This paper presents a deep-learning-based proxy modeling approach to efficiently forecast reservoir pressure and fluid saturation in heterogeneous reservoirs during waterflooding. The proxy model is built on a recently developed deep-learning framework, the coupled generative adversarial network (Co-GAN), to learn the joint distribution of multidomain high-dimensional image data. In our formulation, the inputs include reservoir static properties (permeability), injection rates, and forecast time, while the outputs include the reservoir dynamic states (i.e., reservoir pressure and fluid saturation) corresponding to the forecast time. Training data obtained from full-scale numerical reservoir simulations were used to train the Co-GAN proxy model, and then testing data were used to evaluate the accuracy and generalization ability of the trained model. Results indicate that the Co-GAN proxy model can predict the reservoir pressure and fluid saturation with high accuracy, which in turn, enable accurate predictions of well production rates. Moreover, the Co-GAN proxy model also is robust in extrapolating dynamic reservoir states. The deep-learning proxy models developed in this work provide a new and fast alternative to estimating reservoir production in real time.

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