Recovery of Ethanol from Fermentation Broths by Catalytic Conversion

Dec 28, 1981 - 3.09 X 10'. kEM. 2.26 X lo6 19.6 2.86 X lo6. kMA. 6.66 X lo4 19.7 9.95 X lo5. AM. 1.04 X lo5 19.7. 4.93 X lo6. kMN. 9.49 X lo4 19.8 1.1...
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Ind. Eng. Chem. Process Des. Dev. 1083, 22, 452-457

452

V. Summary of R a t e Parameters Obtained from Kinetic Model 2. Kentucky No. 6 C o a l high-temp range low-temp range (392-444 “C) (337-390 “C) rate parameter Aa Eb A E

Table

kCM kMH kHM kMN kNM

ME

kEM kMA

AM

9.80 2.45 3.35 9.49 1.96 3.27 2.26 6.66 1.04

X

lo5

x 10’ x lo5 X X X

lo4 lo5 10’

lo6 lo4 X lo5 X X

19.6 19.7 19.7 19.8 19.5 19.6 19.6 19.7 19.7

6.02 X l o 5 3.91 x 10’ 8.34 x l o 5 1.10 X105 4.61 X i o 5 3.09 X 10’ 2.86 X l o 6 9.95 X l o 5 4.93 X l o 6

Frequency factor parameter, min-’. energy parameter, kcal/g-mol. a

19.6 19.6 19.4 19.2 18.6 19.8 19.9 19.6 19.4

Activation

the large polar multifunctional compounds are intermediates which are formed by the initial breakup of the “coal molecules”. These multifunctional compounds are later converted into smaller and less polar compounds. Kinetic model two has been shown to describe this observation satisfactorily and to describe the coal liquefaction kinetics in the low-temperature region as well for Kentucky No.

6 coal and by Mohan and Silla (1981) for Illinois No. 6 coal. Model two, which does not account for retrogressive reactions, appears not to be affected by the observed solids formation in the high-temperature region, most likely because the amount of solids formed is small. The optimum kinetic parameters for model two are shown in Table V. The activation energy for all the reaction steps ranges from 18.6 to 19.9 kcal/g-mol. Mohan and Silla (1981) report activation energies of 17.2 to 29.3 kcal(g-mol for Illinois No. 6 coal. Acknowledgment The suggestions and help given by Dr. G . Mohan of Becton Dickinson Co., NJ, are appreciated. Registry No. Tetralin, 119-64-2; decalin, 91-17-8.

Literature Cited Han, K.; Dixit, V. 8.; Wen, C. Y. Ind. Eng. Chem. Process Des. Dev. 1976, 17, 18. Mohan, G.; Silla, H. Id.Eng. Chem. Process Des, D e v . 1981, 20, 349. Painter, P.; Yamada, Y.; Jenkins, R. G.; Coleman, M. M., Walker, P. L., Jr. Fuel 1979, 58, 293. Wakeby, L. D.; Davis, A.; Jenkins, G.; Mltchell, G. D.; Walker, P. L., Jr. fuel I979* 58, 379.

Received for review December 28, 1981 Accepted September 23, 1982

Recovery of Ethanol from Fermentation Broths by Catalytic Conversion to Gasoline Davld R. Whitcraft,+ Xenophon E. Veryklos, and Rajakkannu Yutharasan’ Depaflment of Chemical Engineering, Drexei Unlversity, Wladeiphia, Pennsylvania 19 104

The technical and economic feasibility of recovering ethanol from fermentationbroths by catalytic conversion to gasollne was investigated. Reactkns of diethyl ether, ethanol, and aqueous 95 wt % ethend over a shapsselecthre zeolite catalyst were studled In terms of product distributions, and the effects of pressure, temperature, and space velocity were established. Higher pressure was found to decrease the amount of gaseous hydrocarbons produced, while increasing the space veioclty had the opposite effect. An optimum temperature of 623 K was found to maximize the amount of liquid paraffins and aromatics with a corresporiding minimum in gaseous hydrocarbons. No significant effect of the presence of water in the feed stream was observed. A prelhninary analysis revealed that the proposed process could offer significant economic advantages over traditional processes of ethanol recovery.

