Ind. Eng. Chem. Res. 1987, 26, 976-982
976
(3) An ash layer is formed near the exposed surface, and the BL starts moving inward, sandwiched between the ash layer and the unreacted core. The zero-order approximation is the SI model. The duration of this period is 4R. (4) After the solid has become entirely converted to ash, the ash becomes saturated with the gaseous component. This time range could be disregarded altogether, since the reaction is completed before it. The four time ranges hold in an asymptotic sense, and they are separated by transition regions. The transition region between stages 2 and 3 is one in which the BL thickness decreases from l/(4R)1/z to 1/4R. This is different from what the FR model assumes to be the first stage. Time range 3 above is equivalent to the second stage of the FR model, and the transition between 3 and 4 is equivalent to the last stage. In this limited sense, the FR model is identified as the first-order approximation for the singular limit, l/@R = 0. The SI model is the exact zero-order approximation for the same limit. The VR model is not recovered asymptotically. To within the order of approximation which justifies the VR model assumptions, the phenomenon is entirely controlled by the intrinsic kinetics. The VR model retains terms which are of the same order of magnitude as terms which have been neglected. The TS model is not recovered in any asymptotic sense. Whenever a discontinuity is approached, the value of a to the left of it approaches unity, contrary to the assumption of the TS model. The longest of the time ranges, the third one, is left out of the picture in the TS model. It is possible that the solution of the TS model equations may approach that of the general model for intermediate values of 4; however, for such values numerical integration of the general model is easy, and thus there seems to be no pragmatic case where use of the TS model is suggested. Nomenclature a = concentration of gaseous component, mol/cm3 a. = value of a at exposed surface, mol/cm3
b = concentration of solid reactant, mol/cm3 bo = initial value of b, mol/cm3 D = diffusivity, cm2/s
f = dimensionless kinetic function k = kinetic constant, s-l L = thickness of slab, cm p = stoichiometric coefficient R = concentration ratio, R = bo/pa, t = time, s t* = equilibration time, s u = stretched coordinate x = distance from exposed surface, cm y = dimensionless distance, y = x f L Greek Symbols a = dimensionless concentration of gas ,B = dimensionless solid concentration e = thickness of reaction layer p = dimensionless position of front = dimensionless time, T = k t 4 = dimensionless kinetic constant, 4 = k L 2 / D Operators 6w = variation of w over integration field [w]= variation of w across boundary layer Subscripts L, R = to the left and right of the boundary layer
Literature Cited Ausman, J. M.; Watson, C. C. Chem. Eng. Sci. 1962, 17, 323. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions;Wiley: New York, 1984; Vol. 1. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1979. Ishida, M.; Wen, C. Y. Am. Inst. Chem. Eng. J . 1968, 14, 311. Mantri, V. B.; Gokarn, A. N.; Doraiswamy, L. K. Chem. Eng. Sci. 1976, 31, 779. Ramachandran, P. A.; Doraiswamy, L. K. Am. Inst. Chem. Eng. J. 1982,28, 881. Stefan, J. Ann. Phys. Chem., N . F. 1891, 42, 261.
Received f o r review October 17, 1985 Accepted November 17, 1986
Separation of Dodecane-Biphenyl Mixtures Using Supercritical Ethane, Carbon Dioxide, and Ammonia Shashank V. Dhalewadikar, A n d r e w J. Seckner, and Mark A. McHugh* Department of Chemical Engineering, The Johns Hopkins University, Baltimore, Maryland 21218
T e r r y L. Guckes' Exxon Chemical Company, Florham Park, New Jersey 07932
Experimental data are presented on the high-pressure phase behavior of ternary mixtures consisting of a supercritical fluid solvent, dodecane, and biphenyl. Supercritical ethane at 76.8 "C and 86.7 atm and a t 125.6 "C and 126.8 atm, carbon dioxide a t 53.7 " C and 104.8 atm and a t 97.7 "C and 188.1atm, and ammonia a t 156.5 "C and 139.5 atm are used in an effort to determine the selectivity of these solvents for an aromatic hydrocarbon relative to a paraffinic hydrocarbon when these hydrocarbons form a liquid mixture. The phase behavior of the ternary mixture is modeled by using the Peng-Robinson equation of state. The experimental data show that these supercritical fluid solvents do not exhibit high selectivity, thus indicating that the aromatic-paraffinic interactions present in the liquid phase dominate the selectivity behavior. Model calculations suggest that better selectivities might be obtained a t temperatures and pressures other than those investigated experimentally. Supercritical fluid (SCF) solvent extraction has been suggested as a viable alternative to other separation
* Author to whom correspondence should be addressed.
