A Finite Volume Approach with Triangular Grids in Reservoir Simulation

Abstract

A technique is presented to improve the 7 numerical modelling of flow in reservoirs with complex geometries. A finite volume formulation is used to discretize the fluid flow equations in irregular triangular grid networks. Effects of grid orientation in multiphase flow in reservoirs with arbitrarily shaped boundaries and containing internal faults are also discussed. Introduction Efficient approaches to simulate multiphase flow in reservoirs with complex geometries are strongly dependent on the type of grid system used in the discretization process. Despite the simplicity of grid construction and easy handling of numerical approximations, finite difference schemes with Cartesian grid, widely used in reservoir simulation, show severe limitation in treating irregular domains with arbitrarily shaped internal and external boundaries. In using standard finite difference approaches, special grid refinement techniques are needed to have adequate resolution in the areas around producing wells, faults, pinchouts, and highly heterogenous internal zones. Pedrosa and Aziz applied a hybrid grid approach to improve the treatment of wells in reservoir simulators. Forsyth and Sammon addressed the modelling of faulted reservoirs through the use of local mesh refinement coupled with adaptive implicit algorithms. A careful treatment of finite difference approximations at the composite grid interfaces is required, as pointed out by Quandalle and Besset. Grid orientation effect is a drawback of standard finite difference schemes with Cartesian grid. Several nine-point schemes have been used in reservoir simulation to reduce this spurious effect. As an additional difficulty, these higher-order schemes do not properly handle irregular contours. Recently there has been an increasing interest in applying flexible gridding techniques to solve fluid flow problems in arbitrarily shaped reservoirs. Heineman et problems in arbitrarily shaped reservoirs. Heineman et al described a flexible method for using irregular triangular grid network in reservoir simulation. They reported that the method provided a good approximation of reservoir geometry, simple treatment of boundary conditions and reduced grid orientation effect. Another attempt was the use of a conformal mapping approach to generate a smooth orthogonal curvilinear grid that conforms to external and internal boundaries of arbitrary geometry, as presented by Sharpe and Anderson. In this paper we describe a finite volume approach that employs a triangular grid network for solving two phase flow problems in reservoirs with complex geometries.

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