Equation of State for Supercritical Extraction - American Chemical

7 Equation of State for Supercritical Extraction J. S. Haselow, S. J. Han, R. A. Greenkorn, and K. C. Chao

Downloaded by PENNSYLVANIA STATE UNIV on September 18, 2013 | http://pubs.acs.org Publication Date: March 24, 1986 | doi: 10.1021/bk-1986-0300.ch007

School of Chemical Engineering, Purdue University, West Lafayette, IN 47907

Nine equations of state are evaluated regarding their ability to describe supercritical extraction. Experimental data on 31 binary mixture systems are compared with calculations from the equations of Redlich-Kwong, Soave, Peng-Robinson, Schmidt-Wenzel, Harmens, Kubic, Heyen, Cubic Chain-of-Rotators, and Han-Cox-Bono-Κ wokStarling. Interaction constants of the equations determined from the experimental data in the course of the evaluation are reported.

Supercritical extraction has received much attention recently for its many applica tions and potential applications. Supercritical carbon dioxide is used to decaffeinate coffee, denicotinize cigarettes, and extract spices ( j_j2 ). Carbon dioxide flooding has assumed major importance in petroleum production ( 3 ). Extraction of coal with a supercritical solvent has been the subject of investigation by the British Coal Board ( 4J) ), Maddocks et al. ( 6 ), Blessing and Ross ( 7 ), Ross and Blessing ( 8 ), and Vasilakos et al. ( 9 ). Kerr McGee Oil Company developed supercritical extrac tion for the deashing of coal liquefaction reactor products in the ROSE process (10). The design and operation of a supercritical extraction process requires the estima tion of solute solubility in a supercritical solvent. Equation of state can be useful to satisfy this need. In this work, equations are screened regarding their applicability to the calculation of supercritical solubility, and the applicable equations are evaluated regarding their ability to quantitatively describe experimental solubility data. 0097-6156/ 86/ 0300-0156S07.00/ 0 © 1986 American Chemical Society

In Equations of State; Chao, K., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

7.

H A S E L O W ET A L .

Supercritical Extraction

157


The Equations of State

From the large number of equations of state that have been proposed in the litera ture, we have found only a small number of them to show promise of being useful for the estimation of supercritical solubility. A severe limitation is the availability of the equation constants. Equations that require their constants to be determined by fitting extensive experimental data on the pure substances to the equation are not useful, for rarely are experimental data available for the complex solutes of interest. We are thus forced to discard complex equations such as the Benedict-WebbRubin ( U ), Jacobsen ( 12 ), Goodwin ( JL3 ), Perturbed-Hard-Chain ( 14 ), and Chain-of-Rotators ( 1_5 ). For detailed evaluation, we have selected nine equations from among those that have been in use in phase equilibrium calculations and newer equations that show promise. Eight of these are cubic equations, and one (Han-Cox-Bono-Kwok-Starling) is complex. But all have been generalized to express the equation constants in terms of critical properties, which are known for a large number of substances. Group con tribution ( 16,17 ) and other methods ( 18,19 ) are widely used for the estimation of the critical properties where experimental values have not been reported. Table I presents the nine equations of state that are studied in this work. Table II shows the critical properties of the substances that are used in the calculations. For many higher molecular weight compounds T , p , and ω were estimated, T and p by the method of Lydersen ( 18 ) and υ by the method of Edmister ( 19 ). c

c

c

c

Mixing rules described in the original papers are used in the calculations reported here for the Redlich-Kwong, HCBKS, Peng-Robinson, Kubic, Heyen, and CCOR equations. No interaction constant was employed by Soave in the mixing rules for his equation. We introduced an interaction constant k to the constant a, as we found it quite necessary. The Schmidt-Wenzel and Harmens-Knapp equations con tained no mixing rules at all. We employ the classical one-fluid mixing rules to extend these equations to mixtures as follows: 1 2

i J

Where θ may be either a or b, and the cross parameter θ

ι}

a

is given by

= (l-kyKauajj) ^ 1

y


c

equation of state parameters

r

kjj

binary interaction parameter

η

number of data points in a binary system

ρ

pressure

p°

vapor pressure

R

gas constant

Τ

temperature

u

equation of state parameter

V

molar volume

V

s

w y

solid molar volume equation of state parameter fluid

phase mole fraction

Greek Letters ρ

molar density

φ

fugacity coefficient of fluid phase

φ°

fugacity coefficient of saturated vapor

ω

acentric factor

Ω

objective function

Subscripts 1 2 c

solid component fluid

component

critical property

Acknowledgment Funds for this research were provided by the Department of Energy through con tract DE-FG22-83PC60036.


178

EQUATIONS OF STATE: THEORIES AND APPLICATIONS

Literature Cited 1. Zosel, K. Chem. Int. Ed. (1978) 17, 702. 2. Hubert, P.; Vitzthum, O.G. Agnew. Chem. Int. Ed. (1978) 17, 710. 3. Irani, C.A.; Funk, E.W. Recent Developments in Separation Science Volume 3, part A, p. 171; CRC Press, West Palm Beach, 1977.


4. Bartle,K.C.,Martin, T.G.; Williams, D.F. Fuel 54, 226. 5. Martin, T.G.; Williams, D.F. Phil. Trans. Roy. Soc. London (1981) A300, 183. 6. Maddocks, R.R., Gibson, J.; Williams, F. Chem. Eng. Progress (1979) 75, 16, 49. 7. Blessing, J.E.; Ross, D.S. Organic Chemistry of Coal ,p. 171 et. seq., Am. Chem.Soc.,1978. 8. Ross, D.S.; Blessing, J.E. Fuel (1979) 58, 423. 9. Vasilakos, N.P., Dobbs, J.M.; Parisi, A.S. Ind. Eng. Chem. ProcessDes.Dev. (1985) 24, 121. 10. Adams, R.M., Knebel, A.M.; Rhodes, D.E. Hydrocarbon Processing (1980), May 150. 11. Benedict, M., Webb, G.B.; Rubin, L.C. J. Chem. Phys. (1940) 8, 334. 12. Jacobsen, R.B. Ph.D. Thesis, Washington State University, Pullman, WA (1972). 13. Goodwin, R.D. "The Thermodynamic Properties of Methane from 90 to 500K at Pressures to 700 Bar", NBS Tech. Note 653 (1974). 14. Donohue, M.C.; Prausnitz, J.M. AIChE J. (1978) 24, 849. 15. Chien, C.H., Greenkorn, R.A.; Chao, K.C. AIChE J. (1983) 29, 560. 16. Klincewicz, K.M.; Reid, R.C. AIChE J. (1984) 30, 1, 137. 17. Lydersen, A.L. "Estimation of Critical Properties of Organic Compounds", Univ. Wis. Coll. Eng. Exp. Stn. Rep. 3, Madison, WI, April, 1955. 18. Edmister, W.C. Pet. Refiner. (1958) 37, 4, 173. 19. Lin, H.M.; Chao, K.C. AIChE J. (1984) 30, 981. 20. Reid, R.C. "Creativity and Challenges in Chemical Engineering", University of Wisconsin, Madison, WI (1982). RECEIVED

November 5, 1985


Equation of State for Supercritical Extraction - American Chemical

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