Solution to the Two-Phase Flow in Heterogeneous Porous Media Based on Physics-Informed Neural Network

Data-driven machine learning models have weak physical interpretability and stability. Physics-Informed Neural Network (PINN) solves partial differential equations by adding partial differential equations describing physical laws and their definite solution conditions to the loss function. The physical laws of the reservoir fluids flow are clear. Aiming at the two-phase Darcy flow problem in the heterogeneous reservoir model, a surrogate model based on PINN is established, and the model control equation is added to the loss function, so that the model obeys both the training data and the governing equation constraint. The model proposed in this article calculates the loss function through the decoupled governing control equation of the implicit pressure explicit saturation method (IMPES), calculates the residual of the pressure equation based on the finite difference method, and uses the Peaceman well model to calculate the flow between the reservoir and the wellbore, thus improve continuity between neighboring grids in heterogeneous reservoirs. The results show that the PINN model agrees well with the calculation results of the reservoir numerical simulator, is insensitive to the number of observation points, has strong stability, and can be well used for simulation calculations and history matching.