Abstract: The characteristic curves for oil displacement by water currently used in prediction of reservoir performance is a straight line on the lg F paper for recovery factor vs water-oil ratio. An improved equation for prediction is proposed, showing at the same time that ahere are practically two types of changes of the rate of recovery with recovery factor and the corresponding relative oil-water permeability curves. The first one derived from the equation proposed by Iraj Ershaghi and Osazuwa Omoregie is expressed on E_R-lgF chart by curves deviating toward the E_R axis, and the other one from the equation proposed by the author by curves deviating toward the lgF axis. Application of both equations may give accurate predictions of changes of rate of water cut with recovery factor as well as the ultimate recovery, and produce relative oil-water permeability curves from available data. In the last part of the paper, calculations are made of data from two dilfferent oil fields in proof of the fact that the theoretical curves agree well with the field data.