0 0
Prediction of Liquid-Liquid Phase Equilibria
0 0
0
E. N. PENNINGTON AND S. J. MARWIL Chemical Engineering Division, Phillips Pefroleum Co., Barffesvilfe, Okla.
T
I
HE separation of hydrocarbon mixtures into various components and fractions is one of the major problems confronting the chemical engineer in the petroleum and petrochemical industries. There are in general use many means of effecting these separations. Among these is liquid-liquid extraction which effects separations by distribution of the components between two liquid phases. In many industrial applications, hydrocarbon mixtures may be separated by liquid-liquid extraction where separation by distillation or absorption is difficult or impossible. As an engineering practice in the process industries, liquid-liquid extraction is relatively new and is seldom used for precise separations. Although there are many commercial extraction processes in use in the petroleum industry in the refining of lube oils and the upgrading of distillates, these processes do not produce sharp separations. In order to develop liquid-liquid extraction as a process for making precise separations in the petroleum industry, a large amount of liquid-liquid phase equilibrium data is required. But the present knowledge of phase equilibrium relationships in nonideal hydrocarbon-solvent systems is inadequate for the solution of most problems involving separation of components by liquid-liquid extraction. The relatively small amount of data in the literature, with exception of a few quaternary systems, is confined to binary and ternary syatems. Equilibrium data for more complex systems are practically nonexistent. The time required for experimental determination of component distribution in liquid-liquid systems to provide sufficient data for the solution of even a limited number of problems makes a convenient means of predicting equilibrium data very desirable. In the past, this problem of predicting component distribution has been studied by the rather unsatisfactory methods of empirical extrapolation and interpolation of existing data. Treybal has reviewed the work done by these methods (9). A more fundamental approach to the problem is possible through the concepts of thermodynamics. The development of the thermodynamic approach has been presented by Carlson and Colburn ( I ) , Treybal (Q), and Wohl (11). Although these relationships are available, they are complicated and laborious to use, even for ternary systems. The purpose of this paper is to present a relatively simple method of predicting component distribution between two liquid phases in equilibrium and to prove its applicability to hydrocarbon-solvent systems. Although the method is based on the thermodynamic concept of activity, it is not entirely rigorous. However, it will be shown that the predicted data are sufficiently accurate for engineering calculations. Also the ternary equilibrium data are quickly calculated from mutual solubility data which are relatively easily determined by experimental means. Development
of Equations
Liquid-liquid extraction is a diffusional process in which separation is effected by distribution of the components between two liquid phases. The study of component distribution between two liquid phases under equilibrium conditions may be a p
proached through the criteria for thermodynamic equilibria. These considerations require that when two immiscible phases are in equilibrium, the activity of a given component is the same in both phases (6), or aav=
aih’
(1)
A more convenient function, activity coefficient, may be defined as the ratio of a component’s activity to its mole fraction in the phase considered, or
and (3)
where y is the activity coefficient, a is the activity, is the concentration in mole fraction in the light phase, and z is the concentration in mole fraction in the heavy phase. If Equations 2 and 3 are combined with Equation 1, the following equilibrium relationship is obtained:
(4) Thus, the ratio of the concentration of a component in the light phase to its concentration in the heavy phase may be evaluated from the inverse ratio of the activity coefficients of the same component in the two phases. It may be proved by Gibbs’ concept of chemical potential ( 4 ) that Equation 4 is rigorous and applies regardless of the number of components present. This equation is a convenient equilibrium relationship when the activity coefficients can be estimated by some other means. Activity coefficients, therefore, offer a convenient starting place for equilibrium calculations. Another relation involving the activity coefficient is the GibbsDuhem equation
which was rigorously derived from thermodynamic functions. This equation shows that if the activity coefficients are plotted on a logarithmic scale versus the mole fraction of one of the components, the ratio of the slopes of the curves must be equal to the negative reciprocal of the mole fraction of the two components. Equation 5 is of value in studying and evaluating experimental data, but cannot be used to evaluate activity coefficients without being integrated. Several studies have been made to obtain convenient solutions to this equation. These studies are summarized by Carlson and Colburn (1) and are discussed and compared by Wohl (11). I t has been found that the equations derived by van Laar (8)usually give values consistent with experimental liquid-liquid phase equilibria. However, for some sys1371
INDUSTRIAL AND ENGINEERING CHEMISTRY
1372
terns other solutions of the Gibbs-Duhem equation do show hetter agreement with experimental data. The van Laar equations,
Table I.
