Boundary element techniques in petroleum reservoir simulation

Pressure transient behaviour of heterogeneous reservoirs with complex geometry can be mathematically simulated by means of numerical methods. In this paper, the applicability of the boundary element method to this class of problems is studied. ee-space Greenʹs function satisfying two-dimensional pressure diffusion equation in the Laplace space is used as a weighting function for the Greenʹs second identity integral equation. The pressure field within the investigated domain is therefore defined analytically and only the reservoir boundary is discretized into a number of boundary elements. scale reservoir heterogeneities are represented by zones of homogeneous rock properties. Uniform flux vertical fractures are simulated by integrating a line sink over the fracture length. Two different ways of incorporating the sources and sinks into the model are investigated. del is applied to several simple systems and the results are compared with known analytical solutions. The performance of linear, quadratic, and cubic isoparametric boundary elements is examined.