Ind. f n g . Chem. Process Des. Dev. 1985, 2 4 , 537-541
537
Literature Cited
Different results were instead obtained with the total holdup model. The optimal order of the reaction changed depending on the reactants and the active components of the catalysts; variations of activity and selectivity of the catalysts may partially justify these results. A kinetic analysis made with a reador without so strong an influence of hydrodynamics as a trickel-bed reactor would help in choosing the most appropriate model. At the moment, however, the TH model does not seem very attractive. Acknowledgment The help of E. Scappatura in carrying out the experimental runs is gratefully acknowledged. Nomenclature cf, c, = outlet and inlet concentration of the reacting component (w/w % for S; ppm for V and Ni) d = particle diameter, m If,and (DJapp= intraparticle diffusivity for evenly and unevenly wetted particles respectively, m2 s-l E = activation energy, kcal/kmol he, h, = external and total liquid holdup, dimensionless k* = intrinsic kinetic rate constant, h-’ (kmol/m3)l-” kapp= apparent kinetic constant, h-’ (kmol/m3)’-” k,, k , = fit-order kinetic constantsfor reactive and refractory fraction respectively, h-’ k:, k,’ = first-order apparent kinetic constants for reactive and refractory fraction, respectively, h-’ k , = frequence factor, h-’ (kmol/m3)’” n = apparent order of the reaction, dimensionless T = temperature, K vL = superficial liquid velocity, m/s
Baldi, G. I n “Multlphase Chemical Reactors”, Rodriguez, A. E.; Cab. J. M.; Sweed. N. H., Ed.; Sijthoff and Noordhoff Alphen aan den Rijn. The Netherlands, 198 1. Bertoiacini, R. J.; Forgac, J. H.; Kim, P. K.; Pellet, R. J.; Robinson, K. K. I n “Proceeding 3rd Internatlonai Conference on Chemistry and Uses of Molibdenum”, Barry, H. F.; Mitchell, P. C. H., Ed.; Climax Molibdenum Co.; Ann Arbor, MI, 1980. Burgio, G. Chem. Eng. Thesis, Polltecnico dl Torino, Italy, 1981. Cecil, R. R.; Mayer, F. 2.; Cart. E. N. Paper presented at AIChE Meetlng, Los Angeies, 1968. Chur, C. I.; Wang, 1. Ind. Eng. Chem. Process. Des. Dev. 1982, 2 7 , 338. Cir. J.; Cirova, A. Int. Chem. Eng. 1979, 79, 671. Colombo, A. J.; Baldi, G.; Sicardi, S. Chem. Eng. Sci. 1978, 37, 1101. Dautzenberg, F. M.; Van Kiinken, J.; Pronk, K. M. A,; Sie, S.T.; WiJffels,J. B. ACS Symp. Ser.1978, 65, 254. De Bruijn, A. Proc. Int. Congr. Cafal. 6th 1976, 951. De Bruijn, A.; Naka, I.; Sonnemans, W. M. Ind. Eng. Chem. Process Des. D e v . 1981. 