493
Ind. Eng. Chem. Fundem. 1984, 23, 493-499
diagrams which are shown separately in Figures 3 and 6. Comparing them with the experimental figures, the most dense packing appears on the coarse-fine axis in Figures 2 and 3, respectively, and inside the triangular diagrams in the Figures 5 and 6. Including the configurations of isoporosity lines, we can see a general agreement between the theory and the experiments. These results suggest wide application of the proposed theory. Nomenclature
C(D)= coordination number, dimensionless Q,Di= diameter of particle, m
D = average diameter of particles from eq 1, m f ( D ) = number frequency size distribution of particles, fi = fractional number of ith component, dimensionless rn = number of components composed of particles of different sizes, dimensionless N = total number of particles, dimensionless n = number of hypothetical spheres, dimensionless ii = average value of n, dimensionless VB (rn) = total packed volume of rn-component mixture in question, m3 VB (rn - 1)= packed volume of an (rn - 1)-componentmixture, m3 VBT = total packed volume of mixture in question, m3 V, (0)= total volume of space allocated to a specified particle, m3
V,,,(D) = volume of spherical shell, m3 Vu(rn - 1)= solid volume of an (rn - 1)-componentmixture, m3 Vu (rn) = total solid volume of rn-component mixture in question, m3 ui = fractional solid volume of ith component, dimensionless u (rn - 1) = fractional solid volume of an (rn - 1)component mixture, dimensionless Greek Letters z = overall average porosity of mixed packing, dimensionless zo = overall average porosity of packing of uniformly sized spheres, dimensionless t A = surface porosity around a particle, dimensionless tij = overall average porosity of packing of components i and j , dimensionless t (rn - 1) = overall average porosity of an (rn - 1)-component mixture, dimensionless t,(D) = average porosity of a spherical shell, dimensionless Literature Cited Cunningham, G. W. React. M t e r . 1983, 6, 1. Kawamura, J.; Aokl, E.; Okusawa, K. Kagaku K q k u 1971, 35, 777. Ouchiyama, N.; Tanaka. T. I&. Eng. Chem. Fundem. 1981, 20, 66. Standlsh, N.; Borger, D. E. Powder Techno/. 1979, 22, 121. RMgway, K.; Tarbuck, K. J. Chem. Recess Eng. 1988, 49, 103.
Received for review August 31, 1983 Accepted April 11,1984
High-pressure Phase Behavior of Binary Mixtures of Octacosane and Carbon Dioxide Mark A. McHugh,' Andrew J. Seckner, and Thomas J. Yogad Department of Chemical Engineering, Universlty of Notre &me, Notre Dame, Indkna 46556
The high-pressure fluid phase behavior of binary mixtures of octacosane and COPis experimentally investigated. Solubilities of octacosane in supercritical CO, and mixture molar volumes are determined for isotherms of 34.7, 45.4, 50.2, and 52.0 OC over a range of pressures from 80 to 325 atm. The solubility data are obtained by two different experimental techniques. The pressure-temperature projection of the two branches of the three-phase solid-liquid-gas freezing point depression curve is also determined. The octacosane-CO, LCEP is determined as 32.2 OC and 72.6 atm. The UCEP, which is at a pressure greater than 650 atm, could not be determined due to the pressure limitation of the experimental apparatus. Phase diagram constructions are used qualltatively to explain the observed phase behavior and to provide Information on the expected phase behavior of the octacosane-CO, system at pressures higher than those experimentally investigated.
Introduction
Supercritical solvent extraction (i.e., extraction with a solvent which is a t a temperature above its critical temperature and a pressure above its critical pressure) is currently being considered as an alternative to conventional separation techniques, such as liquid extraction and distillation. Although supercritical solvents have been used for a variety of separation problems (Schneider et al., 1980; Paulaitis et al., 1983; McHugh, 1984), there is still a need for fundamental research with supercritical solvents to fully understand and capitalize on the unique processing capabilities of these types of solvents. The high-pressure fluid phase behavior of mixtures is one area of research t U.S.Steel
Chemical Research, Monroeville, PA. 0196-4313/84/1023-0493$01.50/0
with supercritical solvents which needs to be expanded. Of interest in this study is the phase behavior of one class of binary mixtures which consists of a heavy nonvolatile solid and a light supercritical fluid. In this instance the melting temperature of the heavy solid, T,,, is greater than the critical temperature of the light component, T,,, and the molecular size, shape, structure, and critical conditions of the two components differ substantially. The phase behavior for this type of binary mixture is depicted in the P-T diagram shown in Figure 1 (Rowlinson and Richardson, 1959). CD and MH are the pure component vapor pressure curves, MN the heavy component melting curve, and EM the pure heavy component sublimation curve. Points D and H represent pure component critical points. For this type of system, the critical mixture curve which represents the critical conditions for mixtures of 0 1984 American Chemical Society
4B4 Ind. Eng. Chem. Fundam., Vol. 23, No. 4, 1984
1f
I$
0
- T: 35 B0C
O-T.495'C
I
TC I
TM2
100
TC 2
0
TEMPERATURE
0.10
0.10
0.15
0.20
BIPHENYL MOLE FRACTION
Figure 1. Pressure-temperature diagram for a highly asymmetric mixture.
