New non-equilibrium matrix imbibition equation for double porosity model

Andrey Konyukhov; Leonid Pankratov

doi:10.1016/j.crme.2016.02.011

New non-equilibrium matrix imbibition equation for double porosity model

Andrey Konyukhov ^1,²; Leonid Pankratov ^2,³

¹ Joint Institute for High Temperatures of the Russian Academy of Sciences, Izborskaya 13 Bldg, 2, Moscow, 125412, Russian Federation
² Laboratory of Fluid Dynamics and Seismic, Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russian Federation
³ Laboratoire de mathématiques et de leurs applications, CNRS – UMR 5142, Université de Pau et des pays de l'Adour, av. de l'Université, 64000 Pau, France

Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 510-520.

Abstract

The paper deals with the global Kondaurov double porosity model describing a non-equilibrium two-phase immiscible flow in fractured-porous reservoirs when non-equilibrium phenomena occur in the matrix blocks, only. In a mathematically rigorous way, we show that the homogenized model can be represented by usual equations of two-phase incompressible immiscible flow, except for the addition of two source terms calculated by a solution to a local problem being a boundary value problem for a non-equilibrium imbibition equation given in terms of the real saturation and a non-equilibrium parameter.

Received: 2015-07-11
Accepted: 2016-02-22
Published online: 2016-03-30

DOI: 10.1016/j.crme.2016.02.011

Keywords: Porous media, Double porosity, Homogenization, Two-phase flow, Non-equilibrium model

Author's affiliations:

Andrey Konyukhov ^{1, 2}; Leonid Pankratov ^{2, 3}

¹ Joint Institute for High Temperatures of the Russian Academy of Sciences, Izborskaya 13 Bldg, 2, Moscow, 125412, Russian Federation
² Laboratory of Fluid Dynamics and Seismic, Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, Moscow Region, 141700, Russian Federation
³ Laboratoire de mathématiques et de leurs applications, CNRS – UMR 5142, Université de Pau et des pays de l'Adour, av. de l'Université, 64000 Pau, France

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Andrey Konyukhov; Leonid Pankratov. New non-equilibrium matrix imbibition equation for double porosity model. Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 510-520. doi : 10.1016/j.crme.2016.02.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.02.011/

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