Id.Eng. Chem. Process Des. Dev. 1983, 22, 577-582
577
Mass Transfer Characteristics of Bubble Columns in Recirculation Flow Regime Katsuml Nakao Department of Chemlcal Enginmdng, Yamaguchi Universi!y, Tokiwadai, Ube, Yamaguchi 755, Japan
Hlroshl Takeuchl' Department of Chemical Engineedng, k g o y a University, Chlkusa-ku, Nagoya 464, Japan
HlrosM Kataoka Institute of Applied Bkhemlstry, Unlvefsi!y of Tsukuba, Ibarakl305, Japan
Hisatsugu Kajl Nlshiki Research laboratory, Kureha Chemical Industry Company, Ltd., Nishlkknechi, Iwakkshi, Fukushlm 974, Japan
Tsutao make Department of Chemical Englnmrlng, Osaka University. Toyonaka, Osaka 580, Japan
Terukatsu Miyauchl Department of Chemical Engineering, Unlversi!y of Tokyo, Bunkyo-ku, Tokyo 113, Japan
I n a bubble column of 80 cm 1.d. with a conical bottom sectlon, values of the IiqukJ-phase volumetric mass transfer coefficient k,a were obtained by absorbing or desorbing oxygen into or from water. The superficial gas velocity ranged from 1 to 8 cm/s, where an Internal recirculating flow was confirmed to be well developed. The kLavalues were about twice as great as those for the conventknal bubble columns. The liquid-phase mass transfer coefficient k , was separated from kLa using the gas-liquid Interfacial area a . The present k , data and the results for the large-scale bubble column of 550 cm i.d., with a similar geometry, were shown to be proportional to the square root of the average bubble diameter, being about 1.6 times as great as those in the conventional columns. Furthermore, the mass transfer behavior in the present type column can be reasonably interpreted by assuming perfect mixing In both gas and liquid phases.
Introduction Bubble columns are widely used for gas-liquid systems because of their simple construction, being in most cases operated in the bubble flow regime where the gas velocity is low and bubbles rise almost separately after being uniformly dispersed at the bottom of the column. Many studies have therefore been conducted in such a bubble flow regime. Recently, it has attracted special interest to operate a bubble column in the high gas feed regime: the recirculation flow regime (Ueyama et al., 1980). For example, such an operation has been successfully utilized for hightemperature steam cracking of petroleum asphalt, a process named Eureka (Takahashi and Washimi, 1976). In the bubble column of the process, 550 cm in diameter and 700 cm in height, a recirculating flow is easily developed by injecting gas through multi-nozzles normal on a circle on the wall of conical bottom section (Ueyama et al., 1980). The characteristics of flow (Koide et al., 1979; Kojima et O I 9 6 ~ 3 0 5 / 8 3 /1 122-0577$Ol.50/0
al., 1980) and mass transfer (Kataoka et al., 1979) in the bubble column have been studied by The Research Team on Large Scale Bubble Column (Koide et al., 1979). In these studies, the performances of the column were compared with those of the conventional bubble columns which are less than 60 cm i.d. and have a single nozzle or ringsparger as gas distributor a t the flat bottom. However, since it was impossible to distinguish clearly between the effects of column dimension and column shape, further studies were performed by using a 60-cm (i.d.) bubble column, with the same shape as the 550-cm column. The behavior of gas bubbles has been reported earlier by Ueyama et al. (1980). The purposes of this work are (a) to obtain the values of liquid-phase volumetric mass transfer coefficient kLa in the 60-cm column mentioned above by absorbing or desorbing oxygen into or from water, (b) to separate the liquid-phase mass transfer coefficient kL from the kLu using the data on the flow behavior of bubbles, (c) to clarify the 0
1983 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983
578 IO
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for either absorption or desorption. A. Perfect Mixing in Both Gas and Liquid Phases. The equation for an absorption run is derived as follows. Introducing
which results from the balance of oxygen for the entire column together with p = P ( p t / P J , eq 1can be integrated with the initial conditions (t = 0, C = Co) to yield
G a s velocliy
us
I cm/sl
Figure 1. Schematic diagram of experimental apparatus.