Vol. 45, No. 6
Mutual Solubility (Continued)
2,2,5-Triinetliylliexaiie-Furfural ?,2,5-Trimeth lhexane, Cyclohexane-Furfural Temp., C. mole Temp., C. Cyclohexane, mole 9iO 14 8 2.39 17.2 11.68 33.5 3.61 21.1 12.89 48 6 4.99 35. 3 17.01 63 5 6.98 43.0 19.54 79.6 51.6 24.94 IO. 17 92.9 58.2 13.04 30.18 19.91 64.7 39.90 99 9 100.6 19.91 66.3 40.66 104.1 66.2 60.02 30.09 104.4 69.73 39.99 65.8 103.4 60.2 79.10 49.98 100.0 59.80 54.3 84.31 92.2 Yl. 25 38.7 69.60 76.4 93 30 28.7 79.73 63.6 30 4 84.77 93.35 48.1 94.33 26.4 90.01 92.01 38.5 27.0 94.61 30.2 94.68 93.63 23.0 23.2 94.96 94.78 16.3 Methylcyclopentane-Furfural , ~Iethyloyclohexane-Furirirfiiral Methylcyclopentane, M e thylcyclohe xane, Temp., C. mole % Temp., C . mole RC . 10.2 10.49 13.9 7.81 21.2 24.5 12.60 9.70 19.6 12.66 37.2 12.82 14.80 46.4 30.3 15.69 56.5 44.7 19.98 20.22 25.22 69.0 53.7 30.29 72.8 60.0 30.11 39.49 73.2 65.0 39.50 49.70 65.0 72.6 39.67 60.01 67.3 49.72 69.9 69.88 57.69 61.3 67.3 79.90 63.5 65.6 69.68 84.85 40 8 79.80 59.0 90.19 32.8 50.8 83.28 92.29 46.9 87.12 92.31 32.8 94 22 24.0 46.9 87.35 38.7 89.81 25.6 91.59 Cyclopentane-Furfural Cyclopentane, mole RC Temp., C. 19.3 20.09 23.61 27.7 30.4 24.82 29,72 38.2 41.4 86.82 35.3 89.70 25.2 92.79 94.52 18.0 16.2 94.78
3
may be shown by differentiation to be mathematically cor rect solutions of Equation 5. But because of certain assumptions made in the derivation, the van Laar equation8 are not entirely rigorous. The constants, A and 61, may be evaluated by the following equations: A _ B
--
:(
+
E)
[PP ( V t J X q og
9 + @ + 2 ZiYL 27
Y?
-2
(XllYl)
(7)
log ( Y J X L 1
2,Y, log (X?/Y,)
Table I. Mutual Solubility Methylc yclopentane- Aniline Methylcyclopentane, Temp., C. mole % 14.8 17.53 25.2 24.79 32.4 39.82 32.6 66.27 28.7 78.68 24.9 84.20 21.0 87.65 11.8 91.51 22-Dimethylbutane-Furfural 2,2-Dimethylbutane, mole % 6.13 8.15 9.93 11.05 92.49 92.43 93.82 94.52 96.11
Temp., ' C. 14.5 27.6 35 8 43.8 40.1 43.5 35.2 30.6 19 0
Temp.,
n-Hexane-Furfural C. n-Hexane, mole % '
Temp.,
n-Heptane-Furfural C. n-Heptane, mole %
=-
2-Methylpentane-Furfural 2-Methylpentane, Temp.. C . mole % ' 21.5 6.76 37.0 9.00 52.0 11.91 45.1 10.65 60.0 14.30 52.5 89.84 43.2 91.71 34.0 93.77 20.8 95.87 2,3-Dimethylbutane-Furfui a1 2,3-Dimethylbutane, Temp., ' C. mole Yo 12.0 6.24 23.4 8.07 24.3 7.98 35.8 10.01 37.5 10.83 50.0 13.09 28.4 94.71 18.4 96.01 40.0 92.47 2,4-Dimethylpentane-Furfural 2,4-Dimethyl entane, Temp., C. mole 4.01 9.9 28.3 5.71 45.2 8.20 55 8 10.08 64.0 11.91 74.7 14.95 68.0 83.98 84.90 66.6 51.3 89.99 34.8 93.19 24.8 94.97 17 0 95.95 Iso-octane-Furfural Temp., C. Iso-octane, mole 70 6.2 2.89 25.5 4.48 39.2 5.65 54.9 8.16 64.6 9.94 82.1 15.00 91.8 19.98 90.4 69.72 76.5 80.03 49.6 90.00 39.1 92.15 25.2 94.90
4
