Application of Physics-Informed Neural Networks to Solve Two-Phase Flow Model in Porous Media

Abstract

Summary In recent years, modern information technologies have been actively used in various industries. The oil industry is no exception, since high-performance computing technologies, artificial intelligence algorithms, methods for collecting, processing and storing information are actively used to solve problems of enhanced oil recovery. Deep learning has made remarkable strides in a variety of applications, but its use for solving partial differential equations has only recently emerged. In particular, it is possible to replace traditional numerical methods with a neural network that approximates the solution of a partial differential equation. Physics-informed neural networks (PINN) embed partial differential equations in the loss function of a neural network using automatic differentiation. The method of automatic differentiation for calculating derivatives of network outputs with respect to network inputs is considered. Given the fact that a neural network is a composition function, automatic differentiation repeatedly applies the chain rule to calculate derivatives. This article discusses the implementation of physics-informed neural networks for solving the Buckley-Leverett model for two-phase flow in porous media. This paper considers the prediction of fluid flow in a porous medium using PINN. The architecture of physics-informed neural networks for solving the Buckley-Leverett model is built. The tensorflow deep learning library for PINN implementations is considered. A comparison of the numerical algorithm with the solution of physic-informed neural networks with optimally selected hyperparameters for the problem under consideration is carried out. Gradient optimizers like Adam, L-BFGS and gradient descent are considered to minimize the loss function of a neural network. PINNs have been tested using multiple hidden layers and neurons for best results. The results of numerical solution and prediction of the PINN neural network for solving the Buckley-Leverett equation are obtained. It was found that PINNs are able to predict the direction of the solution quite well and the results are close to the solution of the numerical algorithm.