Multiscale Finite Volume Method for Multi-Phase Flow in Porous Media: Black Oil Formulation of Compressible, Three-Phase Flow with Gravity and Capillarity Force

Seong H. Lee, Chevron ETC; Christian Wolfsteiner, Chevron ETC; Hamdi A. Tchelepi, Stanford University

The MSFV method has been extended to standard black oil formulation (i.e., three phase, compressible flow with solution gas and gravity/capillarity), in which the mass transfer between oil and gas phases is described by solution gas.   An operator splitting is employed to decompose the pressure equation into elliptic part, buoyancy/capillary force dominant part, and inhomogeneous part with source/sink (wells) and accumulation. Flow and transport equations are decoupled and solved sequentially. An accurate coarse grid operator is derived for the flow equation (pressure and velocity) and a local fine grid solution is reconstructed via basis functions.  In addition, adaptive computation is extensively implemented for numerical efficiency.  The MSFV method of black oil formulation allows us to study a large class of practical problems. We analyze the numerical efficiency of MSFV and demonstrate the robustness and computational efficiency of the MSFV, using large heterogeneous reservoir models.