where L and y are equilibrium concentrations which may be obtained froin a mutual solubility phase diagram. As presented, these equations are for binary systems. Sirnilar equations for multicomponent systems are very comple.: and require a greater amount of data. However, in hydrocarboiisolvent systems. rf it may be assumed that the effect of the hvdrocarbons on each other is negligible in comparison with the effect of the solvent, then it follows that the activity coefficient of a hydrocarbon dissolved in a solvent is a function of the solvent concentration only and is independent of the number of hvdrocarbon components present Thus, the activity coefficients obtained from the individual h j drocarbon-solvent binary systems may be used to eetiniate the component distribution in multicomponent hydrocarbon-solvent systems, provided that the solvent concentration in the multicomponent system is used to determine the activity coefficients from the binary systems. For example, the activity coefficient of a hydrocarbon in a solution of several hydrocarbons and a solvent may be taken to be the activity Coefficient the hydrocarbon would have in the binaiy hydrocarbon-solvent system if the solvent were the same concentration in the binary system a8 in the multicomponent q a tern. This value may be read directly from the binary activity coefficient curve a t a concentration corresponding to the concentration of the solvent in the multicomponent system. Mutual Solubilities and Activity Coefficients Mutual solubility data were experimentally determined foi twelve hydrocarbon-furfural systems and one hydrocarbonaniline system. The hydrocarbons used in the evperimentnl
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1953
1373
stants in the van Laar equations are found to be A = 1.023 and B = 1.358. These constants should be checked by calculating the activity coefficients a t the concentrations corresponding to the mutual solubility data and substituting these values in Equation 4. The van Laar activity coefficients for the system cyclohexanefurfural a t 86" F. are shown in Figure 2. Similar plots for the n-heptane-furfural system a t 86" F. are shown in Figure 3. Van Laar constants for these two systems and seven others are presented in Table 11. Prediction of Component Distribution
0.0 Figure 1.
0.2 MOLE
0.4 0.6 0.8 FRACTION HYDROCARBON
1.0
Mutual Solubilities for Iso-octane, n-Heptane, n-Hexane, and Cyclohexane with Furfural
The proof of the approximation method which was previously developed is in its prediction of experimental data. In order to prove the method of calculation, equilibrium data were calculated for two ternary systems and were compared with experimentally determined equilibrium data. Three duplicate equilibrium determinations were made for each system. Weighed quantities of the three components were placed in a 1-liter separatory funnel and agitated a t 30-minute intervals for 2 hours a t 86" F. At the end of this period, the two li uid phases were allowed to settle over a period of 2 hours. %he phases were then se arated, weighed, and analyzed. A portion of the h drocarbon pffase was titrated with a standardized potassium Kydroxide solution to determine the concentration of furfural. The remaining portion of the hydrocarbon phase was washed with sodium bisulphite solution and water t o remove the furfural; the Sam le was then dried and analyzed by a density determination. T i e hydrocarbon in the solvent phase was removed by distillation and analyzed by a density determination. . .
