Adaptive Multiscale Finite-Volume Framework for Reservoir Simulation

Abstract

Summary A multiscale finite-volume (MSFV) framework for reservoir simulation is described. This adaptive MSFV formulation is locally conservative and yields accurate results of both flow and transport in large-scale highly heterogeneous reservoir models. IMPES and sequential implicit formulations are described. The algorithms are sensitive to the specific characteristics of flow (i.e., pressure and total velocity) and transport (i.e., saturation). To compute the fine-scale 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 framework 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, which triggers the selective updating 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.

Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible, three-phase flow with gravity

“…Although the numerical efficiency of this new blackoil MSFV simulator has not been fully examined, the numerical efficiency gains shown in Jenny et al [16,17] and Tchelepi et al [23] are expected to hold. This is because all the nonlinearities due to the presence of compressibility, gravity, and capillary pressure are resolved locally.…”

“…Our approach extends the sequential implicit MSFV method [17,23] to the nonlinear black-oil model. An operator-splitting multiscale algorithm is devised to compute the fine-scale pressure field, which is used to compute the fine-scale velocity field.…”

“…The upstream weighted phase velocities are used to solve the transport equations on the fine scale. We use a block-based Schwarz overlap scheme, where the blocks are the primal coarse cells [23].…”

“…These steps can be iterated until convergence of all variables at the current time level. The MSFV approach can be easily adapted to a sequential fully implicit treatment [17,23]. The MSFV implementation allows for performing an IMPES, traditional sequential [4], or a fully implicit scheme.…”

“…Jenny et al [15][16][17] described in a series of papers a multiscale finite-volume (MSFV) method for single-phase flow, adaptive implicit pressure-explicit saturations (IMPES), and sequential implicit treatment of incompressible multiphase flow in heterogeneous porous media. The MSFV framework is a general approach for sequential solution of the flow (pressure and total-velocity) and transport (saturation) problems [23]. To compute the fine-scale flow field, dual basis functions, which are solutions of local problems on the dual grid, are used to construct a global coarse scale system of equations.…”