Efficiency Study of the Multiscale Finite Volume Formulation for Multiphase Flow and Transport a Report Submitted to the Department of Energy Resources Engineering of Stanford University in Partial Fulfillment of the Requirements for the Degree of Master of Science

Multiscale methods have been developed to solve multiphase flow and transport problems in large-scale heterogeneous porous media accurately and efficiently. In this report, the computational efficiency of the multiscale finite-volume method (MSFV) is analyzed. The power of MSFV lies in its ability to combine local basis functions with a global coarse-scale problem to solve highly details heterogeneous models. In the first part of this report, we compare MSFV with conventional sequential strategies for solving coupled multiphase flow and transport that employ state-of-the-art linear solvers. Specifically, conventional sequential implicit methods with algebraic multigrid (AMG) for the pressure equation and incomplete LU factorization (ILU) for the saturation equations are used as the reference. We developed modular object-oriented simulation codes for both the multiscale and fine-scale simulation methods. Our results indicate that the adaptivity in pressure (reuse of the basis functions), velocity, and saturation calculations employed in MSFV leads to more efficient computations compared with the conventional fine-scale sequential implicit method. In the two test cases described here, the MSFV simulations are, respectively, eight and two times faster than the sequential fine-scale simulation using AMG and ILU. The efficiency study in this part serves as a solid basis for further development of MSFV as a general algebraic approach for solving nonlinear flow and transport in highly detailed heterogeneous reservoir models. In the second part, we employ an MSFV-based upscaling strategy for multiphase flow and transport, where the original MSFV algorithm is used to construct accurate