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A novel finite element double porosity model for multiphase flow through deformable fractured porous media
Author(s) -
Lewis Roland W.,
Ghafouri Hamid R.
Publication year - 1997
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/(sici)1096-9853(199711)21:11<789::aid-nag901>3.0.co;2-c
Subject(s) - discretization , finite element method , porous medium , multiphase flow , flow (mathematics) , fluid dynamics , mechanics , porosity , galerkin method , mathematics , geology , geotechnical engineering , mathematical analysis , geometry , engineering , physics , structural engineering
Based on the theory of double‐porosity, a novel mathematical model for multiphase fluid flow in a deforming fractured reservoir is developed. The present formulation, consisting of both the equilibrium and continuity equations, accounts for the significant influence of coupling between fluid flow and solid deformation, usually ignored in the reservoir simulation literature. A Galerkin‐based finite element method is applied to discretize the governing equations both in the space and time domain. Throughout the derived set of equations the solid displacements as well as the fluid pressure values are considered as the primary unknowns and may be used to determine other reservoir parameters such as stresses, saturations, etc. The final set of equations represents a highly non‐linear system as the elements of the coefficient matrices are updated during each iteration in terms of the independent variables. The model is employed to solve a field scale example where the results are compared to those of ten other uncoupled models. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered. © 1997 by John Wiley & Sons, Ltd.