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Numerical simulation of nonclassical waves for immiscible three‐phase flow in heterogeneous porous media
Author(s) -
Abreu Eduardo
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700077
Subject(s) - porous medium , nonlinear system , flow (mathematics) , partial differential equation , mechanics , numerical analysis , two phase flow , phase (matter) , computer simulation , shock (circulatory) , multiphase flow , shock wave , mathematics , porosity , computer science , physics , geology , mathematical analysis , geotechnical engineering , quantum mechanics , medicine
Abstract In this paper we present accurate two‐dimensional numerical results, based on a new fractional time‐step method, for the numerical solution of a highly nonlinear system of partial differential equations modeling three‐phase immiscible water‐gasoil flow problems in heterogeneous petroleum reservoirs. The new numerical procedure was used to extend theoretical results for one‐dimensional three‐phase flow available in the literature by providing numerical evidence of the existence of nonclassical transitional shock in heterogeneous twodimensional three‐phase flows. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)