Introduction In view of the national and international critical energy situation, non-petroleum materials are expected to become important energy sources during the next several decades. Particular attention has been directed in recent years tuward the utilization of coal as an alternative energy source. The difficulties and the environmental problems associated with the direct use of coal as a fuel are well-known. A second alternative for energy production from non-petroleum materials is offered by biomass utilization. Biomass represents the only replenishable, environmentally acceptable energy resource which could be developed and become available as a near to mid-term option. Research efforts in this field were undertaken in the period during ‘Joseph E. Seagrams & Sons Inc., Relay, MD 21133.

and after the second World War and have been intensified in recent years of energy scarcity. Thus, today, biomass is looked upon as an abundant, renewable, and attractive feedstock for both direct and indirect production of energy, chemicals, and intermediates. The first step toward the utilization of biomass as an energy source involves the production of ethanol from biomass. This process can be carried out in three steps: (1) pentosan hydrolysis of cellulose to fermentable sugars (glucose), (2) fermentation of pentosans and hexosans to alcohol, and (3) recovery of alcohol from the fermentor broth. The last step is the most energy-intensive one, primarily because ethanol is produced in small concentrations (typically 8-10 w t %) in the fermentor broth and because of the existence of an azeotrope in the ethanolwater system at an ethanol concentration of about 95 w t %. Thus, from the purely economic point of view, the use 0 1983 American Chemical Soclety

Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 453 2 9 Ib m o l e E

7 . 3 Ib molcrw

E :

Ethanol

Q3 :

5 1 0 , 7 0 0 Btu

W : Water Q1 : 2 , 4 1 4 , 8 0 0 B t u Q P : 1,102,600Btu Q,

:

1.036,300 B t u

Q8

:

86,600 Btu

Q.7 :

133,000 B t u

Q,

506,800 B t u

:

0.11:

1, 681,700 B t u IsuPPlemental

heat

1 1 . 4 Ib moles

36.3 Ib moles W

Figure 1. Energy flow diagram of the proposed process.

of biomass-based ethanol as a fuel becomes unattractive as compared to gasoline. Background The process economics of fermentation alcohol production center around the energy intensive step of ethanol separation from the broth (Chambers et al., 1979; Scheller, 1978). Several investigations on energy efficient means of ethanol separation have been carried out recently. For example, Ladisch and Dyck (1979) and Fanta et. al(1980) studied adsorbent drying, Black (1980) suggeated improved distillation method, Gregor and Jeffries (1979) investigated membrane processes, and Leeper and Wankat (1982) explored extraction techniques. In this paper we present a proposed scheme of recovering ethanol by conversion directly to hydrocarbons, which, being immiscible with water, require no energy expenditure for separation. It has been reported that energy required for ethanol recovery by distillation can be reduced tenfold if the ethanol concentration in the product is allowed to drop from 100 to 80%. In the past few years, scientists at the Mobil Oil Corporation Laboratories have succeeded in developing a process to convert methanol into high octane gasoline (Voltz and Wise, 1976; Meisel et al., 1976). This novel process offers a direct route for gasoline production from natural gas and from coal since the conversion of coal to methanol via synthesis gas is a well-established commercial technology (Danner, 1970). This technical breakthrough was achieved by the development of a new family of shape-selective molecular sieve (zeolite) catalysts. The most important characteristic of these catalysts (ZSM-5) is their particular pore structure which has appertures of such a size as to allow passage of molecules only as large as gasoline molecules (Change and Silvestry, 1977). Thus, only molecules in the gasoline boiling range can be produced. Other important aspecta of these catalysts include their favorable deactivation and regeneration characteristic~(Chang, 1980; Chang et al., 1978;Yurchak et al., 1979; Liderman et al., 1978) and the fact that they operate efficiently in the presence of steam at high concentration

