Correlation of Vapor-Liquid Equilibria Data for Nonideal Ternary Systems EDWARD G . SCHEIBELI AND DANIEL FRIEDL4ND2 Polytechnic Institute of Brooklyn, Brooklyn, A‘. Y . simple empirical method is proposed for correlating and predicting the \apor-liquid equilibria for a ternary system from the data for the three binary systems. The method is based on an interpolation of the activity coefficients for the ternary system. The method has been applied to the published data on nine ternary systems, and i t has been found to predict bubble points with an accuracy of within 1” C,, and vapor compositions with an average deviation of about 2 % or less. The agreement appears to be almost within the limits of reliability of the original ternary data.
T
HE field of aaeotropic distillation and of extractive distillation to separate azeotropes or close boiling compounds has 3een receiving increasing attention in recent years. There have 3een several extremely large scale applications in the production )f toluene and synthetic rubber from petroleum; the number of small scale applications 1% hich are possible is practically limitless. The basic mechanism for these processes depends on the devia-ions of the various binary equilibria data from ideality as defined by Raoult’s law. Thepe deviations are different for all jystems. Although there are some generalizations by which it is Dossible to predict qualitative variations ( I I ) , there is no reliable nethod for predicting quantitative deviationg from ideality in Tinary system. Also, there is no general method for correlating or predicting *he vapor-liquid relations of a ternary system fiom the binary Jquilibria data. The binary data are relatively simple to deternine, and the data on numerous systems have been reported in -he literature. Hoi\ever, ternary data are much more difficult -0 determine; and, although there are more ternary systems pos.ible than binary systems, the available data on them are scarce. Carlson and Colburn (8) described a method for predicting the Ternary equilibria data n hich they considered unsatisfactory be:awe it was not in agreement xith the Gibbs-Duhem equation n a hypothetical case. Colburn and Schoenborn (9) found that -his method gave good agreement nith the data for a ternary Jystem involving one ideal binar? misture, but observed that it :odd not be applied where all three binary systems were nondeal (9). Khite (38)applied the van Laar equation (23, 24) to the analy.is of ternary equilibria data and proposed methods for evaliating the necessaiy constants. The method was applied to -hrcc ternary systems, t n o of nhich involved one ideal binar) nixture, and the agreement n a s good. HorTever, the van Laar Aquation is not accurate for manv binary systems, and the method raa not found applicable to the data on many other ternarj Pms reported in the literature (58). The empirical method proposed in this work was the result of a *awful analysis of the equilibria data presented in a previous %per (67),and a preliminary in,pection revealed its applicability -0 practically all the published data on ternary systems. In the .resent analysis some data may have been overlooked, but the method was found to give excellent agreement in almost all the tems studied. To generalize on this method, it was found necessary to classify Present address, Hoffniann-LaRoche Inc , Xutley, S J . Present address, Truland Chem:,-el and Engineering Company. Inc + w o n . S . J.
,
the various nonideal systems into three distinct classes based 0x1 the qualitative deviations from Raoult’s law which are observed in the different binary systems. Raoult’s law states that the partial pressure of a component from a mixture is equal to the product of the vapor pressure of the pure component a t the given temperature and the mole fraction of the component in the mixture. \Then this relation holds, the mixture is considered ideal, and, when deviations are observed, the correction factor which is introduced into this relation is called the activity coefficient Thus, pi = YlP;xl
where p l = partial pressure of component in equilibrium with liquid P: = vapor pressure of pure component at given temperature .rl = mole fraction of component in liquid yl = activity coefficient The value of y1 may be either less than or greater than unity, and for these cases the deviations are defined as negative or positive, respectively, as related to the logarithm of the activity coefficient. Kegative deviations tend to produce maximum boiling azeotropes, whereas positive deviations tend to produce minimum boiling azeotropes. Thus, the following three groups have been defined to include all known ternary systems. There are some other possibilities involving one or more ideal systems; however, they have been omitted because of the absence of any specific information on such ternary systems. TYPEI. Ternary systems made up of the three binary systems which all show the same qualitative deviations from Raoult’s law-that is, all positive or all negative deviations. TYPE11. Ternary systems made up of one ideal binary system and two nonideal systems which give the same qualitative deviations from Raoult’s law. TYPE111. Ternary srstems made up of one rionideal binary system Ivhich evhibits a deviation from Raoult’s lrrrv the opposite of the deviation of the othei two binary systems. +illof these types require a different method for predicting the ternary equilibrium data, and they will, therefore, be considered separately. CORRELATION OF TERNARY SYSTEMS OF TYPE I
The systems in which all the binary systems indicate positive deviations from Raoult’s law are by far the most common, and several such systems have been studied. The data can be correlated by plotting the lines of constant activity coefficient for all the three components on a ternary dia-
1329
INDUSTRIAL AND ENGINEERING CHEMISTRY
1330
TABLEI. COllPARIsON
OF
CALCULATED AND EXPERIVEST.4L VAPOR-LIQUID EQCILIBRIA DhT.4 ACETONE-METHANOL-WATER SYSTEM
KO.
