Effects of thermophysical property estimation on process design

Compvtm and &mid

Britain Engineering, Vol.1,pp. 18349. Pergamon Press, 1977. F’rintedinGreat

EFFECTS OF THERMOPHYSICAL PROPERTY ESTIMATION ON PROCESS DESIGN RICHARDS. H. MAH Department of Chemical Engineering, Northwestern University, Evanston, IL 60201,U.S.A. (Received 29 April 1977) Ah&act-This paper demonstrates the importance of relating thermophysical data estimation procedures to the design application of the information so generated. Examples are given of the utility of vapor-liquid equilibrium and solubility data in distillation and extra&e distillation. Computer-aided design techniques were employed to generate the property estimates and to evaluate their effects on distillation column designs. Specihc guidelines are developed on screening of data sources, determination of data requirements and verification of correlations. Scope-A distinct characteristic of process design is the use of large varieties of thermophysical properties. Accurate thermophysical properties are needed to predict process performance and to size processunits.But these properties are often tedious to gather, correlate or compute. The time and effort required in this step may be greatly reduced through the use of computer-aided process design (CAPD) systems such as FLOWTBAN. In these systems pure component properties such as critical temperature, pressure, compressibility, solubiity parameter, acentric factor, vapor pressure and enthalpy constants are stored in the data base. Retrieval for those components in the data base can be effected by simple instructions such as ‘DISPLAY METHANE ETHANE’[l]. For those components not in the data base facilities are provided to compute the coefficients for pure component physical property correlations from basic physical constants and experimental data on heat capacity, liquid density and vapor pressure. Since a substantial fraction of chemical processing involves solutions which deviate signitkantly from ideal solution behavior, many CAPD systems also provide capabilities for processing experimental phase equilibrium data to compute the parameters for liquid-phase activity coefficient correlations. In this paper we shall discuss the use of such CAPD techniques as well as the pitfalls of misusing them. Although the specific illustrations are based on the use of FLOWTRAN[l], the observations and conclusions are generally applicable to the use of other CAPD systems also. The effects of thermophysical property estimation on process design were studied cenchudertsaud~~ with reference to the design of a process to produce ethanol by diiect hydration of ethylene. The spechk examples considered are the extractive distillation of alcohols and the ether stripper distillation. The different vapor-liquid equilibrium estimations were evaluated in terms of their impact on the distillation column design. It was found that extensive extrapolation of binary data into ternary regions based on plaustble physical reasoning can be dangerous even when good quality data are available for the constituent binaries. Similarly it is dangerous to place too much significance on the values of the individual coefficients in any activity-coefficient correlation. On the other hand the use of bmary solubility data could be both simple and effective, when the components are sparingly soluble and no great extrapolation is involved. So long as the range of coverage is adequate the computing time for correlation may be reduced signiicantly by judicious selection of data points.

CORRELATION OFPEASE EQUII5IUlJM DATA For the sake of concreteness we shall illustrate our

remarks with reference to the design of a process to produce ethanol by direct hydration of ethylene[2]. The principal reactions in this case are: CaH, + Hz0 = CaHsOH 2C&OH

= (C&I&O + HaO.

Clearly any adequate representation of the process must require the thermophysical data of ethylene, water, ethanol and diethyl ether. But it is the presence of impurities in the feed and the occurrence of side reactions in the process, which immensely complicate the task of process design. The extent to which by-products such as higher alcohols (fuse1 oil), aldehydes and other unsaturates are accounted for in the process representation affects not only the number of species whose pure component data must be provided for in the design computation, but it multiplies combinatorially the

amount of experimental data needed to represent the phase equilibriumbehaviors. This assessment is based on the fact that for an n-component mixture the number of possible binary pairs is “Cz. Experimental data for all binary pairs will be needed, if they each behave nonideally and if all components are present at a given point in the process. Neither of these provisos should, of course, be taken for granted. Indeed a very useful feature of FLOWTRAN is that experimental equilibrium data are required only for those pairs which deviate significantly from ideal or regular solution behaviors. However, care must be taken in extrapolating the phase equilibrium correlations. As an example, let us consider the separation of ethanol and isopropanol by extractive distillation using water as the mass separating agent. The solution behaviors of binary pairs, ethanol-water and isopropanol-water, are both very far from ideal as manifested by the formation of minimum boiIing azeotropes. However, ample experimental data on these two binary pairs are available. One might conjecture that the be-

