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CMMSE 2019: an explicit algorithm for the simulation of non-isothermal multiphase multicomponent flow in a porous medium

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Abstract

An explicit computational algorithm is developed to simulate complex flow of multiphase multicomponent slightly compressible fluid through porous media in view of heat sources. The proposed algorithm is based on the original model of porous media flow constructed by the analogy with the quasigasdynamic system of equations including the total energy conservation equation and modified to change the continuity equation type from parabolic to hyperbolic. It is approximated by a three-level explicit difference scheme having the second order of approximation in time and in space with a rather mild stability condition. The model takes into account gravitational and capillary forces, includes strongly nonlinear functions of the relative phase permeability. For the description of mass and energy transfer between the phases the model is generalized to account for multicomponent fluid structure. Conservation laws are formulated now for the components in terms of mass concentrations of components in the phases. The dependence of phase density and dynamic viscosity on pressure, temperature and multicomponent composition should be noted. Constants of the phase equilibrium close the system of equations. The created approach has been verified by test predictions of two- and three-phase fluid flows. Physically correct results were obtained, a good agreement with results by other authors was observed.

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Acknowledgements

The work is supported by the Russian Foundation for Basic Research (Grants 16-29-15095-ofi-m, 18-01-00405-a and 18-01-00587-a).

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics RAS, Moscow, Russia

    Marina Trapeznikova, Natalia Churbanova & Anastasia Lyupa

  2. Moscow Automobile and Road Construction State Technical University (MADI), Moscow, Russia

    Marina Trapeznikova & Natalia Churbanova

Authors
  1. Marina Trapeznikova
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  2. Natalia Churbanova
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  3. Anastasia Lyupa
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Correspondence to Marina Trapeznikova.

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Trapeznikova, M., Churbanova, N. & Lyupa, A. CMMSE 2019: an explicit algorithm for the simulation of non-isothermal multiphase multicomponent flow in a porous medium. J Math Chem 58, 595–611 (2020). https://doi.org/10.1007/s10910-019-01088-z

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  • DOI: https://doi.org/10.1007/s10910-019-01088-z

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