Flow Simulation in Heterogeneous Reservoirs using the Dual Reciprocity Boundary Element Method and the Green Element Method

Green’s functions are established tools for solving petroleum engineering flow problems. Their utility and rigor was extended to arbitrarily shaped reservoirs using the Boundary Element Method (BEM). Traditional BEMs are limited to single-phase flow in homogeneous reservoirs. Earlier authors have developed techniques to handle heterogeneity. These methods are perturbationbased and computation-intensive. The current work adapted the most recent developments in boundary element methods to reservoir engineering problems. The transient pressure (diffusion) and convection-diffusion equations were solved in heterogeneous media using the Dual Reciprocity Boundary Element Method (DRBEM) and the Green Element Method (GEM). Numerical experiments showed that DRBEM is more accurate than a standard finite difference method. However like finite difference methods, DRBEM is subject to spurious oscillation at high Peclet numbers. DRBEM also requires the solution of a dense system of equations. GEM, which is a hybrid boundary element/finite element method, overcomes these disadvantages. The method was found to produce very accurate solutions to convection-diffusion problems and only shows small oscillations in the solution at very high Peclet numbers. A further important advantage is the sparse nature of the matrix system. GEM is also amenable to solving transient nonlinear problems, which makes it the basis for a new technique for multiphase flow simulation. The current work has developed an IMPES black oil reservoir simulation technique based on GEM.