+Currentlyat W. R. Grace and Co., Columbia, MD 21044.
techniques for hard-to-do separations (Paulaitis et al., 1983; McHugh and Krukonis, 1986). Although supercritical fluid solvents have been applied extensively to separating alcohol-water solutions (Paulaitis et al., 1981; de Fillippi and Vivian, 1982; Moses et al., 1982; McHugh et al., 1983; Kuk
0888-5885/87/2626-0976$01.50/0 0 1987 American Chemical Society
Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987 977 and Montagna, 1983; Kander and Paulaitis, 1984; Diandreth and Paulaitis, 1984; Paulaitis et al., 1984), very little phase behavior information has been published on using SCF solvents to separate liquid hydrocarbon mixtures (Chang et al., 1985). As a guide to estimating selectivity qualitatively, Williams (1981) suggests that the differences in the structure, aromaticity, and unsaturation of mixture components is of secondary importance when compared to size and polarity differences. However, Kulkarni et al. (1974) show that decane can be extracted from 2methylnaphthalene with carbon dioxide, indicating that when the sizes of the liquid components are reasonably close aromaticity and structure become very important variables. In the present study we report on the phase behavior of model ternary liquid mixtures consisting of a paraffinic hydrocarbon, an aromatic hydrocarbon, and a supercritical fluid. The objective of this study, which can be considered an extension of the work of Kulkarni et al. (1974), is to determine whether these SCF solvents will selectively solubilize one class of compounds relative to another (i.e., a paraffin vs. an aromatic) when the heavy solutes form a liquid mixture. Dodecane is chosen as the model paraffin, and biphenyl is chosen as the model aromatic. Both of these compounds are well-characterized organic hydrocarbons with the same number of carbon atoms but with slightly different molecular weights. Supercritical carbon dioxide, supercritical ethane, and supercritical ammonia are used in this study. Both carbon dioxide and ethane have similar critical temperatures (i.e., 31.03 and 32.2 "C, respectively), while ammonia's is 132.3 "C. A qualitative estimate of the selectivity of a supercritical fluid solvent can be obtained by considering the phase behavior of the three binary mixtures (i.e., SCF-biphenyl, SCF-dodecane, and dodecane-biphenyl) which comprise the ternary system. The pressure-composition isotherms for the C0,-dodecane system (Stewart and Nielsen, 1954) exhibit behavior which is similar to that of the ethanedodecane system (Lee and Kohn, 1969). In both of these cases, only moderate pressures are needed to obtain a totally miscible mixture, regardless of the binary composition. There is no information available in the literature on the behavior of the SCF-liquid biphenyl systems of interest in this study. However, McHugh and Yogan (1984) have shown that there are differences in the phase behavior of the solid biphenyl-COz and solid biphenyl-ethane systems. On the basis of the characteristics of the pressure-temperature (P-T) trace of the solid-liquid-gas (SLG) line for both solid-SCF systems, they reason that solid biphenyl is more soluble in ethane than in C02at very 'high pressures. The same ordering of solubility levels should be evident with liquid biphenyl, and, therefore, for a given solubility level higher operating pressures will be needed with supercritical C02. There is no information in the literature on the dodecane-biphenyl system. The interactions between these two components in the liquid phase can have a very large effect on the ternary mixture phase behavior. Using the above-mentioned binary phase behavior information, we conjecture that either C02or ethane should preferentially extract dodecane from a liquid mixture of dodecane and biphenyl. The situation with supercritical ammonia is slightly different. There is evidence in the literature that liquid ammonia at approximately room temperature will preferentially extract an aromatic hydrocarbon from a paraf-