effect of column geometry on kL using the present data as well as the results for the 550-cm column, and (d) to discuss the mechanism of mass transfer between gas and liquid phases in the recirculation flow regime. Experimental Section Figure 1 shows a rough scheme of the experimental setup. The bubble column made of transparent PVC resin consisted of a cylindrical section, 60 cm in i.d. and 300 cm in height, and a conical bottom section. The full details are available elsewhere (Ueyama et al., 1980). Gas was blown into the column through 16 nozzles of 3.9 mm i.d. The bubble column was charged with tap water; nitrogen gas was sparged into water for enough time required to completely desorb oxygen dissolving in the liquid. As soon as the supply of nitrogen was turned off, air was sparged into the column at a desired flow rate, thus starting an absorption run. Desorption runs of oxygen from water saturated with air were also carried out by the reverse supply of the two gases. Samples of water in the column were taken into a test bottle of 100 mL at fixed time intervals; dissolved oxygen in the liquid was analyzed on an oxygen meter (Beckman Inc., Model Fieldlab). In most runs, the mouth of a sampling nozzle was located at the axis of the column, but in some rum it was at the midst between the column axis and wall. Average gas holdup EG for each run was determined from the difference between the aerated and unaerated volumes in the column. The liquid depth or the height of unaerated liquid ho was kept at 35,130, and 180 cm above the level where the conical and cylindrical sections were welded. The superficial gas velocity U G ranged from 1 to 8 cm/s; the liquid temperature was at 289 to 291 K. Calculation of Results Although the liquid phase in the bubble column is regarded as perfectly mixed, mixing conditions in the gas phase are not yet well clarified (Kataoka et al., 1979). Thus, theoretical equations to evaluate kLa were derived for the following two cases: (1)perfect mixing in both gas and liquid phases and (2) plug flow in the gas phase and perfect mixing in the liquid phase. In deriving the equations, the following assumptions were made. (a) Liquid-phase resistance controlled the rate of mass transfer. (b) Gas and liquid flowed under steady conditions. (c) Mass transfer through the free liquid surface was negligible. (d) Henry's law held. When the liquid phase is perfectly mixed, an instantaneous change of the dissolved oxygen concentration is given by
where X=
kLaHRTh - kLaHRTVL
-
(1 - ~ V G In the case of a desorption run, the following equation is derived. UG
Equation 4 reduces to eq 3 when Pb = 0. B. Plug Flow in Gas Phase and Perfect Mixing in Liquid Phase. The oxygen balance for a differential column volume at an arbitrary height U G dp kLa(Hp - C) R T dZ is integrated with the initial conditions (z = 0, p = Pb) .by accounting for the variation in hydrostatic head. Defining
-
= ( l / h ) J0h p dZ
eq 1 can be solved with the initial conditions (t = 0, C = Co) to yield
In the case of desorption run, the following equation is also obtained.
Equation 4 and 8 for a desorption operation are the same as the results in the previous paper (Kataoka et al., 1979). Values of kLU/Uc,are not more than about cm-' in a usual bubble column (Akita and Yoshida, 1973), and the value of H for an oxygen-water system is an order of magnitude of mol/L.atm. Thus, in the present experiment, values of X are in the range of 0.02 to 0.08 much less than unity. This leads to the following approximations corresponding to eq 3 and 7, and eq 4 and 8, respectively, for absorption and desorption runs. absorption In
desorption
HPb(P/f'J - C = -- kLU 1 - CG t HPb(P/pt) - CO
(34
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 579
Air
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=
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Figure 2. Time course of dissolved oxygen concentration. 10
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Figure 4. Volumetric mass transfer coefficient plotted against superficial gas velocity (a, sampled between column axis and wall; b, desorption; c, perfect mixing in gas phase; d, plug flow in gas phase; ref 1,Kataoka et al. (1979); 2, Jackson and Shen (1978);3,Towell et al. (1965);4,Akita and Yoshida (1973);5, Fair (1967).