20, 40. Frye, C. G.; Mosby, J. F. ’3”.Eng. frog. 1987, 63(9), 66. Gianetto, A.; BaMi, 0.; Specchla, V.; Slcardi, S . AIChE J. 1978, 2 4 , 1087. Henry, G. H.; Gilbert. J. 0. Ind. Eng. Chem. Process Des. Dev. 1973, 72, 328. Iannibeilo, A.; Marengo, S.;Trlfirb, F.; Villa, P. L. I n “Preparation of Catalysis 11”; Deimon, 8.; Grange, P.; Jacobs, P.; Ponceiet, G.; Elsevier: Amsterdam, 1979. Iannibeilo, A.; Mitchell, P. C. H. I n “Preparation of Catalysis II”, Deimon, B.; Grange, P.; Jacobs, P.; Poncebt, G.; Elsevier: Amsterdam, 1980. Iannibeilo, A.; Marengo. S.; Villa, P. L. I n “Proceedings, 3rd International Conference on the Chemistry end Uses of Molibdenum”, Barry, H. F.; Mitchell, P. C. H., Ed.; Climax Molibdenum Co.; Ann Arbor, MI, 1980. Iannibeilo, A.; Marengo, S.; Gireiii. A. App. &tal. 1982, 3 , 281. Iannibeilo, A.; Marengo, S.;Guerci, A.; Baldi, G.; Sicardi, S . Ind. Eng. Chem. Process Des. D e v . 1983, 2 2 , 594. Koiboe, S. Can. J. Chem. 1969, 47, 352. Koros, R. M. “Proceeding, 4th International Symposium on Chemical Reaction Engineering”; Heildelberg, April, 1976; p 372. Mears, D. E. Cham. Eng. Sci. 1971, 2 6 , 1361. Mears, D.E. Chem. React. Eng. I I , ACS Monograph Ser., No. 733 1974, 266. Mills. P. L.; Dudukovic, H. P. AIChE J. 1981, 27, 893. Newson, E. I . Prepr. Div. Pet. Chem., Am. Chem. SOC. 1970, 141. Paraskos, I.A.; Frayer, J. A., Shah, Y. T. Ind. Eng. Chem. Process D e s . Dev. 1975, 74, 315. Patzer, J. F., 11; Kehi, W. L.; Swift, H. E. J . Catal. 1980, 62, 211. Ross, L. D. Chem. Eng. frog. 1965, 61(10),77. Satterfleld, C. N. AIChE. 1975, 2 7 , 209. Shah, Y. T.; Paraskos, I.A. Ind. Eng. Chem. Process Des. Dev. 1975, 7 4 ,
Greek Letters a = reactive fraction, dimensionless /3 = refractory fraction, dimensionless
e = fitting criterion, defined by eq 11, dimensionless ?I = catalyst effectiveness factor, dimensionless vCE = contacting effectiveness, dimensionless ?It = catalyst effectiveness factor for trickling conditions,
368. Specchia, V.; Baldi, G. Chem. Eng. Sci. 1977, 3 2 , 515. Van Dongen, R. H.; Bode, D.; Van der Eijk, H.; Van Kiinken, I. Ind. Eng. Chem. Process Des. Dev. 1980, 79, 630.
dimensionless yt = Thiele modulus for evenly and unevenly wetted particles, dimensionless Registry No. Mo, 7439-98-7; W, 7440-33-7; Ni,7440-02-0;Co, 7440-48-4; bauxite, 1318-16-7. p,
Received for review May 25, 1983 Revised manuscript received May 30,1984 Accepted June 18, 1984
A Modified Soave-Redlich-Kwong Equation of State for Water-Hydrocarbon Phase Equilibria Vlnayak N. Kabadi’ and Ronald P. Danner Department of Chemical Engineering, The Pennsylvania Sfa fe University, University Park, Pennsylvania 76802
The Soave-Redllch-Kwong equation of state has been modified to apply to water-hydrocarbon phase equilibria in all the regions of the phase diagram. The difficulties in predicting the data in the hydrocarbon-rich and waterqich liquid regions simultaneously have been overcome by the use of an unsymmetric mixing rule. A concentrationdependent term is introduced in the water-hydrocarbon interaction to represent the structural effects in the hydrophobic interactions. The correlation so obtained is applicable over a wide range of temperatures and gives better results than any other generalized correlations available in the literature.