finic-aromatic hydrocarbon mixture (Fenske et al., 1954). We attempted to determine whether the same selectivity would persist at pressures and temperatures which are above the critical point of ammonia. The experimental conditions for this study were determined by first visually identifying regions in P-T space in which a 5050 mixture of dodecane and biphenyl (on an SCF-free basis) with varying amounts of SCF solvent exhibits large volumetric changes for small changes in temperature and pressure. On the basis of this technique, 97.7 "C and 188.1 atm were chosen for obtaining tie-line information for the COPsystem. The second temperature and pressure for obtaining tie-line data, 53.7 "C and 104.8 atm, were chosen so that the temperature is at least 40 deg lower than 97.7 "C and that the two-phase liquid-vapor region covers a wide range of compositions. By use of similar arguments, tie-line data were obtained at 125.6 "C and 126.8 atm and at 76.8 "C and 86.7 atm for the ethane system. For the ammonia system, tie-line information was obtained only at 156.5 "C and 139.5 atm. To obtain an estimate of the phase behavior of dodecane-biphenyl-SCF mixtures at other temperatures and pressures, the phase behavior information obtained in this study is modeled by using the Peng-Robinson equation of state with two fitted parameters for each of the binary mixtures comprising the ternary mixture. The equationof-state parameters are determined by fitting binary data available in the literature. It is necessary to adjust the values of these parameters slightly to obtain a better fit of the ternary data. Ternary phase diagrams are then calculated at conditions other than those investigated in this study.
Experimental Section A detailed description of the experimental apparatus used in this study and the experimental technique used to determine P-T information is available in the literature (McHugh and Guckes, 1985). Only the highlights of the experimental procedure are given here. The basic component of the experimental apparatus is a high-pressure, variable-volume, equilibrium view cell. With this view cell it is possible to observe visually the number of equilibrium phases and it is also possible to adjust the volume of the mixture by displacing a movable piston in the cell. The cell is initially loaded with a known amount of dodecane and biphenyl. The residual air in the cell is purged and then a known amount of ethane, carbon dioxide, or ammonia is transferred into the cell. A t the temperature of interest, the desired operating pressure is obtained by adjusting the piston. At a fixed temperature (maintained constant to within hO.1 "C) and pressure (maintained constant to within h 5 psi), the equilibrium phases are sampled to obtain tie-line information. A sample of approximately 2-4 g of each phase is obtained in the following manner. The stirrer is stopped, and the phases are allowed to separate. Either the top or bottom phase is displaced into a high-pressure sampling bomb by moving the piston forward. During this procedure, the pressure is normally maintained constant to within f25 psi. The loaded sampling bomb is weighed to within f0.02 g and then cooled in a dry ice-acetone bath. At dry ice-acetone conditions, the ethane, COz, or ammonia is slowly vented from the bomb. After fully venting at dry ice conditions, the bomb is further vented while allowing it to come slowly to room temperature. After venting, the bomb is reweighed and the amount of the light gas is therefore determined. A refractometer with a sodium-D light is used at 84.5 "C to determine the weight fraction of biphenyl in the
