  We study modeling of two-phase flow in highly heterogeneous fractured and
porous media. The flow behaviour is strongly influenced by mass transfer
between a highly permeable (mobile) fracture domain and less permeable
(immobile) matrix blocks. We quantify the effective two-phase flow behaviour
using a multirate rate mass transfer (MRMT) approach. We discuss the range of
applicability of the MRMT approach in terms of the pertinent viscous and
capillary diffusion time scales. We scrutinize the linearization of capillary
diffusion in the immobile regions, which allows for the formulation of MRMT in
the form of a non-local single equation model. The global memory function,
which encodes mass transfer between the mobile and the immobile regions, is at
the center of this method. We propose two methods to estimate the global memory
function for a fracture network with given fracture and matrix geometry. Both
employ a scaling approach based on the known local memory function for a given
immobile region. With the first method, the local memory function is calculated
numerically, while the second one employs a parametric memory function in form
of truncated power-law. The developed concepts are applied and tested for
fracture networks of different complexity. We find that both physically based
parameter estimation methods for the global memory function provide predictive
MRMT approaches for the description of multiphase flow in highly heterogeneous
porous media.
