterqcaprolactamqbenzeneqAS
Waterqcaprolactamq1-heptanolqAS
20 40 60 20 40 60 20 20 20 30 40 40 50 20 40 60 20 40 60
Presented model
Chen’s model
D x Ž%.
Dw Ž%.
D x Ž%.
Dw Ž%.
1.4 1.8 2.3 2.4 1.6 2.7 0.9 1.0 0.5 0.2 0.8 0.6 1.8 1.7 1.1 1.6 1.7 1.8 1.8
1.9 2.2 2.0 3.8 2.8 4.3 2.6 2.7 1.6 0.7 1.6 1.0 2.8 1.8 1.0 2.0 2.1 1.3 1.5
1.0 1.5 2.0 2.2 1.9 3.1 1.6 1.7 1.2 0.4 0.9 0.8 1.6 2.1 1.2 1.7 1.8 1.7 1.7
1.7 2.0 1.5 3.8 3.1 4.4 4.8 4.8 3.2 1.0 2.7 1.7 2.6 2.8 1.4 2.2 2.5 1.5 1.7
Source w22x w22x w22x w23x w23x w23x w22x w24x w25x w26x w22x w27x w26x w22x w22x w22x w23x w23x w23x
same physical properties and the same regression and flash routine as the results for the modified model. Results for the water q alcoholq salt systems are given in Tables 1 and 2; the parameters obtained from the regressions are tabulated in Table 3. Some representative results have been plotted in Figs. 3–6. When the model was found to be able to represent the waterq alcoholq salt systems, the model was applied to the ternary and quaternary systems with and without salt of the system
Table 5 NRTL binary interaction parameters for the systems in Table 4. All nonrandomness factors Ž a . are fixed at 0.20, except those for solventqcaprolactam, which were fixed at 0.30 Component 1
Component 2
Water Water Water Benzene 1-Heptanol Water Benzene 1-Heptanol Caprolactam
Benzene 1-Heptanol Caprolactam Caprolactam Caprolactam ŽNH 4 . 2 SO4 ŽNH 4 . 2 SO4 ŽNH 4 . 2 SO4 ŽNH 4 . 2 SO4
Presented model
Chen’s model
A12
A 21
1383.5 1876.7 1171.0 y296.5 953.8 2888.4 4074.0 1620.9 576.0
696.3 y39.8 y649.4 153.5 y734.6 y1369.4 3232.9 4819.1 3598.2
b 12
29.65
A12
A 21
1596.8 2060.0 1155.9 y570.9 3794.3 2974.7 4048.4 1622.2 798.5
829.8 y55.6 y712.7 402.6 y803.7 y1400.4 4382.2 2363.8 3373.2
54
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
Fig. 7. Distribution curve Žin mass fractions. for caprolactam in the system waterqbenzeneqcaprolactam at 208C, 408C and 608C. Markers represent experimental values w22x, lines represent calculations using the NRTL model.
water q ´-caprolactamq solventq AS at 208C, 408C and 608C. For these systems, the built-in temperature dependence of the binary interaction parameters was used and the parameters were used as the difference in the binary interaction energies, divided by the universal gas constant: gi j y g j j Ai j ti j s s . Ž 16. RT T It was not possible to obtain a reasonable fit using the same values for the nonrandomness factors as described above. Therefore, all the nonrandomness factors were fixed at 0.20, except for the solventq caprolactam pairs, which were fixed at 0.30.
Fig. 8. Liquid–liquid equilibrium for the system waterqcaprolactamqAS at 408C. Data are in mass fractions. Experimental data w22x are represented by markers and solid lines. Dashed lines represent calculations with the modified extended electrolyte NRTL.
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
55
Fig. 9. Liquid–liquid equilibrium for the system waterqcaprolactamqAS at 408C. Data are in mass fractions. Experimental data w22x are represented by markers and solid lines. Dashed lines represent calculations with the electrolyte NRTL of Chen and Evans w4x.
