Application of domain decomposition techniques in large-scale fluid flow problems

Abstract

Many large-scale fluid flow problems possess important localized phenomena whose resolution requires local grid refinement. In this paper, the solution of three-dimensional, multiphase flow problems on static, composite grids is discussed. 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. Special finite difference methods have been developed that connect the local and global grid cells in an accurate and mass-conserving manner. Many methods for composite-grid applications generate matrices that have lost their banded structure and must utilize corresponding solution algorithms that are extremely difficult to vectorize for efficiency purposes. Both stand-alone iterative methods and preconditioned gradient-type iterative techniques are discussed that 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 local coning models around any well in a full field-scale application without destroying the efficiency of the original simulator. Multiphase, multiwell problems are also presented. Finally, local time-stepping applications are discussed.