@Article{IJNAM-9-3,
author = {Keilegavlen, E. and Nordbotten, M., J. and Stephansen, F., A.},
title = {Tensor Relative Permeabilities: Origin, Modeling and Numerical Discretization},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2012},
volume = {9},
number = {3},
pages = {701--724},
abstract = {<p style="text-align: justify;">For multi-phase flow in porous media, the fluids will experience reduced conductivity
due to fluid-fluid interactions. This effect is modeled by the so-called relative permeability. The
relative permeability is commonly assumed to be a scalar quantity, even though justifications for
this modeling choice seldom are presented. In this paper, we show that the relative permeability
can yield preferential flow directions, and that furthermore, these directions may vary as a function of the fluids present. To model these effects properly, the relative permeability should be
considered a tensor. As shown in the paper, standard numerical methods cannot simulate tensor
relative permeabilities. We therefore propose two new methods to remedy the situation. One
scheme can be seen as an attempt to amend traditional methods to handle tensor relative permeabilities. The second scheme is a consistent approach to simulate the tensors. We also present
numerical simulations of cases where upscaling leads to tensor relative permeabilities. The results
show that the new methods are indeed capable of capturing tensor effects, moreover, they are in
very good agreement with fine scale reference solutions.</p>},
issn = {2617-8710},
doi = {https://doi.org/2012-IJNAM-655},
url = {https://global-sci.com/article/83508/tensor-relative-permeabilities-origin-modeling-and-numerical-discretization}
}