Catalytic fluidized-bed combustion. Enhancement of sulfation of

Catalytic fluidized-bed combustion. Enhancement of sulfation of calcium oxide by iron oxide. Nirav J. Desai, and Ralph T. Yang. Ind. Eng. Chem. Proces...
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Ind. Eng. Chem. Process Des. Dev. 1083, 22, 119-123

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Catalytic Fluidized-Bed Combustion. Enhancement of Sulfation of Calcium Oxide by Iron Oxide Nlrav J. Desal and Ralph T. Yang' Department of chemlcal Englneerlng, sfat8 University of New York at Buffalo, Amherst, New York 14260

A small amount of iron oxide coated on the surface of dolomite particles Substantially increases both the reaction rate and the ultimate capacity for sulfur dioxide sorption. Although the iron oxide coating catalyzes the sulfation of Tymochtee dolomite, it has an inhibiting effect on Grew limestone. The Interplay of two opposing effects, increase in the chemical rate and a decrease in pore diffusionrate due to pore plugging, has been demonstrated by experiments with pellets made from pulverized Greer limestone. All kinetic data were fitted with a pore closing model with a varying porosity in the product layer. For Tymochtee dolomite with 1.08% (by weight based on CaO) Fe,O, coated on uncalcined stone, it has been shown, through a model, that for 90% sulfur retention a 40% reduction of the sorbent requirement can be achieved over the uncatalyzed case. Fluidization tests at 900 O C showed that no additional attrition of the sorbent particles was caused by the coated iron oxide.

Introduction In recent years, fluidized-bed combustion (FBC) has been recognized as a promising, versatile, and practical technology for clean combustion of coal. One of the crucial factors in determining the economica of the new technology is the overall Ca/S ratio, or the lime requirement. The Ca/S ratio has been assumed to be 2.5 in all of the conceptual designs of a 570MW atmospheric pressure combustor. This is based on using the most reactive limestones, such as the Greer limestone from West Virginia. The desire for new techniques to lower the Ca/S ratio is obvious. To lower the Ca/S ratio, both the reactivity and the capacity for sulfation of the lime would have to be increased. As various models for FBC have demonstrated (Horio and Wen, 1976; Chen and Saxena, 1977; Lee and Georgakis, 1981), the Ca/S feed ratio for the same sulfur retention is very much dependent on the reactivity (as measured with thermogravimetric or fixed bed reactors) as well as the sulfation capacity. The sulfation capacity is defined as the conversion at which the reactivity starts to decrease substantially, and the capacity is as important as the initial reactivity in determining the Ca/S ratio for FBC. Activation of the limestone sorbent can be achieved either physically or chemically. Physical activation involves mainly precalcination which enlarges the feeder pores. Chemical activation involves the use of additives such as NaCl (Gasner and Setesak, 1978). Application of the salt addition, although effective, has been hampered by the corrosion problem. It has been found that Fe203,in small quantities, can effectively catalyze the sulfation reaction (Yang, 1978; Yang and Shen, 1980). It has been suggested that coating of the small amounts of iron oxide on the limestone particles can be achieved by spraying the sorbent prior to feeding to the combustor with an aqueous solution of iron salt, which rapidly decomposes in the combustor leaving a layer of Fe203coating. In this paper, we present our results on studies of the mechanism, as well as the detailed kinetics of the iron oxide catalyzed sulfation reaction. We further discuss various aspects of utilization of the catalytic effeds in FBC. Experimental Section Catalyst Coating Procedure. The sorbent samples were soaked in an aqueous solution of an iron salt (Fez0196-4305/83/1122-0119$01.50/0