Liquid Compn., hlole Fraction Acetone Methanol
Water
Obsvd.
Acetone Calcd.
2 6 10 14 20 24 32 40 50 60
0.3744 0.1665 0.3155 0.0429 0.1120 0 4086 0 8100 0.4242 0.7529 0.5702
0.1246 0,5940 0,1980 0.0861 0.1300 0.4780 0.1029 0 3143 0 0763 0.2263
0.5130 0.4771 0.4865 0.0945 0.2312 0.7160 0.8376 0,6447 0.7852 0.7211
0.515 0.486 0.486 0.122 0,240 0.707 0,858 0,625 0.795 0.710
Run
0.5010 0.2395 0,4865 0.8710 0.7580 0.1134 0.0871 0.2615 0.1708 0.2035
Vol. 39, No. 10
Diff.
+0.002 $ 0 009 0.000 4-0.027 +o, 009
-0.008 -0,020 -0.020 +0.010 -0.011
gram. By reference to the activity coefficient us. composition curves for the binary systems, these curves can be estimated as shown in Figure 1. The point D locates the particular activity coefficient for the component A from the binary with component B, and the point E locates the given activity coefficient for the component A from the binary with component C. The curve of constant activity coefficient is determined by assuming that the radial length from point A varies between AD and A E in a manner proportional to the angle of the radial line. Thus, the point F on the bisector of the angle D A E is located such that the distance AF is half way between the distances A D and AE. Similarly, the points on the bisectors of the two angles DdF and FAE can be located, and these will generally be sufficient to construct A
FOR
Vapor Compn., hlole Fraction hlethanol Obsvd. Calcd. Diff.
Obsvd.
Water Calcd.
0.4384 0.2904 0.4265 0.8710 0.7180 0.1039 0.0933 0.2145 0.1764 0.1687
0,0486 0.2398 0.0870 0.0345 0,0508 0.1811 0,0697 0.1408 0,0384 0.1102
0 041 0 190 0 065 0 033 0 046 0 150 0 049 0 100 0 034 0 078
0.444 0 324 0 449 0 845 0 714 0 143 0 095 0 275 0 171 0 212
+0.006 +0.034 +0.022 -0,026 -0,004 +0.039 +0.002
$0.060 -0.005 4-0.043
_ _ I _
Diff.
-0.M)B -0.048
-0,022 -0 002 -0.005
-0.031 -0,021 -0 041 -0,004 -0,032
The method of correlation was applied to six different systems on which the vapor-liquid equilibria data are known. Table I shows the comparison between the observed data and the predicted values on the acetone-methanol-water system. The ternary data ( 2 7 ) were calculated from the binary equilibria data of the same authors (27). A comparison of the predicted and the observed ternary equilibria data for the ethanol-benzene-water system is shown in Table 11. The ternary data were calculated from the binary data of Fritaweiler and Dietrich (IS) on ethanol-benzene mixtures; the data of Jones et al. (26) on ethanol and water mixtures; and the benzene-mater binary data were calculated from the mutual solubility (21) as indicated by Colburn and Schoenborn (9). The method was also applied to data on four other systems published in the literature, and the summary of the comparison of all six systems is shown in Table 111. The ethanol-dioxane-water ternary data (31) were predicted from the binary data of Jones et al. (28)for ethanol and mater, the data of Hopkins et al. (19) for ethanol and dioxane, and the data of Hovorka et al. (20) for dioxane and water. The ternary data for the n-heptane-methanol-toluene system Rere calculated from the binary data of the same authors (4)OD the methanol and n-heptane system and the methanol and toluene system. The binary data for n-heptane and toluene system were obtained from the work of Bromiley and Quiggle (6).
