An extended critical-scaling equation with a nonlinear order parameter and its use for the fits to vapor/liquid equilibria

In-Seok Yeo; Kyung-Hee Lim

Journal of Industrial and Engineering Chemistry, Vol.20, No.5, 2984-2991, September, 2014

DOI10.1016/j.jiec.2013.11.032 Export Citation

An extended critical-scaling equation with a nonlinear order parameter and its use for the fits to vapor/liquid equilibria

In-Seok Yeo, and Kyung-Hee Lim^†

School of Chemical Engineering and Materials Science, Chung-Ang University, Seoul 156-756, Korea

E-mail:

A method to extend the region of validity of the critical-scaling equations is presented and is tested by fits to the vapor/liquid equilibria (VLE) of ethane, propane, and n-butane. In this method there are two elements. One of them is to find an appropriate order parameter (OP) and the other one is how to fit the equations to equilibrium data. As for the OP, the nonlinear OP Smith and Ferer proposed [7] has been used. For the critical scaling equations, terms different from those they used have been employed. This leads to better results and physically sounder value of exclusion-volume-like fitting parameter b. As for the fitting method, first the critical parameters,Tc and Vc are determined and then linear regressions for the fits to VLE data have been adopted. Otherwise, nonlinear regressions have to be essentially employed. Pre-determination of Tc and Vc and the different terms for critical scaling equations provide relatively significant advantages; (i) it makes fits to VLE binodals linear, (ii) the exclusion-volume-like fitting parameter b is approximately equal to the van der Waals parameter bvdW, and (iii) the fits are in excellent agreement with the VLE data. In fact, the calculated values trace the VLE data almost exactly.

Keywords:Critical-scaling equations;Order parameter;Vapor/liquid equilibrium;Equation of state;Excluded volume

[References]

Lim KH, Statistical Thermodynamics, Hantee Media, Seoul, Korea, 2008
McQuarrie DA, Statistical Mechanics, University Science Books,, Sausalito, California, 2000.
Hill TL, An Introduction to Statistical Thermodynamics, Dover, New York, 1986.
Donohue MD, Naiman DQ, Jin G, Loehe JR, Statistically Designed Study of the Variables and Parameters of Carbon Dioxide Equation of State, The Johns Hopkins University, US, 1991, DOE report #DOE/BC/14200-4 (DE91002240).
Peng DY, Robinson DB, Ind. Eng. Fund., 15, 59 (1976)
Stanley HE, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, New York, 1971.
Smith DH, Ferer M, Fluid Phase Equilib., 113(1-2), 103 (1995)
Aizpiri AG, Correa JA, Rubio RG, Pena MD, Phys. Rev. B, 41, 9003 (1990)
Nakata M, Dobashi T, J. Chem. Phys., 84, 5782 (1986)
Nakata M, Dobashi T, Kuwahara N, Kaneko M, J. Chem. Soc.-Faraday Trans., 2(78), 1801 (1982)
Lim KH, Ferer M, Smith DH, J. Chem. Phys., 100(11), 8284 (1994)
Nagarajan N, Kumar A, Gopal ESR, Greer SC, J. Phys. Chem., 84, 2883 (1980)
Widom B, J. Chem. Phys., 43, 3898 (1965)
Sengers JV, Phase Transitions: Cargese 1980, Plenum, New York, 1982.
Sengers JV, Sengers JMHL, Annu. Rev. Phys. Chem., 37, 189 (1986)
Beysens D, Phase Transitions: Cargese 1980, Plenum, New York, 1982.
Baker GA, Nickel BG, Meiron DI, Phys. Rev. B, 17, 1365 (1978)
Lim KH, Thermodynamics, Free Academy, Paju, Korea, 2011.
Sandler SI, Chemical and Engineering Thermodynamics, 3rd ed., John Wiley, New York, 1999.
Valderrama JO, Ind. Eng. Chem. Res., 42(8), 1603 (2003)
Douslin DR, Harrison RH, J. Chem. Thermodyn., 5, 491 (1973)
Lim KH, Reckley JS, Smith DH, J. Colloid Interface Sci., 161, 465 (1993)
Weast RC, Handbook of Chemistry and Physics, 53rd ed., Chemical Rubber Co., Cleveland, 1972.
Reid RC, Prausnitz JM, Poling BE, The Properties of Gases and Liquids, 4th ed., McGraw-Hill, New York, 1987.
Miniovich VM, Sorina GA, P-V-T-N relations in dilute solutions of propane in ethane near the ethane critical point,, Deposited with the All-Union Institute of Scientific and Technical Information, State Institute of the Nitrogen Industry, 1973.
Khazanova NE, Sominskaya EE, Russ. J. Phys. Chem., 45, 88 (1971)
Beattie JA, Su GJ, Simard GL, J. Am. Chem. Soc., 61(4), 924 (1939)
Lu H, Newitt DM, Ruhemann M, Proc. R. Soc. London A, 178, 506 (1941)
Thomas RHP, Harrison RH, J. Chem. Eng. Data, 27, 1 (1982)
Goodwin RD, Provisional Thermodynamic Functions of Propane, from 85 to 700 K at Pressures to 700 Bar, National Bureau of Standards, Washington DC, U.S.A, 1977.
El A, Mousa HN, Kay WB, J. Chem. Thermodyn., 4, 301 (1972)
Clegg HP, Rowlinson JS, J. Chem. Soc.-Faraday Trans., 51, 1333 (1955)
Beattie JA, Hadlock C, Poffenberger N, J. Chem. Phys., 3, 93 (1935)
Kay WB, Rambosek GM, Ind. Eng. Chem., 45, 221 (1953)
Kay WB, Ind. Eng. Chem., 32, 358 (1940)
Beattie JA, Simard GL, Su GJ, J. Am. Chem. Soc., 61, 24 (1939)
Yeo IS, Lim KH, submitted to Kor. J. Chem. Eng.