978 Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987 Table I. ExDerimental Data for the Dodecane-BiDhenvl-Ethane System Obtained in This Studs vapor phase, wt 3'% liquid phase, wt % loading, wt % DD BP C7Hc DD BP C7Hc DD BP C7Hr T = 76.7 "C and P = 86.7 atm 11.2 54.2 28.1 9.4 62.5 6.0 1.6 92.5 34.6 10.8 28.9 60.3 1.8 1.9 96.4 16.6 57.2 26.2 2.2 93.9 30.5 30.5 39.1 19.8 19.9 60.3 4.0 2.2 96.9 4.5 77.4 18.1 2.9 32.2 64.9 0.9 28.6 20.4 9.8 3.5
11.8 20.0 29.6 36.0
59.6 59.6 60.6 60.5
15.9 10.0 4.6 2.0
T = 125.6 "C and P = 126.8 atm 5.6 78.6 6.1 83.8 89.2 6.2 6.0 92.0
38.2 30.2 13.8 5.9
16.8 32.9 62.7 75.4
45.0 36.9 23.6 18.8
B* 1.21 3.26 1.82 7.04 1.25 1.79 3.37 4.19
Table 11. Experimental Data for the Dodecane-Biphenyl-Carbon Dioxide System Obtained in This Study vapor phase, wt % liquid phase, wt % loading, wt % DD
BP
C02
20.3 6.8 12.2
6.7 21.3 12.4
73.0 71.9 75.4
10.2 6.4 18.9 2.7
10.4 19.7 6.4 23.4
79.4 73.9 74.7 73.9
DD
BP T = 53.7 "C and P 0.7 3.0 0.6 0.8 2.00 1.0"
COZ DD = 104.8 atm 96.3 33.6 15.3 98.6 97.0° 27.2
BP
C02
P*
10.5 53.8 31.9
55.9 30.9 40.9
1.34 4.69 2.35
29.4 57.2 9.1 68.8
46.3 28.3 65.6 27.2
1.76 2.63 1.16 6.45
T = 97.7 "C and P = 188.1 atm 6.1 2.6 14.5 1.2
4.2 3.9 4.5 3.2
89.7 93.6 81.0 95.6
24.3 14.5 25.3 4.0
"Vapor-phase sample was not obtained at this condition. The data listed here represent a composition based on interpolation of the vapor solubility curve in Figure 3. Table 111. Experimental Data for the Dodecane-Biphenyl-Ammonia System Obtained at 156.5 O C and 139.5 atm loading, wt % vapor phase, wt % liquid phase, wt % DD 10.4 18.5 6.2
BP 10.6 6.3 19.2
NH3 79.0 75.2 74.5
DD 7.8 16.7 3.3
BP 7.2 5.6 7.0
remaining sample solution. It is necessary to heat the bomb to obtain a representative liquid sample since biphenyl solidifies at 69.5 "C. To obtain an indication of the reliability of our sampling technique and analysis procedure, we closed a mass balance on each tie line. After obtaining a sample of each of the equilibrium phases, the mixture remaining in the view cell is forced into a one-phase region at the system temperature by increasing the pressure. A sample of the one-phase mixture is then obtained and analyzed as previously described. With this information we are able to close a mass balance generally to within f3.0%. The error in the weight fractions of the equilibrium phases is estimated to be within i2.0%. Materials. The dodecane, 99% purity, was obtained from Fisher Scientific Company, and the biphenyl, 99% purity, was obtained from Aldrich Chemical Company. The COz, bone-dry grade (99.8% pure), ethane, CP-grade (99% pure), and the ammonia, anhydrous-grade (99.99% pure), were obtained from Linde Corporation. All of these materials were used without further purification.
Results and Discussion The ternary phase behavior of the dodecane-biphenyl-ethane system at 76.8 "C and 86.7 atm is shown in Figure 1. The data at 125.6 "C and 126.8 atm are shown in Figure 2. Also shown in these figures are calculated tie lines, which are discussed in a subsequent section of this paper. The data for this system are tabulated in Table I. The selectivities listed in Tables 1-111 are defined as
P* = (YDD/XDD)/(YBP/XBP)
(1)
where y denotes a mass fraction in the vapor or fluid phase,
NH, 85.0 77.7 89.7
DD 20.8 27.1 10.7
BP 23.7 10.3 33.1 DoDECANE
NH3 55.5 62.6 56.1
P* 1.23 1.13 1.46
LOADING EXPERIMENTAL DATA --.-CALCULATED RESULTS o 0
BIPHENYL
ETHANE
Figure 1. Phase behavior of the dodecane-biphenyl-ethane system at 76.8 "C and 86.7 atm. The open symbols and the solid tie lines represent experimental data, and the dashed lines represent calculated phase behavior.
