Computing flow and pressure transients in heterogeneous media using boundary element methods

This work studied the modeling of well tests, tracer tests and multiphase flow in heterogeneous media using boundary element based methods. The motivation for this work was to provide accurate forward models of these processes to be used with parameter estimation/data integration schemes. Boundary element methods are attractive because of their rigorous Green's function basis. The classical boundary element method is however limited to single-phase flow in homogeneous media. This work explored how to recast the differential equations of practical interest to petroleum reservoir engineers in a form suitable for solution with a boundary element scheme.; For flows in heterogeneous media the integral forms of the flow equations contain domain integrals which can not be treated with the classical boundary element method. To handle these terms two hybrid boundary element methods were considered, the Dual Reciprocity Boundary Element Method (DRBEM) and the Green Element Method (GEM). The theory of both methods was considered, however most of the applications presented used GEM because of its sparse matrix structure and amenability to nonlinear problems.; A numerical method that combines GEM with singularity programming was proposed for the modeling of well tests in heterogeneous reservoirs. The method showed excellent accuracy when reproducing the pressure and pressure derivative curves. These results were compared to finite difference simulations which suffer from significant numerical artifacts including artificial wellbore storage effects and difficulty reproducing the boundary effects.; Tracer flows governed by the convection-diffusion equation were considered using both DRBEM and GEM. In numerical experiments at a range of moderate to large Paclét numbers GEM suffered much less from spurious oscillations in the solution than DRBEM. The application of GEM to transport in heterogeneous media was demonstrated.; An IMPES (Implicit Pressure Explicit Saturation) scheme for multiphase flow based on GEM was developed and applied. It showed promising results for a Buckley-Leverett flow example. Unfortunately the method is nonconservative so mass balance errors occur when it is applied to problems in heterogeneous media.; A parameter estimation scheme was developed for the estimation of reservoir permeability distributions from pressure data. This scheme was applied to match pressure data from multiple wells.