[Related Articles]

[1] Lim KH, Statistical Thermodynamics, Hantee Media, Seoul, Korea, 2008

[2] McQuarrie DA, Statistical Mechanics, University Science Books,, Sausalito, California, 2000.

[3] Hill TL, An Introduction to Statistical Thermodynamics, Dover, New York, 1986.

[4] Donohue MD, Naiman DQ, Jin G, Loehe JR, Statistically Designed Study of the Variables and Parameters of Carbon Dioxide Equation of State, The Johns Hopkins University, US, 1991, DOE report #DOE/BC/14200-4 (DE91002240).

[5] Peng DY, Robinson DB, Ind. Eng. Fund., 15, 59 (1976)

[6] Stanley HE, Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, New York, 1971.

[7] Smith DH, Ferer M, Fluid Phase Equilib., 113(1-2), 103 (1995)

[8] Aizpiri AG, Correa JA, Rubio RG, Pena MD, Phys. Rev. B, 41, 9003 (1990)

[9] Nakata M, Dobashi T, J. Chem. Phys., 84, 5782 (1986)

[10] Nakata M, Dobashi T, Kuwahara N, Kaneko M, J. Chem. Soc.-Faraday Trans., 2(78), 1801 (1982)

[11] Lim KH, Ferer M, Smith DH, J. Chem. Phys., 100(11), 8284 (1994)

[12] Nagarajan N, Kumar A, Gopal ESR, Greer SC, J. Phys. Chem., 84, 2883 (1980)

[13] Widom B, J. Chem. Phys., 43, 3898 (1965)

[14] Sengers JV, Phase Transitions: Cargese 1980, Plenum, New York, 1982.

[15] Sengers JV, Sengers JMHL, Annu. Rev. Phys. Chem., 37, 189 (1986)

[16] Beysens D, Phase Transitions: Cargese 1980, Plenum, New York, 1982.

[17] Baker GA, Nickel BG, Meiron DI, Phys. Rev. B, 17, 1365 (1978)

[18] Lim KH, Thermodynamics, Free Academy, Paju, Korea, 2011.

[19] Sandler SI, Chemical and Engineering Thermodynamics, 3rd ed., John Wiley, New York, 1999.

[20] Valderrama JO, Ind. Eng. Chem. Res., 42(8), 1603 (2003)

[21] Douslin DR, Harrison RH, J. Chem. Thermodyn., 5, 491 (1973)

[22] Lim KH, Reckley JS, Smith DH, J. Colloid Interface Sci., 161, 465 (1993)

[23] Weast RC, Handbook of Chemistry and Physics, 53rd ed., Chemical Rubber Co., Cleveland, 1972.

[24] Reid RC, Prausnitz JM, Poling BE, The Properties of Gases and Liquids, 4th ed., McGraw-Hill, New York, 1987.

[25] Miniovich VM, Sorina GA, P-V-T-N relations in dilute solutions of propane in ethane near the ethane critical point,, Deposited with the All-Union Institute of Scientific and Technical Information, State Institute of the Nitrogen Industry, 1973.

[26] Khazanova NE, Sominskaya EE, Russ. J. Phys. Chem., 45, 88 (1971)

[27] Beattie JA, Su GJ, Simard GL, J. Am. Chem. Soc., 61(4), 924 (1939)

[28] Lu H, Newitt DM, Ruhemann M, Proc. R. Soc. London A, 178, 506 (1941)

[29] Thomas RHP, Harrison RH, J. Chem. Eng. Data, 27, 1 (1982)

[30] Goodwin RD, Provisional Thermodynamic Functions of Propane, from 85 to 700 K at Pressures to 700 Bar, National Bureau of Standards, Washington DC, U.S.A, 1977.

[31] El A, Mousa HN, Kay WB, J. Chem. Thermodyn., 4, 301 (1972)

[32] Clegg HP, Rowlinson JS, J. Chem. Soc.-Faraday Trans., 51, 1333 (1955)

[33] Beattie JA, Hadlock C, Poffenberger N, J. Chem. Phys., 3, 93 (1935)

[34] Kay WB, Rambosek GM, Ind. Eng. Chem., 45, 221 (1953)

[35] Kay WB, Ind. Eng. Chem., 32, 358 (1940)

[36] Beattie JA, Simard GL, Su GJ, J. Am. Chem. Soc., 61, 24 (1939)

[37] Yeo IS, Lim KH, submitted to Kor. J. Chem. Eng.