183

R. S. H. MAH Table 1. Van Laar coefficients for ethanol-water and isopropanol-water Data points

System Ethanol(l)-water&) Isooronanol(l)_water(2)

43 63

-0.0677 -0.481 Max error % 1 2 14.4 30.5

x

MODEL

0

MCOELII

-.-

CARSON

2 3x)z 0 f

-

aI2

ba,

b 12

1.3371 1.141

361.79 597.92

119.10 540.40

a21 f

d21

c21

0.01603 0.603

0 0.00149

Avg error % 1 2

7.5 10.6

2.3 4.6

1.4 1.7

I

ROBINSON

ET

AL (19541

AND

GILLILAND

! k2.0._

/

/

(1950)

/

/

/

,,

‘-\

.X’

/’

'\X \

/

/

\

O/

5

/

/ _...

/

/ ,’

X

/O

/ / / /’

./

./

/

,O/' / ,

/ /

I

OH' 0.0

0

I

IO

I

x)

I

30

1’

I

40

t

50

1

GO

I

70

1

90

I

90

I00

*

Water concentmtion (mole %I Fig. 1. Relative volatility of isopropanol to ethanol (etbanol/isopropanol = 20).

havior of the homologous pair (ethanol-isopropanol) will be closely approximated by an ideal solution.* Would a

correlation based on such a model give accurate prediction of phase equilibrium behavior? On the basis of a brief literature survey the experimental data of Othmer et al. [3] and Otsuki & Williams [4] were selected for the correlation of ethanol-water equilibrium and the experimental data of Wilson & Simons [5] and Barr-David & Dodge [a] were selected for the correlation of isopropanol-water equilibrium. Preliminary investigations indicate the van Laar equation as modified by Null[7] to be the most satisfactory representation for the liquid-phase activity coefficients in this case. Least-squares estimates of the van Laar coefficients[l] formulated with the logarithms of vaporization equilibrium ratios as the dependent variables are given in Table 1. As the magnitudes of the errors indicate, the binary data are quite satisfactorily correlated using the van Laar equation. By assuming ideal solution behavior for the homologous pair, ethanol-isopropanol, the ternary equilibrium behavior may be predicted using this model which will be referred to as Model I. Experimental data on the ternary mixture at great dilution of water were reported by Tobin et al. [9] and by

*For the binary system at 1 atmosphere this conjectnre is indeed borne out by experimental observations[l].

Carlson et aL[lO]. Figure 1 displays a comparison between the predicted values and experimental values of relative volatility at ditIerent dilutions of water but a constant ethanol-isopropanol ratio of 20: 1. Figure 2 displays a similar comparison at 80 mole percent water and diRerent ethanol-isopropanol ratios. In both cases the prediction deviates markedly from experimental data in both magnitudes and trends. As an alternative, we experimented with a model (Model II) in which the van Laar coefficients of the pair, ethanol-isopropanol, are adjusted to fit the limited ternary data. Nine data points at dilutions of 80,85 and 90% water were selected and only the lirst two van Laar coefficients were used. The results are shown in Table 2. In this case the curve fitting is quite rough, but the prediction using Model II gives a far better representation of experimental data than Model I, as shown in Figs. 1 and 2.

MTRACTME

DETILLATION OF ALCOEOLS

We next investigate how the accuracies of the thermophysical data correlations would be reflected in the process design. The design of an extractive distillation column to separate ethanol and isopropanol was discussed by Robinson & Gilliland. They carried out stageto-stage calculations using the relative volatility data of Tobin et al. Using a reflux ratio of 41.3 and introducing the feed on the 14th plate from the bottom, it was found

IXects

185

of thermophysicalpropertyestimationon process design

Table 2. Van Laar coe5cient.s for ethanol-isopropanol System

Data points

a21

a12

9

-3.243

-4.171

Ethanol(l~ isopropanol(2)water(3)

Maximumerror 46 1 2 3

Average error 96 1 2 3

40.1

17.9

27.2

34.5

15.9

16.3

t x

3.0 -

MOOELI

z

0

MODELE

f 8

•I

CARLSON ET AL

-

FtOBN9ON AND GILLILAND

0954) (1950)

5 g e 2.0 /

P ._ B r, .E

,x’

