An Adaptive Multiphase Multiscale Finite Volume Simulator for Heterogeneous Reservoirs

Abstract We developed an adaptive reservoir simulator for accurate modeling of multiphase flow and transport in large scale heterogeneous reservoirs. The simulator is based on a multiscale finite volume (MSFV) method. We describe both IMPES and sequential implicit formulations. The algorithms are sensitive to the specific characteristics of flow (i.e., pressure and total velocity) and transport (i.e., saturation). To obtain the fine scale (i.e., fine grid) flow field, two sets of basis functions - dual and primal - are constructed. The dual basis functions, which are associated with the dual coarse grid, are used to calculate the coarse scale transmissibilities. The fine scale pressure field is computed from the coarse grid pressure via superposition of the dual basis functions. Having a locally conservative fine scale velocity field is essential for accurate solution of the saturation equations (i.e., transport). The primal basis functions, which are associated with the primal coarse grid, are constructed for that purpose. The dual basis functions serve as boundary conditions to the primal basis functions. To resolve the fine scale flow field in and around wells, a special well basis function is devised. As with the other basis functions, we ensure that the support for the well basis is local. Our MSFV simulator is designed for adaptive computation of both flow and transport in the course of a simulation run. Adaptive computation of the flow field is based on the time change of the total mobility field and triggers selective updates of basis functions. The key to achieving scalable (efficient for large problems) adaptive computation of flow and transport is the use of high fidelity basis functions with local support. We demonstrate the robustness and computational efficiency of the MSFV simulator using a variety of large heterogeneous reservoir models, including the SPE 10 comparative solution problem.