Relative permeability and capillary pressure functions define how much oil can be recovered and at what rate. These functions, in turn, depend critically on the geometry and topology of the pore space, on the physical characteristics of the rock grains and the fluids, and on the conditions imposed by the recovery process. Therefore, imaging and characterizing the rock samples and the fluids can add crucial insight into the mechanisms that control field-scale oil recovery. The fundamental equations of immiscible flow in the imaged samples are solved, and one can elucidate how relative permeability and capillary pressure functions depend on wettability, interfacial tension and the interplay among viscous, capillary and gravitational forces. This knowledge enables one to answer questions such as: Can a change of injected brine salinity increase oil recovery and by how much? How much more oil would be recovered if advancing contact angles could be modified? Does water injection help to recover sufficiently more oil or is it just for pressure maintenance? How can water imbibition be enhanced and oil trapping limited? Can relative permeabilities be modified with a polymer or with a chemical agent, such as an electrolyte or surfactant? Can one rely on gravity drainage of oil films to increase recovery? These and many other questions may be answered through a combination of imaging and calculations presented here. This paper summarizes the development of a complete quasi-static pore network simulator of two-phase flow, "ANetSim," and its validation against Statoil's state-of-the-art proprietary simulator. ANetSim has been implemented in MATLAB® and it can run on any platform. Three-dimensional, disordered networks with complex pore geometry have been used to calculate primary drainage and secondary imbibition capillary pressures and relative permeabilities. The results presented here agree well with the Statoil simulations and experiments.