Two major arrangements describing the oil-by-water displacement process, i.e., Muskat's model without taking into account the surface tension on the free boundary and the Buckley-Leverett model based on the surface tension, are considered. These arrangements were subject to theoretical and numerical study, which made it possible to uncover their self-contradictoriness. The focus was on construction of a numerical solution at the microlevel using the direct method with pressure correction.