Introduction The more successful approaches to predicting the vapor-liquid equilibria of hydrocarbon and nonhydrocarbon systems have been based on the use of activity coefficient 0196-4305/85/1124-0537$01.50/0
correlations for the liquid phase and equations of state for the vapor phase. These approaches, therefore, consist of a combination of a few correlations. It would be more desirable to have a single cubic equation of state for both 0
1985 Amerlcan
Chemical Society
538
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985
the liquid and the vapor phases. The equation of state of Peng and Robinson (1976a,b) (henceforth called the PR equation) and the modification of the Redlich-Kwong equation of state by Soave (1972) (henceforth called the SRK equation), have been applied successfully to the vapor-liquid equilibria of hydrocarbon-hydrocarbon and some hydrocarbon-nonhydrocarbon systems. (Also, see Graboski and Daubert, 1978a,b, 1979). Attempts at applying these equations to water-hydrocarbon systems have been only partially successful. Water-hydrocarbon systems exhibit immiscibility in the liquid phase. The generalized PR and SRK equations have been unsuccessful in predicting phase equilibria involving the water-rich liquid phase. Peng and Robinson (1976b) were able to correlate the hydrocarbon-rich liquid region data fairly accurately with constant values for the interaction parameters, 6,. For five hydrocarbons they also developed temperature-dependent 6ij in the water-rich liquid region. Kabadi and Danner (1979b) regressed separate sets of temperature dependent 6, and kij, with PR and SRK equations for the hydrocarbon-rich liquid phase, for the 3 ater-rich liquid phase, and for the vapor phase. Their work covered 14 hydrocarbon-water systems. Good resulta were reported in all the regions of the phase diagram. The main limitation of this method is that it is very specific and cannot be applied to other hydrocarbon-water systems for which data are not available. Also, extrapolation to temperatures beyond the range used in development of the method cannot be recommended. It was, therefore, decided to carry out a systematic study on the SRK equation of state in order to develop a more generalized method for phase equilibrium evaluations with water-hydrocarbon systems. Development of the Method Use of Vapor Pressure Data To Obtain a of Water. The parameter a of the SRK equation is given as a(T) = a,a (1) where a, is the value of a at the critical point, and a is a function of the reduced temperature and acentric factor of the compound and is obtained by a regression of the vapor pressure data. If the original Soave a function is used for water, the results show an underprediction of the vapor pressure of water by an average of about 5% in the 32-705 O F temperature range. A new a function was regressed for water from the vapor pressure data (Steam Tables of Keenan et al., 1969) in the 32-705 OF temperature range. The functional form used for the a function was the same as the original SRK a function. a1/2 = 1 C1(1 - TrCz) (2)
+
The optimum values of the constants C1and Czobtained were 0.6620 and 0.80, respectively. The new a function predicted the vapor pressure data within 0.5% average error. Modification of Mixing Rule for Water-Hydrocarbon Systems. Kabadi and Danner (1979b) developed temperature-dependent kij sets for different waterhydrocarbon systems. They observed that different kij sets were needed not only for different systems but also in the different phases. The original SRK geometric mixing rule for the parameter a was used in that work.
where ai, = (uiuj)1/2and kij = 0, if i = j . The parameter a is a measure of the intermolecular attraction forces. In the above mixing rule, the attraction
between water and hydrocarbon molecules is assumed to be proportional to the geometric mean of the attractions between two water molecules and two hydrocarbon molecules. This assumption works very well for a binary system compaeed of similar components, especially if both are nonpolar components which interact only through dispersion forces. Thus, for hydrocarbon-hydrocarbon binary systems, the binary interaction parameter kij is very close to zero, but for water-hydrocarbon systems, this assumption is a very poor one. This was the reason why different sets of kij in different phases were required to correlate the water-hydrocarbon equilibrium data. In this work, it was therefore decided to eliminate this assumption and to examine the following mixing rule n n