0.0
0.2 0.4 0.6 0.8 1.0 MOLE FRACTION FURFURAL
Figure 9. Activity Coefficientsfor Cyclohexane-Furfural at 86" F.
van Laar constants: A
=
1.023, 8 = 1.358
work were all Phillips pure grade hydrocarbons, 99 minimum mole % purity. The furfural used was originally obtained as technical grade furfural from the Quaker Oats Co. This material was further purified each day by distillation with only the heart cut being used. The aniline was obtained as chemically pure from Baker and Co. It was freshly distilled each day with an 80% heart cut being used. The mutual solubilities of the hydrocarbon-solvent systems were determined by the cloud point temperature of weighed samples in equipment similar to the familiar aniline point apparatus. The solubility measurements were limited to the data which could be obtained a t atmospheric pressure; data were not obtained a t temperatures above the boiling point of the mixtures. The experimental mutual solubility data for the hydrocarbonsolvent systems are presented in Table I. In addition, the data for the iso-octane-, n-heptane-, n-hexane-, and cyclohexanefurfural systems are shown in Figure 1. The van Laar constants may be calculated using Equations 7 and 8. Solutions of these equations have been plotted by Colburn and Schoenborn (8). From the mutual solubilities of cyclohexane-furfural a t 86" F. (xi = 0.154 and y i = 0.936) the con-
I .o
0.0
0.2 0.4 0.6 0.8 1.0 MOLE FRACTION FURFURAL
Figure 3. Activity Coefficients n-Heptane-Furfural at 86" F.
for
van Laar constants: A = 1.334, 8 = 1.383
Table 11.
van Laar Activity Coefficient Constants
System Furfural with n-Hexane n-Heptane Iso-octane Cyclohexane
a Calculated
A
B
1.239 1.334 1.446 1.023
1.116 1.365 1.371 1.358
86 86 86 86
1,248 1.371 0.918 0.861 1.041
1.309 1.284 1.089 1.117 1.140
77' 77 77 77 77
from d a t a as indicated by references.
Temp.,
O
F
INDUSTRIAL AND ENGINEERING CHEMISTRY
1374
Table 111. Experimental and Estimated Equilibrium Concentrations in n-Heptane-Cyclohexane-Furfural System a t
Table V.
86" F. Case No. 1 2 3 4 a Experimental E:quilihrinm Concentration. ?vIole Fract. -
Hydrocarbon phase n-Heptane Cyclohexane Furfural
0.745 0.194 0.061
0.752 0.188
0,060
~
0.490 0.450 0,060
0.483 0.445 0.072
0.180 0.761 0.069
~
__
1.000
1.000
1.000
1,000
1.000
0.050 0.012 0.930
0.052 0.020 0.928
0.060
0.038
0.039 0.061 0.900
0.016 0.114 0.870
0.016 0,114 0.871
1.000 1 . 0 0 0 1 000 1.000 1.000 Estimated Equilibrium Concentration, ;\lole Fract.
1.000
Solrent phase n-Heptane Cyclohexane Furfural
0 056 0.025 0,919
0.056 0.024 0.919
_- _-
1.000 1.000 Concn. of n-Heptane in Solvent Phase, Experimental 0.716 0.717 Estimated 0.690 0.698
0.902
0.042 0.064 0.894
__
0.042 0.064 0.894
0.018 0.120 0.862
_ __ _
1.000 1.000 1,000 Solvent-Free Basis, Mole 0.389 0.387 0.122 0.399 0.398 0.133
Solvent phase Iao-octane n-Hexane Furfural
0.790 0.149 0.061
0.781 0.148 0.071
0.495 0.444 0.061
0.494 0.444 0.062
1,000 Fract.
6
0,194 0.749 0.057
0.197 0,746 0.057
1.000
1.000
1 000
1.000
1,000
0,948
0.040 0.012
0.038 0.011 0.951
0.027 0.036 0.937
0 026 0.037 0.937
0.011 0.060 0,929
0.011 0.060 0.929
1.000
1.000
1.000
1.000
i.ooo
__ 1.000
Estimated Equilibrium Concentration, Mole Fraot. Solvent phase Iso-octane n-Hexane Furfural
0.046 0.012 0.942
__
0.046 0.012 0.942
0.031 0.036 0.933
0.031 0.036 0 933
0.013 0.064 0.923
1.000 1.000 1.000 1.000 1,000 Concn. of Iso-octane in Solvent Phase, Solvent-Free Basis, Mole Experimental 0.769 0.766 0.495 0.419 0.150 Estimated 0.800 0,800 0,464 0,464 0.172
0.0468 0.0134
0.065
Table VI.