x denotes a mass fraction in the liquid phase, subscript
DD denotes dodecane, and subscript BP denotes biphenyl. A t both experimental conditions, the values of the selectivities indicate that dodecane is more soluble than biphenyl in supercritical ethane. This solubility behavior is consistent with the binary ethane-dodecane and ethane-biphenyl phase behavior described previously. At the lower temperature and pressure, the loading or amount of heavy components in the ethane-rich phase is only on the order of 2-7 wt % . Therefore, it would take a large amount of ethane to extract dodecane from biphenyl. At the higher
Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987 979
A
o LOADING
A
EXPERIMENTAL DATA ----CALCULATED RESULTS
BIPHENYL
o LOADING 0
EXPERIMENTAL DATA
ETHANE
Figure 2. Phase behavior of the dodecane-biphenyl-ethane system at 125.6 "C and 126.8 atm. The open symbols and the solid tie lines represent experimental data, and the dashed lines represent calculated phase behavior. 'ODECANE
Figure 4. Phase behavior of the dodecane-biphenyl-carbon dioxide system at 97.7 "C and 188.1 atm. The open symbols and the solid tie lines represent experimentaldata, and the dashed lines represent calculated phase behavior.
LOADING EXPERIMENTAL DATA ----CALCULATED RESULTS o
o LOADING
0
0
BIP~ENYL Figure 3. Phase behavior of the dodecane-biphenyl-carbon dioxide system at 53.7 "C and 104.8 atm. The open symbols and the solid tie lines represent experimentaldata, and the dashed lines represent calculated phase behavior.
temperature and pressure, where dodecane is now miscible over the entire range of binary dodecane-ethane compositions, the selectivities are not significantly different than those at the previous condition. However, the loading of heavy component in the ethane-rich phase now ranges from 8 to 21 wt 5%. With these higher loadings, smaller amounts of ethane are needed to extract dodecane from biphenyl. The ternary phase behavior of the dodecane-biphenyl-carbon dioxide system at 53.7 "C and 104.8 atm is shown in Figure 3 and at 97.7 "C and 188.1 atm is shown in Figure 4. Also shown in these figures are calculated tie lines, which are discussed below. The data for this system are tabulated in Table 11. As shown in Figure 3, dodecane is more soluble than biphenyl in supercritical carbon dioxide. Again this solubility behavior is consistent with the binary phase behavior of COP-dodecane and C02-biphenyl described previously. The loading and selectivity behavior of the dodecane-biphenyl-carbon dioxide system are very similar to that of the dodecanebiphenyl-ethane system. At the lower temperature and pressure, the loading of heavy components in the carbon dioxide rich phase is quite low, while at the higher temperature and pressure the loading increases greatly. Unfortunately, the selectivities for the carbon dioxide system
EXPERIMENTAL DATA
AMMONIA
Figure 5. Phase behavior of the dodecane-biphenyl-ammonia system at 156.5 O C and 139.5 atm.
at the two P-T conditions considered in this study are not significantly different from each other-that is, the tie lines did not change slope between the two conditions. Funk (1985) has also shown that supercritical carbon dioxide at 40 "C and 100-200 atm does not selectively extract saturated hydrocarbons from aromatic hydrocarbons. The phase behavior of the dodecane-biphenyl-ammonia system at 156.5 "C and 139.5 atm is shown in Figure 5 and listed in Table 111. The selectivity values for supercritical ammonia are all very close to one, while those for saturated liquid ammonia (Fenske et al., 1954) are much greater than one. Although Fenske et al. (1954) do not explain the selectivity behavior of liquid ammonia, it seems reasonable to assume that aromatics are preferentially extracted from aromatic-paraffinic mixtures because ammonia, a strong Lewis base, interacts with the aromatics (Lewis acids) rather than with neutral paraffins. These interactions are probably less dominant with supercritical ammonia because of its lower density and the elevated operating temperatures (Anderson et al., 1962). It is not possible to obtain higher ammonia densities since the mixture becomes a single phase at higher pressures. The three solvents used in this study can be compared by plotting the selectivity factor as a function of the loading of the solutes in the vapor (extract) phase as shown in Figure 6 (Barton, 1986). In all three cases, the selectivity
980 Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987
'
Table IV. Interaction and Size Parameters for the Binary Mixtures which Comprised the Ternary Mixtures Investigated in This Study adjusted fitted values values system source for binary data qv 'iJ qzl DD-C,H6 Lee and Kohn, 1969-0.020 0.010 0.02 0.01 DC-BP 0.03 0.01 BP-C,H6 McHugh and Yogan, 1984 0.015 -0.017 0.03 -0.02 BP-CO, McHugh and Yogan, 1984 0.085 -0.02 0.08 0.00 DD-CO, Stewart and Nielsen, 1954 0.095 -0.010 0.09 0.00
\\,
where u is the molar volume, a accounts for interactions between the species in the mixture, and b accounts for size differences between the species of the mixture (Peng and Robinson, 1976a,b). For the pure components
Solute
Weight
Fraction n Vapor Phase
Figure 6. Variation in the selectivity as a function of the loading of biphenyl and dodecane in the vapor phase for all three supercriethane at 76.7 "C and 86.7 atm, tical solvents used in this study: (0) (0) ethane at 125.6 "C and 126.8 atm, (v)CO, at 53.7 "C and 104.8 NH3 at 156.5 'C and atm, (A) C02 at 97.7 "C and 188.1 atm, and (0) 139.5 atm.