amix= CEuijxixj i=lj=l
(4)
where aij = ( ~ i j ) l /if~ i = hydrocarbon, j = hydrocarbon or i = water, j = water, and aij = (1/2)awj,if i = water, j = hydrocarbon. If i refers to water and j to hydrocarbon, aij is not related to ai or a .. However, if i and j are both hydrocarbons, then aij is stid given by the mean geometric rule. Henceforth, we shall denote ai, corresponding to water-hydrocarbon interaction by (1/2)uk, where i refers to hydrocarbon and in an n-component system i can vary from 1 to (n - 1). Values of uk for different hydrocarbons at different temperatures can be calculated from the binary phase equilibrium data and then regressed with reduced temperature and hydrocarbon properties to obtain a genera l i i relation for uk. For this approach to be acceptable, identical values of awi must be obtained in both the water-rich and the hydrocarbon-rich liquid phases. Preliminary calculations were made with a few data points for systems for which vapor-liquid equilibrium data are available in both the water-rich and the hydrocarbon-rich regions. Unfortunately, but not surprisingly, it was found that the uk values in the water-rich liquid phase were consistently higher than those in the hydrocarbon-rich liquid phase. For example, for the n-butane-water system at 220 O F , the value of aWiin the water-rich liquid region was 0.2455 X lo4 atm me and that in the hydrocarbon-rich liquid region was 0.1173 X lo4 atm ms. The mixing rule given by eq 4 was, therefore, judged unacceptable. Since water is a strongly hydrogen-bonded fluid, the addition of a hydrocarbon to it has very significant effects on the water structure (see Franks, 1973). The work with some associating polar fluids has shown that the use of a concentration-dependent association factor successfully predids the vapor-liquid equilibria of these fluids (Marek and Standard, 1954; Jenkins and Gibson-Robinson, 1977, Savkovie-Stevanovie et al., 1982). Based on these facts, we decided to divide the water-hydrocarbon interaction term uk into two terms: ( a&J as a measure of moleculemolecule attraction between water and hydrocarbon and a concentration-dependent term (a’&& as a measure of the structural effect of the hydrocarbon on water. We assumed the structural effect term to be a linear function of the water concentration. a,.
=
a L + U’&jXW
(5)
If one substitutes eq 5 into eq 4, one obtains
where ai, = aii; ai, = if i and j are both hydrocarbons; and ai. = (1/2)a&jif i is water and j is a hydrocarbon. Since &e functionality of a- with respect to the
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985 538
concentrations has changed in eq 6, from that of the original mixing rule of Soave a new expreyion for the fugacity coefficientsof the individualcomponents had to be derived ’ for the
In
SRK equation of state.
fi bi = -(z
xip
b-
- 1)- In ( z - B) r
L
J
where
B=-
RT
and n ti
= C(2x,pj - xsj)a’kj (if i refers to water) j=l
n
ei =
xSr&- C xw2x,u‘ij
(if i refers to hydrocarbon)
j=1
The fugacity coefficient equation for water is different from that for hydrocarbons, which should be expected for the type of mixing rule used. Evaluation of a h and a’h. In the mixing rule (eq 6) one has to evaluate two parameters, a L and a”,. at a given temperature for a given water-hydrocarbon system. As these values should be the same in all three phases, they have to be evaluated so that data in all of the phases are predicted satisfactorily. The data for all of the evaluations were taken from the compilation given in the API Technical Data Book (1982). A nonlinear regression program based on the steepest ascent, steepest descent algorithm of Marquardt (1963) was used for the evaluations. Flash calculations in either three-phase vapor-liquid-liquid, or two-phase vapor-liquid, or two phase liquid-liquid equilibrium regions were carried out. Errors in the prediction of compositions in two of the coexisting phases were minimized. ak and ark were generated for 32 waterhydrocarbon systems for a total of 91 temperatures. To generate a h and a’& at a given temperature with a fair degree of accuracy, the data had to include at least one point in both the water-rich liquid and the hydrocarbonrich liquid regions. No data are available for solubifity of water in acetylenes. The solubilities