e Figure 1. Estimation of Curve of Constant Activity Coefficient for Ternary Systems with Three Xonideal Binaries Ha, ing Similar De\iations from Raoult’s Law (Type I)
the curve of constant activity coefficient. This procedure IS repeated for all activity coefficients for all the components. When activity coefficients greater than those of one of the binary systems are encountered, the curves can be estimated by interpolah ing a cross plot at constant concentrations of the particular component. This can be accurately accomplished because usually more than half of the curve is already established and the limiting value at the other end is known. When the activity coefficients for any mixture are knov n, it is possible to calculate the bubble point of the liquid and the composition of the vapor in equilibrium with the liquid. This is done by a trial and error process of estimating a temperature and calculating the partial pressure of the three components from their activity coefficients and the vapor pressures of the pure liquids a t this temperature, as previously defined. The sum of the partial pressures must be equal to the total pressure on the system. If the total is too high, a lorver temperature is chosen for the second trial, and if the total is too low, a higher temperature is tried until the calculations check the desired total pressure.
Figure 2. Estimation of Curve of Constant Activity Coefficient for Ternary Systems with One Ideal Binary, BC (Type 11)
The ternary data for the n-heptane-methylcyclohexane-tuluene system (6) \Yere predicted from binary data of the same authors and the data of Quiggle and Fenske (Sf)on the methylcyclohexane and toluene system. The comparison of the very recent data of Drickamer, Brown, and White (10) with the calculated values based on the binary data used by these authors shows the poorest agreement of xII
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1947
1331
The equations of the particular family of curves used in this method could not be deVapor Compn , Mole Fractions Liquid Compn., veloped because there is no hlole Fraction Ethanol Benzene Water Ethanol Benzene Water Obsvd. Calcd. Di5. Obsvd. Calcd. Di5. Obsvd Calcd. Diff. general equation tvhich repre0.222 0 443 0 335 0 . 2 4 1 0 , 2 4 4 + O 003 0 549 0 , 5 2 2 -0.027 0 210 0 234 +o 024 sents all the binary activity 0,458 0.314 -0.006 0 034 0 508 0 . 4 2 9 0 . 4 4 7 + O 018 0 320 0 251 0 239 -0 012 coefficients. Also, the graphi0.335 0 214 0 451 0 , 2 5 7 0.300 + O 043 0 531 0 500 $0.031 0 212 0 200 -0 012 0.468 0 . 5 7 6 +o 026 0 519 0 . 5 5 0 0 124 0,110 -0,014 0 013 0 326 0 314 -0 012 cal construction is much simpler 0.271 0,486 -0,044 0 530 0 036 0 693 0 . 2 5 8 0 . 2 9 3 1 0 035 0 212 0 221 +o 009 0.251 0 , 3 3 4 +o 022 0.417 - 0 , 0 0 7 0 732 0 312 0 424 0.017 0 264 0 249 -0 015 than the c:ilculation of the 0 245 0 005 0 750 0 . 5 0 3 0 . 4 6 3 -0 040 0 138 0.177 4-0.039 0 359 0 360 +o 001 0 . 7 8 1 +o 012 0.105 0 864 0 033 0 103 0.769 0 126 0 . 1 2 7 +0.001 0 092 -0 013 curves from any algebraic equa0.070 +0.004 0.879 0 017 0 104 0 , 8 2 6 0 . 8 3 3 + O 007 0 066 0 108 0 097 -0 011 tion that might be derived for 0.394 +0.044 0.396 0 542 0 062 0.350 0 537 0.500 - 0 , 0 3 7 0 106 -0.007 0.113 special cases where all binary data obey the van Laar equaTABLE 111. SUhIMARY OF COMPARISoN O F CALCULATED VAPOR LIQUIDEQUILIBRIA tion. However, the interpolated activity K I T H OBSERVED D.4TA O S T E R N d R Y SYSTEMS O F TYPE1 Arithmetic Deviations coefficients for the acetone-methanolVapor Compositions water system were t,ested for thermoS o . of Temp., 1st compd., 2nd compd. 3rd compd. Ternary System Citation Runs C. mole fraction mole fractioh mole fraotioh dynamic soundness graphically deAcetone-methanol-water (27) 60 0.5 0.013 0,024 0.017 termining the partial derivatives and Ethanol-benzene-water (2) 15 l,? 