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These equations show that values of kLa can be obtained independently from mixing conditions in the gas phase, by using a semilogarithmic plot of fractional unsaturation or incomplete desorption against contact time. Figure 2 shows a rearrangement of the typical data on both absorption and desorption runs based on eq 3a and 7a, and eq 4a and 8a, respectively. The kLa values can be then calculated from those slopes, provided that the gas holdup t G is known. Values of kLa evaluated from eq 3 and 7 for perfect mixing in the gas phase were found to be only a few percent greater than those from eq 4 and 8 for plug flow in the gas phase. There are significant differences between the values of kLa in this work and those evaluated using eq 4 and 8 for a desorption of carbon dioxide from water in the earlier work (Kataoka et al., 1979). This comes from the fact that the value of X for the C02 desorption run was about 3, which is much greater than that in the present experiment.
Results and Discussion A. Liquid-PhaseVolumetric Coefficient kLa The values of average gas holdup tGobtained under conditions of the absorption and desorption runs are plotted against uG in Figure 3. The figure indicates that tG values are almost independent of D T and ho,being also little affected by the gas distributor and the geometry of the column bottom. Figure 4 shows the values of kLa obtained in this work, together with the previous result for the 550-cm column and other ones. All of the literature values are converted to the kLa for oxygen at 290 K, assuming that the liquidphase mass transfer coefficient k L for a solute is propor-
.
tional to the square root of its molecular diffusivity. In Figure 4, the present kLa values for the absorption and desorption runs are in good agreement with each other. The two different positions of sampling tap gave almost the same values of kLa. This fact indicates that the assumption of perfect mixing in the liquid phase is valid. The data of Jackson and Shen (1978) are for a large-scale column, D T = 1.8-7.6 m and ho = 6-13 m. Although in their work the relatively small values of uGwere employed, the kLa values almost fall on a smooth-extrapolated line of the k ~ vs. a UG plot for the case of the greater UG. In addition, little distribution of both concentration and temperature was observed in the liquid phase. This suggests that in bubble columns of large DT and ho a recirculating liquid flow is easy to develop even at small gas flow rates. On the other hand, a correlation of Fair (1967) gives appreciably smaller kLa than those for the present type columns. In Figure 4, however, it is noticed that the present kLa data are roughly twice as great as the previous data as well as the prediction from a correlation of Akita and Yoshida (1973) and the data of Towell et al. (1965), whereby the latter two are for usual bubble columns. This leads to a working hypothesis that for the shape of the present column, scaling up from 60 cm to 550 cm in DT decreases kLa by a factor of 2. Also for a column of DT N 60 cm, changing the column bottom from usual cylindrical shape to conical as in this work increases kLa by a factor of 2. B. Gas-Liquid Interfacial Area 8 . The gas-liquid interfacial area per unit volume of aerated liquid a can be calculated from =6 t ~ / d ~
(9)
When all the bubbles in a dispersion are spherical, the specific surface mean diameter of bubbles d B is equal to the volume-surface mean diameter of bubbles d,, defined by d , = C n i d : / C n i d t . For the gas bubbles of the same volume, the d B values decrease with an increase in the degree of their deformation from sphericity. Figure 5 shows values of dB and d , obtained previously with the electrical resistivity probe technique and by the photographic method, respectively, as a function of UG (Ueyama et al., 1980). The figure also shows the data for the 550-cm column (Koide et al., 1979), d B obtained by Ueyama and Miyauchi (19771, d,, predicted from a correlation of Akita and Yoshida (1974), and dB calculated as 6eG/a where a was measured by the chemical absorption
580
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, I983 Probe
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d,, or d, ( c m ) Figure 8. Liquid-phase mass transfer coefficient as a function of average bubble diameter (ref 1, Akita and Yoshida (1974);2, Calderbank and Moo-Young (1961);3, Valentin (1967).