of water in 1-butyne, 1-pentyne, 1-hexyne, and 1-octyne were therefore calculated by the Hibbard and Schalla (1952) correlation which is at present t4e recommended method for solubility of water in hydrocarbons in the API Technical Data Book (1982). With these values and experimental solubilities of these acetylenes in water (McAuliffe, 1966), a h and a”,,, were generated for these water-acetylene systems. Better a’, and a ’ h could be generated in the future, if experimental solubility data in the hydrocarbon-rich liquid region become available for these systems. For some hydrocarbons, viz. methane, ethane, ethylene, propyne, and cyclopropane, data are available only in the drater-rich liquid region. Hence, simultaneous evaluation of a 6and a ” ~ was not carried out with these data. However, once a generalized regression equation was obtained for a these data were used for the generation of a l ’ ~ . Regression Equation for ah. The term a h was assumed to represent molecule-molecule interactions between water and hydrocarbons. It was therefore decided
ai,
Table I. Best Fit Values of Serier
k,i
for Different Homologous
ki
homologous series alkanes alkenes dialkenes acetylenes naphthenes cycloalkenes aromatics
0.500 0.393 0.311 0.348 0.446 0.355 0.315
to regrew it by an expression similar to the geometric mean rule of the original SRK equation. However, attempts to obtain one generalized regression fit for all the hydrocafbons were not successful. The best regression equation obtained was uniformly positively biased for alkanes and naphthenes and negatively biased for alkenes, dialkenes, cycloalkenes, acetylenes,and aromatics. For the evaluation of solubility of water in hydrocarbons, this equation would overpredict for alkanes and naphthenes and underpredict for alkenes, dialkenes, cycloalkenes, acetylenes, and aromatics. Improved results, therefore, could be obtained if different regression equations were used for different homologous series. The original SRK geometric mean rule with different kij values for different homologous series gave good correlations
a h = 2 ( ~ 4 ~ ) ‘ /-~kwi) (1
(8)
where i refers to hydrocarbon. The hydrocarbons were divided into seven homologous series. Table I gives the best fit values of k,. for the different homologous series. Very good correlations were obtained with the average error in the calculated values of a’, equal to 2.9%. Group Contribution Method for a’&,. For a few hydrocarbons,viz., methane, ethane, ethylene, acetylene, and cyclopropane, data are available only in the water-rich liquid region. It was important that a’d values be available for these systems to obtain a better regression equation for With the regression equation for a h developed in the last section, these data were used to generate a‘h for these systems. The next step was to obtain a regression equation for a’Li with the 138 values generated for different waterhydrocarbon systems at different temperatures. A careful observation of these values showed a definite trend with hydrocarbon properties and temperature. In our physical explanation of the mixing rule given by eq 6, the term (a’hx,) was introduced to represent the structural effect of hydrocarbon on water. It would therefore seem reasonable to assume that a’& would depend only on the size and shape of the hydrocarbon molecule and on the properties of water. A preliminary analysis showed that a group contribution method in terms of individual groups constituting a hydrocarbon molecule with a temperature dependency in terms of the reduced temperature of water might work. The following form of equation was chosen
where Gi is the sum of the group contributions of different groups which make up a molecule of hydrocarbon i n
Gi = Cgj j-1
Tis the temperature in K, T, is the critical temperature of water in K, and c1 is a regression constant. Equation 9 assumes the two boundary conditions, a’Li = Gi, when
540
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 3, 1985
Table 11. Groups Constituting Hydrocarbons and Their Group Contribution Paramters g;, atm m6 x lo6 group j CH, 1.3580 -CH3 0.9822 -CHz1.0780 >CH0.9728 quaternary carbon 0.8687 -CH2(cyclic) 0.7488 >CH- (cyclic) 0.7352 -CH=CH(cyclic)" 0.6180 CHz=CHz 1.7940 CHz=CH1.3450 CHZ=C< 0.9066 CH=CH 1.6870 CHEC1.1811 -CH= (aromatic) 0.5117 >C= (aromatic) 0.3902 "This value is obtained from very little data. Might not be reliable.
