This paper presents the development and design of an artificial neural network that is able to predict the breakthrough oil recovery of immiscible displacement of oil by water in a two-dimensional vertical cross section. The data used in training the neural network was obtained from the results of fine-mesh numerical simulations. Several network architectures were investigated and trained using the back propagation with momentum algorithm. The neural network that gave the best predictive performance was a two-hidden layer network with 8 neurons in the first hidden layer and 8 neurons in the second hidden layer. This network also performed well against a cross validation test. The reservoir simulation data used so far in the training process was for a homogeneous reservoir, the more general case is still under investigation.