Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

Interval Mathematics Applied to Critical Point Transitions

Palabras clave

Critical Points
Interval Analysis
Computational Methods
Puntos Críticos
Análisis de Intervalos
Métodos Computacionales

Cómo citar

Stradi, B. A. (2005). Interval Mathematics Applied to Critical Point Transitions. Revista De Matemática: Teoría Y Aplicaciones, 12(1-2), 29–44.


La determinación de puntos críticos de mezclas es importante tanto por razones prácticas como teóricas en el modelamiento del comportamiento de fases, especialmente a presiones altas. Las ecuaciones que describen el comportamiento de mezclas complejas cerca del punto crítico son significativamente no lineales y con multiplicidad de soluciones para las ecuaciones del punto crítico. Aritmética de intervalos puede ser usada para localizar con confianza todos los puntos críticos de una mezcla dada. El método también verifica la no–existencia de un punto crítico si una mezcla de composición dada no tiene dicho punto. Este estudio usa un algoritmo denominado Newton–Intervalo/Bisección–Generalizada que provee una garantía matemática y computacional de que todos los puntos críticos de una mezcla han sido localizados.Estos problemas cubren los modelos de ecuaciones cúbicas de estado; sin embargo, la técnica es de propósito general y puede ser aplicada en el caso de otros problemas no lineales.


Baker, L. E.; Kraemer, D. L. (1980) “Critical points and saturation pressure calculations for multicomponent systems”, Soc. Pet. Eng. J. February: 15–24.

Boberg, T. C.; White, R. R. (1962) “Prediction of critical mixtures”, Ind. Eng. Chem. Fund. 1(1): 40–44.

Boshkov, L. Z.; Yelash, L. V. (1997) “Closed-loops of liquid-liquid immiscibility in binary mixtures predicted from the Redlich-Kwong equation of state”, Fluid Phase Equil. 141: 105–112.

Debenedetti, P. G. (1996) Metastable Liquids: Concepts and Principles. Princeton University Press, New Jersey.

Deiters, U.; Schneider, G. M. (1976) “Fluid mixtures at high pressures. computer calculations of the phase equilibria and the critical phenomena in fluid binary mixtures from the Redlich-Kwong equation of state”, Ber. Bunsenges. Physik. Chem. 80(12): 1316–1321.

Enick, R.; Holder, G. D.; Morsi, B. I. (1985) “Critical and three phase behavior in the carbon dioxide/tridecane system”, Fluid Phase Equil. 22: 209–224.

Grieves, R. B.; Thodos, G. (1962) “The critical temperature of ternary hydrocarbon systems”, Ind. Eng. Chem. Fundam. 1(1): 45–48.

Hansen, E. (1992) Global Optimization using Interval Analysis. Marcel-Dekker, New York.

Heidemann, R. A. (1975) “The criteria for thermodynamic stability”, AIChE J. 21(4): 824–826.

Heidemann, R. A. (1983) “Computation of high pressure phase equilibria.”, Fluid Phase Equil. 14: 55–78.

Heidemann, R. A.; Khalil, A. M. (1980) “The calculation of critical points”, AICHE J. 5: 769–779.

Hicks, C. P.; Young, C. L. (1977) “Theoretical prediction of phase behavior at high temperatures and pressures for non-polar mixtures”, J. Chem. Soc. Faraday II 73: 597–612.

Hua, J. Z.; Brennecke, J.; Stadtherr, M. A. (1998) “Enhanced interval analysis for phase stability: Cubic equation of state models”, Ind. Eng. Chem. Res. 37: 1519–1527.

Hua, J. Z.; Brennecke, J. F.; Stadtherr, M. A. (1996) “Reliable phase stability analysis for cubic equation of state models”, Computer Chem. Engng. Suppl. 20: S395–400.

Hurle, R. L.; Jones, F.; Young, C. L. (1977) “Theoretical prediction of phase behavior at high temperatures and pressures for non-polar mixtures.”, J. Chem. Soc. Faraday II 73: 613–617.

Hurle, R. L.; Toczylkin, L.; Young, C. L. (1977) “Theoretical prediction of phase behavior at high temperatures and pressures for non-polar mixtures.”, J. Chem. Soc. Faraday II 73: 618–622.

Hytoft, G.; Gani, R. (1996) IVC-SEP Program Package. Danmarks Tekniske Universitet, Lyngby, Denmark.

Imre, A.; Martinas, K.; Rebelo, L. P. N. (1998) “Thermodynamics of negative pressures in liquids”, J. Non-Equilib. Thermodyn. 23: 351–375.

Kearfott, R. B. (1987) “Some tests of generalized bisection”, ACM Transactions on Mathematical Software 13(3): 197–220.

