Petroleum reservoir engineering applications of the dual reciprocity boundary element method and the green element method

Petroleum reservoir engineering requires solutions to the transient diffusion and convection-diffusion equations. Traditionally these calculations are carried out using finite difference methods. Prior workers have used perturbation-based boundary element methods for single phase flow in heterogeneous media. The current work applies the Dual Reciprocity Boundary Element Method (DRBEM) and the Green Element Method (GEM) to flow in heterogeneous media and to the convection-diffusion equation. GEM is a domain-based scheme incorporating the singular integral theory of BEM in an element-by-element fashion. It is very suitable for large problems such as those that can be generated in reservoir engineering because it produces sparse matrices. The performance of DRBEM and GEM are compared for convection-diffusion problems. Numerical experiments showed GEM to be more accurate and more stable than DRBEM at high Peclet number. Both methods allow reservoir heterogeneity to be treated more efficiently than with perturbation-based methods.