0

0

/ 0

/

/

X’

/

0

,

0

/’

Fo 1 1.0 ,-x-

.z ;

o*oh

IO

/A

/--

I

I

20

30

.X’

I

40

50

I

I

I

60

70

80

Ethanol /( ethanol + isopmpanal 1, ( male %

1

I

90

loo

*

Fig. 2. Relative volatility of isopropanol to ethanol (water concentration = 80%).

that 24 theoretical plates were needed to meet the design specifications summarized in Fig. 3. To provide a direct comparison rigorous distillation designs were carried out using the same reflux ratio and the same number of theoretical plates with enthalpy and phase equilibrium data generated using Models I and II respectively. The FLOWTRAN block, FRAKB, which is a Thiele-Geddes method proposed by Ball[ll] was used for this purpose. Liquid concentration profiles derived

Mot fmction of water =0.95 A /(

Dilute

ethanol

Spacificaticns: 99%

ethanol

isqwapard

recovery

with not war

on (I water free

0.2%

basis

Fig. 3. Extractive distillation system for isopropanol-ethanol.

from these computations are shown in Table 3. Vaporization equilibration ratios for the two FLOWTRAN cases are shown in Table 4 along with the relative volatilities reported by Robinson & Gilliland[9]. In all respects the design based on Model I data departs signi6cantly from the base case of Robinson & Gilliland, indicating the danger of extrapolating even when excellent binary data are available and used.

In practice the van Laar equation should be viewed as a purely empirical correlation: no significance should be ascribed to the numerical value of an individual coefficient. Since the computing time for data correlation increases with the number of data points, much time can often be saved by thinning out closely packed neighboring data points. As an illustration the van Laar coefficients were computed using 42 data points from Othmer et al. [3] and later recomputing using 21 of the 42 data points. The results shown in Table 5 give rise to comparable correlations, but the computing time was reduced from 33.4 to 21.5 system seconds. Notice also that the coefficients look very different from those shown in Table 1 even though predictions based on these coefficients are in fact quite comparable. In the extractive distillation example above, we showed the advantages of using ternary experimental data in mixtures of three or more components to avoid extensive extrapolation. But ternary data are generally more difficult to measure accurately than binary data and they are not always available. As an alternative, liquidphase activity coefficients can sometimes be estimated

R. S. H. M.u+

186

Table 3. Liquid concentration profiles in e&active distillation of alcohols (%) Robinson & GiBiland Ethanol Isopropanol Water Overhead 24 ;; 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Bottoms

14.5 4.63 6.0 7.44 8.86 10.1 11.05 11.8 12.3 12.6 13.0 13.4 13.5 13.55 13.6 13.65 13.7 13.7 13.7 13.8 13.8 13.8 13.8 13.35 10.4 4.76

36.7 10.4 8.89 7.23 5.63 4.2 3.01 2.15 1.54 1.13 0.87 0.71 0.6 0.505 0.42 0.355 0.293 0.24 0.1% 0.16 0.127 0.10 0.0785 0.057 0.033 0.0096

48.8 84.9 85.1 85.3 85.5 85.7 85.9 86.0 86.2 86.2 86.1 85.9 85.9 85.9 85.9 85.9 86.0 86.0 86.0 86.0 86.0 86.0 86.0 86.5 89.5 95.2

Ethanol

Model I Isopropanol

Water

Ethanol

Model II Isopropanol

Water

21.65 6.42 7.70 9.29 10.80 11.79 12.27 12.47 12.56 12.63 12.77 13.22 13.27 13.30 13.32 13.33 13.33 13.34 13.34 13.35 13.34 13.29 13.06 12.14 9.23 4.14

38.0712 8.8653 7.3461 5.0347 2.6874 1.1953 0.5169 0.2575 0.1651 0.1333 0.1230 0.1216 0.0537 0.0235 0.0103 0.0045 0.0019 0.0008 0.0004 o.ooo2 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000

40.28 84.71 84.% 85.67 86.51 87.01 87.21 87.28 87.28 87.24 87.10 86.66 86.67 86.68 86.67 86.67 86.67 86.66 86.66 86.65 86.66 86.71 86.94 87.86 90.77 95.86

