Petroleum production from reservoirs and finding ways to increase recovery has always been a challenging task. Reservoirs are heterogenous in nature, leading to complex fluid flow mechanism and displacement process. During displacement, frontal movement can be affected by dimensional permeabilities. Variations in vertical permeability with reference to horizontal permeability can affect the production and hence the recovery from a reservoir. As production of oil has always been a point of focus, so to increase its production various methods have been designed and analyzed owing to different advantages and disadvantages. In this study in-depth analysis of water and water alternating gas (WAG) injection as enhanced oil recovery method (EOR) has been done, while incorporating the vertical permeability variations with reference to horizontal permeabilities. The obtained results show better displacement is obtained with the increase in vertical to horizontal permeability ratio and hence leading to maximum recovery in case of maximum vertical permeability.