Despite several decades of artificial neural network reserach in other engineering disciplines, only recently work has been reported on its use as a prediction tool in petroleum engineering applications. Existing methods for the prediction of fluid now in porous medium include numerical simulation techniques and laboratory core flood experiments. Both of these methods are generally expensive and time consuming. However, neural networks, once successfully trained, can be used to predict reservoir performance in a short time with a personal computer. An artificial neural network was developed using data obtained from fine-mesh numerical simulation to predict the breakthrough oil recovery of immiscible displacement of oil by water in a two-dimensional vertical cross section. The network is able to predict the results of the fine-mesh numerical simulations without actually performing these simulation runs. Various neural network connections were investigated using the back-propagation with momentum algorithm for error minimization. This paper describes the design, development, and testing of the neural network.