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 horizontal well problems in relatively complex situations.

A major advantage is 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 reduction in problem dimensions allows three-dimensional problems to be modeled using two-dimensional grids.

This paper provides a summary description of the main features of the algorithm. The application of the algorithm is demonstrated using two examples involving horizontal wells.

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