0.936 0.846
__
0.7432 0.1743
__
0.0602
1.0000
0.9175
Estimation of Distribution in Solvent Phase Activity Coefficient
Coinponent wHeptane
Mole Fract. 0.7040
Cyclohexane
0.2060
3 Yh
yb
-tu
1 3 . 4 8 1.013 7.80
1 016
Estd. Hydrocarbon Concn. in Solvent Phase
13.31
(0.7940) (0.9400)/13.31 = 0.0561 (0.2060) (0.9400)/ 7 68 = 0.0252
7.68
0.0813
Tabie VII.
0.120 0 131
1.000
__
0.059
Solvent Phase Soly. a t 86" F., mole fract. Partial furfural soly.
__
86" F.
Hydrocarbon phase Iso-octane n-Hexane Fiirf nrnl
0.7940
0.018 0.120 0.862
Table IV. Experimental and Estimated Equilibrium Concentrations in Iso-octane-n-Hexane-Furfural System a t Case S o . 1 2 3 4 5 Experimental Equilibrium Concentration, Mole Fraot.
Hydrocarbon Phase Soly. a t 86' F., mole fract. Partial .?o!y. furfural
0.2060 -
0.178 0.764 0.058
1.000
Solvent phase n-Heptane Cyclohexane Furfural
n-Heptane Cyclohexane
Estimated Furfural Concentrations
Mole Fraot.
Component 6
Vol. 45, No. 6
0,013 0.064 0.923 1,000 Fract.
0.150 0,174
Estimated Furfural Activity Coefficients in Equilibrium Phases
Hydrocarbon Phase, 0 0600 Mole Fract. Furfural SolventPartial free activity ooinpn. YU ooeff.
Component n-Heptane Cyclohexane
0.7940
0.2060 -
16.0 14.2
1.0000
0 . 6 9 0 0 . 1.030 1.020
12.70 2.93 15.63
t
Solvent Phase 0.9175 Mole Fract. Fuifuial SolventPartial free activity oompn. Y/$ cooff. 0.711 0.316
0.3100 __
__
1,0000
1.027
I
//
0*4 //
1
0.2 0.0
L
The experimental equilibrium data are presented in Tables I11 and IV. The method of predicting ternary equilibrium data will be illustrated with the n-heptane-cyclohexane-furfural system a t 86 F., using n-heptane-furfural and cyclohexane-furfural binarv solubility data. The problem is to estimate the furfural content of the hydrocarbon phase and the composition of the solvent phase when the hydrocarbon phase has a solvent-free composition of 0.7940 mole fraction n-heptane and 0.2060 mole fraction cyclohexane. Solution of the above problem involves a trial and error method of calculation, which is illustrated by the folloa ing example: Step 1. The concentration of furfural in each of the two ternary phases is estimated by assuming that it will be the weighted average of the furfural concentration in the binary systems. For the first trial calculation, the solvent-free composition of the h-ydrocarbon phase is used to estimate the furfural concentration in both phases; this usually gives a good first approximation. The estimated furfural concentrations will be confirmed or rejected by subsequent calculations. The initial O
9.4 0.6 0.8 1.0 MOLE FRACTION ?7-HEPTANE SOLVENT PHASE
0.0
0.2
Figure 4. Liquid-Liquid Phase Equilibria for n-Heptane-Cyclohexane-furfural at 86" F. Curve estimated from van Laar equations
0 Experimenlellv determined
estimation of the furfural concentration in both phases is shown in Table V. The estimated furfural concentration in mole fracion is 0.0602 for the hydrocarbon phase and 0.9175 for the solvent phase. Step 2. Determine the activity coefficients for normal heptane and cyclohexane at the furfural concentrations estimated in step 1. For the purpose of this illustration the activity coefficients will be obtained a t the nearest 0.0025 concentration. From the n-heptane-furfural binarj- activity coefficient curves, Figure 3, n-heptane has an activity coefficient of 13.48 in 0.9175 mole fraction furfural and 1.013 in 0.0600 mole fraction furfural. From Figure 2, the activity coefficients of cyclohexane are 7.80
June 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY
0.0 0.0 0.2 0.4 0.6 0.8 LO MOLE FRACTION [SO-OCTANE SOLVENT PHASE
0.0 0.0 0.2 0.4 Ob 00 I .o MOLE FRACTION ??-HEXANE SOLVENT PHASE
Figure 5. Liquid-Liquid Phase Equilibria for Iso-octane-n-Hexane-Furfural a t 8 6 " F.