increases as the solute loading decreases. Interestingly, the ammonia data fall close to the high-temperature carbon dioxide data and between the two sets of ethane data. If the selectivity values of the 125.6 "C ethane data, the 97.7 "C carbon dioxide data, and the 156.6 "C ammonia data a t a loading of 10 wt 70 are compared to their relative volatilities [PDDvap(T)/P~p"p(~] (Reid et al., 1977), we find that ammonia and carbon dioxide both "promote" the solubility of biphenyl whereas ethane does not. This suggests that supercritical ammonia and carbon dioxide are not acting as neutral, nonselective solvents. Unfortunately, as the solubility of biphenyl in ammonia and carbon dioxide increases, the selectivity tends toward a value of one, whereas ethane maintains a high value of the selectivity even at moderately high solute loadings. Data Reduction. We model the ternary phase behavior by using the Peng-Robinson equation of state (EOS). Model-generated phase diagrams can be used to determine other possible pressures and temperatures at which the loading and selectivity relationships may be more favorable. At equilibrium the fugacities of each mixture component in each of the phases are equal. i = 1, 2,
..., n
(2) where fk is the fugacity of component i in the liquid phase, fy is the fugacity of component i in the gas or fluid phase, and n is the number of components. The fugacities can be written as f,L
=
fiG
fiL
= Xi+jLP = yj+pp
(3)
(4) where x i is the mole fraction of component i in the liquid phase, 4iLis the fugacity coefficient of component i in the liquid phase, yi is the mole fraction of component i in the gas phase, and $?is the fugacity coefficient of component i in the gas phase. The fugacity coefficientsare determined by using an equation of state. We have chosen to use the Peng-Robinson equation of state a(T) p = - -R T (5) u - b U(U + b ) + ~ ( I -J b) fjG
h = 0.07780(RTC/P,)
(6)
479 = a(T,)a(T,,w)
(7)
a(TJ = O.45724(R2TC2/Pc) cuO.'(TR,o)= 1
+ m ( l - TR0,5)
(8)
(9)
m = 0.37464 + 1,542260 - 0 . 2 6 9 9 2 ~ ~ (10) where T , is the critical temperature, P, is the critical pressure, TR is the reduced temperature, and w is the acentric factor. For mixtures, we use the mixing rules i, j = 1, 2, ..., n a = CCxixjaij (11) and aij = (1 - 8i,)a:."aj",5
(12)
where aij is an interaction parameter obtained by regressing experimental P-x data and i, j = 1, 2, ..., n b = CCxixjbij (13) and bij = (1 - qij)(bi + hj)/2
(14)
where qij is a size parameter, determined along with a i j by fitting the equation of state to P-x data. Peng and Robinson usually set qij equal to zero, which reduces eq 13 to b = Cxibi i = 1, 2, ..., n (15) Deiters and Schneider (1976) suggest that both parameters are needed when using a cubic equation of state for calculating the high-pressure phase behavior of binary mixtures which differ considerably in structure, molecular size, and polarity. We also retain two parameters per binary pair. Due to the polarity of ammonia, the dodecane-biphenyl-ammonia system was not analyzed by using the Peng-Robinson EOS. The values for the parameters ai, and vij, obtained from a fit of binary data available in the literature, are listed in Table IV for the five binary pairs which comprise the dodecane-biphenyl-ethane system and the dodecane-biphenyl-carbon dioxide system. For the ethane-dodecane system, pressure-composition (P-x) isotherms are fit over a temperature range of 0-100 "C (Lee and Kohn, 1969). Not surprisingly, the second parameter, vij, greatly improves the fit of the data. Temperature-independent values for 6, and vij are obtained from a least-squares fit of the data. The value for 8, obtained in this study, 0.02, is reasonable based on the order of magnitude values recommended by Robinson and Peng (1978), who regress data with only a single parameter, Jij.
Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987 981
For the carbon dioxide-dodecane system, pressurecomposition isotherms are fit at two temperatures, 15.6 and 32.2 OC (Stewart and Nielsen, 1954). The resultant parameter values, also temperature independent over this limited temperature range, provide good first estimates for our calculations. Again the value of 6, for this system is reasonable based on the order of magnitude values recommended by Peng and Robinson (1978). Since P-x data are not available for either the ethanebiphenyl system or for the carbon dioxide-biphenyl system, the P-T trace of the three-phase solid-liquid-gas (SLG) line originating at the normal melting point of biphenyl and ending at the system's upper critical end point (McHugh and Yogan, 1984) is fit to obtain values for 6, and qij: In this instance, three fugacity relationships must be satisfied along the SLG line fBPG
= fBPL
(16)
fLCG
= fLCL
(17)
fBPG
= fBPs
(18)
Figure 7. Effect of temperature on the calculated dodecane-biphenyl-ethane diagram at a fixed pressure of 125 atm. OOOECANE
where the subscripts BP and LC denote biphenyl and the light component, respectively; f is the fugacity; and superscripts G, L, and S denote gas, liquid, and solid phases, respectively. The fugacities in the gas and liquid phases are calculated by using the Peng-Robinson equation of state. The fugacity of pure, solid biphenyl is given by P fBPs
@]
= pBPsub(T)'#'BPSub(T)[ e x p ~ B p e u $ v B P s / ~ T ) (19)
where is the sublimation pressure of solid biphenyl (Bradley and Cleasby, 1953), '#'BpsUbis the fugacity coefficient of biphenyl at its sublimation pressure, and uBPs is the molar volume of solid biphenyl. For these calculations, the molar volume of solid biphenyl, 132.05 cm3/mol, is assumed to remain constant (Vaidya and Kennedy, 1971). Although the fit of the P-T trace of the SLG line for these systems is, semiquantitative, at best, it did provide a reasonable first estimate of 6ij and qij. The value of aij for the ethane-biphenyl system is similar to the value suggested by Robinson and Peng (1978) although it is slightly smaller than the value found by Schmitt (1984). Neither Schmitt nor Peng and Robinson included qij in their analysis of experimental data. Although using temperature-dependent values for dij and qij would have improved the fit of the SLG line, we chose a single value for each parameter. Similar trends are found for aij and qij for the carbon dioxide-biphenyl system. Since we did not have information on the phase behavior of the dodecane-biphenyl system, we initially choose zero valuea for 6, and qii. We obtained nonzero values for these parameters by fitting tie lines for the dodecane-biphenyl-ethane system at 76.7 "C and 86.7 atm. These nonzero values were then used for modeling the dodecane-biphenyl-carbon dioxide system. To obtain a good fit of the ternary phase behavior, we found it necessary to adjust the parameter values slightly for the ethane-biphenyl, C02-dodecane,and C02-biphenyl systems. The adjusted parameter values shown in Table IV are not significantly different from those obtained from fitting binary data. The fit obtained for the dodecane-biphenyl-ethane system is shown in Figures 1and 2. The calculated tie lines are very close to the experimentally obtained tie lines. Likewise, the fit for the dodecane-biphenyl-carbon dioxide system is shown in Figures 3 and 4. In this case, the calculated and experimental data are not in as good
Figure S. Effect of pressure on the calculated dodecane-biphenyl-ethane diagram at a fixed temperature of 125 "C.