0 029 0.025 0,011 substituting in the Gibbs-Duhem equaEthanol-dioxane-water (SS) 19 0.2 0,011 0.022 0 019 n-Heptane-merhanol-water (4) 8 1.2 0,010 0.017 0,009 tion for ternary mixtures, as expressed n-Heptane-methylcyclohexane-toluene (6) 17 b 0.004 0,004 0.004 by Lewis and Randall ( 2 5 ) . Three points Slethylcyclohexane-toluenenear the center of the ternary diagram phenol (IO) 79" 1.8 0.029 0.037 0.011 were chosen, and the agreement was a Of the reported runs, 10 evenly distributed points were compared. well vithin the accuracy of the basic 6 No temperature data were reported. binary data. The additional systems were not tested in this wav because frequently the binary data themselves are the previous systems. Their ternary data on the isooctanenot entirely thermodynamically sound. toluene-phenol system was also estimated with less agreement; Carlson ( 7 ) has noted that the particular construction used in consequently the results were not tabulated. Several distributed this method coincides with the two-suffix equations proposed by points were studied, and the calculated temperatures averaged Benedict et ul. ( 4 ) when the three constants in this equation are about 2 O C. too high. The phenol vapor compositions agreed to equal. When the constants are different, the, methods do not about 0.02 mole fraction, but the calculated hydrocarbon concengive the same solution. I n order to obtain precise correlation of trations were considerably in error. There appears to be no extheir data, Benedict et al. (4)found the two-suffis equation inadeplanation for the failure of the method in this system; homver, quate and introduced additional constants to obtain a four-suffis it was observed that, if the curves of constant activity coefficient equation. The present method gives good agreement on the nwere drawn as straight lines between the binary systems on the heptane-methanol-water system studied by the previous investernary diagram, the predicted activity coefficients agreed with tigators (Table 111). The present method is much simpler to the ternary data as well as the method of White (58), which was apply than the equations of Benedict et al. ( 4 ) . used to correlate the original data. These lines appeared to intersect at the same point for phenol and isooctane, and were parallel CORRELlTION OF TERNARY SYSTEMS OF TYPE I1 for the toluene activity coefficients. The vapor compositions These systems which contain one ideal binary system are not calculated by this method agreed well with the observed comi o common as those of type I. However, they are almost as positions; however, the calculated temperatures averaged about important, for they include many of the various evtractive distil3' to 4' C. below the observed values. lation and azeotropic distillation systems for the separation of I n general, it is obvious that the method previously described close boiling compounds such as occur in petroleum fractions. can be used to predict reliably ternary equilibrium data from The hydrocarbon mixtures in these latter systems can frequently known binary data Frequently in systems where a ternary azeotrope is known, it is possible to check the method with the be considered as essentially ideal. Another well knovn evample of this system is the ethanol-methanol-water system which has observed activity coefficients at this one point. .4t any rate, a been thoroughly studied. few experimental points to check the calculated results would suffice t o establish the validity of the correlation for the given sysIt is apparent that if the binary system BC in Figure 2 is ideal tem, and thus the vapor-liquid equilibria for the entire ternary it will be impossible to employ the previous technique to locate the lines of constant activity coefficient for components B and C wstem could be easily determined.
TABLE11. COMP.4RISOK
O F C.4LCvLATED A S D EXPERIMENTAL VAPOR-LIQUID EQUILIBRIA DATA FOR ETHANOL-BENZENE-WATER SYSTEM
-
TABLE IT'. COlfP44RISON O F CALCULATED
AYD EXPERIVENT4L VAPOR-LIQUID EQUILIBRIA D 4 ~ 4FOR >\IETHANOL-ETH4SOG\~7.4TER SYSTE\I
Run Y O
1
2 3 4 7 8 9 I1 14 15
Liquid Compn , l l o l e Fraction Methanol Ethanol 0 517 0 106 0.188 0 459 0 383 0 281 0 064 0 683 0 141 0 266 0 121 0 242 0 040 0 808 0 286 0 061 0 331 0 188 0 274 0.415
Water 0,377 0.353 0.336 0.253 0.593 0.637 0.152 0,653 0.481 0.311
Ohsvd 0.183 0 297 0 431 0 865 0 529 0 313 0 921 0 152 0 531 0 603
Methanol Calcd 0.182 0 308 0.437 0.849 0.531 0.274 0,912 0 143 0.563 0.596
Diff. -0.001
+0.011 +0.006 -0.016 $0,002 -0.039 -0.009 -0.009 +0.032 -0,007
Vapor Compn , Mole Ethanol Obsvd. Calcd. 0 579 0.579 0 493 0 481 0 386 0 382 0 051 0 049 0 224 0 193 0 408 0 383 0 035 0 026 0 521 0 477 0.215 0 265 0 255 0.249
Fraction Water Di5. +0.006 -0,012 -0.004 -0.002 -0 031 -0,025 -0.009 -0.044 -0,040 -0.006
O b s v d Calcd. 0 244 0 210 0 183 0.084 0.247 0 279 0 044 0 327 0 204 0.142
0.239 0.211 0,181 0.102 0 276 0.343 0.062 0.380 0.222 0.155
Diff. -0.005 fO.OO1 -0,002
+0.018
+0.029
i-0.064
f0.018 f0.053 +O.OlS f0.013
1332
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLEv.
