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. 

Water flooding is a well known secondary mechanism for improving oil recovery. Conventional approach to evaluate the performance of a water flooding process (e.g. breakthrough and post breakthrough behavior) is to establish a reliable geological reservoir model, upscale it, and then perform flow simulations. To evaluate the uncertainty in the breakthrough time or post breakthrough behavior, this procedure has to be repeated for many realizations of the geological model, which takes many hours of CPU time. Moreover, during the early stage of reservoir life, when data is scare, breakthrough and post breakthrough time behavior prediction are usually based on analogues or rules of thumb. Alternative statistical approach is to use PERCOLATION theory to predict breakthrough and post breakthrough bahavior. The main contribution is to evaluate the applicability of the existing scaling laws of the breakthrough time by the numerical flow simulation results using the Burgan formation dataset of Norouz offshore oilfield in the south of Iran. Moreover, we extend the scaling to the post breakthrough behavior. There is good agreement between the predictions from the PERCOLATION based expressions and the numerical simulation results. Moreover, the prediction from the scaling law took a fraction of a second of CPU times (as it only needs some algebraic calculations) compared with many hours required for the conventional numerical simulations.

Please click on PDF to view the abstract.