13.44 4.35 5.35 6.31 7.12 7.72 8.13 8.44 8.75 9.17 9.82 10.97 11.11 11.30 11.53 11.78 12.05 12.30 12.54 12.74 12.90 12.98 12.86 12.03 9.23 4.19

37.3563 8.4991 7.3330 5.9775 4.5315 3.2264 2.2358 1.5778 1.1761 0.9422 0.8118 0.7581 0.7081 0.6421 0.5637 0.4781 0.3915 0.3098 0.2373 0.1763 0.1272 0.0889 0.0593 0.0357 0.0164 0.0042

49.21 87.15 87.32 87.71 88.35 89.05 89.63 89.98 90.07 89.89 89.37 88.27 88.19 88.06 87.91 87.74 87.56 87.39 87.23 87.08 86.97 86.93 87.08 87.93 90.75 95.81

Table 4. Relative volatilities and K-values in extractive distillationof alcohols Vaporization equilibriumratios

Relative volatilities Robinson & Gilliland Isopropanol Overhead

Model I Water

1.50

: 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

-

1.635 1.65 1.62 l.%

-

-

0.188 0.18 0.148 0.114

Model II

Ethanol

Isopropanol

Water

Ethanol

Isopropanol

Water

1.363 3.370 3.256 3.217 3.320 3.497 3.622 3.678 3.6% 3.693 3.667 3.582 3.597 3.602 3.604 3.603 3.602 3.600 3.599 3.597 3.5% 3.606 3.649 3.835 4.570 6.837

1.073 4.295 4.733 5.747 7.459 9.217 10.310 10.791 10.%3 11.002 10.957 10.764 10.894 10.949 10.%9 10.975 10.973 10.%9 10.964 10.959 10.958 10.976 11.072 11.491 13.057 17.321

0.736 0.476 0.473 0.481 0.510 0.549 0.576 0.589 0.594 0.595 0.595 0.593 0.597 0.598 0.599 0.599 0.609 0.600 0.609 0.600 0.600 0.601 0.602 0.608 0.637 0.748

0.6% 3.115 3.197 3.319 3.483 3.662 3.824 3.949 4.022 4.032 3.964 3.777 3.777 3.769 3.755 3.737 3.716 3.694 3.674 3.655 3.641 3.638 3.672 3.848 4.565 6.804

1.145 4.464 4.651 4.973 5.485 6.140 6.808 7.355 7.705 7.824 7.688 7.192 7.206 7.211 7.207 7.198 7.187 7.174 7.161 7.147 7.140 7.156 7.267 7.759 9.650 15.062

0.%9 0.555 0.557 0.557 0.558 0.559 0.563 0.569 0.576 0.582 0.586 0.587 0.5% 0.592 0.594 0.5% 0.597 0.5% 0.599 0.599 0.600 0.601 0.603 0.609 0.637 0.746

from solubility data, if two of the components are sparingly miscible. Diethyl ether-water is such an example. Again the adequacy of such a representation depends on the application. In the context of our illustrative exam-

ple, the application is the design of an ether stripper column which separates ether and light ends from alcohols and water. In addition to the binary data sources cited previously, we also have binary data on ethanol-

l

.

187

Effects of thermophysicalpropertyestimation on process design Table 5. Van Laar coefficients for ethanol-water System

Data points

a21

at2

b2,

brz

42 21

0.8312 0.7385

1.8775 1.9131

50.851 99.026

24.905 47.054

Ethanol(l)_water(2) Ethanoltlkwatert2)

d2,

c21

0.8156 0.002 1.1717 0.003

Max error % 1 2

Avg error % 1 2

15.0 12.2

3.6 3.8

10.0 9.7

4.8 4.8

hypothetical liquid state at lOOOKether and water form an ideal solution, i.e. ln ylm= 0. On this basis the temperature effects may be estimated. The van I.aar coefficients so estimated (Model III) are listed in Table 6 along with those estimated from ternary data (Model IV). On the face of it, these two sets of coefficients certainly look quite different. To determine the impact on the design, we carried out an ether stripper design with the FRAKB block using these two sets of coefficients in turn. The design conditions are specified in Fig. 4 and the liquid concentration profiles for the two cases are shown in Table 7. It is evident that the results of the design calculations do not differ greatly, even though a very simple and rough procedure was used to estimate the liquid-phase activity coefficients from the solubihty data.

