Invasion Percolation in Presence of Gravity

Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displacement of two fluids when both the gravity and viscous effects are negligible. In particular, the characteristic of the percolating cluster and the other important percolation properties at the breakthrough can be inferred. However, with the inclusion of the gravity forces, the behavior may change. For example, as the magnitudes of the gravity forces are comparable to the capillary forces, we have observed a transition in the structure of the interface (i.e. invasion front) depending on the dimensionless Bond number (i.e. ratio of gravity to capillary forces). We have taken a numerical study of the displacement of two immiscible fluids in the presence of the gravity force in a network of random pores. The main contribution is to investigate the effect of heterogeneity by considering various throat size distributions. We consider the injection to take place from one side of the system and displace the displaced fluid from the other side. The condition of the stability or instability of the front (or interface) is observed to be dependent on the dimensionless bond number as well as the heterogeneity of the system.