Generative adversarial neural networks for the heuristic modelling of a two-phase flow in porous media

Data-driven simulation is a promising approach to the development of heuristic models of complex physical systems. Within this approach, an artificial neural network is trained to directly predict the dynamics of a hydrodynamic model. In this study the data-driven approach is successfully used to approximate saturations of every grid cell for a chosen timestep in a two-phase flow in a porous media setting. The uncertainties that inevitably arise in many specific tasks of the oil and gas industry make research of such heuristic methods highly relevant. In a computational experiment a deep convolutional neural net work is trained with the use of the adversarial training technique. The original architecture and training procedure are used for the training, including a non-trivial sequence of weight updating for the two encoder networks and one decoder/generator. Also, following the methodology of adversarial training, a discriminator network is used, the objective function for which is set to contradict the objective functions of the main training loop. The results of the experiment have proven the ability of the proposed architecture to successfully generalize patterns learned from a set of training data. The developed heuristic model obtains results that are comparable to the reference of traditional numerical simulation for the test initial conditions. The heuristic model exceeds the speed of traditional solvers by 2-3 orders of magnitude. The satisfactory accuracy of the heuristic model makes it applicable to the tasks of synthetic reservoir modelling.