TY - JOUR
T1 - Numerical Treatment of Two-Phase Flow in Capillary Heterogeneous Porous Media by Finite-Volume Approximations
AU - Friis , H. A.
AU - Evje , S.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 505
EP - 528
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/644.html
KW - two-phase flow, heterogeneous media, capillary pressure, finite volume, MPFA, unstructured grids.
AB - <p style="text-align: justify;">This paper examines two-phase flow in porous media with heterogeneous capillary
pressure functions. This problem has received very little attention in the literature, and constitutes
a challenge for numerical discretization, since saturation discontinuities arise at the interface
between the different homogeneous regions in the domain. As a motivation we first consider a
one-dimensional model problem, for which a semi-analytical solution is known, and examine some
different finite-volume approximations. A standard scheme based on harmonic averaging of the
absolute permeability, and which possesses the important property of being pressure continuous
at the discrete level, is found to converge and gives the best numerical results. In order to
investigate two-dimensional flow phenomena by a robust and accurate numerical scheme, a recent
multi point flux approximation scheme, which is also pressure continuous at the discrete level, is
then extended to account for two-phase flow, and is used to discretize the two-phase flow pressure
equation in a fractional flow formulation well suited for capillary heterogenity. The corresponding
saturation equation is discretized by a second-order central upwind scheme. Some numerical
examples are presented in order to illustrate the significance of capillary pressure heterogeneity in
two-dimensional two-phase flow, using both structured quadrilateral and unstructured triangular
grids.</p>