733
Ind. Eng. Chem. Process Des. Dev. 1886, 25, 733-736
= dispersed-phaseviscosity, kg/ (ms) v, = kinematic viscosity, m2/s ai = interfacial tension, kg/s2
Fr = dV/g = D P / g = Froude number g = acceleration due to gravity, m/s2 h = distance from bottom plate, m H = distance from first to last plate, m N = agitator speed, rev/s Re = dVp/p, Reynolds number V, = continuous-phase superficial velocity based on the empty column cross section, m/s v d = dispersed-phase superficial velocity based on the empty column cross section, m/s V, = characteristic velocity, m/s V, = relative velocity, m/s We = dVp/a, Weber number Xd = dispersed-phase holdup, fraction Z = coalescence coefficient in eq 3 and 5 Greek Symbols 4 = fractional plate free area Ap = density difference, kg/m3 pc = continuous-phase density, kg/m3 Pd = dispersed-phase density, kg/m3 p, = continuous-phase viscosity, kg/ (ms)
kd
Literature Cited Bibaud, R. E.; Treybai, R. E. AIChf J . 1866, 12, 472. Bell, R. L.;Babb. A. L. Ind. Eng. Chem. Process Des. D e v . 1988, 8 , 393. Deflves, D.; Schnekler, G. Genie Chlm. 1861, 85, 246. Fischer, E. A. Ph.D. Dissertation, Swiss Federal Institute of Technology, Zijrich, 1973, Dlssertatlon No. 5016. Koide, K.; Hirahara, T.; Kubato, H. Kagaku Kogaku 1867, 5 , 38. Klee, A.; Treybal, R. E. Chem. Eng. J . 1856, 2 , 444. Kumar, A.; Vohra, D. K.; Hartland, S. C a n . J . Chem. f n g . 1880, 58, 154. Logsdaii, D. H.;Thornton, J. D.; Pratt, H. R. C. Trans. Inst. Chem. f n g . 1957, 35, 301. Misek, T. Collect. Czech. Chem. Commun. 1864, 29, 1755. Misek, T. Collect. Czech. Chem. Commun. 1963, 28, 1613. Misek, T.; Marek, J. Br. Chem. Eng. 1870, 15, 202. Strand, C . P.; Olney, R. 8.; Ackerman, G. H. AIChE J. 1962, 8 , 252. Thornton, J. D. Chem. Eng. Sci. 1856, 5 , 201. Zenz. F. A. Pet. Refln. 1957, 3 6 , 8.
Receiued for review February 19,1985 Revised manuscript received November 12,1985 Accepted January 9,1986
L-L-E Data for Aromatics Extraction Calculations Using a Modified UNIFAC Model Mamata Mukhopadhyay' and Avlnash S. Pathak Chemical Engineering Department, I.I.T. Bombay, Bombay-400
076, Indla
A modified UNIFAC model has been used for prediction of L-L-E data of multicomponent aromatics extraction systems. The isobaric activity coefficients at infinite dilution have been employed for evaluation of the group-interaction parameters between the CH,-sulfolane pair of groups and their temperature coefficients. These parameters along with the other group-interaction parameters evaluated earlier have been employed in the modified UNIFAC model. The valldity of these parameters has been tested by comparing the predicted results with the corresponding experimental data from the literature. The good agreement justifies the capability of the modified UNIFAC model and improvement of interaction parameters evaluated from the infinite dilution activity coefficients over those evaluated earlier by utilizing the mutual solubility data.
The applicability of the UNIFAC model (Fredenslund et al., 1977) in the prediction of multicomponent L-L-E data needed in the process engineering calculations for extraction of light aromatics from reformed naphtha with sulfolane as the polar solvent were discussed in an earlier publication (Mukhopadhyay and Dongaonkar, 1983). The binary-group-interaction parameters for all possible pairs of groups involved in the calculations except the CH2sulfolane were evaluated from the V-L-E data of the miscible binaries, whereas those for the latter pair were evaluated from the mutual solubility data (Karvo, 1980) of the partially miscible binaries. In the present work, isobaric activity coefficients at infinite dilution have been employed for evaluation of the CH2-sulfolane pair of group-interaction parameters. The modified UNIFAC model (Kikic et al., 1980, 1982) with the temperature dependency on the interaction parameters as suggested by Larsen et al. (1983) has been considered for the prediction of the multicomponent L-L-E data.