or Fe(N0,)J at room temperature, followed by drying and thermal decomposition. The amount of iron salt coated on the sorbent was controlled by varying the concentration and the soaking time. The iron salt decomposed rapidly to iron oxide below 570 "C in the thermogravimebic (TG) reactor. The amount of iron oxide coated on the sorbent was determined by measuring the weight loss due to thermal decomposition and comparing such a loss from a blank sample. Weight loss due to moisture was below 150 "C and distinct from the weight loss due to thermal decomposition of ferric nitrate/ferric sulfate. Some of the iron oxide-coated samples were examined by cutting the particles and inspecting the distribution of the reddish iron oxide. For all the coated samples examined, it was clear that the iron oxide was coated only on the exterior surface. The method of determining the amount of iron oxide coated on the sorbent was verified by atomic absorption on one sample (as analyzed by Galbraith Laboratories, Knoxville, TN). Measurement of Reactivity and Capacity of Sorbent. The reactivity and capacity of the sorbent was measured in a TG reactor. The TG measurements were performed at 1atm total pressure with a Mettler 2000C thermoanalyzer system which had a sensitivity of 5 Fg. A small quartz boat with an area of about 0.85 cm2was used as the sample holder. About 60 mg of the sorbent was spread into a thin layer on the holder. The sample was then heated at 25 OC/min to the desired sulfation temperature in a flowing gas mixture of 95% argon and the balance oxygen. The end of the calcination was indicated by a zero weight loss on the thermoanalyzer system. Sulfation immediately followed the calcination reaction. Three Tylan mass flow controllers were used to control the flows which were proportioned to simulate the combustion gas (0.3% SOz, 5.0% 02, and the balance Ar). Flow rates of the sulfating gas for reaction and argon for calcination were equivalent to a linear velocity of about 3 cm/s. The velocity was predetermined to be high enough to minimize gas-film diffusion resistance. Materials. The Greer limestone (originally from Morgantown, WV) was obtained from Argonne National Laboratory. It gave the following chemical analysis: CaC03 = 80.4%, MgCO, = 3.5%, Si02 = 0.39%, FezO3= 1.24%, A1203 = 3.19%, Na20 = 0.23%, and 1.17% H20. The Tymochtee dolomite (originally from Huntsville, OH) was obtained from Argonne National Laboratory and gave 0 1982 American Chemical Society

120

Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983

Table I. Amounts of Fe,O, Coated o n Uncalcined Tymochtee Dolomite soaking time, concn and iron salt min

batch no.

Fe(NO,), Fe(NO,), 2 M Fe(NO,), 1M Fe(NO,), 1 M Fe(NO,), 1 M Fe(N0,L ..- t 1% snc1, 2 M Fe(NO,),

1

sat. sat.

2 3 4 5 6

I 8 9

1M Fe,(SO,), + 1 % SnC1, 1M Fe(NO,), t 1%NaNO, 1 M Fe(NO,-), 1MFe(NO,), t 1% KNO, 1 MFe(NO,), t 1%Cu(NO,), 1 M Fe(NO,),

11

12 13 14 15

I

I

I

% Fe,O,

on CaO

10

0.91

6 6 10 5 5

0.88 0.85 0.12 0.67

10 5 5

1.08 0.51 0.51

15

0.80

15

30

0.83 -3.2

30

-3.2

30

-3.2

0.61

0

,

I

0

-3

I

30

I

60

I

90

1

120

I

150

so

$0 120 TIME, WIN

150

la0

Figure 2. Effect of Na20 aa a promoter for Fe20s-catalyzed sulfation. Batch numbers are: 11 (A)and 12 (0).

I

4ot-

30

lk

TIME, MIN.

Figure 1. Iron oxide-catalyzed sulfation of Tymochtee dolomite (12-20 mesh) at 900 O C , 1 atm in 0.3% SOz, 5% 02,and 94.7% Ar. Batch numbers (see Table I) are: 1 ( O ) , 2 ( O ) , 3 (A),4 and 5 0 , 6 (A), 7 ( O ) , 8 and 9 (0) (lowest), 13 to 15 (e), and uncoated (m).

the following analysis: CaC03 = 51.5%, MgC03 = 43.0%, SiOz = 3.6%)A1203 = 1.5%, Fez03 = 0.4%) Na20 = 0.07%. The chemicals used were reagent grade and the gases were prepurified grade.

