c = critical property Li, Y.-H., K. H. Dillard and L. Robinson, Jr.: /. Chem. M = mixture property Eng. Data, 26, 52 (1981). r = reduced property Newton, R. H.: Ind. Eng. Chem., 27, 302 (1935). rl, r2 = reference fluid Nishiumi, H. and S. Saito: /. Chem. Eng. Japan, 8, 356 1,2,i,j = component 1, 2, /,j (1975). Ohgaki, K. and T. Katayama: Fluid Phase Equilibria, 1, <Superscripts> 27 (1977). (r),(rl),(r2) = reference fluid Plocker, U., H. Knapp and J. M. Prausnitz: Ind. Eng. (0) = simple fluid (l),(2),(0 = component 1, 2, / Chem., Process Des. Dev., 17, 324 (1978). Sagara, H., Y. Arai and S. Saito: /. Chem. Eng. Japan, 5, 339 (1972). Literature Cited Soave, G.: Chem. Eng. ScL, 27, 1197 (1972). 1) Bender, E. : 5th International Congress of Chemical Engi- Sprow, F. B. and J. M. Prausnitz: AIChEJ., 12, 78 (1966). neering, CHISA 75, Section F2.25 (1975). Streett, W. B. and J. C. G. Calado: /. Chem. Thermodyna- 2) Benham, A. L. and D. L. Katz: AIChEJ., 3, 33 (1957). mics, 10, 1089 (1978). 3) Chang, S.-D. and B. C.-Y. Lu: Chem. Eng. Progr., Symp. Stryjek, R., P. S. Chappelear and R. Kobayashi: /. Chem. Ser.9 63 (81), 18 (1967). Eng. Data, 19, 340 (1974). 4) Cine, M.R., J.T. Roach, R. J. Hoganand C. H. Roland: Teja, A. S.: AIChEJ., 26, 337 (1980). ibid., 49 (6), 1 (1953). Teja, A. S. and P. Rice: Ind. Eng. Chem., Fundam., 20, 5) Cooper, H. W. and J. C. Gold frank: Hydrocarbon Process., 77(1981). 46 (12), 141 (1967). Teja, A. S., S. I. Sandier and N. C. Patel: Chem. Eng. J., 6) Figuiere, P., J. Horn, S. Laugier, H. Renon, D. Richon and 21, 21 (1981). H. Szwarc: AIChE J., 26, 872 (1980). Wichterle, I. and R. Kobayashi: /. Chem. Eng. Data, 17, 9 7) Grau0, L., A. Fredenslund and J. Mollerup: Fluid Phase (1972). Equilibria, 1, 13 (1977). Williams, R. B. and D. L. Katz: Ind. Eng. Chem., 46, 2512 8) Hanson, G.H., R. J. Hogan, F. N. Ruehman and M. R. (1954). Cines: Chem. Eng. Progr., Symp. Ser., 49 (6), 37 (1953). Yorizane, M., S. Yoshimura, H. Masuoka and T. Naka: 9) Lee,B. I.andM. G. Kesler: AIChEJ.,21, 510(1975). Kagaku Kogaku, 35, 691 (1971). SOLUBILITY OF SOLID NAPHTHALENE IN GASEOUS ETHYLENE AT HIGH PRESSURES Hirokatsu MASUOKAand Masahiro YORIZANE Department of Chemical Engineering, Hiroshima University, Hiroshima 730 Solubility of naphthalene in compressed ethylene was measured with a single-pass, continuous- flow apparatus at temperatures of 35, 50 and 65°C respectively and for a pressure range of 8 to 62atm. A calculation method is presented for determining the solubility of a heavy solute in a super- critical gas solvent. The modified BWRequation of Lee and Kesler together with a pseudo- critical method was used to calculate fugacity coefficients of the solute in subcooled liquid and vapor phases. The utility of the method presented is illustrated by a calculation of the ethylene- naphthalene system at temperatures between 12 and 65°C and over a pressure range of 8 to 300 atm. The supercritical gas extraction process is based on the Intro duction ability of a supercritical gas to enhance the volatility Fluid fuels and chemical feedstocks derived from of the heavy organic compounds present in coal, coal are becoming increasingly attractive as a sub- provided high pressure is maintained. stitute for oil. Supercritical gas* extraction of coal The solvent effect of compressed gases was recog- is promising in many liquefaction techniques12K * Each fluid has its owncritical temperature. At tempera- Received June 5, 1981. Correspondence concerning this afticle should be tures exceeding its critical temperature the fluid cannot be lique- addressed to H. Masuoka. fied and is referred to as a supercritical gas. VOL. 15 NO. 1 1982 nized as far back as in 1879 by Hanay and Hogarth6}. librium for the solute is given by Fank3) reports the pronounced solvent power of super- /!=/;à" (i) critical water. Weale21) has presented an excellent f\ = (p\Pyi (2) discussion of solubility of solids in compressed gases. Hagenbach5) demonstrated enhanced solvent proper- where f°±s is the fugacity of pure solid, y1 is the mole ties of supercritical polar gases. Paul and Wise15) fraction of the solute in the solution, and <p\ is the have shown from theoretical considerations that the fugacity coefficient of the solute in the vapor mixtures. volatility enhancement is greatest when the tempera- Arranging Eqs. (1) and (2), solid solubility is expressed ture at which the extraction is carried out is near the as critical temperature of the extracting gas. Gangoli yi =(f?lfoil)(<p°il/<pl) (3) and Thodos4) have given an extensive technical re- where f{1 is the fugacity of pure subcooled liquid and (pll is the fugacity coefficient of the pure subcooled view of supercritical gas extraction. liquid solute. The fugacity ratio of component 1, The ethylene-naphthalene system