Table 111. Group Constitution of a Few Representative Hydrocarbons hydrocarbon group constitution methane 1CH4 ethane 2CH3 2CH3, lCHz propane 2CH3,6CHz n-octane 3CH3,lCH 2-methylpropane 5CH3,1CHz, ICH, 1C 2,2,4-trimethylpentane 6CHz (cyclic) cyclohexane 5CH2 (cyclic), 1CH (cyclic), lCH3 methylcyclohexane 4CH2 (cyclic), lCH=CH (cyclic) cyclohexene lCHZ=CHZ ethene lCH3, lCHz=CH propene 2CH3, lCHz=C 2-methylpropene 2CHz=CH 1,3-butadiene 1CH4H ethyne lCH3,1CHZ, lCHfC 1-butyne 6 CH (aromatic) benzene 5CH (aromatic), 1C (aromatic), lCH3 methylbenzene 5CH (aromatic), IC (aromatic), lCH2=CH ethenylbenzene
T = 0 and alai = 0, when ?' = Tcw. A total of 15 groups were necessary to represent all the hydrocarbons. The group contribution parameters gj for each group and the regression constant cl were obtained by regressing the a",,+ values with the groups constituting Table IV. Comparison of the Present Method with UNIFAC
1. 2. 3. 4. 5. 6. 7. 8.
quantity XHC in water-rich V-L region XHC in water-rich liquid in VLL and IAIAregions XHCa t 77 "F Xw in HC-rich liquid in VLL and LL regions Kw in water-rich V-I, region Kw in LL region KHC in water-rich V-L region KHc in LL region
no. of Doints 426 457 55 283 30 132 30 132
different hydrocarbon molecules and with temperature T. The best fit value of c1 obtained was 0.812. It was rounded to 0.80. Table 11gives the 15 group and the corresponding group contribution parameters. A reasonably good correlation was obtained with an average percent error of 5.8%. Table I11 gives the group constitution of a few representative hydrocarbons. Method Summary. The development of the modified SRK method fc water-hydrocarbon phase equilibria calculations is no , complete. In summary, it uses the SRK equation of state with a modified CY for water given by eq 2 with c1 = 0.6620 and cp = 0.80. The mixing rule for parameter a has been modified and is given by eq 6. The resulting new equation for fugacity coefficients is given by eq 7. The term ad in the mixing rule is given by eq 8, with the kwi for different hydrocarbon homologous series as listed in Table I. The term a '6in the mixing rule is given by eq 9 with c1 = 0.80 and Gi is the sum of the group contributions of the different groups constituting the hydrocarbon. The group contribution parameters for the groups are given in Table 11. Results and Discussions Comparisons with Experimental Data and Other Correlations. To compare the values predicted by the modified Soave equation with the experimental data, the data were divided as follows: (1)solubility of hydrocarbons in water (XHc)under vapor-liquid-liquid, vapor-liquid, and liquid-liquid equilibria; (2) solubility of water in hydrocarbons (X,)under vapor-liquid-liquid, vapor-liquid, and liquid-liquid equilibria; (3) water content of hydrocarbon vapors (Y,) in the vapor-liquid-liquid region and the two vapor-liquid regions; (4) equilibrium ratios K , and KHcin the different regions of phase equilibria. In the two-phase liquid-liquid equilibria, K's are defined as the ratio of concentration in the hydrocarbon-richphase to the concentration in the water-rich phase. The new method was evaluated with the experimental data and compared with other correlations available in the literature. Data on hydrocarbons up to Clo were covered. The only generalized method available in the literature for phase equilibria calculations with water-hydrocarbon systems is the UNIFAC activity coefficient method (Fredenslund et al., 1975, 1977). The UNIFAC method has a limitation that it can be applied only in the temperature range of 32-230 O F . The present method can be applied
__ UNIFAC av abs error 0.00048 0.0002 0.000026 0.0023 0.0016 1.6 6900 3100
-
_.
av % error 174 104 68.7 106 5.1 3.6 75 49
modified SRK no. of av abs Doints error 1274 0.00038 809 0.00028 62 0.000064 689 0.013 175 0.022 0.015 314 1695 175 314 5217
av % error 34.6 56.6 104.4 38.1 17.9 35.7 34.2 38.1
Table V. Comparison of the Present Method with Some Specific Correlations Available in Literature _I_____-_._ __^..__________I __ no. of correlation .. quantity points De Santis correlation Yw in water-rich V-L region 478 YWin HC-rich V-L region 107 Hibbard and Schalla correlation Xw in HC-rich liquid under VLL equilibrium 283 Leinonen and MacKay correlation X H in~ water-rich liquid at 77 "F 67 Kabadi and Danner nomograph XHc in water-rich liquid a t 77 "F 72 Cysewski and Prausnitz correlation XH, in water in water-rich V-L region 762 ____I__I
1.