Figure 8 shows the relationship between kL and dg, together with the correlations mentioned above. As the figure shows, the data for the present column and for the 550-cm column are roughly correlated by a linear relationship between kL and dg1I2. Furthermore, for a fixed value of bubble diameter, these kL values are about 1.6 times as great as those from the Akita and Yoshida's equation, whereas data of Towell et al. (1965) agree well with the results from their equation. Such discrepancies in kL values are considered to arise from the difference in gas-liquid flow patterns depending on the column geometry. According to Figures 5 and 8, on the other hand, kL should vary with UG as represented by the broken line in Figure 7. Also, such a variation of kL with uG has been observed in perforated plate columns for DT = 10-15 cm by Kawagoe et al. (1975). As for the two bubble columns with a conical bottom section, DT = 550 cm and 60 cm, since both the columns are considered to have almost the same recirculation flow pattern, the difference in the kL values would be responsible for dB values depending on DF The data of Towell et al. (1965) for DT = 40.7 cm are in a good agreement with
Ind. Eng. Chem. Process Des. Dev., Vol. 22, No. 4, 1983 581
the results from the Akita and Yoshida's equation with DT = 30 cm, as discussed in the above section. This implies that in their columns dB values are of almost the same she, where the bubble breakup is dominant enough to produce smaller bubbles as the recirculating flow is easy to develop in a column of a relatively large DT. Data of Tadaki and Maeda (1963) for DT = 6 cm and ho = 70 cm are greater for uG < 3 cm/s than the results from the Akita and Yoshida's equation, whereas both of them agree well for U G > 5 cm/s. From such discussion, we may conclude that in a small-scale column the higher gas flow rate is required to ensure the bubble breakup dominant enough to produce such small bubbles as in the large scale column. D. Mass Transfer for Bubble Swarms in the Recirculating Flow Regime. Valentin (1967) has given the relationship between the kL value for a single bubble and its equivalent diameter de as shown in Figure 8, wherein the dotted line represents the data for the dissolution of air single bubbles into pure water. The upper dash-dot line is for the result calculated by assuming that mass transfer occurs under potential flow conditions. The lower dash-two dots line corresponds to a rigid sphere with mass transfer determined in terms of diffusion and boundary layer flow. In either case, it can be seen that when de is greater than 0.2 cm, the kL values decrease with increasing de, being inversely proportional to This differs remarkably from the results for bubble swarms. Such a discrepancy in kL values between single bubble and swarm bubbles may be due to the difference in the slip velocities between bubble and liquid, resulting from the bubble deformation or the bubble coalescence and breakup. On the other hand, as was shown in Figure 5, the relationship between d B and U G for the present column suggests that the recirculating flow develops well 90 that rates of the bubble coalescence and breakup are increasing in the range of U G from 5 to 50 cm/s. In this region, the results measured on an electric probe approximately follow that d~ a 11G1/5. Also, according to Ueyama and Miyauchi (1979), the slip velocity usin a usual column of 60 cm i.d. increases with uG in the range of 4 to 40 cm/s. Such behavior corresponds to the increase of the bubble coalescence and breakup rates with uG. For 4 < UG < 40 cm S, their result may be approximately expressed as u, 0: U G6 5 . Thus, according to the Higbie penetration model (1935), kL for a given physical system is expressed as follows.
The relation of kL a u G 1 / l 0 in eq 10 is approximated by the broken line in Figure 7, where U G is in the range of 5 to 20 cm/s. Also, as was shown in Figure 8, the results for the present type columns substantiate the relation kL a dgl/'. Furthermore, the relation us0: dB' is derived from eq 10, suggesting that the difference between u, = 70-100 cm/s for the 550 cm column (Koide et al., 1979; Kojima et al., 1979) and u, = 25 cm/s (Ueyama and Miyauchi, 1979) may be explained in terms of d B = 1.3 cm for the larger column and d B = 0.6 cm for the smaller column.
Conclusions Liquid-phase volumetric mass transfer coefficients kLa were measured in the bubble column of 60 cm i.d. by absorbing or desorbing oxygen into or from water. Superficial gas velocity U G was in the range of 1to 8 cm/s, where an internal recirculating flow was confirmed to be
well developed. The following conclusions are drawn from the present data, together with the results for the 550-cm column in the previous work. 1. Values of the kLa are about twice as great as those for the conventional bubble columns at a fixed value of UG.
