Pore-scale modelling of dynamic capillary pressure: the role of fluid viscosities and length scale

Traditional theories of multiphase flow rely on capillary pressure and saturation relationships that are measured under equilibrium conditions. To incorporate transient behaviour, new multiphase flow theories have been proposed. These include an extended capillary pressure-saturation relationship that is valid under dynamic conditions. In this relationship, the difference between the two fluid pressures is called dynamic capillary pressure, and is assumed to be a function of saturation and its time rate of change. The dependency is through a so-called damping coefficient. In this work, a dynamic pore-scale network model is applied to investigate the parameters this coefficient depends on. The model consists of a three-dimensional lattice of cylindrical pore throats connected to each other by spherical pore bodies. In our numerical drainage experiments, nonwetting fluid is PCE and water is wetting fluid. Following Stauffer (a), we investigate the dependencies of the damping coefficient, focussing on the influence of fluid viscosities and length scale. For the drainage experiments in unsaturated porous media, Stauffer found a constant damping coefficient. In our previous work, the damping coefficient has been shown to be a function of saturation. We now show that the damping coefficient also depends on the interplay of the two fluid viscosities. Finally, the influence of length scale on the value of the damping coefficient will be discussed. a) Stauffer, F., Time dependence of the relations between capillary pressure, water content and conductivity during drainage of porous media, Proceedings of International IAHR Symposium on Scale Effects in Porous Media, Thessaloniki, Greece, August 29-Sept 1, 1978