Shortest path algorithm for pore-scale simulation of water-alternating-gas injection

For simulation of three-phase flow processes, such as water-alternating-gas injection (WAG), accurate descriptions of the three-phase capillary pressures and relative permeabilities as functions of the phase saturations are essential. Instead of deriving these functions from experiments, which is very difficult, they may be obtained from pore-scale network simulations. During multiple injection processes, especially under mixed-wet conditions, isolated clusters of the three phases occur. These clusters may still be mobilized, even under the assumption of capillary-dominated flow, as part of so-called multiple displacement chains of adjacent clusters stretching from inlet to outlet of the model. To determine the most favourable displacement chain requires implementation of an efficient shortest path algorithm. For the present problem the distances or costs are the capillary entry pressures between the various phase clusters. Because these entry pressures can also be negative, so-called negative cost cycles arise, which invalidate traditional algorithms. Instead, we have implemented an efficient shortest path algorithm with negative cycle detection If negative cycles arise, the corresponding cyclic displacement chains are carried out before any linear displacement from inlet to outlet. Negative cost cycles correspond to spontaneous displacements, for which the prevailing invading phase pressure is higher than required. Additionally, and probably even more significant, the shortest path algorithm determines in principle the pressures of all phase clusters in the network. These pressures are in turn used in the accurate calculation of the three-phase entry pressures, as well as the film and layer volumes and conductances in pore corners. Some WAG network simulations in mixed-wet media have been carried out using the new algorithm to demonstrate the occurrence of long displacement chains and the much improved efficiency, also for increasing network sizes. A significant number of negative cycles occurred, but the corresponding displacement chains were short. Additionally, we have analysed the obtained values of the cluster pressures.