Different-Scale Simulation of Flows in Porous Media

Keldysh Institute of Applied Mathematics RAS, RU-125047 Moscow, Russia

^* Corresponding author: mtrapez@yandex.ru

Published online: 26 April 2021

Abstract

The paper considers the development of algorithms for an adequate description of processes of different scales in porous media. The choice of a computational technique is determined by the reference size of the problem being solved. Models of porous medium flow under Darcy’s law, neglecting the medium microstructure, are used for the simulation at macro-scale. While at micro-scale, a direct description of fluid flow in porous channels with complex geometry by means of gas dynamic equations is used. In the first case the proposed model of non-isothermal multiphase multicomponent flow in a porous medium includes the mass balance and total energy conservation equations modified by analogy to the known quasi-gas dynamic equations. The model features are the introduction of minimal reference scales in space and in time and the change of the system type from parabolic to hyperbolic to increase the stability of explicit difference schemes applied for approximation. In the second case the dimensionless form of the quasi-gas dynamic system with pressure decomposition, developed by the authors earlier, is adapted to the simulation of flows in the pore space. The fictitious domain method is proposed to reproduce the core microstructure. The developed approaches have been verified by test predictions.