The Multiscale Finite-Volume (MSFV) method has been recently developed
and tested for multiphase-flow problems with simplified physics (i.e.
incompressible flow without gravity and capillary effects) and proved
robust, accurate and efficient. However, applications to practical
problems necessitate extensions that enable the method to deal with
more complex processes. In this paper we present a modified version of
the MSFV algorithm that provides a suitable and natural framework to
include additional physics. The algorithm consists of four main steps:
computation of the local basis functions, which are used to extract the
coarse-scale effective transmissibilities; solution of the coarse-scale
pressure equation; reconstruction of conservative fine-scale fluxes;
and solution of the transport equations. Within this framework, we
develop a MSFV method for compressible multiphase flow. The basic idea
is to compute the basis functions as in the case of incompressible flow
such that they remain independent of the pressure. The effects of
compressibility are taken into account in the solution of the
coarse-scale pressure equation and, if necessary, in the reconstruction
of the fine-scale fluxes. We consider three models with an increasing
level of complexity in the flux reconstruction and test them for highly
compressible flows (tracer transport in gas flow, imbibition and
drainage of partially saturated reservoirs, depletion of gas-water
reservoirs, and flooding of oil-gas reservoirs). We demonstrate that
the MSFV method provides accurate solutions for compressible multiphase
flow problems. Whereas slightly compressible flows can be treated with
a very simple model, a more sophisticate flux reconstruction is needed
to obtain accurate fine-scale saturation fields in highly compressible
flows. (c) 2006 Elsevier Inc. All rights reserved.