The continuing depletion of light oil supplies and the rapidly growing demand for energy are forcing oil and gas companies to explore unconventional oil extraction techniques. The structure and flow rate implies an impact on the trapping and mobilization of oil in the reservoir. This article studies the effect of pore geometry and dynamics on water-oil displacement as a two-phase flow system. The pore geometries of sandstone were extracted using the non-destructive 3D micro computational tomography (micro-CT) technique. Two-phase flow simulations were performed using COMSOL Multiphysics on the micro-CT images to show the effect of the capillary number and the flow pattern. Velocity and relative permeability of the non-wetting phase at different points of the porous structure was computed. The effect of viscosity of wetting fluid on the pore structure was also studied to evaluate the parameters affecting enhanced oil recovery (EOR). © 2021 Trans Tech Publications Ltd, Switzerland.