A Twophase Multirate-Mass Transfer Model for Flow and Transport in Porous Media

Abstract:

We present an upscaled non-local model for two-phase flow and transport in
highly heterogeneous porous media. The media under consideration are
characterized by sharp contrasts in the hydraulic properties typical
for fractured porous media, for example. A two-scale expansion gives
an upscaled flow and transport formulation that models multirate
mass transfer between mobile (fracture) and immobile (matrix) medium
portions. The evolution of saturation due to viscous dominated flow
in the mobile domain and mass exchange with the immobile zones through
capillary countercurrent flow. The medium heterogeneity is mapped onto
the mass transfer parameters, which are encoded in a memory function
that describes the non-local flux between mobile and immobile zones.
The upscaled model is parameterized by the medium heterogeneity and the
distribution of hydraulic parameters. Breakthrough of the displaced fluid
shows characteristic heavy tails due to fluid retention in immobile zones.