Results and Discussion A complete study was made of the catalytic effects of Fe203on the sulfation of Tymochtee dolomite. Table I gives the sample preparation and designations for all samples included in the kinetic study. Figure 1shows the rates of sulfation of the various samples listed in Table I. It is clearly seen from the results that both the reactivity and capacity of the dolomite are increased by small amounts of coated Fe203. However, this was not true of samples which were coated with a solution containing ferric sulfate (samples no. 8 and no. 9). As seen from Figure 1, the sulfation capacity for samples coated with ferric sulfate is reduced by about 12.0% in comparison to the untreated dolomite. This could be explained by the fact that the

Sod2-ions in a solution containing ferric sulfate could neutralize some of the surface carbonate causing partial plugging of pores and also partial conversion of lime to calcium sulfate. This would also explain the decrease in the initial rate of sulfation. In contrast to this, a solution containing NO, ions (asin a solution of ferric nitrate) may also neutralize some surface carbonate forming calcium nitrate. However, calcium nitrate decomposes at 400 "C, which is much lower than calcination temperatures normally encountered in fluidized-bed combustors (near 900 "C). In contrast to this, calcium sulfate does not decompose at the FBC temperature (it decomposes at about 1250 "C), thus leaving a partially plugged structure on calcination of the dolomite at 900 "C. As seen from Figure 1, dolomite coated with approximately 1.1% Fez03 (from nitrate solution) showed the maximum capacity and reactivity. After 3 h of sulfation, the capacity was 65% higher than that for the uncoated dolomite. For samples with a higher Fe203loading, Le., 3.2%, the initial rates were higher but the "capacity" was lower than samples with lower Fez03 loadings. Promoters for Catalyzed Sulfation. It was also intended to see if a small amount of promoter, of the order of 1% by weight of the catalyst, could enhance the catalytic effect. Ferric oxide is an n-type semiconductor oxide with excess electrons, and it was thought that increasing the electron density would increase the activity (Ashmore, 1963). Thus the addition of oxides such as Sn02 would increase the activity, and K+ or Cu2+should decrease it. These oxides have been tried in our study. As seen in Figure 2, the addition of sodium oxide as promoter showed a considerable increase in the reactivity and the capacity. After 3 h the conversion was increased by 11%. Other experiments with promoters such as K20 and CuO showed a small increase in reactivity with no significant increase in capacity. It was also observed (Figure 1) that SnClZhas an inhibition effect on the sulfation reaction. From these results, the electron transfer mechanism (between SO2and the surface) is not likely the rate-limiting step in the lime sulfation reaction. Effects of Fea03on Other Lime Sorbents. The catalytic effects of Fe203 were also studied with other sorbents. Besides Tymochtee dolomite, Greer limestone has been the other popular sorbent being used in the U.S. The aforementioned coating procedure (from nitrate solution) was applied to 12-20 mesh size (US.mesh is used throughout the paper) uncalcined Greer limestone, and the results are shown in Figure 3. Both the rate and the capacity for this sorbent was decreased by FezO3coating. Thus Fe203coating actually decreased the overall rate. To

Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983 121

2.0

0

30

60 TIME,MIN.

Figure 3. Sulfation of Greer limestone particles of 12-20 mesh size under conditions same a~ in Figure 1, for uncoated sample (O),Fe203 (ca. 1%) coated sample (O),and the following samples which were pulverized to 200-325 mesh followed by repelletization and reduction to 12-30 mesh: uncoated (A), mixed with 1% Fe203powder (01, and coated with 2.0% Fe203(0). i5,1(@,,

,

PORE MUIETER(pm) 10, , , , ( , , f , , , , , (r o . l r , ,

, w 7

2.4

il g .3 >

t

k1 &,, 0

1

10

100 P R E k b Y

io'

, , ,,,,,,, , , 109

0.9 111011 OXIDE,%

Figure 5. Effect of the amount of iron oxide coated on dolomite on the reaction rate constant at 900 OC.

120

90

0.7

,

j

)

Figure 4. Cumulative pore volume distribution for sorbents calcined at 900 OC: Greer limestone (A), Tymochtee dolomite (01, and pulverized and repellatized Greer limestone (0).

understand the influence of pore structures on the catalytic action, we used pulverized and repelletized samples. The stone was pulverized to 200-325 mesh and the powder was pelletized with a small amount (of the order of 1-2%) of water-based Sauerisen cement. The cement is a silicate based material which has no sulfation activity. The pellets were further reduced to 12-20 mesh size. Compared with the original stone, this procedure increased the total porosity from 0.494 to 0.61 and the surface area (BET N2) from 4.8 to 11.17 m2/g. The effect of Fez03 coating on the pulverized-repelletized sample is also shown in Figure 3, and a positive effect is indeed seen. The rate and capacity were substantially enhanced with the blank sample over the original 12-20 mesh sample. Fe203,both coated and physically mixed, further increased the sulfation rate and capacity, as shown in Figure 3. Before the rates are analyzed in terms of chemical rates and pore diffusion rates, as will be done in the following section, it is desirable to have qualitative understanding of the conditions when the Fe203 coating process would apply. To this end, complete pore size distributions for the following three calcined samples were measured with a mercury porosimeter: Greer limestone, Tymochtee dolomite, and the pulverized/repelletized Greer limestone (Figure 4). The only plausible interpretation from the pore size analysis as shown in Figure 4 is that the applicability of the Fe203coating process depends on the pore

