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A finite element solution of a fully coupled implicit formulation for reservoir simulation
Author(s) -
Sukirman Y.,
Lewis R. W.
Publication year - 1993
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610171002
Subject(s) - discretization , finite element method , mathematics , partial differential equation , compressibility , reservoir simulation , stability (learning theory) , flow (mathematics) , fluid dynamics , porous medium , compressible flow , mechanics , computer science , mathematical analysis , porosity , engineering , geotechnical engineering , geometry , petroleum engineering , thermodynamics , physics , machine learning
Abstract An iterative method is presented for solving a fully coupled and implicit formulation of fluid flow in a porous medium. The mathematical model describes a set of fully coupled three‐phase flow of compressible and immiscible fluids in a saturated oil reservoir. The finite element method is applied to obtain the simultaneous solution (SS) for the resulting highly non‐linear partial differential equations where fluid pressures are the primary unknowns. The final discretized equations are solved iteratively by using a fully implicit numerical scheme. Several examples, illustrating the use of the present model, are described. The increased stability achieved with this scheme has permitted the use of larger time steps with smaller material balance errors.