A Fully Implicit Reservoir Simulation Using Physics Informed Neural Network

Abstract

The accuracy of simulation of multiphase flow in porous media is critical for reservoir management but is hindered by the nonlinear, coupled nature of governing equations and truncation errors in mesh-based numerical solvers. This study introduces a mesh-free, fully implicit Physics-Informed Neural Networks (PINN) framework for two-phase immiscible oil–water flow, where feedforward neural networks simultaneously approximate continuous pressure and saturation fields, embedding the governing PDEs, boundary, and initial conditions directly into the loss function. Three network topologies of single-row (N1), dual-row (N2), and branched-layer (NY) were tested across nine configurations which include variants of the networks. The novelty lies in the fully implicit PINN formulation of branched networks architectures with capability to reduce interference between pressure and saturation predictions. Benchmarking against the commercial simulator (Eclipse©) showed the NY achieved the best performance, with a mean squared error of less then 1.0×10-10. The N1 showed the ability to maintain stability at successive timesteps, while N2 models converged more slowly. The deep and narrow networks yielded higher accuracy but required almost double computation per iteration. Results demonstrate that even though with higher computational cost, the proposed PINN-based approach delivers high-fidelity solutions for complex reservoir problems without spatial meshing, offering a promising alternative to common numerical methods for both regular and irregular geometries.