Mathematical Models and Computer Simulations

, Volume 2, Issue 6, pp 782–787 | Cite as

Thermodynamically consistent model of a multicomponent mixture with phase transitions

  • A. V. Koldoba
  • E. V. Koldoba


The paper considers a thermodynamically consistent model of compressible multicomponent mixtures with phase transitions. For the isothermal case, this enables one to obtain surfaces of phase equilibrium and other thermodynamic functions in analytic form. Use is made of simple model equations of state and the model Gibbs potential, which are known to adequately describe the phase behavior of solutions in some practically important range of parameters. Such a thermodynamically consistent model is convenient for the numerical simulation of the filtration of multicomponent solutions with phase transitions—in this way we achieve a significant reduction in the execution time and reliability of numerical computation, and also exclude some unphysical solutions.


multicomponent mixtures thermodynamic model 


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  1. 1.
    K. Aziz and E. Settari, Petroleum Reservoir Simulation (Warren & Root, 1963; Nedra, Moscow, 1982).Google Scholar
  2. 2.
    M. D. Rozenberg and S. A. Kundin, Multiphase Multicomponent Filtration during Oil and Gas Extraction (Nedra, Moscow, 1978) [in Russian].Google Scholar
  3. 3.
    F. M. Orr, Theory of Gas Injection Processes (Stanford, 2005).Google Scholar
  4. 4.
    V. S. Mitlin, “Two-Phase Multicomponent Filtration: Instabilities, Autowaves and Retrograde Phenomena,” J. Fluid Mech. 220, 369–395 (1990).CrossRefGoogle Scholar
  5. 5.
    S. M. Walas, Phase Equilibrium in Chemical Engineering (Bulterworth Pub., Sydney, 1985; Mir, Moscow, 1989).Google Scholar
  6. 6.
    O. Yu. Batalin, A. I. Brusilovskii, and M. Yu. Zakharov, Phase Equilibriums in the Natural Hydrocarbon Systems (Nedra, Moscow, 1992) [in Russian].Google Scholar
  7. 7.
    A. V. Koldoba and E. V. Koldoba, “Model Equation of State for the Numerical Solution of the Problems of Multicomponent Filtration with Phase Transitions,” Geokhim., No. 5, 573–576 (2004) [Geochem. Int. 42, No. 5,493 (2004)].Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. V. Koldoba
    • 1
  • E. V. Koldoba
    • 2
  1. 1.Institute for Mathematical ModelingRussian Academy of SciencesMoscowRussia
  2. 2.Faculty of Mathematics and MechanicsMoscow State UniversityMoscowRussia

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