Vol. 39, No. 1C
The data for the ethanol-cellosolveSLXMARY O F COMPARISOS O F CALCUL.4TED \'APOR LIQUIDEQCIL~BRI.~ n-ater sl-stem \\-ere predicted from the WITH OBSERVED D.4TA O X TERXARY SYSTEMS O F TYPE 11 binary data of the same authors ( 1 ) or. 7
Ternary System
Citation
Methanol-ethanol-water
(15) (16) (1)
Ethanol-Cellosolve-water
To. of Runs 40
Temp.,
72
0.7
C.
0.4
-Arithmetic Deviations---Yapor Compositions 1st compd., 2nd compd., 3 r d c o m x mole fraction mole fraction mole fraction 0.017 0.028 0 034 0.022
For this system it is possible to assume that the activity coefficient's for components Band Cn-ill be functions only of the amount of component -4 present in the mixture, and independent of the relative amounts of components B and C present. Thus, the lines of constant. activity coefficient for B and C will be parallel to the base BC of the triangle similar to the line GH, and they can be located from the data of their binary systems with component A . The constant activity curves for component A are located as described for t,ype I.
the Cellosolve and water system, and on the ethanol and Cellosolve systea nhich was found tobe ideal, The binary data of Jones et nl. (21) were used for 0.006 0.0'4 the ethanol and water system. The agreement in this ternary system i. even bet,ter than in the previous case, and this is doubtless within the limits o: accuracy of the ternary equilibria data. The summary of the cornparision of the calculat,ed and observed equilibria. data for both ternary systems of type I1 is shon-n in Table V. The predicted activity coefficients for t,he methanol-ethanolwater system were also tested for thermodynamic soundnesf b!. means of the Gibbs-Duhem equation as in the previous sectiori The agreement was well within the accuracv of the graphical wi1culations and the basic binary data. CORRELATION OF TERNARY SYSTEMS OF TYPE 111
8
C
Figure 3. Estimation of Curves of Constant Activity Coefficients for Ternary Systems w-ith One Binary System Having Deviations Opposite from Those of the Other Two Binary Systems (Type 111)
A cornparision of the calculated and observed equilibria data for the methanol-ethanol-rrater system is s l ~ o n nin Table IT'. The ternary data for the methanol-etl~anol-\ater systeln ( 1 5 ) calculated frQmthe binary data of the same authors The boiling point data for these mixtures TTere published separately (16) and used as one of the methods of analysis for the ternary mixtures. I n this case also the maxiInum errors occurred in the dilute alcohol region \There the vapor is sensitive to liquid composition. .bJso, in this region the accuracy of the method of analysis was the poorest, and deTy point calculatiom on the vapor compositions agreed better with the observed liquid composition. Thus, it is not impossible that, the calculated q u i libria are more reliable in this case than the observed equilibria.
TABLE\TI, CO-\fPa4RISOS O F
The ternary systems of t,his type contain one binary sys-cen; Kith negative deviations from Raoult's lam and two binary systems with positive deviat,ions, or one binary system with positive deviations and two binary Fystems vvith negative deviationt These ternary systems are probably the least common, and they have little practical application at the present time. The data o r only one such system have been reported; these were studied more as a unique case to broaden t,he present knodedge of vaporliquid equilibria rather than because of their practical utility. A study of the activity coefficients for this system will indicatt that neither of the methods used for the previous types are applicable to this case. In Figure 3 component A has a positive deviation from Raoult's law in the binary system ryith B component and a negative deviation in the binary system with component C I n this case the line of unity act,ivity coefficient of component -4 must lie between lines A B and BC, and, as a first approsiniatiorz it may be considered as perpendicular to side BC, as shonn. The1 all the other lines of constant activity coefficient may be d r a m t,hrough their proper points on the binary sides of the triangle anci parallel to the previous line. The binary RC also shoxvs positirt deviations; consequently the lines of con5tant activity for cornponent c are similar to that for component 9 and are dra\m prrpendicular t'o the 9 B side of the triangle. The lines of constanl activity coefficient of component C are located as curves by the Same method as 'Ised for systems Of type I. This method of correlation FT-as applied to the data on the acttone-benzene-chloroform system (%?), and the resuits are ijhowr. in Table VI. The average arithmetic deviations in this systen were based on the comparison of tIyenty-four evenly distributed runs out of the total 231 reported by Reinders and Dehlinjer (32, The average temperature deviation vias 0.7' C. in these twentyfour runs.
