A system and method for modeling technology to predict accurately water-oil relative permeability uses a type of artificial neural network (ANN) known as a Generalized Regression Neural Network (GRNN) The ANN models of relative permeability are developed using experimental data from waterflood core test samples collected from carbonate reservoirs of Arabian oil fields Three groups of data sets are used for training, verification, and testing the ANN models Analysis of the results of the testing data set show excellent correlation with the experimental data of relative permeability, and error analyses show these ANN models outperform all published correlations