volume of pores larger than ca. 0.5 pm. These large pores may be called feeder-pores. The majority of the pores are smaller pores, with sizes of 0.1 to 0.4 pm for the three samples. These smaller pores are more subjective to pore plugging by Fez03 during impregnation. The feeder-pores are less likely to be affected. Thus in Greer limestone, due to the lack of the feeder-pores, Fe203decreases the overall rate, whereas in the two other samples in which the volume of feeder-pores is relatively large, Fe203 coating increased the rate. Chemical Rates from Initial Rate Data. Although the mechanism of the sulfation reaction is not understood fully, it is known that the degree of sulfation of MgO in dolomite is negligibly small as compared with that of CaO (Yang et al., 1975). Thus the rate of sulfation of dolomite as well as limestone may be represented as rate = k,S,Coq g-mol of CaO/s (1) where k, = reaction rate constant per unit surface area, S = internal surface area, Co = ambient concentration of and q = effectiveness factor, used to represent the degree to which the reaction occurs within the internal structure of the solid. The rate constant for the sulfation reaction may be determined by

Sb2,

k , = sS, L d dtx / t-oG

(2)

At low conversions (X), q = 1. Thus the chemical rate constant may be determined by the initial rate using eq 2.

Figure 5 shows the dependence of the reaction rate constant k, with the amount of iron oxide coated on the dolomite. It is seen that the dependence is linear up to a concentration of 1 % Fe203. Higher concentrations of iron oxide on the dolomite do not increase the rate constant appreciably. Interplay of Chemical Reaction and Pore Diffusion. A number of mathematical models have been proposed in order to quantitatively account for the interactions between chemical and diffusional resistances for the lime sulfation reaction (Pigford and Sliger, 1973; Hartman and Coughlin, 1976; Ramachandran and Smith, 1977; Georgakis et al., 1979; Lee, 1980; Bhatia and Permutter, 1981; Christman and Edgar, 1981). The computational difficulties encountered in detailed gas-solid reaction models limit their use in the modeling of SO2 absorption in fluidized bed combustors. In view of this, we have used a simple pore closing model to fit our experimental results (Ramachandran and Smith, 1977; Lee, 1980). Figure 6 shows that the model predictions are satisfactory at low conversions (X below 15%). The fitting parameter D (effective diffusivity through the product sulfate layer)

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Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 1, 1983

/

1' 0

10

20

-_-

1

10 20 CONVERSION( X ),%

30

TIME,min

Figure 6. X-t behavior for sulfation of dolomite under conditions same as in Figure 1: experimental data ( O ) ,predicted by models of Ramachandran and Smith (with D = 1.2 X lo4 cmz/s) (lower curve) and of Lee with D = 8 X lo4 cmz/s (upper curve).

Figure 8. Variation of porosity ae calculated by eq 3 and the pore closing model for samples no. 1 ( O ) , 2 (A), and 3 (0).

1

8,

0

10 Ca/S

2.0 RATIO

30

40

Figure 9. Predicted sulfur retention in a fluidized bed combustor operated at 900 OC,0.6 m/s gas velocity and 2 m bed height using the following Tymochtee dolomite: uncoated (A) and Fez03-coated Batch no. 7 ( O ) , 11 (O), 13-15 (0). 0

0.1

0.2

03

CONVERSION (X)

Figure 7. Variation of effective pore diffusivity in product layer with overall conversion for dolomite samples Batch no. 1 ( O ) , 2 (A), and 3 (0).

took the value 0.8 X cm2/s. This is comparable to values obtained previously, i.e., 1.2 X cm2/s (Ramachandran and Smith, 1977) and 6 X cm2/s (Hartman and Coughlin, 1976). One of the major drawbacks of the pore closing model is the assumption of a constant diffusion coefficient in the product layer p . In reality, since calcium sulfate has a molar volume about three times larger than that of calcium oxide, the accumulation of reaction product causes the porosity to decrease and diffusional resistance to increase. Thus in order to obtain a better fit at higher conversion, the effective diffusivity in the pores was varied with conversion. Figure 7 shows the diffusivity profile with conversion for three different coated samples of dolomite. Diffusion in porous bodies may be described by (Desai and Yang, 1982).

