Abstract
Reservoir simulation is a powerful tool to mimic the formation behaviour during primary production and later on for planning enhanced oil recovery (EOR) pattern. However, all available commercial and developed scien-tific/academic software for this purpose is based on either finite difference method (FDM) or finite volume method (FVM). Recently finite element method started to gain more attention in the scientific and commercial practices due to its robust results and the ability to deal with complex boundaries. COMSOL Multiphysics is a finite element method (FEM)-based software, having very special features, which are different from standard reservoir engineering software packages like Eclipse or CMG, which are black box-type software. The most important feature of the COMSOL is that user can see equation and modify it - customize for specific conditions and objectives, as well as couple different physics together and apply different solvers, which are under user’s disposal. In this paper, short background of FEM will be illustrated and then the mathematical models of two-phase immiscible flow of water and heavy oil will be reviewed and simulated using COMSOL Multiphysics on the famous inverted five-spot model. The comparison between the results of Comsol Multiphysics and Eclipse shows good agreement. This study is the first step in applying Comsol Multiphysics to reservoir simulation. Further steps will involve simulating thermal enhanced oil recovery using steam flooding technique and coupling Comsol Multiphysics with CMG software package to enhance simulation inputs and outputs.
Highlights
Reservoir simulation combines mathematics, physics, reservoir engineering, and computational science to develop a tool for predicting oil and gas reservoirs performance at different operating patterns [1]
Finite element method While finite difference method (FDM) and finite volume method (FVM) can be considered as easier methods in terms of programming language, finite element method (FEM) is a little bit difficult to program due to its speciality in equation discretization
Multiphysics® software are different from the traditional reservoir simulation software packages owing to the speciality in discretization procedure used in FEM that is significant difference compared to FDM and FVM
Summary
Physics, reservoir engineering, and computational science to develop a tool for predicting oil and gas reservoirs performance at different operating patterns [1]. To describe the fluid flow inside an oil or gas reservoir a set of partial differential equations (PDE’s) must be solved with the use of consistent set of initial and boundary conditions. Short background of FEM will be illustrated and the mathematical models of two-phase immiscible flow of water and heavy oil will be reviewed and simulated using COMSOL Multiphysics on the famous inverted five-spot model. 2. Finite element method While FDM and FVM can be considered as easier methods in terms of programming language, FEM is a little bit difficult to program due to its speciality in equation discretization. To solve PDE using Galerkin approach the following steps should be followed [2]: multiply the original equation with a test function; integrate the equation and apply boundary conditions to produce weak form of the original equation; write the finite element solution as linear sum of a set of basis function (in the Galerkin method, test functions and basis functions are identical); apply the finite element solution into the weak form equation; solve the set of algebraic equations produced at the previous step; perform the error analysis
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