has been exten- sively studied by Diepen and Scheffer2) at five tempera- fVlfl1 can be evaluated by the relation ture levels from 12 to 60°C and at various pressures in the range of 40-270atm. Tsekhanskaya et al.18) ln7F~^V rr tTVt~1) also studied extensively the influence of pressure levels AC Tt JF on the extractive property of supercritical ethylene and " !Tln T~ RT{P~Pt) (4) carbon dioxide acting on naphthalene. These obser- where Tt and Pt are the triple-point temperature vations are limited to higher pressures, down to 40 and pressure, respectively, ASf is the molar entropy atm. of fusion of the solute, and ACPand AVare the dif- At moderate pressures a virial equation of state is ferences between the liquid and solid molar heat used to calculate the solubility9K At higher pres- capacities and molar volumes, respectively. sures, however, the utility of the equation is limited by The fugacity coefficients of the pure solute in sub- lack of knowledge about higher-orderv irial coefficients. cooled liquid and those of the solute in vapor mix- Vetere20) has recently presented a predictive method tures were calculated from the generalized equation of for calculating the solubility of solids in supercritical state of Lee and Keslern) together with the pseudo- gases. He reported that good agreement was ob- critical method8'13', as described in the following sec- tained between experimental and calculated data for tion. the ethylene-naphthalene system. He treated the An alternative expression of solubility is expressed supercritical gas mixture as a hypothetical liquid mix- as J>l=l ' TDsat> ±J V[(P-Plat) ture in phase equilibrium determinations. However, _£ v ^ (5) it was pointed out by the authors14} that his paper Jr) exp RT contains some errors and that his predictive method where (p\at is the fugacity coefficient for the saturated leads to erroneous results. Thus, at present, thermodynamically predictive vapor, and this is essentially unity. This equation, methods for the solubility of heavy compounds in comparedto ofEq. (3), does not require the subcooled supercritical solvents are limited in application due to liquid properties but requires vapor pressure data of lack of understanding of the behavior of both the the solute. If the virial equation, truncated after the second dense-fluid state and highly asymmetric mixtures of substances. virial coefficient, is assumed in vapor phase at mode- The purpose of this work is to obtain experimental rate pressures, one obtains data for the solubility of solid naphthalene in ethylene In (pvl=^-(y1Bn -\-y2B12)-ln Zm (6) in the lower pressure range and to propose a new predictive method for calculating the solubility of If it is further assumed that P>Pjai, the enhancement solids in supercritical gases. factor, which is a measure of enhanced solubility, maybe expressed as 1. Thermodynamics of Solid-Vapor Equilibria In E=\n (PyJPl**) The solubility of a nonvolatile solute in a super- critical gas is determined from standard thermody- = ( Vt+ytB22 -2ylB12y£Y (7) namics16}. Solid-vapor equilibria considered in this This equation is often used in a consistency test of study are those for which the solid phase is assumedto experimental phase equilibrium data. be pure solute (component 1) and the vapor phase is a saturated solution of the solute in the solvent (com- 2. Generalized BWR Equation of Lee-Kesler, and ponent 2). For such a system, the equation of equi- Its Application to Mixtures by the Pseudocritical JOURNAL OF CHEMICAL ENGINEERING OF JAPAN Method In calculating the solubility according to Eq. (3), an equation of state capable of representing the thermodynamic properties of subcooled liquid is required. For this purpose the Lee and Kesler11} three-parameter corresponding-states correlation was chosen from considerations similar to those in a pre- vious paper13} on the solid solubility in liquid. The Lee and Kesler equation is an extended and im- proved version of the Pitzer-Curl tables based on a modified BWR equation of state. The compressi- bility factor of a real fluid is related to properties of a simple fluid (w=0) and to those of octane as a ref- erence fluid. Z=Z(0H-^7(Z(i2) -Z(0)) (8) where a>(R] =0.3978. Other thermodynamic functions librium cell or sampling tube can cause serious experi- (fugacity coefficients and enthalpy departure) have mental errors, and it is difficult to minimize this ef- been derived from Eq. (8). fect. These circumstances are similar to measure- In applying the Lee-Kesler equation to mixtures, ment of vapor pressures of high boiling-point sub- we used the pseudocritical method8'13). According stances. We used a single-pass, continuous-flow (also re- to the three-parameter corresponding-states theory, ferred to as gas saturation) method1)7'10'17).