D = D,-

€2

r

(3)

D,is the gas-phase diffusivity, t is the porosity of the solid, and 7 is the tortuosity factor. Assuming constant tortuosity through the course of the reaction, the porosityconversion relationship may be calculated from eq 3. The porosity-conversion relationship is plotted in Figure 8. To discuss the pore closing model with a varying porosity in the product layer, it is helpful to visualize the reaction system. A lime particle contains many small grains. As the reaction proceeds, the outer grains experience higher conversions than do the inner ones. So as the overall conversion is increased, the porosity in the product layer is expected to decrease, as suggested by Figure 8 from our

data fitting, and the effective diffusivity through the product layer is decreased as suggested by Figure 7. Predicted Performanceof FBC Using Fe203Coated Dolomite. Although several models for FBC performance exist, the computational complexities involved in the detailed gas-solid reaction models prohibit their use in the modeling of SO2absorption in fluidized bed combustors. The simple semianalytical expression obtained by Georgakis et al. (1979) will now be applied to predict the performance of FBC based on our data on the catalyzed sulfation of dolomite. The two parameters, p* (the pore plugging constant) and 7,f (the sulfation time), can be estimated from sulfation reaction data. (4)

By plotting In (1 - ( a / a J vs. time the value of p* is obtained by linear regression and eq 4. The sulfation time may be calculated by 7,f

=

p*(MW a-p,*x,

(5)

Using typical values of Uo, the superficial gas velocity, and h, the expanded bed height in a fluidized bed, the fractional SO2retention vs. Ca/S ratio relationship was computed by the model developed by Georgakis et al. (1979) (Figure 9). Figure 9 contains four sorbents based on our kinetic data. In all the computations, the fluidization voidage was assumed to be 0.45, Uo= 0.6 m/s, and h = 2 m. I t can be seen that for a calcium to sulfur ratio of 2.5, sulfur retention is increased by about 30% for the 1% FeaOgcoated dolomite. On the other hand, by using coated dolomite (sample 7, with 1.08% Fe203),the amount of calcium required for 90% sulfur retention is 40% less than

Ind. Eng. Chem. Process Des. Dev. 1083, 22, 123-129

that for the untreated dolomite. Attrition. The question of attrition concerns both the loss of iron oxide and the loss of lime. We have measured the iron contents and the size distributions before and after the fluidized-bed sulfation experiments. The sulfation was done at 900 "C for 5 h at a fluidization velocity of 3 ft/s. The sulfator was a 1-in. diameter quartz tube, operated batchwise. Neither loss of Fez03 nor additional size attrition was detected in these experiments. Detailed data have been reported (Yang and Shen, 1978). Acknowledgment Dr. Ming Shing Shen (presently at Laramie Energy Technology Center) contributed in the initial phase of this research. This work was supported by the Department of Energy under Contract DE-AS21-80MC14617. The thermogravimetric analyzer was purchased under a grant from National Science Foundation No. CPE-8012357. Nomenclature C = concentration of SOz at exit of dense bed, g-mol/cm3 Co = ambient concentration of SOz, g-mol/cm3 D = effective pore diffusivity in roduct layer, cmz/s D, = diffusivity in gas phase, cm /s h = expanded bed height, cm or m k, = rate constant, cm/s MW = molecular weight of calcium carbonate, g/g-mol p* = pore plugging constant, g-mol.s/cm3 S, = surface area of calcined sorbent, m2/g or cm2/g t = time, s Uo= superficial velocity, cm/s or m/s X = fractional conversion of CaO to CaS04 X , = weight fraction of calcium carbonate in uncalcined stone

