Abstract
The mathematical formulation of a three-phase, three-dimensional fluid flow and rock deformation in fractured reservoirs is presented in this paper. The present formulation accounts for the significant influence of coupling between the fluid flow and solid deformation, an aspect usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time. The final set of equations, which contain the additional cross coupling terms as compared to similar existing models, are highly nonlinear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables. A field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme. The results illustrate a significantly different behavior for the case of a reservoir where the impact of coupling is also considered.
Highlights
Productivity of a reservoir, to some extend, depends on the microseismic fissures that exist in the oil formation
A continuum approach based on the double porosity model introduced by Barenblatt et al (1960), and later extended by Warren and Root (1963) is more suitable in this scenario
Alternative of Aifantis’ formulation were given latter by others in this area, e.g. Valliappan and Khalili (1990), Cho et al (1991), Bai et al (1993), Berryman and Wang (1995), Ghafouri and Lewis (1996), Chen and Teufel (1998), in chronological order. The majority of these works, concentrated on single-phase flow phenomena in a deformable geo-material, which has its special utility in civil engineering application like footing analysis etc
Summary
Productivity of a reservoir, to some extend, depends on the microseismic fissures that exist in the oil formation. Valliappan and Khalili (1990), Cho et al (1991), Bai et al (1993), Berryman and Wang (1995), Ghafouri and Lewis (1996), Chen and Teufel (1998), in chronological order The majority of these works, concentrated on single-phase flow phenomena in a deformable geo-material, which has its special utility in civil engineering application like footing analysis etc. Direct application of such models to a deformable oil reservoir is an idealization far from realistic as far as the petroleum industry is concerned. To recast the governing equations based on a multiphase flow formulation and to present a numerical analysis of the proposed model
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