50
0.05
I
0.20
Mole Fraction of Naphthalene
Figure 2. Experimental solubilities of solid naphthalene in supercritical ethylene at 25, 45, and 50 "C (Diepen and Scheffer, 1953).
different composition has two branches. One branch, which starts at the critical point of the heavy component, H, intersects the three phase solid-liquid-gas (S-L-G) freezing point depression curve at the upper critical end point (UCEP). The other branch of the critical mixture curve starts at the critical point of the light component, D, and intersects the S-L-G line at the lower critical end point (LCEP). The freezing point depression of the heavy solid is a consequence of the solubility of the light component in the heavy liquid. If this solubility were large, the S-L-G curve would start at the melting point of the heavy solid and run continuously to lower temperatures. Also, the critical mixture curve would run continuously between the critical points of the two pure components (Rowlinson and Richardson, 1959). In the present case, however, the light component is only slightly soluble in the heavy liquid phase and, hence, the freezing point depression of the heavy solid is also only slight. As shown in Figure 1,the S-L-G line rises steeply and intersecta the critical mixture curve at the LCEP and the UCEP. At these critical end points the liquid and gas phase of the S-L-G line merge into a single fluid phase in the presence of excess solid (Diepen and Scheffer, 1948a). Supercritical solvent extraction of solids would occur in the gas-solid region which exists between the two branches of the S-L-G line. A variety of high-pressure phase behavior can exist even for binary mixtures which are very similar, such as naphthalene-ethylene and biphenyl-COD Both naphthalene and biphenyl are heavy, nonvolatile solids with melting temperatures well above room temperature, 80.2 and 69.5 "C, respectively. Both ethylene and COz are gases at ambient conditions with relatively mild critical conditions, 9 "C and 49.7 atm and 31.05 "C and 72.8 atm, respectively. Shown in Figure 2 are three solubility isotherms for the naphthaleneethylene system (Diepen and Scheffer, 1953). Notice that the 50 "C isotherm exhibits a large solubility
Figure 3. Solubility of biphenyl in supercritical C02 at 35.8, 49.5, and 55.2 "C (McHugh, 1981; McHugh and Paulaitis, 1980).
enhancement which is sensitive to small changes in pressure around 175 atm. Notice also that for an isobar of approximately 200 atm the increase in the solubility of naphthalene in ethylene from 45 to 50 "C is substantially greater than that from 25 to 45 "C. The sensitivity of the solubility to small changes in pressure as well as temperature near 175 atm and 50 "C is a consequence of operating extremely close to the naphthalene-ethylene UCEP (i.e., 52.1 "C and 174 atm (van Welie and Diepen, 1961b)). Also, the loading of solid naphthalene in supercritical ethylene can be quite substantial near the UCEP (i.e., 15 mol % naphthalene corresponds to approximately 45 w t % naphthalene in supercritical ethylene). Compare the solubility behavior of the previously described naphthalene-ethylene system to that exhibited by the biphenyl-C02 system shown in Figure 3 (McHugh, 1981; McHugh and Paulaitis, 1980). The 55.2 "C isotherm of the biphenyl-C02 system has certain characteristics which are similar to the 50 "C isotherm of the naphthalene-ethylene system. The 55.2 "C isotherm exhibits a large solubility enhancement which is also sensitive to small changes in pressure near 460 atm. The isobaric solubility behavior of the biphenyl-C02 system near 450 atm is also similar to the previously described naphthalene-ethylene system near 200 atm. The increase in the solubility of biphenyl in supercritical COzfrom 49.5 to 55.2 "C is substantially greater than that from 35.8 to 49.5 "C. The sensitivity of the solubility to small changes in pressure as well as temperature near 460 atm and 55 "C is a consequence of operating extremely close to the biphenyl-COz UCEP (i.e., 55.1 "C and 469.0 atm (McHugh, 1981; McHugh and Paulaitis, 1980; McHugh and Yogan, 1984). Also, as with the naphthalene-ethylene system, the loading of solid biphenyl in supercritical C02 is very high near the mixture UCEP (Le., 15 mol % biphenyl is equivalent to aproximately 38 wt 70).The similarity in the P-x behavior near the UCEP for naphthaleneethylene and biphenyl-C02 suggests that the location of the UCEP can be estimated solely from solubility data (McHugh, 1981; McHugh and Paulaitis, 1980; Gitterman and Procaccia, 1983; Procaccia and Gitterman, 1983). However, at a temperature near the UCEP temperature and at pressures greater than the UCEP pressure, these two systems exhibit radically different solubility behavior. At 55.2 "C and at pressures greater than 460 atm, the solubility of biphenyl in supercritical COz decreases dramatically for a small increase in pressure; at 50 "C and at pressures greater than 174 atm, the solubility of naphthalene in supercritical ethylene increases for a small increase in pressure until at higher pressures the solubility eventually reaches a limiting value. Even though the location of the mixture UCEP can be determined from the behavior of the P-x isotherms, the interpretation of these isotherms is not always a straightforward task. However,