* To whom the correspondence should be addressed. 01 96-430518611125-0733$01.50/0
Table I. Experimental vs. Temperature Data for the Systems Sulfolane-Cyclohexane, Sulfolane-n -Heptane, and Sulfolane-n -Hexane temp, K
347.6 352.6 354.6
7; temp, K Sulfolane(l)-Cyclohexane(2) 129.90 546.2 98.87 552.7 90.00 555.6
4.768 4.329 3.842
363.3 368.1 370.5
Sulfolane(1)-Heptane( 2) 120.68 546.2 108.30 552.5 102.84 555.5
5.615 5.114 4.592
334.6 339.2 341.4
Sulfolane(1)-Hexane (2) 139.85 546.3 121.43 552.7 110.58 555.6
4.693 4.609 4.390
7;
Group-Interaction Parameters The isobaric infinite dilution activity coefficients have been determined by using the differential ebulliometric technique for three partially miscible binaries, n-hexanesulfolane, n-heptane-sulfolane, and cyclohexane-sulfolane @ 1986 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986
734
(Pathak, 1984), and are presented in Table I. The binary group-interaction parameters between the CH,-sulfolane pair of groups have been evaluated by reduction of these data, adopting the simplex search technique modified by Nelder and Mead (Beveridge and Schechtor, 1970). This involves statistical regression analysis over all experimental data points for minimizing a selected objective function which incorporates the temperature variations of the isobaric ~~y~~~~data as =
(
fI:
Y?,exptl
- ?'T,calcd)l
+
$(
Yzexpt:
Y2,exptl
Ycexptl
i=l
Y~,cakd)'
i
(1) where i and j indicate, respectively, the two temperatures at which yT,exptland yF,exptl have been determined at a particular pressure and p is the number of isobaric data sets. yycalcd and Y&alcd have been calculated by using the modified UNIFAC model at the respective temperatures. The temperature dependency of the interaction parameters has been considered am, = ahn[l + gh,(T - 298.15)] (2)
The parameters a;, and g;, have been evaluated at a reference temperature of 298.1 K. In all, a set of four parameters has been obtained simultaneously for each partidy miscible binary. Yccalcd values are calculated from the combinatorial and residual contributions as In
Yccalcd
= (In YJC"
+ (In yi)R"
(3)
At the limiting conditions, the combinatorial contribution of the two activity coefficients reduces to the form
In the case of three binaries in the present study, evaluation of the residual contributions of the limiting activity coefficients is simplified. Because there is neither any group common to both components nor any mixing of groups in either component as both components individually belong to single groups only, namely, sulfolane is treated as one single group and the hydrocarbons are consisted of CH, and CH3groups classified under the same main group CH2. Consequently, the group activity coefficients rk needed in the evaluation of the residual contribution (In rJRw for the groups CH2 (3), CH3 (4), and sulfolane ( 5 ) reduce to the following form:
[
l n r 4 = Q4 1 + - - e x p
( y)] --
(5b)
The optimized valyes of the set of group-interaction paramete5s a,, a5d a,, along with the temperature coefficients g,, and g,, evaluated separately from the ycexptldata on the three binaries are presented in Table 11. It can be noted that the values are of the same magnitude which
Table 11. Binary Interaction Parameters for the Groups CH2(3)-Sulfolane(S) system data source a&, K gi3,K-l 4 5 , K d 5 , K-' sulfolane-cyclohexane sulfolane-heptane sulfolane-hexane
67.98 -0.003 107 584.80 -0.002 165 79.81 -0.003 419 554.65 -0.003 184 68.26 -0.003 389 564.15 -0.002 616
av value
72.0
-0.003 305 567.87 -0.002 655
Table 111. Selected UNIFAC Group-Interaction Parameters for the Prediction of L-L-E Data (Mukhopadhyay and Dongaonkar, 1983) temp, K interaction parameters K 348.1 373.1 a12 a21 a13
a31 a15 a51
a23 a32 a25
a52
a35(1 a53a
322.8 -213.2 -17.63 65.24 222.6 -40.12 -84.08 62.76 -126.8 2032.0 498.48 60.12
322.8 -213.2 -17.63 65.24 222.6 -40.12 -84.08 62.76 -126.8 2032.0 454.79 54.17
"Estimated in this work using -ym data: 1, ACH; 2, ACCH,; 3,
CH,; 4, CH,; 5, sulfolane.
justifies the reliability of the r,:', tl data. Average values of these four parameters for the tiree sets have been used in the modified UNIFAC model. Further, though the temperature coefficients gkn are small, they are certainly not negligible. Evaluation of these parameters is absolutely essential as the data sources of isobaric ycexptl values of the components are at two widely different temperature levels. The group-interaction parameters between the CH2sulfolane pair evaluated in this work along with those between the remaining pair of groups evaluated earlier (Mukhopadhyay, 1983) by using V-L-E data of the miscible binaries have been presented in Table 111.
