A reservoir simulator was developed for accurate modeling of multiphase flow and transport in large scale heterogeneous reservoirs. The simulator is based on a multiscale finite volume (MSFV) method. In MSFV, the pressure equation is solved on a coarse grid, where coarse scale transmissibilities are computed via dual basis functions (i.e., localized interpolators). The fine scale pressure and velocity field is computed as a superposition of basis functions using the coarse pressure information. These reconstructed properties are very accurate when compared to results from a conventional fine grid simulation. In the second step, a localized and adaptive transport scheme is employed to update the saturation distribution. Both IMPES and sequentially implicit formulations are described. To resolve the fine scale flow field around wells, a special well basis function is devised. The multiscale algorithm is also extended to include gravity, capillary pressure and compressibility.

The multiscale simulator achieves the robustness and computational efficiency through scalable (efficient for large problems) adaptive computation of flow and transport. We establish the accuracy of MSFV relative to conventional methods with several test examples. The multiscale simulator is subsequently applied to large field scale reservoir models to demonstrate its practical use and efficiency, compared with the conventional finite difference simulator.


The trend in modern reservoir characterization is to build geocellular models with an ever increasing level of detail and number of cells. In addition, specific applications (e.g., history matching, Monte Carlo Simulation) may require running large numbers of these detailed simulations. The multiscale framework is a particularly promising method for solving these highly detailed problems directly without resorting to traditional upscaling techniques. In the multiscale approach, the problem is decomposed into a coarse scale operator and local fine scale reconstruction operators. The local problems are small, independent from each other (via appropriate closure assumptions) and typically weak functions of time (for large parts of the reservoir). The resulting method is efficient and scalable.

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