Ind. Eng. Chem. Fundam., Vol. 23, No. 4, 1984 HElSE
PRESSURE GAUGE
GAUGE
495
PRESSURE GAUGE
VENT
8
PRESSURE GENERATOR
L-f-,t I L
--------_----_-_--___---THERMOSTAT I J
HEATING
A g --- - -
FIBER OPTICS
TEMPERATURE READOUT
Figure 4. Schematic diagram of the flow apparatus used to obtain solubility data.
Figure 5. Schematic diagram of the experimental apparatus used for obtaining P-r information.
the differences in the behavior of the naphthaleneethylene and biphenyl-C02 solubility behavior near the mixture UCEP can be readily explained if the P-T trace of the three phase S-L-G line is known. This will be demonstrated in the Discussion section of this paper. The focus of this investigation is to elucidate the highpressure fluid phase behavior of binary mixtures consisting of a long-chain, normal paraffin, octacosane, and a light gas, COP Octacosane is chosen for this work since it is a crystalline solid which melts at a temperature (TM= 64.5 "C) which is greater than the critical temperature of COP Also, the data obtained in this study can be directly compared to those obtained by other investigators for the naphthalene-C02 and biphenyl-C02 systems (McHugh, 1981;McHugh and Paulaitis, 1980;Tsekhanskaya et al., 1964). In this work the P-T trace of the S-L-G line for the octacosane-C02 system will be presented along with P-x isotherms obtained in the solid-gas region of the phase diagram. Two experimental techniques for obtaining P-x data will be described. Phase diagram constructions will be used to explain the experimentally observed phase behavior and to provide information on the expected phase behavior of the &c0sane-CO2 system at pressures higher than those experimentally investigated. Also, the behavior of the biphenyl-C02 system near the mixture UCEP will be explained using the same phase diagram constructions. Experimental Section Two types of experiments are performed in this study. In one, the P-T trace of the two branches of the S-L-G line is determined. In another, the solubility of solid octacosane in supercritical C02 is measured. The experimental technique used to obtain the S-L-G line is described in detail elsewhere (McHugh and Yogan, 1984). The solubility measurements are determined by either a flow or static technique. A schematic diagram of the experimental flow apparatus is presented in Figure 4. Since this technique has been previously described in detail (McHugh, 1981;McHugh and Paulaitis, 1980),it is only briefly reviewed here. COP, compressed and heated to the desired operating conditions, is delivered to two high-pressure columns connected in series. The columns are packed with a mixture of solid octacosane and glass beads. Supercritical C02exits from the second column saturated with octacosane and flows through a high-pressure switching valve (Valco Instruments, Co.) where a calibrated sample loop (0.2092 f 0.00135cm3 (McHugh, 1981))can be isolated for analysis. The volume of C02 in the sample loop is determined by slowly expanding the C02 across a valve and displacing water. The sample loop is then flushed with toluene to recover the octacosane. This solution is then analyzed by standard chromatographic techniques. The pressure of the system is measured with a Heise gauge (0-10000 psig,
accurate to f10 psi) and is typically maintained constant to better than f1.0%. The temperature of the system is measured with a platinum resistance element (accurate to f0.15 OC, calibrated on the 1968 IPTS scale) and is held constant to within f0.15 "C. A schematic diagram of the static experimental apparatus used in this study is shown in Figure 5. The main component of this system is a high-pressure, variablevolume view cell similar to the view cell described by Li et al. (1981).This cell allows for visual determination of the phases present at equilibrium. Carbon dioxide is charged at ambient temperature to the air-operated galliquid compresser where it is compressed and delivered to a holding