Backpropagation neural networks for solving gas flow equations in porous media

Abstract

This study proposes a backpropagation neural network (BPNN) as an alternative solver for nonlinear equations in gas flow simulation through porous media. Conventional solvers like the Newton-Raphson (N-R) method are accurate but may become inefficient for large-scale or heterogeneous systems. We develop a feedforward BPNN architecture with adaptive learning rates to solve discretized residual equations from the one-dimensional gas flow model. The methodology includes finite difference discretization and mapping the nonlinear algebraic system into a four-layer neural network. The BPNN solver is validated against the Newton method across various grid sizes and heterogeneous permeability-porosity distributions. Results show that BPNN achieves high accuracy, with maximum absolute errors (MAE) of only 0.241 psi in the homogeneous model and 0.0418 psi in the heterogeneous model. While the BPNN requires more iterations and longer computation time, especially for finer grids, it exhibits the ability to learn pressure patterns and improve efficiency over time. This approach demonstrates that BPNN can serve as a viable nonlinear solver in reservoir simulation, offering flexibility in handling nonlinearities while maintaining accuracy.