levels (Voltz and Wise, 1976). This property is of particular scientific and practical interest since steam has been found to be detrimental to the operation of many zeolite catalysts (Venuto and Landis, 1968) and since water, at high concentrations, is being produced during the conversion of methanol to gasoline. A process involving the catalytic conversion of ethanol to gasoline offers a direct route for fuel production from renewable biomass resources. From the economic point of view, our preliminary studies show that such a process would be economically feasible. The objective of this study is to investigate the feasibility of converting aqueous ethanol to gasoline over a shapeselective zeolite catalyst (ZSM-5). The effects of process variables such as temperature, pressure, and space velocity on conversion and product distribution are established. A preliminary economic analysis based on the results of this study is also performed. Proposed Scheme The proposed process consists of two stages; in the first stage fermentor broth containing 8-10 wt % ethanol is distilled to 90 wt % solution. In the second stage the concentrated ethanol solution is dehydrated to diethyl ether or fed directly to a conversion reactor where either the ether or ethanol is converted to gasoline by use of a suitable catalyst. A very important consideration in the proposed flowsheet is the energy requirements. In Figure 1, the energy flow and requirements of the proposed scheme is presented on the basis of lo00 lb mol of fermentor effluent containing 3 mol % ethanol (7.32 w t %). The dilute ethanol solution from the fermentor is distilled to 80 mol % (-90 wt %) using heat recovered from the dehydration and conversion reactor. The vapor containing 80 mol % ethanol is heated to 315 OC prior to entry into the dehydration reactor. Both the dehydration and conversion reactions are exothermic to the extent of 5.8 kcal/g-mol ethanol and 19.4 kcal/g-mol of ethanol, respectively. Note that about one-third of the reboiler heat requirement is obtained by condensing the

454

Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983

product and cooling it to 105 O C . The flowsheet shown in Figure 1 depicts the various heat requirements rather than the optimum heat integration. The supplemental heat requirements are estimated to be approximately 1230 Btu/lb of ethanol. With a current energy cost of $8.00/106Btu, the supplemental energy cost of the process translates to less than l&/lbof ethanol processed or 11&/galof gasoline produced. Although corn-based ethanol has been estimated to cost about 7&/lb(Remirez, 1980) a more realistic cost estimat of grain alcohol (95%) is 10&/lb,which translates into $l.lO/gal of gasoline. Additional process costa including capital and operating costs are estimated to be 4t/gal of gasoline based on Mobil's methanol to gasoline process (Voltz and Wise, 1976). Hence the cost of corn based gasoline is approximately $1.25/gal. This cost estimate compares very favorably with the cost of pure grain alcohol which is $1.30-$1.40/gal (Remirez, 1980) keeping in mind that the energy content of gasoline is approximately twice that of ethanol, on a volume basis. It is obvious that the major fraction of the cost originates in the ethanol production steps. Any major breakthroughs in the ethanol production technology will greatly benefit the economics of the proposed process.

Experimental Section The conversion reaction was studied in a tubular, Ushaped, packed-bed reactor immersed in a constant-temperature fluidized sand bath. Each leg of the reactor is 50 cm in length and 12 mm in diameter. The entrance leg of the reactor was packed with 3.2 mm diameter mullite pellets. The catalyst, in amounts from 1 to 10 g, was pelletized to an average size of 0.2 mm and placed in the second leg of the reactor. Five thermocouples run inside a thermocouple well placed in the center of the reactor, and axial temperature profiles were continuously recorded in a multipoint temperature recorder. The reactant feed flow rate is monitored by a rotameter. The feed enters a preheater incased in a furnace where it is vaporized and heated to the reaction temperature. The first leg of the reactor serves as a final preheater. The pressure in the system is controlled by a back-pressure regulator. The existing product vapors flow through an ice-water condenser. The liquid products are collected while the uncondensable products are vented after their flow rate has been measured. Liquid and vapor products are analyzed by use of a gas chromatograph equipped with Porapak Q column, a temperature programmer, flame ionization detector, and thermal conductivity detector. Chromatographic signals are analyzed with a reporting integrator. Results and Discussion The effects of pressure, temperature, and space velocity on product distribution were investigated. In these studies the conversion of the feed was essentially complete. Diethyl ether was used as a feed since ethanol can easily be converted to diethyl ether with existing technology. Furthermore, studies with methanol indicate that diethyl ether might be an intermediate product in the dehydration of ethanol. In industrial operations the dehydration of ethanol to diethyl ether will be preferred since this is an exothermic process. On the other hand, if ethanol is contacted directly with ZSM-5 catalysts, the dehydration product seems to be ethylene, which is an endothermic reaction. Other feeds consisted of pure ethanol and aqueous ethanol at a concentration of 95% (w/w). Experiments with Diethyl Ether. Preliminary experiments with diethyl ether indicated that the catalyst

I

1 300

600 900 1203 Pressure iKPa J

1500

Figure 2. Effect of pressure on hydrocarbon distribution produced by diethyl ether at T = 573 K and WHSV = 0.498.

