In cooperation with SPII our group will try to reveal similarities and differences in the numerical treatment of two-phase flow on the microscale and mesoscale using a dimensional analysis and solving a reference problem. The study should help to map microscale parameters to the mesoscale approach. Furthermore we want to analyse transient physical processes on the meso- and macroscale as a function of fluid and solid phase properties and structural parameters. Effective constitutive relationships will be formulated for the macroscale based on steady-state and transient numerical experiments. Subsequently we would like to extend the constitutive relationships and the balance equations by a dynamic capillary pressure-saturation relationship including hysteresis.

The relevance especially of the dynamic term will be investigated for the macroscale.

Up until now the dynamic capillary pressure-saturation relationship is implemented in the multi-phase simulation code. This new relationship differs from the well-established other parametrizations as shown in Figure 1.

Comparing the old and the new formulation, we see in the imbibition example in Figure 2 how the front calculated with the dynamic term is slowed down in comparison to the other formulation.

There two different kind of hysteresis models implemented in the our multi-phase code. One after Lenhard and Parker is depicted in Figure 3. There are a primary drainage and a primary imbibition curve enclosing all secondary loops. The second model represent a play-type hysteresis, where the primary curves are connected with vertical lines.

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