CALcEL.4TED A S D EXPERI~IESTAL VAPOR-LIQUID ACETOSE-HEXZESE-CHLOROFORSI SYSTEN
EQT-ILIBRI4 D.4T.k FOR
Yapor Cornpn.. Mole Fraction
Run KO. 6 20 50
80 110 140 160 180 200 220
.. Acetone 0.019 0,064 0,260 0.337 0.345 0.361 0.535 0.603 0.673 0.865
Liquid Compn.. AIole Fraction lcetone ~. Benzene Chloroforai Obsrd. Calcd. 0.792 0.189 0.034 0.039 0.630 0.115 0,306 0.118 0.408 0.342 0.366 0 360 0.437 0.226 0,480 0.478 0.157 0,498 0.419 0 401 0.051 0.393 0,588 0.381 0.176 0.648 0.641 0,290 0.126 0.271 0.706 0 . 70.5 0.279 0.048 0. 790 0.785 0.032 0.918 0.103 0.917 Average arithmetic deviatiaNns
Uiff.
+0.005 -0,003 -1-0.016 +0.003 +0.018
+0.012 10.007 +0.001 -0,005 +0.001 0.010
'Obsd 0.697 0 508 0.308 0.323 0.115
0.038 0.130 0,095 0.181 0,024
Benzene Calcd. 0 705 0 500 0,280 0 303 0.102 0 033 0.114 0,055 0 152 0.021
C:iiioroforrii
Diff-0 008 -0 008 -0 02E -0 022 -0 013 - 0 005 -0 016 -0 oin $0 001 -0 003
O.Ol0
Obsrd. 0.269 0.374
0.342 0.19i 0 484 0.581 0,229 0 200
0.029 0.059
Calcd. 0 256 0 38B 0 354 0 0 0 0 0 0 0
211
479 574 238 209 033 061
.-
Diti. -0 01:
+o +o
01 012
4-0 02c
-0 00: -0 00; +O
+o T O +o
one
005 004 001
0 01.
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1947
0 . 5 1 -
ETHANOL- BENZENE-WATER 25OC.
-t-----/
1333
0.5
*DISTRIBUTION DATA OF VARTERESSIAN B F M S K E O T I
0.4
0.3
0.2 0.I
'0
0.1
0.2
0.3
0.4
0
0.5
0.5
0.5
a4
0.4
0.3
03
0.2
02
0.1
01
0 0
0.1
0.2
0.4
0.3
0.5
00 0.0
0.1
0.2
o
0.1
0.2
03
04
05
0.3
a5
0.4
M O L E FRACTION OF SOLUTE IN AQUEOUS PHASE Figure 4.
