Three-dimensional, multiphase flow problems are solved on static, composite grids. The composite grid consists of a global, rectangular coarse grid and a set of locally refined patches around active wells or other areas with important local flow properties. Curvilinear (locally orthogonal) refinements can be utilized to approximate radial or near-radial flow around wells if such flow is assumed to be appropriate. More general localized refinement can be utilized otherwise. Finite differencing is presented which connects the local and global grid cells in an accurate manner.
Other methods for composite grid applications which have appeared in the SPE literature generate linearizations which have lost their banded structure and must utilize corresponding solution algorithms that are extremely difficult to vectorize for efficient solution. Preconditioned iterative techniques will be discussed which allow easy implementation of the composite grid techniques in existing simulators with full vectorization capabilities.
Pressure calculations in a single-phase flow problem with a distribution of injection and production wells exhibit excellent agreement between numerical calculations on locally radial grids and analytical solutions. Water and gas coning results for a single well also show very good agreement between computations on a hybrid grid and a circular cylindrical grid. This indicates the potential for incorporating coning models around any well in a full field-scale application without destroying the efficiency of the original simulator.