2. 3. 4. 5.
modified SRK Method av abs av 70 no. of av abs av % error points error error error ___ ____ 0.061 26.3 467 0.012 10.7 0.090 35.3 94 0.063 24.1 0.00071 32.7 375 0.011 40.2 0.000027 36.6 62 0.000064 104.4 O.ooOo07 13.7 62 0.000064 104.4 0.00011 15.6 1274 0.00038 34.6
Ind. Eng. Chem. Rocess Des. Dev., Vol. 24, No.
with a fair degree of accuracy up to about 500 O F . Comparison of the new method with the UNIFAC correlation for different quantities in the different regions of phase equilibria is given in Table IV. The errors reported are calculated as the difference between the experimental and the calculated values normalized by the experimental value. It can be seen that, even though the new method includes more data points (over a larger range of temperatures), the UNIFAC correlation gives higher errors for most of the quantities evaluated. The relatively large errors observed for the solubility of hydrocarbons in water (XHc) are misleading considering the small magnitudes (order of to lo-’) of these quantities especially for hydrocarbons with high carbon numbers (>C4). A comparison of the new method with the correlations available in the literature for some specific quantities is given in Table V. It is not expected that the new method would give better results than these correlations, as these correlations were developed particularly for one specific quantity and some of them use specific parameters for each hydrocarbon. These correlations are (1)De Santis et al. (1974,1975) correlation for water content of hydrocarbon vapors; (2) Hibbard and Schalla (1952) correlation for solubility of water in hydrocarbons under VLL equilibrium;(3) Leinonen et al. (1971) correlation for solubility of hydrocarbons in water at 25 “C; (4) Kabadi and Danner (1979a) nomogrrlph for solubility of hydrocarbons in water at 25 “C;(5) Cysewski and Prausnitz (1975) correlation for solubility of hydrocarbons in water under VL equilibrium. Table V shows that the new method does reasonably well even when compared to these specific correlations. All the comparisons given above used binary waterhydrocarbon data. Not many data sets are available for ternary and higher component water-hydrocarbon phase equilibria. Two of the more extensive data sets available are the data of McKetta and Katz (1948) on the methane-n-butane-water system and the data of Wehe and McKetta (1961) on the n-butane-1-butene-water system. The new correlation was evaluated with these data. The percentage errors observed for different quantities were 33.9% for X,, 48.9% for XHC,12.5% for Y,, 30.8% for YHc, 14.2% for K,, and 29% for KHC. The results, therefore, prove that the correlation can be used for multicomponent water-hydrocarbon phase equilibria. A major discrepancy was observed with the results of the new correlation, when the calculated solubility curves for hydrocarbons in water were compared with the experimental ones (API Technical Data Book, 1982). The experimental curves are concave upward, whereas the predicted ones are convex upward. This discrepancy may be a result of the temperature function used for u’ai or it may be an indication of some other deficiency in the overall approach. Nevertheless, the modified Soave equation can be used to compute XHCat individual temperatures with a fair degree of accuracy in the recommended temperature range (TI 500 OF). Extrapolation beyond this temperature is not recommended. The experimental and the calculated curves showed much better agreement for the solubility of water in hydrocarbons. Large deviations were, however, observed near the three-phase critical point. Conclusions The modified SRK equation of state for phase equilibrium calculations with water-hydrocarbon systems gives
