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Implicit linearization scheme for nonstandard two‐phase flow in porous media
Author(s) -
Kassa Abay Molla,
Kumar Kundan,
Gasda Sarah E.,
Radu Florin A.
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4891
Subject(s) - linearization , mathematics , monotone polygon , capillary pressure , convergence (economics) , flow (mathematics) , two phase flow , scheme (mathematics) , multiphase flow , function (biology) , nonlinear system , mathematical optimization , porous medium , mathematical analysis , mechanics , geometry , physics , porosity , geotechnical engineering , quantum mechanics , evolutionary biology , engineering , economics , biology , economic growth
Summary In this article, we consider a nonlocal (in time) two‐phase flow model. The nonlocality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed‐point iterative linearization scheme for the resulting nonstandard model. The scheme treats the dynamic capillary pressure functions semiimplicitly and introduces an L ‐scheme type stabilization term in the pressure as well as the transport equations. We prove the convergence of the proposed scheme theoretically under physically acceptable assumptions, and verify the theoretical analysis with numerical simulations. The scheme is implemented and tested for a variety of reservoir heterogeneities in addition to the dynamic change of the capillary pressure function. The proposed scheme satisfies the predefined stopping criterion within a few number of iterations. We also compared the performance of the proposed scheme against the iterative implicit pressure explicit saturation scheme.