Multiscale finite-volume formulation for multiphase flow in porous media: black oil formulation of compressible,three-phase flow with gravity |
| |
Authors: | S H Lee C Wolfsteiner H A Tchelepi |
| |
Institution: | (1) Chevron Energy Technology Co., 6001 Bollinger Canyon Rd., San Ramon, CA 94583, USA;(2) Energy Resources Engineering Dept., Stanford University, Stanford, CA 94305, USA |
| |
Abstract: | Most practical reservoir simulation studies are performed using the so-called black oil model, in which the phase behavior
is represented using solubilities and formation volume factors. We extend the multiscale finite-volume (MSFV) method to deal
with nonlinear immiscible three-phase compressible flow in the presence of gravity and capillary forces (i.e., black oil model).
Consistent with the MSFV framework, flow and transport are treated separately and differently using a sequential implicit
algorithm. A multiscale operator splitting strategy is used to solve the overall mass balance (i.e., the pressure equation).
The black-oil pressure equation, which is nonlinear and parabolic, is decomposed into three parts. The first is a homo geneous
elliptic equation, for which the original MSFV method is used to compute the dual basis functions and the coarse-scale transmissibilities.
The second equation accounts for gravity and capillary effects; the third equation accounts for mass accumulation and sources/
sinks (wells). With the basis functions of the elliptic part, the coarse-scale operator can be assembled. The gravity/capillary
pressure part is made up of an elliptic part and a correction term, which is computed using solutions of gravity-driven local
problems. A particular solution represents accumulation and wells. The reconstructed fine-scale pressure is used to compute
the fine-scale phase fluxes, which are then used to solve the nonlinear saturation equations. For this purpose, a Schwarz
iterative scheme is used on the primal coarse grid. The framework is demonstrated using challenging black-oil examples of
nonlinear compressible multiphase flow in strongly heterogeneous formations. |
| |
Keywords: | Multiscale finite volume Black oil Compressibility Gravity Operator split Reservoir simulation |
本文献已被 SpringerLink 等数据库收录! |
|