diethyl ether and ternary data on ethanol-diethyl etherwater[l21. Instead of using the ternary data, the activity coefficients of diethyl ether-water may be estimated from mutual solubility data. Riddick and Bunger[l3] reported that at 25°C the solubility of diethyl ether in water is 6.04wt% and that of water in diethyl ether is 1.468wt%. Hence, the concentrations for the water-rich phase are XII= 0.0154 and xz’ = 0.985 and the concentrations for the ether-rich phase are xl”=0.!M22 and x,” = 0.05776, where subscripts 1 and 2 refer to diethyl ether and water respectively. For two liquid phases in equilibrium

As an approximation, we shall assume ytn = y2r = 1.

.9lUCTIONOF DATA AND VERIZTCATION

Whereupon we obtain

OF CORUELA’I’IONS

y? = 61.24

and

Even when experimental data are available, a great deal of time and effort can often be saved by carefully considering the following points: (1) Determine the temperature, pressure and composition range of interest and the accuracy required. The range of interest should, of course, be covered adequately by experimental dam, but contrary to one’s first expectation, too broad a range of coverage tends to ‘blur’ the correlation.

y2= = 16.98.

Rounding and extrapolating both coefficients to infinite dilution we get y;=90 and yz”=ZO at 25°C. As we raise the temperature the mutual solubility of ether and water increases. Let us assume that in a

Table 6. Van Laar coefficients for water-diethyl ether System

Data points

asi

at3

Water(lb Diethylether(3)

2

-1.93

-1.29

Water(l)ethanol(2k diethyl ether(3)

35

-13.76

-3.49

bs,

bra

~31

d31

1930 1290

0

0

6052

0

0

1909

Maximumerror 46 1 2 3

Average error % 1 2 3

-

-

-

74.9

-

77.1

417.2 35.4

-

-

27.7

53.3

Table 7. Liquid concentration profiles in ether stripper (%) MODEL III

Water Overhead 13 12 11 10 9 8

27.02 34.49 47.68 77.20 977;31 99.69 99.88

7 6 5 4 3 2 1 Bottoms

99.89 99.89 99.89 99.89 99.89 99.89 99.89 99.99

Ethanol

Isopropanol

69.94 65.24 52.25 22.77 2.68 0.29 0.11 0.10 0.09 0.09 0.09 0.09 0.09 0.09 0.01

MODEL IV

Ether

Water

Ethanol

Isopropaaol

Ether

0.2264 0.1175 0.0431 0.0076 0.0009 O.lMO4

2.8087 0.1512 0.0347 0.0209 0.0157 0.0149

27.79 35.96 51.03 82.50 97.52 99.56

69.62 63.78 48.89 17.45 2.41 0.36

0.2074 0.0956 0.0292 0.0040 O.MlO6 0.0003

2.3854 0.1694 0.0541 0.0515 0.0687 0.0782

0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0000

0.0148 0.0148 0.0149 0.0149 0.0150 0.0151 0.0151 0.0152 o.txtO3

99.77 99.79 99.79 99.79 99.79 99.78 99.78 99.78 99.98

0.15 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.01

0.0093 0.0003 0.0003 0.0003 0.0003 0.0003 o.aoO3 0.0003 o.OtmO

0.0803 0.0813 0.0821 0.0829 0.0837 0.0845 0.0853 0.0861 0.0084

R. S. I-f. MAH

188

Overhead = 0.2

82.96% 9.64% 0.05% 7.35%

Feed

Water Ethanoi lsopropcmal Diethyl ether

Dilute

ethanol

Fig. 4. Ether stripper. (2) Screen the sources of experimental data. For literature data, check to see if the author has (a) critically

evaluated previous data, (b) performed thermodynamic consistency tests, (c) adequately considered experimental equipment limitations and (d) replicated measurements with good agreement. (3) Select the number of data points to be used, bearing in mind that the activity coefficient correlations are, for all practical purposes, empirical and that the computing time required for correlating the data increases with the number of data points used. (4) Select the correlation model (in the case of FLOWTRAN-VLE, the selection will be amongst van Laar, Renon or Wilson equations) and the dependent variable (usually, logarithm of either vaporization equilibrium ratios or relative volatilies). Before carrying out the regression on phase equilibrium data, make sure that the pure component physical properties are correctly represented over the range of interest. In the context of FLOWTRAN the pure component physical properties may be computed and displayed using the ‘report block’, TABLE. Finally, after the regression is completed, compute and display the liquid-phase activity coefficients over the entire temperature and concentration range. In FLOWTRAN this step can be simply carried out using the ‘report block’, GAMX. It is a vital step in checking against the hidden danger of overfitting the experimental data. JIISCUSSION

