Backpropagation neural networks for solving gas flow in porous media
Adrianto, Zuher Syihab, Sutopo and Taufan Marhaendrajana

Department of Petroleum Engineering, Faculty of Mining and Petroleum Technology, Bandung Institute of Technology

Abstract

Reservoir modeling is an essential tool in the petroleum industry to predict the dynamics of fluids in the subsurface over a period of time. Darcy^s law and the continuity equation serve as the governing equations for reservoir simulation. Discretization techniques transform the continuous partial differential equations (PDEs) into a large system of algebraic equations, and the classic iterative Newton method typically solves them. Despite its widespread use and success in many situations, the Newton method has several drawbacks or restrictions. These include the computer time required to generate and inverse the Jacobian matrix, the memory required to store it, and the challenges in achieving convergence due to the sensitivity of the initial estimate and the presence of large nonlinearities.
This study presents an alternative approach to solving the system of linear equations that arises from hydrocarbon reservoir modeling. This linear solver employs feed-forward neural networks and consists of an input layer, two hidden layers, and an output layer. Later, we use this proposed solver to solve one-dimensional gas flow problems in a porous medium, and we verify its accuracy with a solution from the classic Newton method.
The pressure solution generated by the neural network-based solver resembles the Newton method solution. The maximum absolute error for the homogeneous model is around 10^{-7} psi, whereas for the heterogeneous model, it is around 10^{-8} psi. The simulation results show that the learning rate parameter in networks influences convergence speed and accelerates weight updates. However, excessively high learning rates can cause weights to overshoot optimal values, causing instability and poor performance.

Keywords: neural networks, linear solver, reservoir simulation

Topic: Minisymposia Differential Equations