2. The kL values separated from the kLa data by using the gas-liquid interfacial area a are proportional to the square root of the average bubble diameter, being about 1.6 times as great as those for the conventional columns. 3. A recirculating two-phase flow is easier to develop in bubble columns with a conical bottom section than in the conventional ones. In addition, the degree of its development in the present type column is little affected by the ratio of liquid depth to column diameter ranging from 1 to 3. 4. Perfect mixing in both gas and liquid phases can be reasonably assumed in the present type columns for a liquid-phase resistance controlling mass transfer. Acknowledgment The report presents a part of experimental work using a medium-size bubble column conducted by a group consisting of Terukatsu Miyauchi and Korekazu Ueyama (University of Tokyo), Hiroshi Kataoka and Eichi Kojima (Tokyo University of Education), Kozo Koide (Shizuoka University), Hiroshi Takeuchi (Nagoya University), Katsumi Nakao (Osaka University), Shigeharu Morooka and Hisayoshi Matsuyama (Kywhu University) and Hisatsugu Kaji (EUREKA Industry Co., Ltd.). (The position of each member is quoted as of May, 1977.) The above group was organized to carry on a certain portion of the initial functions of The Research Team on large-scale bubble column. The medium-size bubble column used in this research was constructed and equipped by Kureha Chemical Industry Co., Ltd. at its Nishiki Plant. The company also provided valuable accommodations and assistance to the group. The authors are very grateful for the generous cooperation of Kureha and its staff at the Nishiki Plant. Nomenclature a = gas-liquid interfacial area per unit volume of aerated liquid, l/cm C = concentration of gas dissolved in liquid, mol/cm3 C* = equilibrium value of C, mol/cm3 D = gas diffusivity in liquid, cmz/s DT = diameter of bubble column, cm dB = specific surface mean bubble diameter, cm d,, = volume-surface mean bubble diameter, cm H = Henry's law constant, mol/(cm3 atm) h = bubbling bed height, cm ha = settled bed height, cm kL = liquid-phase mass transfer coefficient, cm/s P = total pressure, atm P = P averaged through column, atm p = partial pressure of oxygen, atm p = p averaged through column, atm R = gas constant, (atm cm3)/(mol K) T = temperature, K t = time, s t , = contact time, s U G = superficial gas velocity at pressure P, cm/s u, = mean slip velocity of bubbles, cm/s V , = gas flow rate, cm3 s V , = liquid volume, cm z = height from the bottom of column, cm t G = gas holdup
5
Subscripts
b = bottom of column
0 = initial condition
Ind. Eng. Chem. Process Des. Dev. 1983, 22, 582-588
582
t = top of column m = limiting value observed Literature Cited
Kolkna, E.; Unno, H.; Sato, Y.; Chkla. T.; Imai, H.; E&, K.; I ~ 1.; K&, Y13a d16 , J.; KaJi. H.; Nekanlshi, H.; Y a m a m , K. J . Cbem. Eng. 1960,
m.
_,
Tadaki. T.; Maeda, S. Kamku Kspaku 1963,27, 803. Takahashi, R.; Washimi, K. Pet. Dev. 11176,93. Towell. G. D.; Strand, C. P.; Ackerman, G. H. “Preprint of AIChE-Instn. Ch. E. Joint Meeting”; London, June 1965. Ueyama, K.; Miyauchi, T. Kagaku Kogaku Ronbunshu 1977. 3 , 19. Ueyama, K.; Miyauchi. T. AICM J . 1979. 25, 258. Ueyama. K.; Morooka, S.;Koide, K.; KaJi, H.; Miyauchi, T. Id. fng. Chem. kocess Des. Dev. 1960. 19, 592. Vahtln, F. H. H. “Absorptbn in Qas-Liquid Dispersbns”; E. B F. N. Spon Ltd.: London, 1967; p 52.
