A boundary-element algorithm for modeling three-dimensional fluid flow through porous media involving arbitrarily-oriented wells in arbitrarily-shaped reservoirs

Three-dimensional fluid flow through porous media problems have assumed increased significance and complexity in recent years due to a growing interest in horizontal well applications. Various predictive tools based on analytical and numerical methods have emerged to address such problems. They have various drawbacks. A versatile boundary-element algorithm was developed in this work to provide a viable alternative. The algorithm is capable of solving transient and steady-state problems in isotropic or anisotropic reservoirs and handling finite reservoirs and finite-radius well(s) of arbitrary geometry. It also allows the prescription of arbitrary combinations of the two common types of boundary conditions (Dirichlet and Neumann). It can thus be used to solve a wide variety of three-dimensional fluid flow through porous media problems in relatively complex situations, such as those associated with horizontal wells.; To verify its validity and demonstrate its application, the algorithm was used to model six problems with known analytical solutions. Good to excellent agreement between model and analytical solutions was obtained. The usefulness of the algorithm was illustrated further using two example applications involving more complex problems.; Several benefits were gained by adopting the boundary-element approach. Benefit of versatility was gained because of the ability to handle and conform well to irregular domain geometry and complex boundary conditions. Advantages were also gained due to the need to discretize only the domain boundary and not the domain itself, thus effectively reducing the dimensionality of the problem by one and eliminating grid orientation effects and numerical dispersion. The accuracy of solutions was also enhanced due to the "semi-analytic" nature of the technique.; To obtain accurate result, it was found essential that the order of quadratures used be high enough. The algorithm is thus computationally intensive. This is no major concern because of prevailing rapid advances in computing technology. Also, when solving problems that involve major flow variation near domain boundary, local grid refinement must be applied to obtain accurate early-time solutions. This is due to the use of linear shape functions in the interpolation of field variables. The use of higher order shape functions may eliminate or alleviate this undesirable sensitivity.