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 the set of weights of an artificial neural network is optimized to predict directly the characteristics of the calculation blocks representing a system studied. The data-driven approach is applied for the first time to simulate the two-phase flow in a porous medium; specifically, to determine the saturations of two immiscible phases during their filtering in space at an arbitrary instant. A computational experiment is performed, in which a deep convolutional neural network is adversarially trained using statistical estimates of the deviation from reference numerical solutions, which serves the objective function. A network of original architecture and a training process including nontrivial weight updating sequence for subnetworks (two encoders and one decoder/generator) are considered. Within the methodology of adversarial training, a discriminator network is used, whose objective function is set to contradict the objective functions of the main subnetworks. The results of training of an artificial neural network of specified configuration proved the ability of the proposed architecture to successfully generalize the regularities learned from the set of training data. The developed technique, implying the existence of two main objective functions for optimizing the set weights for each subnetwork, allowed the heuristic model to obtain results comparable with those of reference imitative simulation of two-phase flow on the basis of numerical methods. The specificity of the tasks solved in the oil and gas industry is the inevitable occurrence of uncertainties in geological and hydrodynamic reservoir models, a circumstance making urgent research in the field of heuristic methods of hydrodynamic simulation. The data output rate for the developed model is 2 to 3 orders of magnitude higher than that of conventional solvers (with comparable accuracy values). Thus, the proposed synthetic simulation is applicable to the tasks of predicting hydrocarbon deposits and planning their development.