/

i

W H S V Lwt/wt/hr

Figure 3. Effect of space velocity on hydrobarbon distribution produced by diethyl ether at T = 573 K and P = 790.8 kPa.

was indeed active and that conversion to hydrocarbons did take place. The effect of pressure on the hydrocarbon distribution is shown in Figure 2 with a weight hourly space velocity (WHSV)of 0.498 g of catalyst per g of feed per hour. A t the highest pressure which was used a decrease in gaseous products and an increase in liquid products are evident. Figure 3 shows the effect of space velocity on product distribution at a pressure of 790.8 kPa (100 psig). Increase in space velocity resulted in an increase of gaseous paraffins with a corresponding decrease in liquid paraffii and aromatics. These experiments were conducted at a temperature of 300 OC. Experiments with Ethanol at Low Space Velocity. The details concerning the products obtained from the experiments conducted with 10 g of catalyst in the reactor are shown in Figures 4 through 6. Figure 4 shows the effects of temperature on product distribution. At each pressure used, the amount of gaseous hydrocarbons produced was minimized at 623 K, as shown in Figure 4 for a pressure of 790.8 kPa and a WHSV of 2.370. This reduction was anticipated when increasing the temperature

Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 455

90 -

80

-

70 -

60 -

5

50-

5

: 40-

0

B

?.

0 30-

30-

n > I

20-

20-

10-

10-

573

623

2

673

Figure 4. Effect of temperature on hydrocarbon distribution produced by ethanol at P = 790.8 kPa and WHSV = 2.370.

4

6

8

IO

12

W H S V ( w t /wf/hr I

Temperalure l K 1

Figure 6. Effect of space velocity on hydrocarbon distribution produced by ethanol at T = 623 K and p = 790.8 kPa.

toor 100

90

70

;40-)p=; Aromotics C5. Paraffins

-

30-

D

I” 20-

c1- c4

10-

Pressure l K P o 1

Figure 7. Effect of pressure on hydrocarbon distribution produced by aqueous 95% ethanol at T = 623 K and WHSV = 2.395.

mospheric pressure and 790.8 kPa. Further increase of pressure to 1480.3 kPa did not have a significant effect. Increasing the pressure also appeared to have the effect of increasing the aromatic to liquid paraffin ratio by a slight amount. From Figure 6 it is evident that increasing the space velocity results in an increase in the percent of gaseous hydrocarbons produced with a corresponding decrease in the amount of liquid hydrocarbons. This is expected to occur in view of the hypothesized reaction path in which light paraffins react further to produce heavier paraffins and aromatics. This trend occurs regardless of the temperature and pressure which was used. Experiments with Aqueous 95% Ethanol. In Figure 7 the effect of pressure on the hydrocarbon distribution produced by aqueous 95% ethanol at a temperature of 623 K and a WHSV of 2.395 is shown and appears to be very similar to the results from experiments with pure ethanol. The effect of space velocity at the same temperature and a pressure on 790.8 kPa is shown in Figure 8 and is again similar to that observed for pure ethanol. It appears that

456

Id.Eng. Chem. Process Des. Dev., Vol. 22, No. 3, 1983 I

1001

30

-

20 * 10 -

i . , . . . i 20 40 60 80 la 120 WHSV iwl/wt/hrl

Figure 8. Effect of space velocity on hydrocarbon distribution produced by aqueous 95% ethanol at T = 623 K and P = 790.8 P a . C, - C q

C5*ParaffIns

1 OOr

Aromatics I

I

80

60 40

20

i/I ROH

DEE

EtOH

DEE

DEE

EtOW

Figure 9. Comparison of hydrocarbon distributions produced by diethyl ether (WHSV= 2.124) and ethanol (WHSV= 2.370) at T = 573 K and P = 1480.3 kPa.