tank located in a forced convection air bath. The temperature of the air, maintained constant to within fO.l "C (American Scientific Products, YSI 63RC controller), is measured with an accuracy of f0.26 "C using a platinum resistance element (Degussa Inc.) calibrated on the 1968 IPTS scale. With valves 1 and 2 closed (see Figure 5),the pressure of the gas is measured with a Bourdon-tube Heise gauge (Dresser Industries, Model CM), with a range of 0-10 OOO psig and an accuracy of f10 psi, to determine when the gas attains thermal equilibrium with the bath air. This normally takes approximately 30 min. The amount of gas in the holding tank is determined from the gas density obtained from the literature data of Michels and Michels (1937)and the volume of the holding tank. The gas is then transferred to the view cell which has been previously charged with a known amount of octacosane measured to within f0.00002 g (Mettler balance, Model HL52). The amount of gas transferred is determined by a mass balance based on the density of the gas remaining in the holding tank and the transfer lines, and the volume of the tank and lines. The variable-volume, high-pressure view cell (316S.S., 2 in. 0.d. X 0.75 in. i.d., 45 cm3working volume) is designed to operate to 10000 psig at 500 O F . The view cell is maintained at a constant temperature normally within fO.l "C as determined by a platinum resistance element located on the outside skin of the cell. The cell contents, illuminated by a 0.25 in. fiber light pipe (Dolan-Jenner Industries, Model 180),are viewed through a 0.5 in. diameter quartz window (Esco Products) which is secured by a cell end cap which has a 0.25 in. by 0.75in. view slit. The cell contents are mixed by a magnetic stirring bar activated by a magnet (Permag Central Corporation, Model H-109)located below the cell. The contents can be compressed to the desired operating pressure by a movable piston fitted with Teflon O-rings and driven by a low vapor pressure silicon fluid which is pressurized by a syringe type pressure generator (High Pressure Equipment Co., Model 87-6-5).In this manner the pressure of
498
Ind. Eng. Chem. Fundam., Vol. 23,No. 4, 1984 700~
'
6001
1
1
1:1I
i
I
CPCOZ,
1
PC) Figure 6. Experimentally determined P-T diagram for the octacosane-C02 system. TEMPERATURE
Table I. Experimental Pressure-Temperature Data for the Octacosane-C02 Solid-Liquid-Gas Line Ending at t h e Lower Critical End Point pressure, atm temp, "C 13.5 47.1 15.0 48.8 16.3 50.5 17.9 52.5 19.0 53.9 20.7 55.9 22.0 57.3 23.5 60.0 25.1 61.7 26.6 63.7 27.9 65.8 29.5 68.2 31.0 70.9 32.2" 72.6"
"LCEP.
the octacosane-C02 mixture is adjusted isothermally at fixed overall composition by varying the mixture volume. The solubility of octacosane in supercritical C02 is determined in the following manner. The pressure of the octacosaneCOz mixture is isothermally increased until all of the octacosane is solubilized in the C02. At this point a clear, single fluid phase is present in the view cell. The mixture is now slowly decompressed until octacosane precipitates from solution. At this point two phases exist in the view cell. Hence, the actual solubility point is in the pressure interval between this two-phase state and the previous single, fluid phase state. The octacosane is alternately solubilized and precipitated a number of times in an effort to decrease the two-phase, one-phase pressure interval to within approximately &1.5% of the absolute pressure. Materials. Sigma Chemicals, Inc., supplied the octacosane at a stated purity of 99+%. Hence, it was used without further purification. The carbon dioxide, "bone dry" grade 99.8% minimum purity, was supplied by Linde Company. It was also used without further purification. Results The P-T trace of the two branches of the S-L-G line for the octacosane-C02 system is shown in Figure 6 and listed in Tables I and 11. The LCEP for this system is 72.6 atm and 32.2 "C. As shown in Figure 6, the mixture LCEP is very close to the critical point of pure COz (72.8 atm and 31.05 "C). The close proximity of the mixture LCEP to the critical point of pure COz indicates that very little octacosane dissolves in the COP The UCEP for this system is at a pressure which is greater than 649.5 atm and a temperature which is greater than 62 "C. However, the
A-AD
1I
-3
-7.52
- m - -7.50 0--7.34
0
ooc 2' C 7*C
0 0005 0 0010 OCTACOSANE MOLE FRACTION
Figure 7. Solubility of octacosane in supercritical COPat 34.7,45.4, 50.2, and 52.0 OC. The open symbols represent data obtained with the flow apparatus and the solid symbols represent data obtained with the view cell apparatus.