Akita, K.; Yoshlda, F. Ind. Eng. Chem. Process D e s . Dev. 1973, 12, 76. Akita, K.; Yoshlda, F. Ind. fng. Chem. procesS Des. Dev. 1974, 13, 64. Calderbenk, D. H.; Moo-Young, M. B. Chem. Eng. &/. 1961, 16, 39. Fair, J. R. Chem. Eng. 1967, 74(14), 67. Higbie, R. Trans. A I C M 1935,31, 365. Jackson, M. L.; Shen, C. C. A I C M J . 1978, 24, 63. Kataoka, H.; TakeucM, H.; Nakao, K.; Yagi, H.; Tadaki. T.; Otake, T.; Miyaw chi, T.; Washimi, K.; Watanabe, K.; Yoshkla, F. J . Chem. Eng. Jpn. 1979, 12, 105. Kato. Y.; Nishiwaki. A. Kaflku Kogaku 1971,35. 912. Kawagoe, M.; Nakao, K.; Otake, T. J . Chem. fng.Jpn. 197b,8 . 254. Kdde, K.; Morooka, S.; Ueyama, K.; Matswra. A.; Yamashlta. F.; Iwamoto, S.; Kato, Y.; Inoue, H.; Shigeta, M.; Suruki, S.; Akehata, T. J . Chem. Eng. Jpn. 1979,12, 96.
Received for review December 29, 1981 Revised manuscript received February 4,1983 Accepted February 28, 1983
Correlatfon and Prediction of Solid-Supercritlcai Fluid Phase Equilibria David H. Zlger and Charles A. Eckert’ Department of Chemlal Englneedng, University of Illlnols, Urbana, Illinois 6 180 1
A semiempirical correlation has been developed to describe quantitatively the solubility of heavy nonpolar solis in slightly subcritical and supercritical solvents using only one temperatusindependent pure component parameter for each component. The method, based partly on regular sobtion theory and the van der Waats equatlon of state, correlates available solubility data for 24 binary solld-fluid systems within an average standard deviatlan of 25 %
with ethylene, ethane, and carbon dioxide as s o h ” . The range of solubility correlated was lo-’ to lo-* mole fraction, 20-80 “C,and 80-500 bar. Pure-component parameters for solutes are presented for naphthalene, anthracene, triphenylmethane, phenanthrene, fluorene, pyrene, 2,3-and 2,6dlmethylnaphthalene, biphenyl, hexamethylbenzene, and hexachloroethane along with solvent parameters for ethylene, ethane, and carbon dioxide.
Introduction Although supercritical fluids have been noted as excellent solvents of heavy hydrocarbon solids for nearly a century (Hannay and Hogarth, 1879, Biichner, 1906), a quantitative understanding of the underlying phenomena has eluded investigators. The obvious difficuIty researchers encounter when modeling two-component solid-fluid equilibrium is adequately describing complex, usually asymmetric, interactions present in the lighter phase. Applications taking advantage of solubility enhancements of 103-108 are numerous and varied because supercritical fluid extraction often has several advantages over more conventional liquid-liquid extraction. The most important of these is the relative ease in which a solute may be cleanly loaded and unloaded in a separation process when a supercritical fluid is used as the soIvent. This is possible since the solvating power of a supercritical fluid is directly related to its relative density. By using a fluid whose critical point is readily accessible, a lighter solvent phase may be heavily loaded as the fluid is in a very dense, supercritical state. By slightly manipulating process conditions downstream below the solvent’s critical point (e.g., lowering the pressure), the solvent’s density and solvating power are decreased dramatically, causing the vast bulk of solute to be precipitated and collected easily. If the chosen solvent’s critical point is near ambient temperature, large thermal savings are normally realized over conventional extraction methods since an energy-intensive 0198-4305/83/1122-0582$01.50/0
distillation operation is avoided. Final considerations are the low cost, low viscosity, and low toxicity of useful supercritical fluids compared to ordinary organic liquid solvents. The coal, food, and oil industries, in particular, have found supercritical fluid extraction either profitable or promising (Paulaitis et al., 1982). Perhaps the greatest liability limiting the use of supercritical fluids has been the lack of a reliable correlation for existing sold-fluid equilibrium data. Due to the complicated nature of the supercritical phase, proposed thermodynamic analyses usually involve the use of one or more temperature dependent solutesolvent cross parameters which are difficult to correlate generally or are applicable only to a few well-studied systems. In this paper, a quantitative semitheoretical corresponding states treatment will be discussed which involves only two correlated temperature-independentpure-component parameters. Theory 1. Background. In general, the light component is virtually insoluble in the solid phase, for which the fugacity of the heavy component is given by its pressure (except for solid COP,where 42sis needed) modified by a Poynting correction.
If the ratio between the observed solubilities to that pre0
1983 American Chemical Society