the existence of steam in the feed does not significantly alter the route of the reaction and the distribution of the products. It is believed that steam mechanistically affects the catalyst performance in terms of its activity and selectivity. No attempt was made in this investigation to characterize the role of steam. Nevertheless, in most of the experiments, conversion was in excess of 90%;thus the steam concentration over a significant portion of the reactor was very high. Effect of Feed. A comparison of hydrocarbon distributions produced by diethyl ether and ethanol under nearly identical conditions is shown in Figure 9 The higher amount of gaseous hydrocarbons produced by ethanol can be explained by the possibility that diethyl ether is the intermediate product in the initial dehydration of ethanol in the reaction. By the elimination of a reaction step, the conversion to hydrocarbons for the diethyl ether would proceed further and result in a higher percentage of aromatics produced. Experiments with Ethanol at High Velocity. In experiments conducted using only 1 g of catalyst at 623 K, the effect of space velocity on conversion was investigated. Results are shown for a pressure of 101.4 W a in Figure 10. Logically, the higher the space velocity, the lower the conversion. In addition to the effect on conversion, there is also a shift in product distribution resulting in all hydrocarbons formed being lass than CJ. The effect of pressure which was addressed earlier was evident

.

WHSV l w t / w t / h r l

Figure 10. Effect of space velocity on conversion of ethanol at T = 623 K and P = 101.4 kPa. Table I. Comparison of Hydrocarbon Distributions of Liquid Product and Gasoline wt % compound

this work

gasoline

pentanes hexanes heptanes octanes benzene toluene xylenes

18.91 19.87 11.02 6.84 0.00 8.48 12.79 22.01

14.15 15.90 12.64 12.52 1.17 10.10 13.35 20.25

c 9 -k

in this series of experiments and another effect appeared to be on the conversion, with higher pressure resulting in increased conversion. Again, the differences between runs at 790.8 kPa and 1480.Wa were minimal. Product Quality. No attempt was made in this study to investigate the quality of the liquid hydrocarbons produced from the conversion of ethanol. Nevertheless, a sample of commercial unleaded gasoline was analyzed as to the distribution of the various components. Table I shows the composition of commercial gasoline and the composition of the gasoline obtained in the laboratory. The composition of the ethanol derived gasoline is very close to that of commercial gasoline, which indicates that the qualities of both are very similar.

Summary and Conclusions The results obtained in this study established the technical feasibility of converting biomass derived ethanol to liquid hydrocarbon fuels which can be readily used as an energy source. The effects of process variables on the distribution of the products were investigated, but no opthimtion was attempted. Nevertheless, it is shown that over 80% of the hydrocarbons produced are in the liquid state. The light hydrocarbons produced can be recycled into the reactor so as to essentially produce only liquid products. This is supported from the results of this study, which indicate that an oligomerization process is taking place during the reaction, and from the results of other investigations (Voltz and Wise, 1976) using methanol as the feed over the same catalyst. The distribution of the liquid products obtained very closely resembles the components present in commercial unleaded gasoline.

Ind. Eng. Chem. PIocess Des. Dev. 1983, 22, 457-462

A preliminary conservative economic analysis shows that the proposed method of recovery of ethanol from fermentation broths is significantly less costly than other methods. Furthermore, important other advantages are realized when ethanol is converted to gasoline as compared to the direct use of ethanol as a fuel. The cost of producing gasoline from biomass is still significantly higher than the cost of petroleum-based gasoline. Nevertheless, biomass has an important advantage over petroleum: it is renewable.

457

Chang, C. D.; Kuo, J. C. W.; Lang, W. H.; Jacob. S. M.; Wise, J. J.; Silvestri, A. J. Ind. Eng. them. Process Des. D e v . 1978, 17, 255. Chang, C. D. Chem. Eng. Scl. 1980, 35, 619. Danner, C. A.. Ed. “Methanol Technobgy and Economics”, Chem. Eng. Rogr. S y v . Ser. No. 98, AIChE: New York, 1970; p 66. Fanta, G. F.; Bwr. R. C.; Orton, 0. L.; Doene, W. M. Science 1980, 210, 646. Qregor. H. P.; Jeffrles, T. W. Oovwnmnt Repart Announcement Index (US), 1979, 79(18), 215. Report order NTIS-PE-295645. Ladlsch, M. R.; Dyck, K. Science 1979, 205, 898. Leeper, S. A.; Wankat, P. C. In d. Eng. Chem. Process Des. Dev. 1982, 21, 331. Llederman, D.; Jacob, S. M.; Voltz, S. E.; Wise. J. J. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 340. Meieel, S. L.; McCullough, J. P.; Lechthaler. C. H.; Welsz, P. 8. CHEMTECH 1978, 6 , 86. Remkrez, R. Chem. €41.1980, 87(6), 57. Schelkr, W. A. “Energy Requirements for Grain Alcohol Productlon”, presented at 176th Natbnal Meeting of the American Chemical Soclety. Miaml Beech, FL. a p t 10-15, 1978. Venuto, P. B.; Landls, P. S. A&. Catel. 1988, 18, 259. Voltr, S. E.; Wise, J. J. “Development Studies on Conversion of Methanol and Related Oxywnates to Qaiesdlne”, Flnal Report to ERDA under Contract EX078C-01-1773, NTIS No: FE-1773-25, 1976. Yurchak, S.; Voltz, S. E.; Warner, J. P. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 527.