Comparison of Calculated Distribution Data with Observed Data on \ arious Ternarj Systems
over the entire system. However, if thr lines of constant activity The predicted activity coefficients were also tested for thermocoefficient were drawn parallel a t the proper sngle to coincide dynamic soundness by the Gibbs-Duhem relation for ternary miuwith the activity coefficient a t the known saddle point instead tures, and the agreement n-as also nithin the accuracy of the of perpendicular to the base, the calculated vapor-liquid equilibria basic binary data. The lack of complete data on additional sysn-odd probably be w l l within the limit. of accuracy of any tems of this type makes it impossible to ascertain whether this reexrm-imental work. markable agreement is coincidental for this particular case; however, the method is invaluable in predicting the vapor-liquid equilibria for the entire system n ith a niininium of experimental PREDICT103 OF LIQUID DISTRIBI TIOY DATA data. One point might be used to determine the proper slopes for the lines of conatant activity of components d and C, and anSeveral methods (8, 28, 28.34) have been proposed for predictother point or tn o might establish the curvature of these lines. ing the liquid distribution data from vapor-liquid equilibria. Thus, it would be possible to predict the equilibria for remaining These methods mere summarized and tested by Treybal ( S d ) , mho system from only a feiT observed points. also suggested a nen- method. They are all based on different I n cases n-here the system exhibits a ternary azeotrope xhich is interpolations of the activity coeffjcient for the ternary system. knon-n, this )Jill suffice to check the method of correlation. As an illustration of this, the given method was used to predict the ternary saddle T ~ B L EF'II. SOURCES O F LIQCIDDI~TRIBUTIOX DATA ASLI \ ' - A P O R - ~ ~ I Q K I D point azeotrope in the acetone-chloroform-n~ethDATAUSED TO C A L C U L ~DISTRIBT-TION TE DATA m o l system. This system was studied by Enell Vapor Equilibria Liquid at and Welch ( l a ) ,who reported the saddle point at dtmospheric Pressure 21.8% methanol, 32.2% acetone, and 46.0% chloroA Solvent B Distribution Data form by weight. The average error of the calTernary System Temp., bmwFy. binary, Solute Solvent A Solvent B Citation O C. citation citation culated vapor composition a t this point was about I _ _
2 7 , ( 3 5 ) . This is about the maximum interpolation of the binary data and indicates that the average error in the vapor liquid equilibria calculated by the present method would be less than 1%
~~~~~~~
Acetone Acetone Acetic acid
Water ~ ~ ~ $ ~ e t a t eT a t e r Benzene Water Monochlorbenzene W-ater BenEene Water
(2,37:
(29, (17)
25 20 45 25-26 25
j15,36)
(2%
(96) (52) (26)
(92) (98) C28)
($0)
(14)
1334
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLE krIII. COlfPARIsON O F PRESENT LfETHOD O F PREDICTINQ TERNARY DISTILLATION DATAWITH PREVIOUS XETHODS
System Methanol-ethanol-water Ethanol-Cellosolve-water Ethanol-bensene-water
Method Colburn et al. (X) White (98) Present W h i t e (98) Present W h i t e (38) Present
Arithmetic Av. Deviations of Calcd. Vapor Compn., Mole Fraction 1st 2nd 3rd compd. compd. compd. 0.024 0.042 0.022 0.035 0.022 0.018 0.034 0.017 0.028 0.018 0,016 0,005 0.024 0,022 0.006 0.025 0,018 0.017 0.011 0.029 0,025
The empirical method described in this work has also been used to predict the liquid-liquid equilibria; the results are shown in Figure 4. The sources of the data for these calculations are given In Table VII. The agreement between the observed data and the calculated curves is seen to be excellent; the method can be used with good assurance when the vapor liquid equilibria and mutual solubility data are known. The method has been applied to other systems where the vaporliquid equilibria was estimated from one known point, such as the azeotrope temperature and composition. The results in these instances were indifferent; this indicates the futility of applying an accurate treatment t o uncertain data. Where the basic vaporliquid equilibria are uncertain, the simplest method-namely, that of Hildebrand (I@, Fhich ignores the mutual solubility data-could preferably be used to approximate the liquid distribution data. The present method gives exceptionally good agreement with all the observed distribution data, even a t high solute concentrations. All the previous methods fail in some of these systemj.
Vol. 39, No. 10
Ewell, R. H., and Welch, L. M.,Ibid., 37, 1224 (1945). Fritaweiler, R., and Dietrich, K. R., Angew Chem., 46, 241 (1933).
Gilmont, R., and Othmer, D. F., IND.ENQ.CHEM.,36, 1061 (1944).
Griswold. J . . and Dinwiddie. J. A.. Ibid.. 34. 1188 (1942). Griswold, J.: and Dinwiddie, J. .4., IND. ENO.CHEM.,’ANAL ED., 14, 299 (1942). Hand, D. B., J . Phys. Chem., 34, 1961 (1930). Hildebrand. J. H., “Solubility of Yon-Electrolytes,” 2nd ed. D. 184. Xew York. Reirihold Pub. Coro.. 1936. Hopkins, R. N., Yerger, E. S., and Lynch, C. C., J . Am. Chem SOC.,61, 2460 (1939). €Iovorka. F., Schaefer. R. A,. and Dreisbach. D.. Ibid., 58 2264 (1936). International Critical Tables, Vol. 111, p. 389 (1828). Jones, C. A , , Colburn, A. P., and Schoenhorn, E. M., ISD.E s o CHEM.,35, 666 (1913). Laar, J. J . van, 2. anorg. u. allgem. Chem., 185, 35 (1929). Lam, J. J. van, Z . physik. Chem., 72, 723 (1910): 83, 599 (19131.
