Physics-Informed Neural Networks Help Predict Fluid Flow in Porous Media

Abstract

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 203033, “Prediction of Fluid Flow in Porous Media Using Physics-Informed Neural Networks,” by Muhammad M. Almajid, SPE, and Moataz O. Abu-Alsaud, SPE, Saudi Aramco. The paper has not been peer reviewed. The authors of the complete paper write that the realm of reservoir engineering is considered to belong to the small-data regime because of the complex physical systems involved and the inherent uncertainty of the problems. The objective of the paper is to present a physics-informed neural network (PINN) technique that is able to use information from the fluid-flow physics and observed data to model the Buckley-Leverett problem. Fractional-Flow Theory Through their study of fluid displacement in sands, Buckley and Leverett introduced the fractional-flow theory. The theory estimates the rate at which one fluid displaces another and, consequently, the change in fluid saturations. The theory has been applied to many fluid-flow processes in porous media such as waterflooding, carbonated waterflooding, alcohol flooding, miscible flooding, steam flooding, foam flooding, low-salinity waterflooding, and carbon sequestration. The authors use the fractional-flow theory to simulate the displacement of water-filled porous media by gas, a process detailed in the complete paper. Once the Buckley-Leverett solution is obtained, the saturation profile of gas or water can be plotted at different times. It is noteworthy that a gas viscosity of 0.2 cp in this case is used so that the shock is visually apparent in the Buckley-Leverett solution. Additionally, having this large of a gas viscosity is justified. For instance, foamed gas can develop apparent viscosities orders of magnitude larger than unfoamed gas. Fig. 1 plots the gas-saturation profile along the dimensionless distance. Obtaining the corresponding water-saturation profiles is trivial. The authors compare the analytical solution and the PINN prediction with respect to water saturation.