Traditional multi-phase flow models use an algebraic relationship between capillary pressure and saturation. This relationship is based on measurements made under static conditions. However, this static relationship is then used to model dynamic conditions, and evidence suggests that the assumption of equilibrium between capillary pressure and saturation may not be justified. Extended capillary pressure-saturation relationships have been proposed that include an additional term accounting for dynamic effects. In the present work, we study the underlying pore-scale physical mechanisms that give rise to this so-called dynamic effect. The study is carried out with the aid of a simple bundle-of-tubes model wherein the pore space of a porous medium is represented by a set of parallel tubes. We perform virtual two-phase flow experiments in which a wetting fluid is displaced by a non-wetting fluid. The dynamics of fluid-fluid interfaces are taken into account, and we consider systems in which viscosity differences influence the displacement process. From these experiments, we extract information about overall system dynamics, determine coefficients that are relevant to the dynamic capillary pressure description, and determine large-scale effects that are associated with viscosity differences between the two fluids. Based on these results, we then speculate about possible scale effects and the significance of the dynamic term.
All Science Journal Classification (ASJC) codes
- Water Science and Technology
- Geotechnical Engineering and Engineering Geology
- Ocean Engineering
- Mechanical Engineering