Water flooding is commonly used to recover oil from porous rocks using pressurized water. Present study focuses on fully resolved pore-scale level multiphase Direct Numerical Simulations (DNS) of oil-water flows through homogeneous porous rocks. A second order accurate implicit Immersed Boundary Method (IBM) is used to resolve fluid-solid interactions on a non-body fitted Cartesian computational grid. Dynamic evolution of the fluid-fluid interface is tracked by a mass conservative sharp interface Volume of Fluid (VOF) method. The IBM and VOF method are coupled by a prescribed contact angle boundary condition at the fluid-fluidsolid contact line. Our method has been extensively validated especially for the test cases involving oil-water flows. Simulations of water flooding process through periodic homogeneous configurations of spheres are performed based on typical pore-scale capillary and Reynolds numbers. Effect of wettability on the mobility of oil through oil-wet and neutrally-wet rocks has been quantified as well.