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Development of a finite element computer simulation platform for a coupled reservoir and geomechanics system

Abstract:

The aim of this article is to describe the development of a finite element computer platform for the modeling, analysis, and simulation of a coupled reservoir and geomechanics system. The conditions that are assumed are the simplest possible, so that we assume homogeneity and isotropy in the material, an elastic behavior of the rock with small deformations, a quasi-static equilibrium, the absence of fractures and isothermal state. The study evolves sequentially in stages, from the flow of a single fluid in a porous medium, through the two-phase case, up to the three-phase black oil model. The starting point is based on a mathematical model that is an extension of Biot's theory for flow in porous media, and which accounts for coupling the reservoir of fluid flow to the rock deformation and stress states. The mathematical model is reformulated in variational terms, in order to get a proper formulation that enables us to apply the weighted residuals methods of Galerkin with linear interpolation functions. The use of linear interpolant functions reduces the computational work but at the cost of having to face some inestabilities in the solutions. Once the model is discretized, we make use of appropriate software to built an unstructured meshing domain using tetrahedral elements. We carried out a computational model founded in the design of a program based in the C++ language, to perform the tasks of numerical calculations of the coefficients, assembling the stiffness element by element matrices, and for solving the resulting equations. It is intended to develop the computer program in a modular structure, so that the solution of the coupled geomechanics/reservoir system can be performed through an iterative procedure. The development of this code is still in its initial stage, but the approachs show promise. At the end two case studies are presented, which are compared with analytical solution for verification of the approach. Copyright 2014, Society of Petroleum Engineers.