3, 1985 541
fairly good results in all the regions of the phase diagram. It predicta the instability in the liquid phase and the liquid-liquid equilibria data with a fair degree of accuracy. It gives better results and is applicable over a wider range of temperatures than the UNIFAC correlation. It also does reasonably well when compared to some correlations for specific quantities, available in the .literature. Nomenclature a = parameter in the SRK equation of state A = as defined in eq 7 B = as defined in eq 7 f = fugacity g = group contribution of each group G = s u m of the group contributions by all the groups constituting a hydrocarbon molecule kij = binary interaction parameter in the SRK equation of state K = equilibrium constant defined as concentration in the lighter phase divided by concentration in the heavier phase P = pressure R = gas constant T = temperature X = mole fraction in the liquid phase Y = mole fraction in the vapor phase z = compressibility factor cy = vapor pressure function in the SRK equation of state e = as defined in eq 7 Subscripts HC = hydrocarbon w = water wi = water-hydrocarbon mix = mixture of water and hydrocarbon Literature Cited American Petroleum Institute “Technical Data Book-Petroleum Reflning”; API: Washington, DC, 1982. Cysewski, G. R.; Prausnitz, J. M. Ind. Eng. Chem. Fundam. 1975, 15, 304. De Sentis, R.; Breedveid, G. J. F.; Prausnitz, J. M. Ind. fng.Chem. Process Des. Dev. 1974, 13 374. De Santis, R.; Merrelll, L.; Sandulll, M. Chem. Eng. Scl. 1975, 30, 659. Franks, F. “The Solvent Properties of Water”, I n “Water-A Comprehensive Treatise”, Vd. 2, Franks, F., Ed.; Penum Press: New York, 1973. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. A I C M J . 1975, 21, 1088. Fredenslund, A,; Gmehling, J.; Rasmussen, P. “Vapor-Liquid Equlllbria Using UNIFAC”; Elsevler Sclentlfk PuMlshlng Co.: New York. 1977. Graboski. M. S.; Daubert. T. E. Ind. Eng. Chem. Process Des. D e v . 1978a, 17, 443. Graboski, M. S.; Daubert, T. E. Ind. Eng. Chem. Process Des. D e v . 1978b, 17, 448. Graboski, M. S.; Daubert, T. E. Ind. Eng. Chem. Process Des. Dev. W79, 18, 300. Hlbbard, R. R.; Schalla, R. L. ”Solubility of Water In Hydrocarbons”; Natl. Advisory Comm. Aeron, RM. E. 52024, 1952. Jenkins, J. D.; Gibson-Roblnson, M. Chem. Eng. Sci. 1977, 32, 931. Kabadi, V. N.; Danner, R. P. Hydrocarbon Process. 1979a, 58, 245. Kabadi, V. N.; Danner, R. P. ”Evaluations of Correlations for Hydrocarbon Water Phase Equilibria”, Presented at the ACS Symposium on “Thermodynamics of Aqueous Systems with Industrial Appikations”; AlrIle House: Washington, DC, 1979b. Keenan. J. H.; Keyes, F. 0.; HIII. P. G.; Moore, J. G. “Steam Tables”; Wlley: New York, 1969. Leinonen, P. J.; Mackay, D.; Phillips, C. R. Can. J . Chem. Eng. 1971, 19, 288. Marek, J.; Standard, G. Collect. Czech. Chem. Commun. 1954, 19, 1074. Marquardt, D. W. J . SOC.I n d . Appl. Math. 1983, 1 1 , 431. McAuiiffe, C. J . Phys. Chem. 1966, 7 0 , 1267. McKetta, J. J.; Katz, D. L. Ind. Eng. Chem. 1948, 4 0 , 853. Peng, D.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1978a. 15, 59. Peng, D.; Robinson, D. B. Can. J . Chem. Eng. 1978b, 54, 595. SavkoviE-StevanovlE, J.; Tasb, A.; Djordjevb, B. Chem. fng. Scl. 1982, 37, 1491. Soave, G. Chem. f n g . Sci. 1972, 2 7 , 1197. Wehe, A. H.; McKetta, J. J. J . Chem. Eng. Data 1981, 6 . 167. ~
Received for review August 24, 1983 Accepted May 18,1984
