This paper deals with pore-scale two-phase flow simulations in carbonate rock using the pore network method (PNM). This method was used to determine the rock and flow properties of three different rock samples, such as porosity, capillary pressure, absolute permeabilities, and oil–water relative permeabilities. The pore network method was further used to determine the properties of rock matrices, such as pore size distribution, topological structure, aspect ratio, pore throat shape factor, connected porosity, total porosity, and absolute permeability. The predicted simulation for the network-connected porosity, total porosity, and absolute permeability agree well with those measured experimentally when the image resolution is appropriate to resolve the relevant pore and throat sizes. This paper also explores the effect of the wettability and fraction of oil-wet pores on relative permeabilities, both in uniform and mixed wet systems.

We present a numerical study of viscous fingering occurring during the displacement of a high viscosity fluid by low viscosity fluid in a circular Hele-Shaw cell. This study assumes that the fluids are miscible and considers the effects of inertial forces on fingering morphology, mixing, and displacement efficiency. This study shows that inertia has stabilizing effects on the fingering instability and improves the displacement efficiency at a high log-mobility-viscosity ratio between displacing and displaced fluids. Under certain conditions, inertia slightly reduces the finger-split phenomenon and the mixing between the two fluids.