Horizontal redistribution of fluids in a porous medium: The role of interfacial area in modeling hysteresis

Recent advances in multi-phase flow theory have shown that the flow of several phases in a porous medium is highly influenced by the interfaces separating these phases. First modeling studies based on this new theory have been performed on a pore scale, as well as on a volume-averaged macro scale using balance equations and constitutive relations that take the role and presence of interfaces into account. However, neither experimental data nor analytical solutions are available on the macro scale so far, although their knowledge is essential for the verification of the new models. In this paper, we derive a semi-analytical solution for the redistribution of two fluid phases in a horizontal one-dimensional and homogeneous porous medium. We start with the macro-scale model including interfacial area. Next, we construct a semi-analytical solution for this problem by using a similarity transformation. We then compare results obtained from a numerical macro-scale model to this semi-analytical solution used as the reference solution.