Figure 6. Liquid-Liquid Phase Equilibria for n-HexaneMethylcyclopentane-Aniline at 77" F.
Curve estimated hom van Laar equations
0 Experimentally determined (Darwent and Winkler, 3)
Curve estimated from van Laar equations
0 Experimentally determined
Table VIII.
Component n-Heptane Cyclohexane
Furfural
1375
Comparison of Calculated and ,Experimental Equilibrium Data Compositions, Mole Fraction Experimental Estimated Hydrocarbon Solvent Hydrocarbon Solvent phase phase phase phase 0 7454 0 0501 0 7462 0 0561 0 1099 0 1936 0 0252 0.1936 0 9187 0 0610 0 9300 0 0602
_-
-
___
__
1 0000
1 0000
1 0000
1 0000
and 1.016 in 0.9175 and 0.0600 mole fraction furfural, respectively. Step 3. From the activity coefficients obtained in step 2, calculate the ratio of the activity coefficient in the solvent phase to the activity coefficient in the hydrocarbon phase for n-heptane and cyclohexane. Use these ratios to estimate the composition of n-heptane and cyclohexane in the solvent phase. The calculations are shown in Table VI. Step 4. Check the furfural concentration in the solvent phase
0.6 0.8 1.0 MOLE fRACTLQ&! n-HEPTANE1 SOLVENT PHASE
0.0
0.2
0.4
Figure 7. Liquid-Liquid Phase Equilibria for n-Heptane-Cyclohexane-Aniline a t 77" F. Curve estimated from ven Laar equations 0 Experimentally determined (Hunter and Brown, 7 )
calculated in step 3 against the value used in step 1 to obtain the activity coefficients for the solvent phase. By difference, the furfural mole fraction is 0.9187 which compares favorably with 0.9175 estimation in step 1. Therefore a second approximation of the furfural concentration in the solvent phase is not necessary. Step 5. Check the furfural concentration in the hydrocarbon phase estimated in step 1, using the activity coefficient8 of furfural in n-heptane and furfural in cyclohexane. The activity coefficients are evaluated a t the estimated furfural concentration in the hydrocarbon phase from step 1 and the calculated furfural concentration in the solvent phase from step 4. The activity coefficient of furfural in each of the ternary phases is estimated by assuming that i t will be the weighted average of the furfural activity coefficients in the binary systems. The calculations are shown in Table VII. The ratio of theactivity coefficient of furfural in the hydrocarbon phase to the activity coefficient of furfural in the solvent phase is 15.63/1.027 = 15.22. Then the calculated furfural concentration in the hydrocarbon phase is equal to the furfural concentration in the solvent phase divided by the inverse ratio of the activity coefficients, or 0.9187/15.22 = 0.0604. The calculated
0.0 0.2 0.4 0.6 0.8 0.1 MOLE FRACTION %HEPTANE SOLVENT PHASE
0.0
Figure 8 . Liquid-Liquid Phase Equilibria for n-Heptane-Methylcyclohexane-Aniline at 77" Curve estimated from van Laar equations 0 Experimentally determined (Varteressian and Fenske,
F.
IO)
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
1376
concentration of 0.0604 provides a satisfactory check with the concentration of 0.0600 estimated in step 1; therefore a second trial calculation is not necessary. The final proof of the method of prediction is how well the calculated compositions check the experimental data (see Table VIII).