Results and Discussion In order to ascertain the applicability of the modified UNIFAC model and to test the validity of the parameters evaluated by reduction of y mdata sets, the L-L-E data have been predicted for three ternary systems, namely, (i) cyclohexane-benzene-sulfolane, (ii) n-hexane-benzenesulfolane, and (iii) n-heptane-toluene-sulfolane, at 75 and 100 "C. The predicted data for all three systems have been found to compare well with the corresponding experimental data from the literature (De Fre and Verhoeye, 1976) for the entire region except near the plait points. Figures 1-6 describe the ternary diagrams where the binodal curves have been plotted with a few tie lines. The standard deviations in the raffinate and extract phases for the three systems i, ii, and iii are 0.0171 and 0.0159,0.0102 and 0.0106, and 0.0133 and 0.0121, respectively. Relatively larger deviations of the predicted values from the corresponding experimental data near the pleat point regions may be attributed to the probable uncertainties in the experimental data near the plait point region where experimentation is quite difficult. However, extraction is never carried out near this region. In the actual liquid-liquid extraction process, the solvent to hydrocarbon feed ratio varies between 2.0 and 3.5 (Jones, 1973), and the hydrocarbon feed contains 20-30% aromatics. For such mixtures, the agreement between the experimental L-L-E data and the predicted values are exemplary. The standard deviations in this work are even smaller than those estimated in the earlier work (Muk-
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986 735 TBnporature 3 L 8 . 1 5 ~ --+-Expenmental (4 m. +Predicled C Cycloharane 8 - Benzene s - Sulfolano
im)
-
, S - Sullolane
\
f-
Mole lroction of
C
5
-
-
t Mole lmcllon of H
Figure 1. Ternary diagram for cyclohexane-benzene-sulfolane.
Figure 4. Ternary diagram for n-hexane-benzene-sulfolane.
Temperature 373 15K Temperature 3 1 8 15H
- - 0- - Experimental (LO)
- - 0 -Eaperimonlal ( 4 0 )
--s-
Predicted C - Cyclohoxone B - Benzene
\
A Predicled
~
0.9
08
07
06
04
05
03
02
01
-
5
Figure 2. Ternary diagram for cyclohexane-benzene-sulfolane. t Mole traction of
HP- n-Heptane T Toluene
C
n c Mole Iracttcn of
HD
S
-
Figure 5. Ternary diagram for n-heptane-toluene-sulfolane.
Tempratum 348.15 K --..=---Expenmental (LO) -PreQlcled H n-Hexane
-
S
+
Mole fraction of H
S
__
Figure 3. Ternary diagram for n-hexane-benzene-sulfolane.
hopadhyay and Dengaonkar, 1983) where mutual solubility data (Karvo, 1980) were used for evaluation of the CH2sulfolane pair of group-interaction parameters, which justifies the fact that 7-data can be utilized for better estimation of the group-interaction parameters. In a previous article (Mukhopadhyay and Sahasranaman, 1982) where prediction of L-L-E of the same ternary systems were reported by employing the NRTL and UNIQUAC models with standard deviations of little higher magnitude, the number of equilibrium stages required for
- Sultolme
f-
Mole fraction of HD
-
Figure 6. Ternary diagram for n-heptane-toluene-sulfolane.