Acknowledgment

The authors would like to thank Veronica Burrows for her significant contribution on the economic and energy analysis of the process, and Mobil Oil Corporation for providing the catalyst for this study. Registry No. Ethanol, 64-17-5; diethyl ether, 60-29-7. L i t e r a t u r e Cited Black, C. Chem. €ng. Rog. 1980, 78(9), 78. Chambers, R. S.; Heredeem, R. A.; Joyce, J. J.; Penner- P. S. Science 1979, 206, 789. Chang. C. D.; Sllvestry, A. J. J . Cetal. 1977, 47. 249.

Received for review June 28, 1982 Revised manuscript received November 15, 1982 Accepted January 7, 1983

Modified UNIFAC Model for the Prediction of Henry’s Constants Carlos Antunes and Mmitrlos tamlor’ New Jersey

Insme of Technobgy, Newark, New Jersey

07102

A group-contribution model for the correlation and prediction of Henry’s constants in single solvents is presented. The model involves a onaparameter per gas/solvent group pair UNIFAC expresslon extended to incorporate free volume effects. The model Is appHed to t h e gases, CH,, N,, and 02,in alkane solvents and in water. oood results, inckKHng a successful description of the temperature dependency of the Henry’s constants, are obtained with typical accuracy of f 10% .

Introduction

Table I. Values of the Constants in Eq 2

The importance of gas solubilities in the chemical and petroleum industry has led to the development of several methods for the estimation of Henry’s constants in pure solvents. Most of these methods apply to nonpolar solvents (Prausnitz and Shair,1961; Yen and McKetta, 1962; Preston and Prausnitz, 1971; Gunn et al., 1974; Cycewski and Prausnitz, 1976, etc.). The last method is also applicable to polar solvents, but results are not very reliable with predictions to within a factor of 2, if care is exercised. Prediction of Henry’s constants, with a less general scope, however, is discussed by Mathias and OConnell(l979) and by Brandani and Prausnitz (1981). In recent years, group-contribution techniques, especially the UNIFAC model (Fredenslund et al., 1975), have been very successful in terms of accuracy and breadth of applicability for the phase equilibrium prediction of mixtures of subcritical compounds. A method for the prediction of Henry’s constants in pure nonpolar and polar solvents, involving conversion of available Henry’s constant values to symmetric infinite dilution activity coefficients and a modified UNIFAC model also extended to include freevolume effects, is presented in this paper. The method is demonstrated with three individual gases: 02,N2, and CHI in two solvents: water and alkanes. 0196-4305/83/1122-0457$01.50/0

A, A, A, A, A,

= 3.54811 =-4.74547 = 1.60151 = -0.87466 = 0.10971

T h e Proposed M e t h o d

Symmetric infinite dilution activity coefficient for a gaseous solute i in a given solvent (rim) are calculated from the corresponding Henry’s constant (Hi) at a pressure of 1 atm by using the following relationship .yi-

Hi -

fiL

where ft is the fugacity of hypothetical liquid i, at the system temperature and pressure of 1atm, obtained from the correlation of Prausnitz and Shair (1961). Their graphical correlation was fitted to the following polynomial In (fiL/Pc,) = A.

+ AITr;l + A2T,,+ A3Tr: + A,Tr:

(2)

where P, is the critical pressure of solute i and Triis the solute reduced temperature. Values for the constants A,, Al, A2,As, and A4 in eq 2 are presented in Table I. No 0

1983 American Chemlcal Society