Vol. 45, No. 6
for which comparisons were made were taken from the literature and are of unknown accuracy. The system n-hexane-methylcyclopentane-aniline shown in Figure 6 indicates poor agreement between experimental and predicted data. There is indication that the hydrocarbons used by Darwent and Winkler ( 3 ) for the experimental determinations with this system may have contained impurities which would have caused inaccuraries in the results. Good agreement is shown between the predicted and experimental data for the other four systems: n-heptane-cyclohexane-aniline ( 7 ) in Figure 7, n-heptane-methylcyclohexaneaniline (IO) in Figure 8, n-heptane-methylcyclohexane-furfural ( 5 ) in Figure 9, and n-heptane-methylcyclohexane-methylcarbito1 (6) in Figure 10. The good agreement obtained with five of these seven systems indicates the proposed method of calculation may be used for engineering purposes. I n fact, because of inaccuracies and inconsistencies in some experimental data. in some cases the predicted data may be better than the experimental. I n some cases the predicted separation between the tn,o hydrocarbons is greater than the experimental separation, and in others not as great. Therefore, a definite trend in the calculations could not be established. Correlation of Partition Coefficients
MOLE FRACTiON HEPTANE I N SOLVENT PHASE
Figure 9. Liquid-Liquid Phase Equilibria for n-Heptane-Methy fcyclohexane-furfura I at 140 O
F.
Curve ortimated from activity coefficients 0 Experimental data b y Herbolrheimer (5)
Since the comparison of predicted and experimental values of equilibrium concentrations has proved the acceptability of the assumption that paraffin and naphthene hydrocarbons form ideal solutions in each other, the method of prediction may be extended to multicomponent systems of these hydrocarbons. The ratio of activity coefficient in the solvent phase to the activity coefficient in the hydrocarbon may be defined as the partition coefficient. If the assumption of ideal hydrocarbon solutions is valid, the partition coefficient becomes a function of temperature and the concentrations of the hydrocarbon components. Therefore, at constant temperature a. system of K charts similar to vapor-liquid equilibria K charts can be plotted. These charts are a plot of partition coefficient versus solvent concentration in one phase with solvent concentration in the equilibrium phase serving as parameter, as illustrated in Figure 11. These charts may be used to determine component distribution between phases for multi-
7.501----7
7 .oo
0.0 0.0
0.2 0.4 0.6 0.8 MOLE FRACTION HEPTANE I N SOLVENT PHASE
1.0 (HYDROCARBON PHAS
Figure I O .
Liquid-Liquid Phase Equilibria for n-Heptane-Methylcyclohexane-Methylcarbitol at
140" F.
,
Curve estimated lrom activity coefficients 0 Experimental data b y Herbolsheimer (5)
On a solvent-free basis, the concentration of n-heptane in the solvent phase is 0.716 mole fraction (experimental data). The estimated value is 0.690. This agreement is considered to be reasonably close and should be satisfactory for most calculations. The ternary phase equilibrium data which were calculated in this manner are compared with experimental data in Tables I11 and IV and Figures 4 through 10. I n general, the agreement between the predicted and experimental data is good. Good agreement is shown in Figure 4 between the estimated and experimental data for the n-heptane-cyclohexane-furfuralsystem. The predicted equilibrium data for the iso-octane-hexane-furfural system shown in Figure 5 are only in fair agreement with the experimental data. However, this system gives the method of prediction a severe test because of the similarity of the two hydrocarbons. The experimental data for the other five systems
0.92 ' a96 ' I.dO 3'50i.80 ' 8.84 ' 0.68 MOLE F R A C T I O N FURFURAL (SOLVENT PHASE)
Figure 11.
Partition Coefficients for CyclopentaneFurfural at 100" F.
component systems if the assumption of ideal hydrocarbon S O ~ U tions can be shown to be acceptable, I n general, for systems involving paraffins, olefins, and naphthenes, in admixture the charts will give good results. However, the present state of knowledge does not permit the prediction of the effect of aromatics on hydrocarbon-solvent systems.
