Secondary Recovery Conference, 2–3 May, Wichita Falls, Texas Abstract This paper presents numerical solutions or the equations describing the imbibition of water and the countercurrent flow of oil in porous rocks. The imbibition process is of practical importance in recovery of oil from heterogeneous formations and heretofore has been studied principally by experimental means. Calculations were made for imbibition of water into both linear and radial systems. Imbibition in the linear systems was allowed to take place through one open, or permeable, face of the porous medium studied. In the radial system, water was imbibed inward from the outer radius. The effects on rate of imbibition of varying the capillary pressure and relative permeability curves, oil viscosity, and the initial water saturation were computed. For each case studied, the rate of water imbibition and the saturation and pressure profiles were calculated as functions of time. The results of these calculations indicate that for the porous medium studied, the time required to imbibe a fixed volume of water of a certain viscosity is approximately proportional to the square root of the viscosity of the reservoir oil whenever the oil viscosity is greater than the water viscosity. Results are also presented illustrating the effects on rate of imbibition of the other variables studied. Introduction The process of imbibition, or spontaneous flow of fluids in porous media under the influence of capillary pressure gradients, occurs wherever there exist capillary pressure gradients in permeable rock which are not exactly balanced by opposing pressure gradients such as those resulting from the influence of gravity. The importance of such capillary movement in the displacement of oil by water or gas was recognized in early investigations and described by Leverett, Lewis, and True in 1942. The methods advanced by these authors for the study of the process by use of dynamically scaled models were rendered more general and flexible by the research of later workers. The influence of capillary forces in laboratory waterfloods has also been discussed by several authors.