The results for the systems with water q caprolactamq solventq AS are given in Table 4; the parameters used are given in Table 5. Fig. 7 gives the results for the salt-free system waterq benzene q caprolactam at 208C, 408C and 608C to show the ability of simultaneous fitting of electrolyte and nonelectrolyte systems. Figs. 8 and 9 give the ternary phase diagrams of the system water q caprolactamq AS at 408C, calculated with the model presented here and with the model of Chen and Evans w4x. These figures illustrate the performance of these models near the plait point. Calculated distribution curves for the system of water q caprolactamq benzene or 1-heptanolq AS at 408C are given in Figs. 10 and 11. It can be seen that the model performs well for the systems with benzene as the solvent, but somewhat less for these systems with 1-heptanol as the solvent.
Fig. 10. Distribution curve for caprolactam in the system waterqbenzeneqcaprolactamqAS at 408C at weight fractions of 0, 0.05, 0.10, 0.15 and 0.30 of AS in the aqueous phase. Markers represent experimental data w22x, lines represent calculations. Data are in mass fractions.
56
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
Fig. 11. Distribution curve for caprolactam in the system waterq1-heptanolqcaprolactamqAS at 408C at weight fractions of 0, 0.05, 0.10, 0.15 and 0.30 of AS in the aqueous phase. Markers represent experimental data w23x, lines represent calculations. Data are in mass fractions.
Attempts to get close to the ternary critical point in the calculations were successful for the modified extended electrolyte NRTL as discussed in this paper, but not for the electrolyte NRTL w4x of the electrolyte systems studied. This probably has to be accounted to the use of the correct derivatives or the use of the BG contribution in the modification of the extended electrolyte NRTL presented here. Chen et al. w6x suggested that the results could be improved by assuming partial dissociation. However, we found no significant improvement by assuming partial dissociation, despite the additional adjustable parameters required.
5. Discussion It may be concluded from the results presented in the tables that the modification of the electrolyte NRTL, which correctly takes into account the influence of the solvent composition on the electrostatic contribution to the solvent activity coefficient, can be used successfully to model liquid–liquid equilibria of mixed solvent electrolyte systems. More important, it can be applied for the modelling and prediction of the liquid–liquid equilibria that exist in an industrial extraction process like the recovery of caprolactam. The modified extended electrolyte NRTL produces only slightly better results than the electrolyte NRTL of Chen and Evans w4x, despite the physically more correct derivation of the solvent activity coefficients. It is more successful than the model of Chen and Evans w4x in performing calculations near the ternary critical point. For systems with demixing in the binary solventq solvent subsystem, the use of the original BG contribution, together with the correct derivatives to the solvent fractions in the solution properties, may provide a better representation of experimental data. Further research is still necessary. Improvements must be found both in the Ž electrolyte NRTL. local composition contribution and in the electrostatic contribution. Regarding the first approach,
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
57
many efforts have been made, but they usually result in an increase of the number of adjustable parameters or they cannot be extended to multicomponent mixtures. The electrostatic contribution may also need improvement. It is well known that the DH model can only be applied to dilute electrolyte solutions. Although the PDH equation is applicable to a broader range of concentrations, its use is still limited to moderate electrolyte concentrations. In the last years, much research has been done into the Mean Spherical Approximation ŽMSA. model w28x. This model explicitly takes into account the influence of ion size on the ionic activity coefficient. It seems that a model based on primitive or nonprimitive MSA theory is worth developing. List of Ax Ai j d e FOBJ gi j GE Ix k M n nc nd NA R r Ti w x zi
symbols Debye–Huckel parameter ¨ NRTL binary parameter Ž Ky1 . Density Žkg my3 . Electronic charge Žs 1.602 = 10y19 . ŽC. Objective function Binary interaction energy ŽJ moly1 . Excess Gibbs energy ŽJ moly1 . Ionic strength at mole base Boltzmann constant Žs 1.381 = 10y23 . ŽJ Ky1 . Molar weight Žkg kmoly1 . Mole number Žmol. Number of components Number of datapoints Avagadro’s number Žs 6.022 = 10 23 . Žmoly1 . Universal gas constant Žs 8.314. Ž J moly1 Ky1 . Born radius Žm. Temperature ŽK. Mass fraction Mole fraction Ionic charge
Greek a b g D ´ r ti j
letters Nonrandomness factor Brønsted–Guggenheim interaction parameter Ž K kg moly1 . Activity coefficient Average deviation Dielectric constant Žs 4p 8.85 = 10y12 ´r . ŽC 2 Jy1 my1 . Closest approach parameter NRTL binary interaction parameter
Subscripts and superscripts BG Brønsted–Guggenheim contribution Born Born contribution
G.H. Õan BochoÕe et al.r Fluid Phase Equilibria 171 (2000) 45–58
58
calc exp i I, II j, k n NRTL PDH
Calculated value Experimental value Ion number Phase number Solvent number Component number Local composition contribution Pitzer–Debye–Huckel contribution ¨
Acknowledgements A grant from DSM Research is gratefully acknowledged.