For non-ideal solutions which are non-electrolytes and which do not exhibit limited miscibility, the Wilson equation is generally preferred even though it is computationally more complex than the van Laar equation. Empirical evidence suggests that it gives a more reliable extrapolation based on binary data. For the system, methanol-ethanol-isopropanol-water, the Wilson constants are given by Ohe et al. [ 141and Hirata et al. [ IS]. Using these constants and applying the Wilson equation to the data in Table 1, we obtained maximum errors of %.4 and 83.4% and average errors of 64.8 and 27.9% for ethanol and water respectively, and 98.0 and 85.0%, and 51.0 and 34.3% for isopropanol and water respectively. Extrapolation to the ternary system using the Wilson equation substantially under-estimates the relative vola-

tility (1.19 for 80% water and 1.28 for 90.5% water). But the extrapolation is monotonic and the changes are more gradual and on this basis one might argue that the Wilson equation gives a better representation of the ternary system than the van Laar equation. However, one must bear in mind the context of these applications, in this case, ethanol synthesis, and the fact that the current generation CAPD systems do not permit the use of more than one set of data estimation methods in a flowsheet simulation-a limitation which it would be desirable to eliminate. In view of the limited miscibility of ether and water, the van Laar equation is a better overall choice than the Wilson equation. The importance of relating thermophysical data estimation procedures to the ultimate application of the information so generated is clearly underlined by the foregoing examples. In a very real sense we cannot answer the question, “Is a given thermophysical property correlation satisfactory?“, without knowing how the data will be used. In the cases of ethanol-water and isopropanol-water, the quality of the binary data and correlations is excellent, but the design of the extractive distillation column requires extensive extrapolation of correlations. The uncertainties of the prediction could be all but eliminated with a minimum of ternary data points. By contrast, the ether stripper example shows the simplicity and effectiveness of using binary solubility data, when the components are sparingly soluble and no great extrapolation is involved. It is evident from the large variations of the numerical values of the coefficients generated from different data points that it is dangerous to place too much signiicance on the values of the individual coefficients. There is no particular merit in correlating excessive number of data points so long as the range of coverage is adequate. In fact, the computing time for correlation may be reduced significantly by judicious selection of data points. Acknowledgements-The examples used in the paper evolved from short courses on “Computer-Aided Design of Chemical Processes” held at Northwestern University during the past two summers. Acknowledgement is made of the contribution of Dr. C. A. W. DiBella of the United States Bureau of Mines and Professor J. D. Seader of the University of Utah in many stimulating discussions with the author.

REFERENCES

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Christopher, Composition of vapors from boiling binary solutions. Recirculation-type still and equilibria under pressure for ethyl alcohol-water system. Ind. Engng Chem. 43, 707 (1951). 4. H. Gtsuki & F. C. Wiiiams, Effect of pressure on vaporliquid equilibria for the system ethyl alcohol-water. Chem. Engng Progr. Symp. Ser. 49(6), 55 (1953). 5. A. Wilson & E. L. Simons. Vauor-liauid eauilibria. 2Propanol-water system. Ind. EhgngChem: 44,22’14 (1952). 6. F. Barr-David & B. F. Dodge, Vapor-liquid equilibriumat high

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189

12. W. P. Moeller, S. W. Englund, T. K. Tsui & D. F. Othmer, Compositions of vapors from boiling solutions. Ind. Engng Chem. 43,711 (1951). 13. J. A. Riddick & W. B. Bunger, Organic Solvents. Physical Properties and Methods of Purification, 3rd Edn, p. 205. Wiley-Interscience (1970). 14. S. Ohe, K. Yokoyama & S. Nakamura, ZHI Engineeting Reoiew (Japanese) 12, 211 (1972),cited extensively in Hirata ct al. (1975). 15. M. Hirata, S. Ohe & K. Nagahama, Computer-Aided Data Book of Vapor-Liquid Equilibria. Kodansha/Elsevier, Tokyo (1975).