Recently, multiscale methods have been developed for accurate and efficient numerical solution of large-scale heterogeneous reservoir problems. A scalable and extendible Operator Based Multiscale Method (OBMM) is described here. OBMM is cast as a general algebraic framework of the multiscale method. It is very natural and convenient to incorporate more physics in OBMM for multiscale computation.

In OBMM, two multiscale operators are constructed: prolongation and restriction. The prolongation operator can be constructed by assembling basis functions, and the specific form of the restriction operator depends on the coarse-scale dis-cretization formulation (e.g., finite-volume or finite-element). The coarse-scale pressure equation is obtained algebraically by applying the prolongation and restriction operators on the fine-scale flow equations. Solving the coarse-scale equation results in a high quality coarse-scale pressure. The fine scale pressure can be reconstructed by applying the prolongation operator to the coarse-scale pressure. A conservative fine-scale velocity field is then reconstructed to solve the transport equation.

As an application example, we study multiscale modeling of compressible flow. We show that the extension of modeling from incompressible to compressible flow is really straightforward for OBMM. No special treatment for compressibility is required. The efficiency of multiscale methods over stan dard fine-scale methods is retained by OBMM. The accuracy of OBMM is demonstrate by several challenging cases including highly compressible multiphase flow in a strongly heterogeneous permeability field (SPE 10).

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