Non-Isothermal Compositional Model for Simulation of Multiphase Porous Media Flows

¹ Keldysh Institute of Applied Mathematics RAS, RU-125047, Moscow, Russia
² Moscow Automobile and Road Construction State Technical University, RU-125319, Moscow, Russia
³ Moscow Institute of Physics and Technology (State University), RU-141700, Dolgoprudny, Moscow Region, Russia

^* e-mail: mtrapez@yandex.ru

Published online: 9 December 2019

Abstract

The research carried out in this work is aimed at the development of an explicit computational algorithm to simulate non-isothermal flow of multiphase multicomponent slightly compressible fluid through porous media. Such a modeling is necessary, for example, at solving practically important problems of hydrocarbon recovery via thermal methods and contaminated soil remediation via the hot steam injection. The original model and algorithm developed by the authors earlier draw the analogy with the quasi-gas-dynamic set of equations. Phase continuity equations were modified to get regularizing terms, while the type of equations was changed from parabolic to hyperbolic for the approximation by an explicit scheme with a mild enough stability condition. Since an adequate description of temperature-dependent porous media processes requires an explicit consideration of the transfer of mass and energy between the phases, the present work focuses on the generalization of the proposed approach to the case of multicomponent composition of fluids. Conservation laws are currently formulated for the components in terms of the mass concentrations of components in the phases. Constants of the phase equilibrium were used to close the set of equations. The developed model and algorithm have been verified numerically via test predictions of twoand three-phase flows, and, the phase transition of water into the gas phase at heating has been reproduced correctly.