References w1x A.J.F. Simons, N.F. Haasen, in: T.C. Lo, M.H.I. Baird, C. Hanson ŽEds.., Handbook of Solvent Extraction, Krieger, Malabar, 1991, pp. 557–566. w2x C.C. Chen, H.I. Britt, J.F. Boston, L.B. Evans, AIChE J. 28 Ž4. Ž1982. 588–596. w3x H. Renon, J.M. Prausnitz, AIChE J. 14 Ž1. Ž1968. 135–144. w4x C.C. Chen, L.B. Evans, AIChE J. 32 Ž1986. 444–454. w5x Y. Liu, S. Watanasiri, Fluid Phase Equilib. 116 Ž1996. 193–200. w6x C.C. Chen, P.M. Mathias, H. Orbey, AIChE J. 45 Ž7. Ž1999. 1576–1586. w7x Abovsky, V.Y. Liu, S. Watanasiri, Fluid Phase Equilib. 150–151 Ž1998. 277–286. w8x R. de Santis, L. de Marelli, P.N. Muscetta, Chem. Eng. J. 11 Ž1976. 207–214. w9x K.S. Pitzer, J. Am. Chem. Soc. 102 Ž9. Ž1980. 2902–2906. w10x C. Christensen, B. Sander, A. Fredenslund, P. Rasmussen, Fluid Phase Equilib. 13 Ž1983. 297–309. w11x H.L. Friedman, J. Sol. Chem. 1 Ž5. Ž1972. 387–417. w12x N. Koak, Some computational and experimental aspects of polymer solution phase behaviour, PhD thesis, Calgary, 1997. w13x S.M. Walas, Phase Equilibria in Chemical Engineering, 1984, Stoneham. w14x A.A. Rashin, B. Honig, J. Phys. Chem. 89 Ž26. Ž1985. 5588. w15x R. Lide ŽEd.., CRC Handbook of Chemistry and Physics, 76th edn., 1995, Boca Raton. w16x R. Perry ŽEd.., Perry’s Chemical Engineer’s Handbook, 7th edn., 1997, New York. w17x J.M. Sørensen, W. Arlt, Liquid–liquid data equilibrium collection, DECHEMA Ž1980. Frankfurt. w18x R.A. Robinson, R.H. Stokes, Electrolyte Solutions, 1959, London. w19x V. Gomis, F. Ruiz, N. Boluda, D. Saquete, J. Chem. Eng. Data 44 Ž1999. 918–920. w20x V. Gomis, F. Ruiz, M. Ramos-Nofuentes, M.J. Fernandez-Torres, Fluid Phase Equilib. 149 Ž1998. 139–145. ´ w21x Z. Li, Y. Tang, Y. Liu, Y. Li, Fluid Phase Equilib. 103 Ž1995. 143. w22x A.B. de Haan, S. Niemann, in: Proceedings International Solvent Extraction Conference ’99, 1999, Žin press.. w23x M. Wijtkamp, G.H. van Bochove, Th.W. de Loos, S. Niemann, Fluid Phase Equilib. 158–160 Ž1999. 939–947. w24x I.G. Shubtsova, N.I. Nikurashina, S.K. Rybalov, Russ. J. Phys. Chem. 49 Ž1. Ž1975. 35. w25x K. Tettimanti, M. Nogradi, Period. Polytech. 5 Ž1. Ž1960. 15. w26x S. Vecera, J. Sladky, Coll. Czech. Chem. Commun. 20 Ž1955. 557. w27x A.J. Gucwa, K. Makal, J. Azymczak, Przem. Chem. 55 Ž8. Ž1976. 420. w28x L. Blum, J.S. Hoye, J. Phys. Chem. 81 Ž13. Ž1977. 1311.