A two-dimensional study on the impact of pore space connectivity on the immiscible two-phase flow in a water-wet, water-oil system under steady state conditions

Immiscible displacements in porous media are unquestionably of great significance in numerous natural and industrial processes. It has been well established and accepted that in addition to the immiscible fluid properties, the morphology of the porous medium also plays a significant role in the final volumetric throughput of a particular fluid. Topological features of the porous medium have been found to exert a strong influence on the hydrodynamic behaviour of single and two-phase flows as they express a measure of pore space and consequently flow path connectivity and availability. The current study investigates the effect of the pore space connectivity, expressed through the Euler characteristic, on the hydrodynamic behaviour of a water-wet, oil-water two-phase system at steady state. Two-dimensional simulations are conducted in artificially generated porous media with constant diameter circular solid grains using a multi-relaxation time lattice-Boltzmann model. It is shown that topological features of the porous medium can significantly affect the macro-scale capillary pressure and relative permeability curves for drainage and imbibition but in different ways. It is also demonstrated that pore space connectivity has a strong influence on the fluid phase distribution and fragmentation patterns in the porous structure depending on the displacement process.