-- 90 0
0-T:
347°C
A-T=
454°C
0-T:
502°C
I 40'
I20
'
160
200
240
280
PRESSURE ( a i m )
Figure 8. Octacosane-CO, mixture molar volume data obtained at 34.7, 45.4, 50.2, and 52.0 "C with the flow apparatus.
UCEP could not be determined due to the pressure limitations of the view cell. The most striking feature of the phase behavior observed for the octacosane-C02 system is the large degree of asymmetry exhibited by the two branches of the S-L-G line shown in Figure 6. Had the S-L-G line not intersected the critical mixture curve, it is highly unlikely that the critical mixture curve would have been a continuous curve as suggested by the schematic P-T diagram shown in Figure 1. Worth noting are two features of the branch of the SL-G line which starts at the melting point of pure octacosane and runs to the UCEP. One is the temperature minimum in the S-L-G line which occurs at approximately 140 atm and 52.5 "C (Le., as the pressure is increased the S-L-G line begins with a negitive slope (dP/dT), passes through a temperature minimum, and then continues with a positive slope to the UCEP). This temperature minimum is a consequence of the influence of the pure melting curve for octacosane and of the limited solubility of C02in liquid octacosane alone the S-L-G line (De Swaan and Diepen, 1963). The other unique feature of the S-L-G line is that a phase inversion of the supercritical fluid and liquid phases occurs at approximately 260 atm and 54.7 "C. At this condition the supercritical fluid phase becomes denser than the liquid phase and, hence, as the pressure is increased above 260 atm the clear supercritical fluid phase is now located below the liquid phase at conditions along the S-L-G line. Present in Table I11 and shown in Figure 7 are the experimental solubility and mixture molar volume data for solid octacosane in supercritical COPobtained with the flow apparatus. Also listed in Table I11 and shown in Figure 8 are the experimental mixture molar volume data obtained with the flow apparatus. The reported mole fractions and mixture molar volumes represent an average
Ind. Eng. Chem. Fundam., Vol. 23, No. 4, 1984
Table 11. Experimental Pressure-Temperature Data for the C02-Octacosane Solid-Liquid-Gas Line Starting at the Melting Temperature of Pure octacosane pressure, atm temp, "C 1.7 62.0 61.0 13.6 60.3 17.6 59.1 21.2 56.9 38.7 57.3 43.1 53.4 73.6 52.8 105.1 52.5 139.4 53.0 161.2 53.5 198.6 53.8 226.8 53.9 230.9 54.2 242.2 54.2 242.8 54.5 254.4 54.6 256.7 54.7" 260.2" 54.7 262.9 54.5 267.3 55.0 274.4 55.0 283.0 55.0 294.3 54.8 296.4 55.1 297.4 55.2 299.0 55.1 300.7 55.4 302.7 55.4 308.1 55.2 314.3 55.4 316.0 55.8 329.2 56.0 331.6 56.3 351.5 57.1 387.7 58.0 424.3 58.6 470.7 59.5 526.0 61.0 600.0 62.0 649.5
497
Temperature
Figure 9. Phase behavior for a highly asymmetric mixture with a temperature minimum in the S-L-G freezing point depreesion curve. (b)
I!
I
HEAVY COMPONENT
HEAVY COMPONENT
--__
HEAVY COMPONENT
(e) 114
Td> Tucep s-F
I
HEAVY COMPONENT
IF
i
I
" Phase inversion conditions. value of at least three independent measurements reproducible to better than 3 %. The solubility and volume data obtained at 45.4, 50.2, and 52.0 "C have an average experimental error of less than 1.0%. The solubility and volume data obtained at 34.7 "C have an average experimental error of approximately 3.3%. The experimental solubility data for solid octacosane in supercritical COz obtained with the view cell are presented in Table IV and are also shown in Figure 7. The reported mole fractions have an average experimental error of less than aproximately 2%. The data obtained using the view cell are in excellent agreement with the data obtained with the flow apparatus. It is evident by comparing the results obtained by McHugh (1981) and McHugh and Paulaitis (1980) to the results obtained in this study that the solubility of octacosane in supercritical C 0 2 is almost two orders of magnitude less than the solubility of either naphthalene or biphenyl in supercritical COz at comparable temperatures and pressures. It appears that the order of decreasing solid solubility io naphthalene, biphenyl, and octacosane. In fact, this is also the order of decreasing sublimation pressure of the solids. Hence, it is not entirely obvious whether the dominant factor which determines solid solubility is either the solid sublimation pressure or the solvent power of supercritical CO,. However, for the case of octacosane the sublimation pressure is so low at 35 to 52 "C that its solubility in supercritical COz must be
COMPOSITION+
Figure 10. Pressure-composition isotherms near the UCEP for systems described in Figure 9.