a given separation was computed and the agreement indicated that the predicted data were sufficiently accurate for the process design. In view of still lower standard deviations of the predicted L-LE data in the present work employing the modified UNIFAC model, it can be safely concluded that better accuracy will be reflected in the engineering design. Besides L-L-E concentrations, the solute distribution ratios at infinite dilution can be conveniently predicted with sufficient accuracy by utilizing
736
Ind. Eng. Chem. Process Des. Dev. 1906, 25,736-741
the modified UNIFAC model (Pathak, 1984). On the strength of the above good agreements, for the three ternary systems, the modified UNIFAC model with the binary-group-interaction parameters employed io this study can be recommended with confidence for accurate prediction of L-L-E data of the actual aromatics extraction systems having any number of components. Nomenclature umn= UNIFAC binary interaction parameter for groups m and n, K A, = ith set of UNIFAC parameters (umn) to be evaluated F = objective function 1, = UNIFAC constant for component i , related to r, and qr Nc = number of components NO = number of groups N = number of data points P = pressure, atm Q k = surface area parameters for group k qt = surface area parameters for component i rr = pure-component volume parameter for component i Rk = group volume parameter for group k R = universal gas constant, cm3.atm/ (gmo1.K) T = temperature, K w, = modified molecular volume fraction of component i x , = liquid-phase mole fraction of component i X, = liquid-phase mole fraction of group m z = coordination number Greek Letters yl = activity coefficient of component i rk = activity coefficient of group k rk(l) = activity coefficient of group k in pure component i Or = surface-area fraction for component i
8, = group surface-area fraction for m yk(;) = number of groups of type k in component i rji
,$ ,
= segment fraction for component i = W A C binary group interaction parameter for groups m and n related to a,,
w = acentric factor Superscripts C = combinatorial part of the activity coefficient R = residual part of the activity coefficient Q)
= infinite dilution
Subscripts C = critical value calcd = calculated value exptl = experimental value
Literature Cited Beveridge, G. S. G.; Schechter. R. S. "Optimization: Theory and Practice"; McGraw-Hill: New York, 1970. De Fre, R. M.; Verhoeye, L. A. J. Appl. Chem. BEOtechnd. 1978, 26, 469. Fredenslund, A.; Gmehiing, J.; Rasmussen. P. "Vapor-Liquid Equilibria using UNIFAC"; Elsevier: Amsterdam, 1977. Jones, W. T. Hydrocarbon Rocess. 1973, 52, 91. Karvo, M. J. Chem. Thennodyn. 1980, 12, 1175. Kikic, 1.; Alessi, P.; Rasmussen, P.; Fredensiund, A. Can. J. Chem. Eng. 1980, 58, 253. Kikic, 1.; Alessi, P.; Rasmussen, P.; Fredensiund, A. Can. J. Chem. Eng. 1882, 60, 30. Larsen, 6. L.; Fredensiund, A.; Resmussen, P. Phase Equilib. Separat. Process. 1983, Sep.8307. Mukhopadhyay, M.; Sahsranaman, K. Ind. Ens. Chem. Process Des. D e v . 1982, 27 (4).632. Mukhopadhyey, M.; Dongaonkar, K. R. Ind. Eng. Chem. Process Des. Dev. 1983. _22 _ 131. --,.521. -- Pethak, A. S. M. Tech. Dissertation, I.I.T., Bombay, India, 1984.
_._.
Received for review June 10, 1985 Accepted January 9, 1986
To Break an Azeotrope. The Use of n-Pentane To Break the CO,-Ethane Azeotrope, for COP EOR Gas Processing Jane H. Hong and RIkI Kobayashl' Depsrtment of Chemical Englneerlng, Rice University, Houston, Texas 7725 1
Enhanced Oil Recovery projects utilizing carbon dioxide yield gases which are rich in carbon dioxide throughout
a major portion of the life of the project. This is the first in a series of studies to provide phase equilibria data to separate carbon dioxide from natural gas llquid constituents and to determine the phase equilibrium conditions under which the carbon dbxkle-ethane azeotrope could be broken by using n-pentane as the extractive solvent. The experimental results demonstrate that it does not suffice merely to break the azeotrope to produce greater than 95.0 mol % (speclficatlon set by the companies) carbon dioxide*ich recycle gas. To ensure that such carbon dioxide concentrations are attainable, comprehensive phase equilibrium data were obtained in the high CO, concentration regions as well as in the mldcolumn concentration region. Both pressure and temperature were varied to confirm the range over which the separation could be carrled out. Vapor-liquid equilibria were measured in terms of two quasi-binary systems: (1) a near azeotropic mixture of carbon dioxide and ethane (a 72.17 mol % C02-27.83 mol % C2HBmixture) added to n-pentane and (2) a 95.5 mol % C0,-4.5 mol % ethane mixture added to n-pentane to produce various total pressures at fixed temperatures.
High-pressure enhanced oil recovery processes increase and alter the composition, amount, and cost of gas processing required t o separate and recycle the enhancing constituents back to the reservoir for the entire length of the project. Fields which are projected for COz enhanced 0196-4305/86/1125-0736$01.50/0
oil recovery fall into this category. Recent economic studies (Holmes et al., 1982; Flynn, 1983) indicate that the most economic process by which COz can be separated from C02-richgases huing from C 0 2 EOR fields may be a separation process historically clas0 1986 American Chemical Society