June 1953
INDUSTRIAL AND ENGINEERING CHEMISTRY Conclusions
*
Nomenclature
A simple method has been developed for predicting liquidliquid equilibrium data of sufficient accuracy to be used in engineering design calculations. The equilibrium data are predicted from mutual solubility data which may be easily and accurately determined by experimental means. The method of prediction is based on the assumptions that in hydrocarbonsolvent systems the hydrocarbons form ideal solutions in each other, and the activity coefficients of the several hydrocarbons are functions of the solvent concentration. Although this method of calculation is not rigorous, the results of this study indicate that phase equilibrium data of sufficient accuracy for engineering design calculations may be obtained. It is possible that predictions at temperatures close to the critical solution temperatures of any solvent-hydrocarbon pair may be inaccurate. Therefore, predictions within 20’ F. of a critical solution temperature should be experimentally verified. The results also indicate the assumption that aliphatic and naphthenic hydrocarbons form ideal solutions in each other is acceptable for liquid-liquid phase equilibrium calculations. This method of prediction has given good results for systems of aliphatic and naphthenic hydrocarbons in the solvents furfural, aniline, and methylcarbitol, and would probably give good results for the same hydrocarbons in similar solvents; however, this method of prediction should not be applied to other types of systems without first checking a few experimental points. Acknowledgment
The authors wish to gratefully acknowledge the contributions His ideas and advice were of material aid in the successful completion of this project. The authors also wish to thank the Research and Development Department of Phillips Petroleum Go. for permission to publish this work. of K. H. Hachmuth to this study.
A
= constant in van Laar equations = activity = constant in van Laar equations
‘ i K = partition coefficient
= mole fraction in solvent phase or in solution if only one phase is present y = mole fraction in hydrocarbon phase y = activit coefficient In = logaritlm to the base e log = logarithm to the base 10 Subscripts h pertains to solvent phase i indicates component i j indicates component j Y pertains to hydrocarbon phase z
Literature Cited (1) Carlson, H. C., and Colburn, A. P., IND. ENG.CHEM.,34, 581 (1 942). (2) Colburn, A. P., and Schoenborn, E. M., Trans. Am. Inst. Chem. Engrs., 41, 421 (1945). (3) Darwent, B. de B., and Winkler, C. A., J. Phus. Chem., 47, 442 (1943). (4) Gibbs, J. W., “Collected Works,” New York, Longmans, Green, and Co., 1928. (5) Herbolsheimer, Glenn, dissertation, The Pennsylvania State College, 1942. ( 6 ) Hildebrand, J. H., and Scott, R. L., “Solubility of Nonelectrolytes,” 3rd ed., New York, Reinhold Publishing Corp., 1950 (7) Hunter, T. G., and Brown, T., IND. ENG.CHEM.,39,1343 (1947). (8) Lam, J. J. van, 2. phusik Chem., 72, 723 (1910); 83, 599 (1913). (9) Treybal, R. E., “Liquid Extraction,” New York, McGraw-Hill Book Co., 1951. (10) Varteressian, K. A., and Fenske, M. R., IND. ENU.CHEM.,29, 270 (1937). (11) Wohl, K., Trans. Am. Inst. Chem. Engrs., 42,215 (1946). RECEIVED for review December 12, 1952. ACCEPTEDFebruary 26, 1953. Presented st the Eighth Southwest Regional Meeting of the AMERICAN CHEMICAL SOCIETY, Little Rock, Ark., 1952.
Mass Transfer between Solid Wall and
Dextran-Correction In the Staff-Industry Collaborative Report, Dextran, by Gordon H. Bixler, G. E. Hines, R. M. McGhee, and R. A. Shurter [IND.ENG.CHEM.,45,692 (1953)J, the following sentence should be added on page 694, column 1, line 8: Dextran and gelatin are the only expanders accepted by the Council on Pharmacy and Chemistry of the American Medical Association. The caption for the photograph on page 701 should read: (Left) Vapor Compression Still Supplies 400 Gallons of PyrogenFree Water Each Hour. On page 705, in reference (la),the year should be 1915 instead of 1951.
Ion Exchange-Correction In the Unit Operations Review article on “Ion Exchange’’ [IND.ENG.CHEM.,45, 83 (1953)] the following changes should be made in the Literature Cited. (4) (25) (58) (99) (189) (398)
1377
Fluid Streams-Correction I n the article on “Mass Transfer between Solid Wall and Fluid Streams” [IND. ENG.CHEM., 45, 636 (1953)] the following changes should be made: Page 638, Equation 17 Page 638, Equation 18 Page 638, second column paragraph 3, line 3 Page 644, Figure 7
Change u t6 U Change CT to C? Change 5 t ~ < y +
< 33 to 5
