Hybrid solver with deep learning for transport problem in porous media

In this work, a hybrid solver with deep learning is proposed for numerical modeling of fluid flow in porous media. The classical simulation procedure is complemented with a neural network model to obtain an initial guess for fluid saturation that is closer to the solution in the Newton–Raphson iterative algorithm. The simulation setup is a 3-dimensional immiscible two-phase flow with fluid motion caused by multiple production and injection wells. Approximation of the initial guess with a neural network model accelerates the numerical modeling up to 14% in terms of nonlinear iterations. Extensive experiments with dynamic and static reservoir features revealed that improving predictive accuracy does not necessarily improve fluid modeling. Different training procedures (e.g., different loss functions) and feature spaces (e.g., more past time steps used) can lead to better prediction quality but a higher number of nonlinear iterations. These results demonstrate that not only the closeness to the solution, but also the spatial distribution of residuals affects the “quality” of the starting point in Newton’s method.