Lewis, G. N., and Randall, &I,, “Thermodynamics and the Free Energy of Chemical Substances,” New York, McGrawHill Book Co., Inc., 1923. Othmer, D. F.,IXD.ESG. CHEM.,35, 614 (1943). Othmer, D. F., Friedland, D., and Scheibel, E. G., unpublished work. Othmer, D. F., and Tobias, P. E., IND.ENG. CH~M.,34,696 (1942). Othmer, D. F., White, R. E., and Trueger, E., I b i d . , 33, 1240 (1941). Perry, J. H., Chemical Engineers’ Handbook, 2nd ed., New York, McGraw-Hill Book Co., Inc., 1941. Quiggle, D., and Fenske, M. R., J . Am. Chem. SOC.,59, 1829 (1937). Reinders, W., and De-Minjer, C. H., Rec. trav. chim., 59. 392 (1940). Schneider, C. H., and Lynch, C. C., Ibid., 65, 1063 (1943). Treybal, R. E., IND. ENG.CHEM.,36, 875 (1944). Treybal, It. E., private communication. Tyrer, D., J . Chem. SOC.(London), 101, 1104 (1912). Vateressian, K. A., and Fenske, >I. R., IND.ENG.CHEM.,28. 928 (1936). White, It. R., Trans. Am. Inst. Chem. E ~ Q T s41, . , 539 (1945).
SUMMARY
The graphical methods presented in the previous sections can be used to predict ternary distillation data and liquid distribution data in nonideal systems with a reliability comparable to the accuracy of the binary vapor-liquid equilibria upon which themethod is based. The binary distillation data are known for numerous aystems or can be very readily determined when necessary. The ternary distillation data are relatively scarce and difficult to determine. The method has been found to have broader application than any previous methods and is much simpler to apply. Table VI11 shows a comparison of the application of the present method to diderent systems which have been studied by previous methods. In addition to these systems, the application of the present method has been demonstrated on the data on six other ternsrv system. reported in the literature.
CORRECTIONS Production of Alumina from Clay As a result of an error in drafting the flow sheet (Figure I, page 1055, August 1947), the alumina loss in the residue from the No. 2 filter is given as 491 pounds. The correct figure ie 49 pounds. This will bring the alumina input and output into balance, since the input is 349 pounds from the sinter and 16 pounds from the regenerated solution. The output is 316 pounds in the saturated solution and 49 pounds in the discarded residue. T. P. HIGNET-I TENNESSEE VALLEY~ U T H O R I T I WILSOXDAM,ALA.
LITERATURE CIThIJ
;1) Baker, E. AI,, Hubhard, R. 0. H., Huquet, J. €I., and hlichalowski, S. S., IND. E m . CHEM.,31, 1260 (1939). (2) Barbaudy, J., J . chim. phys., 24, 1-23 (1927). (3) Beech, D. G., and Glasstone, S., J . Chem. SOC.(London), 1938 67. (4) Benedict, M.,Johnson, C. -I.,Solomon, E., and Rubin, L. C.. Tram. Am. Inst. Chem. Engrs., 41, 371 (1945). ( 5 ) Briggs, S. W., and Comings, E. W., IND.ENG.CHEM.,35, 411 (1943). (6) Bromiley, E. C., and Quiggle, D., Ibid., 25, 1136 (1933). (7) Carlson, H. C., private communication. (8) Carlson, H. C., and Colburn, A. P., IND.ENG.CHEW 34, 581 (1942). (9) Colburn, A. P,, and Schoenborn, E. M., Trans. Am. Inst. Chem. Enors.. 41. 421 (1945). (10) Drickamer, H . G.,’Brown, G: G., and White, R. R., I b i d . 41, 555 (1945). (11) Ewell, R. H., Harrison, J. M..and Berg, L., IND.ENCI.CHEM.. 36, 87 (1944).
Handling Fresh Alfalfa before Dehydration The heading for Table I11 of this article, which appeared III the September 1947 issue (pages 1163-1165) is incorrect. It should read as follows:
TABLE111. C.4ROTESE CONTENT O F FRESHALFALFA FROM FIELD NO. 2 As printed on page 1164, it is, inadvertently, a repetition of the heading for Table 11. RALPHE. SILHEH H. H. KINQ KAKSAS AQRICULTURAL EXPERIMENT STATION
U A N H A T T A N , KANS.