strictly a function of the solvent power of supercritical COz. Discussion To provide insight into the phase behavior that can be expected for octacosane-COz mixtures at extremely high pressures near the mixture UCEP, and to explain the behavior of the biphenyl-COz system near the mixture UCEP, let us consider the phase diagrams that can be generated for a system which exhibits a temperature minimum in the S-L-G line. The P-T diagram for this type system is shown in Figure 9 (van Welie and Diepen, 1963). Shown in Figure 10a is an isotherm at a temperature which is greater than the temperature minimum of the S-L-G line but still less than the UCEP temperature (Diepen and Scheffer, 1948b; Zernike, 1955). A variety of phase behavior is exhibited at this temperature since the three-phase S-L-G line is intersected at two different pressures. A t low pressures solid-gas equilibrium is maintained until the S-L-G line is intersected at Pa,where the three equilibrium phases are depicted by a horizontal tie line. Depending on the concentration of the overall mixture, either liquid-gas, solid-liquid, or a single liquid
498
Ind. Eng. Chem. Fundam., Vol. 23, No. 4, 1984
Table 111. Experimental Solubilities and Mixture Molar Volumes for Octacosane in Supercritical C 0 2 Obtained with the Flow Apparatus at 34.7, 45.4, 50.2, and 52.0 "C pressure, octacosane mixture vol, atm mole fraction cm3/g-mol
Table IV. Experimental Solubilities for Octacosane in Supercritical COz Obtained with the View Cell Apparatus at 45.4, 50.2, and 52.0 "C pressure, octacosane atm mole fraction
T = 34.7 "C 121.8 137.7 152.2 162.9 180.3 191.7 220.4 241.7 259.5 277.4
0.000107 0.000110 0.000114 0.000115 0.000116 0.000115 0.000117 0.000116 0.000112 0.000112
T = 45.4 "C 57.3 55.5 54.8 53.6 51.2 50.6 49.3 48.5 47.8 47.4
T = 45.4 "C 117.5 134.2 153.2 173.5 200.3 221.2 249.3 279.9
0.000154 0.000218 0.000276 0.000322 0.000370 0.000390 0.000399 0.000407
68.8 63.1 59.7 57.3 55.1 54.0 51.6 50.8
T = 50.2 "C 80.6 102.2 122.9 139.3 157.8 176.5 185.7 199.0 211.9 226.3 242.0 258.5 279.1
0 0 0.000210 0.000327 0.000493 0.000617 0.000633 0.000702 0.000761 0.000816 0.000838 0.000855 0.000882
0 0 72.9 66.1 61.9 59.3 58.5 57.4 56.5 55.5 54.7 53.7 53.1
T = 52.0 "C 119.2 127.7 141.3 153.7 165.3 170.6 179.4 187.4 194.4 202.5 212.1 219.0 234.0 242.5 261.2 279.9
0.000179 0.000291 0.000385 0.000507 0.000628 0.000659 0.000756 0.000821 0.000899 0.000933 0.000966 0.000987 0.001039 0.001060 0.001100 9.001108
77.9 72.6 67.0 63.6 61.6 60.8 60.0 59.1 58.7 58.1 57.3 56.8 55.9 55.2 54.5 53.6
phase exists as the pressure is increased. For the type of system under consideration the solid-liquid line bends back toward compositions richer in the light component as the pressure increases. The solid-liquid line eventually merges with the liquid branch of the liquid-gas loop when the three-phase line is again intersected at the higher pressure. A t this point the liquid and gas phases are closer in composition than they were when the three-phase line was first intersected at the lower pressure. Solid-fluid equilibrium is maintained at higher pressures and the light phase, now less compressible, quickly attains a limiting solubility value. In fact, at very high pressures, the solubility of heavy solid in supercritical fluid now decreases slightly, reflecting a free volume effect which results from the large size disparity between the large nonvolatile component and the small supercritical component
130.6 175.2
0.000203 0.000325
T = 50.2 O C 124.7 134.1 134.7 136.2 165.6 199.1 211.1 251.0 267.3 306.9 322.4
0.000203 0.000325 0.000325 0.000326 0.000545 0.000698 0.000750 0.000850 0.000863 0.000850 0.000863
T = 52.0 O 119.0 175.9
C
0.000203 0.000750
(McHugh and Paulaitis, 1980; Rance and Cussler, 1974; von Tapavicza and Prausnitz, 1976). At very high pressures, increasing the pressure further reduces the free volume between COS molecules available to the solute molecules and hence reduces the solid solubility. The decrease in solubility which is observed for the naphthalene-ethylene system (van Welie and Diepen, 1961a) the biphenyl-C02 system (McHugh, 1981; McHugh and Paulaitis, 1980), and the naphthalene-methane system (van Hest and Diepen, 1963) is expected for the octacosaneCOz system at pressures higher than those reported here. In Figure 10b the isotherm at T, is reconstructed in a similar manner to Figure 10a to show the results that are obtained with the flow apparatus used in this study (i.e., the solid line depicts the solubility data obtained with the flow apparatus while the dashed lines plus the solid line depict all the possible phase behavior). With the variable-volume view cell it would be straightforward to determine the entire solubility isotherm depicted in Figure 10b since the equilibrium phases are visually determined (van Welie and Diepen, 1961a). As shown in Figure lob, the solubility data obtained with a flow apparatus do not exhibit any discontinuities even though the solubility isotherm represents the gas branch of the liquid-gas region of the phase diagram at low pressures and the fluid branch of the solid-fluid region of the phase diagram at high pressures. This is indeed the case for the bipheny14!02 system at temperatures between 49.3 and 55.1 "C (McHugh; McHugh and Paulaitis, 1980). Entrainment of liquid biphenyl in the supercritical C02-rich phase does not occur with the flow apparatus since the flow rate of C02through the columns is extremely slow and liquid biphenyl is quite dense. However, this behavior is in marked contrast to that of the octacosaneC02system. For solubility isotherms which intersect the three-phase S-L-G line the results from a flow apparatus can be totally spurious as a consequence of the phase inversion exhibited by this system. At pressurrs above 260 atm and temperatures above 54.7 " C supercritical COz pushes the octacosane-richliquid phase out of the columns since the C02-richfluid phase is now the heavier phase. Using the view cell it is immediately obvious when the three-phase S-L-G line is intersected since the equilibrium phases are visually determined, and the liquid-supercritical fluid phase inversion is also easily determined.
Ind. Eng. Chem. Fundam., Vol. 23, No. 4, 1984
Consider an isotherm precisely at the UCEP temperature (see TUCEP in Figure 9). In Figure 1Oc solid-gas equilibrium is maintained at low pressures until the S-L-G line is intersected at P,. As previously described, liquidgas equilibrium, solid-liquid equilibrium, or a single liquid phase will exist as the pressure is further increased depending on the overall composition of the mixture. Note the shape of the solid-liquid equilibrium curve as the pressure is increased. For this type system the solid-liquid equilibrium curve bends from right to left as it approaches the UCEP; i.e., the concentration of heavy component in the liquid phase decreases with increasing pressure. This curve must intersect the liquid-gas loop precisely at the binary liquid-gas critical point and therefore it approaches a negative horizontal inflection at the UCEP pressure (Rowlinson and Swinton, 1981). For systems where the UCEP is at a very high pressure, such as octacosaneCOz, the solid-fluid equilibrium curve decreases sharply to lower heavy component concentrations as the pressure is i.ncreased above the UCEP pressure. This is a consequence of the free volume effect mentioned earlier. In Figure 10d the isotherm at the UCEP temperature is reconstructed to show the solubility data obtained with the flow apparatus used in this study. Again the flow apparatus data are represented by the solid line in this figure. Notice that the solid line depicts solubility behavior which is similar to the biphenyl-COZ 55.2 "C isotherm shown in Figure 3. Hence, the 55.2 OC biphenyl-COz isotherm shown in Figure 3 actually represents liquid-gas equilibrium up to 469 atm and solid-gas equilibrium at pressures above 469 atm. This is in contrast to the 50 "C naphthalene-ethylene isotherm shown in Figure 2 which represents solid-gas equilbrium at all pressures. The 50 "C naphthalene-ethylene solid solubility isotherm does eventually decrease with increasing pressure at very high pressures (van Welie and Diepen, 1961b). However, the 50 "C solid solubility isotherm never intersects the naphthalene-ethylene S-L-G line. The final isotherm considered is one where the temperature is above the UCEP temperature as depicted in Figures 10e and 10f. Notice that the effect of the binary liquid-gas critical point is reflected in the shape of the solid-liquid curve near the UCEP pressure. In Figure 10f the same isotherm is reconstructed to show the results attainable with the flow apparatus used in this study. The data obtained with the flow apparatus are shown as the solid line which begins on the liquid-gas loop at pressures slightly greater than the critical pressure of the light component. At pressures above the binary gas-liquid critical pressure it is possible to jump to the solubilities along the solid-liquid curve since, for this type of system, the solid-liquid curve bends toward lower heavy component solubilities which are accessible in the experimental flow apparatus. This, in fact, is the same type of behavior exhibited by the biphenyl-C02 system for a solubility isotherm at a temperature above the UCEP temperature (McHugh, 1981; McHugh and Paulaitis, 1980). As shown by van Welie and Diepen (1961a), the entire solubility behavior depicted in Figure 10f can be obtained with a
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variable volume view cell similar to the one described in this paper.
