Homogenized model of two-phase capillary-nonequilibrium flows in a medium with double porosity

Voloshin A.S., Konyukhov A.V., Pankratov L.S.
 pdf (538K)

A mathematical model of two-phase capillary-nonequilibrium isothermal flows of incompressible phases in a double porosity medium is constructed. A double porosity medium is considered, which is a composition of two porous media with contrasting capillary properties (absolute permeability, capillary pressure). One of the constituent media has high permeability and is conductive, the second is characterized by low permeability and forms an disconnected system of matrix blocks. A feature of the model is to take into account the influence of capillary nonequilibrium on mass transfer between subsystems of double porosity, while the nonequilibrium properties of two-phase flow in the constituent media are described in a linear approximation within the Hassanizadeh model. Homogenization by the method of formal asymptotic expansions leads to a system of partial differential equations, the coefficients of which depend on internal variables determined from the solution of cell problems. Numerical solution of cell problems for a system of partial differential equations is computationally expensive. Therefore, a thermodynamically consistent kinetic equation is formulated for the internal parameter characterizing the phase distribution between the subsystems of double porosity. Dynamic relative phase permeability and capillary pressure in the processes of drainage and impregnation are constructed. It is shown that the capillary nonequilibrium of flows in the constituent subsystems has a strong influence on them. Thus, the analysis and modeling of this factor is important in transfer problems in systems with double porosity.

Keywords: double porosity, homogenization, two-phase flow, capillary nonequilibrium, dynamic capillary pressure, dynamic relative phase permeabilities
Citation in English: Voloshin A.S., Konyukhov A.V., Pankratov L.S. Homogenized model of two-phase capillary-nonequilibrium flows in a medium with double porosity // Computer Research and Modeling, 2023, vol. 15, no. 3, pp. 567-580
Citation in English: Voloshin A.S., Konyukhov A.V., Pankratov L.S. Homogenized model of two-phase capillary-nonequilibrium flows in a medium with double porosity // Computer Research and Modeling, 2023, vol. 15, no. 3, pp. 567-580
DOI: 10.20537/2076-7633-2023-15-3-567-580
URL: http://crm-en.ics.org.ru/journal/article/3332/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"

Copyright © 2009–2024 Institute of Computer Science