Kearfott, R. B. (1989) “Interval arithmetic methods for non-linear systems and non-linear optimization: An outline and status”, in: Sharda, R.; Golden, B. L.; Wasil, E.; Balci, O.; Stewart, W. (Eds.) Impact of Recent Computer Advances on Operations Research, Elsevier : 533–542.

Kearfott, R. B. (1990) “Interval arithmetic techniques in the computational solution of non-linear systems of equations: Introduction, examples, and comparisons”, Lectures in Applied Mathematics 26: 337–357.

Kearfott, R. B. (1996) Rigorous Global Search: Continuous Problem. Kluwer Academic Publishers, Dordrecht, The Netherlands.

Kearfott, R. B.; Novoa, M. (1990) “Algorithm 681: Intbis. a portable newton/bisection package”, ACM Trans. Math. Software 16: 152–157.

Knuppel, O. (1994) “PROFIL/BIAS- A Fast Interval Library”, Computing 53: 277–287.

Luks, K. D.; Turek, E. A.; Baker, L. E. (1987) “Calculation of minimum miscibility pressure”, SPE Res. Eng. J. November: 501–506.

Michelsen, M. L. (1982) “The isothermal flash problem. Part II, Phase split calculation”, Fluid Phase Equil. 9: 21–40.

Michelsen, M. L. (1984) “Calculation of critical points and phase boundaries in the critical region”, Fluid Phase Equil. 16: 57–76.

Michelsen, M. L.; Heidemann, R. A. (1981) “Calculation of critical points from cubic two-constant equations of state”, AIChE J. 3(27): 521–523.

Modell, M.; Reid, R. C. (1983) Thermodynamics and its Applications. Prentice-Hall, Englewood Cliff, New Jersey.

Moore, R. E. (1966) Interval Analysis. Prentice-Hall, Englewood Cliffs, New Jersey.

Munoz, F.; Chimowitz, E. H. (1993) “Critical phenomena in mixtures. I. Thermodynamic theory for the binary critical azeotrope”, J. Chem. Phys. 99(7): 5438–5449.

Nagarajan, N. R.; Cullick, A. S.; Griewank, A. (1991) “New strategy for phase equilibrium and critical point calculations by thermodynamic energy analysis. Part I. Stability analysis and flash.”, Fluid Phase Equil. 62: 191–211.

Nagarajan, N. R.; Cullick, A. S.; Griewank, A. (1991) “New strategy for phase equilibrium and critical point calculations by thermodynamic energy analysis. Part II. Critical point calculations.”, Fluid Phase Equil. 62: 211–223.

Neaumaier, A. (1990) Interval methods for systems of equations. Cambridge University Press, Cambridge.

Reid, J. M. P. R. C.; Poling, B. E. (1987) The Properties of Gases and Liquids. McGraw-Hill, New York.

Reid, R. C.; Beegle, B. L. (1977) “Critical point criteria in Legendre transform notation”, AIChE J. 5: 726–731.

Rochocz, G. L.; Castier, M.; Sandler, S. I. (1997) “Critical point calculations for semi-continuos mixtures”, Fluid Phase Equilibria 139: 137–153.

Rowlinson, J. S.; Swinton, F. L. (1982) Liquid and Liquid Mixtures. Butterworth Scientific, London.

Sadus, R. J. (1994) “Calculating critical transitions of fluid mixtures: Theory vs experiment”, AIChE J. 40 (8): 1376–1403.

Schnepper, C. A.; Stadtherr, M. A. (1996) “Robust process simulation using interval methods”, Computers Chem. Engng. 20 (2): 187–199.

Scott, R. L.; van Konynenburg, P. H. (1970) “Static properties of solutions”, Discussions of the Faraday Society 49: 87–97.

Spear, R. R.; Robinson, R. L.; Chao, K.-C. (1971) “Critical states of ternary mixtures and equations of state”, Ind. Eng. Chem. Fundam. 10 (4): 588–592.

Stockfleth, R.; Dohrn, R. (1998) “An algorithm for calculating critical point in multicomponent mixtures which can be easily implemented in existing programs to calculate phase equilibria”, Fluid Phase Equil. 145: 43–52.

Stradi, B. A. (2000) Measurement and Modeling of the Phase Behavior of High-Pressure Reaction Mixtures and the Computation of Mixture Critical Points. PhD thesis, Univesity of Notre Dame, Indiana.

Teja, A. S.; Kropholler, H. W. (1975) “Critical states fo mixtures in which azeotropic behavior persists in the critical region”, Chem. Engng. Sci. 30: 435.

Teja, A. S.; Rowlinson, J. S. (1973) “The prediction of the thermodynamic properties of fluids and fluid mixtures-IV. Critical and azeotropic states”, Chem. Eng. Sci. 28: 529–537.

van Konynenburg, P. H. (1968) Critical Lines and Phase Equilibria in Binary Mixtures. PhD thesis, University of California at Los Angeles, California.



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