agreement as for the ethane system. The difference in the fit of the tie lines for the ethane and the COz systems can be explained by considering the method used for fitting 6ij and qij. Recall that the 6, and qij values for dodecane-biphenyl were obtained by fitting the ethane ternary data at 76.7 "C and 86.7 atm. Predictions for the ethane system at 125.6 "C and 126.8 atm, using the parameters thus obtained, are also very good. Since we did not have any binary information on dodecane-biphenyl mixtures, we used the same aij and qij values for the carbon dioxide system. Although these values are probably not the true binary values, we obtain a more reasonable fit of the experimental data than if these parameters are all set equal to zero. The effect of temperature and pressure on the behavior of the ternary systems can now be calculated using the adjusted binary parameters. The results are shown in Figures 7 and 8. In this instance we only show the effect of temperature and pressure on the calculated dodecanebiphenyl-ethane diagrams since the trends with the carbon dioxide diagrams are very similar. Figure 7 shows the effect of temperature on the calculated tie lines at a fixed pressure of 125 atm. As the temperature is increased from 75 to 125 "C, the two-phase liquid-gas region becomes considerably larger. The selectivities at 75 "C are much greater than those at 125 "C-that is, tie lines are more parallel to the biphenyldodecane axis at 75 "C than at 125 "C. The loading of the
982 Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987
heavy components in the ethane-rich phase is also very high at 75 “C and 125 atm. However, the two-phase region at 75 “C and 125 atm is reduced in size relative to the two-phase regions at other conditions. The calculated phase behavior at 75 OC suggests that a biphenyl-rich feed stream can be further enriched by treatment with supercritical ethane. Figure 8 shows the effect of pressure on the tie lines at a fixed temperature of 125 OC. In this case increasing the pressure decreases the two-phase region greatly. At 175 atm and 125 OC, the tie lines are beginning to become more parallel to the biphenyl-dodecane axis, indicating that the selectivities are increasing. However, the two-phase region at 175 atm is also reduced in size, indicating that the separation of dodecane from biphenyl would only occur for feed streams which contain greater than about 60 wt 70 biphenyl (on an SCF-free basis). Conclusions We have presented experimental information on the separation of an aromatic-paraffinic mixture (i.e., biphenyl-dodecane) using supercritical ethane, carbon dioxide, and ammonia. The information is characterized using the Peng-Robinson EOS with two fitted parameters, 6, and qij, for each pair of the three components comprising the ternary mixture. These parameters, initially determined from fitting available binary data, were adjusted slightly to obtain a good representation of the experimental data for the ternary systems. A good estimate of the selectivity behavior of a supercritical fluid solvent can be estimated from the ternary phase diagrams that are generated at other temperatures and pressures using these adjusted binary parameters. Based on our experimental results and on model-generated ternary phase diagrams, none of the solvents, supercritical ethane, carbon dioxide, or ammonia, exhibits both a high selectivity and a high loading for either dodecane or biphenyl. However, the experimental results do suggest that supercritical ethane or supercritical carbon dioxide can be used to further enrich a biphenyl-rich feed stream. Acknowledgment We thank Mike McCann, Ken Mueller, Tom Odar, and Stacy Wenzel for performing many of the experiments reported in this paper. We acknowledge the technical and financial support given by the Exxon Chemical Company. The experimental work was done by S.V.D., A.J.S., and M.A.M. at the Department of Chemical Engineering at the University of Notre Dame, Notre Dame, IN. We wish to express our appreciation for all their help and cooperation during that period. We also acknowledge Paul Barton of the Department of Chemical Engineering at The Pennsylvania State University who suggested that we interpret our data in terms of selectivity factor vs. relative volatility. His review of our paper is most appreciated.
Registry No. DD, 112-40-3; BP, 92-52-4; C2Hs, 74-84-0; COz, 124-38-9;NHB, 7664-41-7.
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Received f o r review December 20, 1985 Accepted October 21, 1986