Conclusion In addition to presenting new experimental information on the high-pressurephase behavior of the octacosaneC02 system, we have attempted to describe two different experimental techniques for obtaining supercritical solubility data. The associated limitations of these experimental techniques in interpreting experimental results are discussed. It is necessary that careful experimental work be performed on even relatively simple binary mixtures such as biphenyl-C02, naphthalene-COz, and octacosane-COz to fully understand the unusual phase behavior which may occur around mixture critical end points. This experimental information is especially important in order to correctly apply thermodynamic models which characterize and predict solid solubilities in supercritical fluids (Gitterman and Procaccia, 1983; Procaccia and Gitterman, 1983). Acknowledgment Some of the experimental work presented in this paper was performed by one of the authors (M.A.M.) while at the University of Delaware. We wish to express our thanks to Dr. M. E. Paulaitis at the University of Delaware for allowing us to publish that work and also for the fruitful discussions and suggestions concerning the presented material. We also wish to acknowledge Jaime Ayarza and Tim Daugherty, who helped to build and operate the view cell apparatus. Registry No. COz, 124-38-9;octacosane, 630-02-4. Literature Cited DeSwaan, A. J.; Diepen, G. A. M. Recueil 1983, 82, 249. Diepen, G. A. M.; Scheffer, F. E. C. J. Am. Chem. SOC. 1948a. 70, 4085. Diepen, G. A. M.; Scheffer, F. E. C. J. Am. Chem. SOC. 1948b, 70, 4081. Diepen, G. A. M.; Scheffer, F. E. C. J. Phys. Chem. 1953, 5 7 , 581. Gitterman, M.; Procaccia, I.J. Chem. Phys. 1983, 78, 2648. Li, Y.-H.; Diiiard, K. H.; Robinson, R. L. J. Chem. Eng. Data 1981, 26, 53. McHugh, M. A. FhD. Thesis, Department of Chemical Engineering, University of Delaware, Newark, DE, 1981. McHugh, M. A. "Extraction with Supercritical Fluids", I n "Recent Deveiopments in Separation Science", Li, N. N.; Caio, J. M. Ed.; CRC Press Inc., Boca Raton. FL, 1984 Voi IX. McHugh, M. A.; Paulaitis, M. E. J. Chem. Eng . Data 1980, 25, 326. McHugh, M. A,; Yogan, T. J. J. Chem. Eng. Data 1984, 2 9 , 112. Micheis, A.; Micheis, C. R o c . R . SOC. London, Ser. A 1937, 160, 348. Pauiaitis, M. E.;Krukonis, V. J.; Kurnik, R. T.; Reid, R. C. Rev. Chem. Eng. 1983, 1, 179. Procaccia, I.; Gitterman, M. AIChE J. 1983, 29, 686. Rance, R. W.; Cussier, E. L. AIChE J. 1974, 20, 353. Rowiinson, J. S.; Richardson, M. J. "Advances in Chemical Physics 11"; Interscience: New York, 1959; p 85. Rowiinson, J. S.; Swinton, F. L. "Liquids and Liquid Mixtures", 3rd ed.; Butterworths: London, 1981; Chapter 6. Schneider, G. M.; Stahi, E.; Wiike, 0. Ed. "Extraction with Supercritical Gases"; Verlag Chemie: Deerfieid Beach, FL, 1980. Tsekhanskaya, Yu. Y.; Iomtev, M. B.; E. V. Mushkina Russ. J. Phys. Chem. 1964, 38, 1173. van Hest, J. A. M.; Diepen, 0. A. M. Symp. SOC. Chem. Ind. 1983, 10. van Weiie, G. S. A,; Diepen, G. A. M. Recueil 198la, 80, 659, 666. van Welie, G. S. A,; Diepen, G. A. M. Recueil 1981b, 80,673. van Welie, G. S. A.; Diepen, G. A. M. J. Phys. Chem. 1983, 6 7 , 7 5 5 . von Tapavicza, S.;Prausnitz, J. M. Int. Eng. Chem. 1976, 16, 329. Zernike, J. "Chemical Phase Theory"; Deventer AE. Kiuwer, 1955.
Received for review December 1, 1983 Accepted April 20, 1984
