[page 681, §1]
[6188.8.131.52] A quantitative prediction of fluid saturation profiles during immiscible displacement remains a fundamental open problem in the physics of porous media. [6184.108.40.206] Despite its well known limitations regarding hysteresis and trapping phenomena, the traditional approach [2, 23, 20, 26] has remained the most popular mathematical model for more than 70 years in applications such as reservoir engineering  or groundwater hydrology .
[6220.127.116.11] Many authors have emphasized the importance of hysteresis between drainage and imbibition [25, 7, 21, 18]. [618.104.22.168] Ad hoc extensions of the existing two phase flow model [21, 24, 19, 14] yield reasonable agreement with laboratory measurements. [622.214.171.124] However, the physical foundations for such hysteresis models are not clear.
[6126.96.36.199] A recent macroscopic theory of capillarity in porous media  proposes to take into account the different hydrodynamic properties of percolating (=connected) and non-percolating (=not connected) fluid parts. [6188.8.131.52] This provides the physical basis for hysteresis in our approach. [6184.108.40.206] In the residual decoupling limit, the traditional constitutive relations between relative permeability and saturation as well as between capillary pressure and saturation are recovered including hysteresis [8, 9]. [6220.127.116.11] Approximate analytical results for a quasi-static displacement have been calculated in . In  and , numerical solutions were calculated for experiments with a closed homogeneous column in gravity. [618.104.22.168] Further, analytic and quasi analytic solutions for the theory were developed in [4, 6, 12]. [622.214.171.124] However, an explicit comparison with experimental data is pending.
[6126.96.36.199] The objective of this paper is to close this gap. [6188.8.131.52] We show that the theory is able to model a laboratory experiment  with a porous column that shows hysteretic behavior.
[6184.108.40.206] The manuscript is structured as followed. [6220.127.116.11] First, we illustrate the experimental setup  that has been used to illustrate hysteretic phenomena in fluid distributions in porous media flow. [618.104.22.168] Section 3 briefly presents the theory of percolating and non-percolating phases and its mathmatical formulation for incompressible immiscible two-phase flow. [622.214.171.124] In Section 4 we discuss the numerical representation of the experiment and its implementation. The results are presented and discussed in Section 5. [6126.96.36.199] The paper closes with concluding remarks.