Y

123

Greek Letters a = fractional conversion of CaO to CaS04 a, = maximum conversion t = porosity 7 = effectiveness factor p*s = density of calcined stone, g/cm3 r = tortuosity factor r,f = sulfation time, s Registry No. SO*, 7446-09-5; CaO, 1305-78-8;Fez03,1309-37-1; dolomite, 17069-72-6. Literature Cited Ashmore. P. G. "Catalysis and Inhlbltlon of Chemical Reactions"; Butterworths: London, 196% Chapter 8. Bhatla, S. K.; Permutter, D. D. AIChE J . 1978, 27, 226. Chen, T. P.; Saxena. S. C. Fuel 1977, 56, 401. Christman. P. G.; Edgar, T. F., Annual AIChE Meetlng. New Orleans, LA, Nov 1981. Desai, N. J.; Yang. R. T. AIChE J . 1982, 28. 237. Gasner, L. L.; Setesak, S.E. "Proceedings,5th International Conference on FluMlzed Bed Combustlon"; MITRE Corp.: McLean, VA, 1978; Vol. 11, p 763. Georgakls, C.; Chang, C. W.; Szekely, J. Chem. Eng. Scl. 1979, 3 4 , 1072. Hartman, M.; Coughlln. R. W. AIChE J . 1978, 22, 490. Horb, M.; Wen, C. Y. "Fluldizatbn Technology"; Keaime. D. L., Ed.; MceawHIII: New York, 1976; Vol. 11, p 289. Lee, D. C.; Georgakis, C. A I C M J . 1981, 2 7 , 472. Lee, H. H. Ind. Eng. Chem. Process Des. D e v . 1980, 19, 242. Plgford, R. L.;Silger, G. Id. €178. Chem. PrOcessDes. Rev. 1973, 72, 85. Ramachandran, P. M.; Smlth. J. M. AICM J . 1977, 23, 353. Yang. R. T. Fuel 1978, 57, 709. Yang, R. T.; Cunningham, P. T.; Wilson, W. 1.; Johnson, S. A. "Sulfur Removal and Recovery"; Pfeiffer, J. B., Ed.; American Chemical Society: Washington, Dc, 1975; p 149. Yang. R. T.; Shen, M. S. "Catalytic FiuMized Bed Combustion"; BNL Report 24653, Brookhaven National Laboratory, Upton, NY, 1978. Yang, R. T.; Shen, M. S. U.S.Patent 4191 115, 1980.

Received for review March 2, 1982 Accepted August 16, 1982

Prediction of Vapor-Liquid Equilibrium from Ternary Liquid-Liquid Equilibrium Data David Yee, Jose Slmonetty, and Dlmltrloo Tassios' Department of Chemical Engineering and Chemistry. New Jersey Institute of Technoey, Newark, New Jersey 07102

Reasonable estimates of ternary vapor-liquid equilibrium can be obtained by using the corresponding liquid-liquid equilibrium (LLE) data with the NRTL, LEMF, and UNIQUAC models. The overall average absolute deviation in vapor-phase concentrations for seven such systems is 0.028, but better predictions are realized along the important, for three-phase distillation calculations, binodai curve. Use of the UNIFAC method gives erratic predictions suggesting caution when applied to such systems. Combination, however, of the LLE data and the UNIFAC method gives the best results with a deviation of 0.020. Prediction of binary VLE behavior from LLE data also yields reasonably good results.

Introduction Vapor-liquid equilibrium (VLE) data are essential in process design calculations, especially distillation. Since such data are not often available, prediction schemes are employed. For binary systems, group contribution techniques, especially the UNIFAC model (Fredenslund et al., 1975; Magnussen et al., 1981),can be used if the necessary interaction parameters are available. For multicomponent systems, good predictions can be achieved if VLE data for the corresponding binary systems are available. If not, the UNlFAC model can be used, with less confidence, however, provided again that the appropriate interaction parameters are known. 0196-4305/83/1122-0123$01.50/0

Another possible prediction scheme involves the use of multicomponent liquid-liquid equilibrium (LLE) data, for in principle at least, one can correlate these data with an appropriate expression for the excess Gibbs free energy to evaluate the parameters for the corresponding binary systems. These parameters can then be used in the prediction of the VLE behavior of the same system, or, combined with parameters obtained from VLE data for other binaries, in the prediction of multicomponent VLE behavior. Since LLE data are plentiful (see, for example, Stephen and Stephen, 1963; Sorensen and Arlt, 1979; Arlt et al., 1981),such an approach, if successful, could provide a very helpful scheme for the prediction of vapor-liquid 0 1982 American Chemical Society