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Calculation of spinodal line and critical point of a mixture

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Abstract

A simple form of two equations that describe the spinodal line on theT-P plane and the critical point of a multicomponent mixture is suggested. This form is easy to implement numerically. An effective solution algorithm for model equations that is based on the parameter continuation method is proposed. Results of computation are compared with the literature data obtained from other models, as well as with experiments. An example of parameter calculation for benzene hydrogénation in supercritical CO2 is given.

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Abbreviations

am, bm:

coefficients in equation of state (5a) for component mixture

Cij, kij :

empirical coefficients describing binary interaction between components (i = 1, 2, ...,N;j = 1, 2,..., N;i⊋j)

f i :

fugacity of the ith component, atm

G:

Gibbs free energy, J

n-N:

dimensional vector of the molar numbers of mixture components, mol

N :

the number of mixture components

P :

pressure, atm

P CI :

critical pressure of the ith component, atm

R :

gas constant, 1 atm/(mol K)

s :

formal parameter (arc length)

S:

entropy, J/K

T :

temperature, K

T Ci :

critical temperature of the ith component, K

V :

mixture volume, 1

V m :

molar volume of the mixture, 1/mol

x-N:

dimensional vector of component concentrations

x :

component concentration, mol. fraction

υ i :

chemical potential of the ith component, J/mol

Ωi :

molecule acentricity factor of the ith component

References

  1. Krichevskii, I.R.,Fazovye ravnovesiya v rastvorakh pri vysokikh davleniyakh (Phase Equilibria in Solutions under High Pressures), Moscow: Goskhimizdat, 1952.

    Google Scholar 

  2. Termodinamika ravnovesiya zhidkost’-par (Thermodynamics of Liquid-Vapor Equilibrium), Morachevskii, A.G., Ed., Leningrad: Khimiya, 1989.

    Google Scholar 

  3. Peng, D.Y. and Robinson, D.B., A Rigorous Method for Predicting the Critical Properties of Multicomponent System from an Equation of State,AIChE J., 1977, vol. 23, no. 2, p. 137.

    Article  CAS  Google Scholar 

  4. Michelsen, M.L., The Isothermal Flash Problem. Part II: Phase Split Calculation,Fluid Phase Equil., 1982, vol. 9, p. 21.

    Article  CAS  Google Scholar 

  5. Heidemann, R.A. and Khalil, A.M., The Calculation of Critical Points,AIChE J., 1980, vol. 26, no. 5, p. 769.

    Article  CAS  Google Scholar 

  6. Reid, R.C., Prausnitz, J.M., and Sherwood, T.K.,The Properties of Gases and Liquids, New York: McGraw Hill, 1977. Translated under the titleSvoistva gazov i zhidkostei, Leningrad: Khimiya, 1982.

    Google Scholar 

  7. Soave, G., Equilibrium Constants from a Modified R.K. Equation of State,Chem. Eng. Sci, 1972, vol. 27, no. 6, p. 1197.

    Article  CAS  Google Scholar 

  8. Anikeev, V.I. and Ermakova, A., Binary-Interaction Coefficients for the Redlich-Kwong-Soave Equation of State,Teor. Osn. Khim. TekhnoL, 1998, vol. 32, no. 5, p. 508.

    Google Scholar 

  9. Choi, S.H., Harney, D.A., and Book, N.L., A Robust Path Tracking Algorithm for Homotopy Continuation,Comp. Chem. Eng., 1996, vol. 20, no. 6/7, p. 647.

    Article  CAS  Google Scholar 

  10. Allgower, E. and Georg, K., Simplical and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations,SIAM Rev., 1980, vol. 22, no. 1, p. 28.

    Article  Google Scholar 

  11. Fidkowski, Z.T., Malone, M.F., and Doherty, M.F., Computing Azeotropes in Multicomponent Mixtures,Comp. Chem. Eng., 1993, vol. 17, no. 12, p. 1141.

    Article  CAS  Google Scholar 

  12. Bertucco, A., Canni, P., and Devetta, L., Catalytic Hydrogenation in Supercritical CO2: Kinetic Measurements in a Gradientless Internal-Recycle Reactor,Ind. Eng. Chem. Res., 1997, vol. 36, no. 7, p. 2626.

    Article  CAS  Google Scholar 

  13. Savage, E.P., Gopalan, S., Mizan, T.I.,et al., Reactions at Supercritical Conditions: Applications and Fundamentals,AlChE J., 1995, vol. 41, no. 7, p. 1723.

    CAS  Google Scholar 

  14. Xiang, T., Johnston, K., Woffort, W., and Gloyna, E., Spectroscopic Measurement of pH in Aqueous Sulfuric Acid and Ammonia from Subto Supercritical Conditions,Ind. Eng. Chem. Res., 1996, vol. 35, no. 12, p. 4788.

    Article  CAS  Google Scholar 

  15. Debenedetti, P.G. and Reid, R.C., Diffusion and Mass Transfer in Supercritical Fluids,AIChE J., 1986, vol. 32, no. 12, p. 2034.

    Article  CAS  Google Scholar 

  16. Uematsu, M. and Frank, E.U., Static Constant of Water and Steam,J. Phys. Chem. Ref. Data, 1980, vol. 9, no. 4, p. 1291.

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Boreskov Institute of Catalysis, Siberian Division, Russian Academy of Sciences, pr. Akademika Lavrent’eva 5, 630090, Novosibirsk, Russia

    A. Ermakova & V. I. Anikeev

Authors
  1. A. Ermakova
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  2. V. I. Anikeev
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Ermakova, A., Anikeev, V.I. Calculation of spinodal line and critical point of a mixture. Theor Found Chem Eng 34, 51–58 (2000). https://doi.org/10.1007/BF02757464

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