Simulating fluid flow in complex porous materials by integrating the governing equations with deep-layered machines

Serveh Kamrava,Pejman Tahmasebi,Muhammad Sahimi

doi:10.1038/s41524-021-00598-2

Serveh Kamrava, Pejman Tahmasebi + Show 1 more

Open Access

https://doi.org/10.1038/s41524-021-00598-2

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Abstract

Fluid flow in heterogeneous porous media arises in many systems, from biological tissues to composite materials, soil, wood, and paper. With advances in instrumentations, high-resolution images of porous media can be obtained and used directly in the simulation of fluid flow. The computations are, however, highly intensive. Although machine learning (ML) algorithms have been used for predicting flow properties of porous media, they lack a rigorous, physics-based foundation and rely on correlations. We introduce an ML approach that incorporates mass conservation and the Navier–Stokes equations in its learning process. By training the algorithm to relatively limited data obtained from the solutions of the equations over a time interval, we show that the approach provides highly accurate predictions for the flow properties of porous media at all other times and spatial locations, while reducing the computation time. We also show that when the network is used for a different porous medium, it again provides very accurate predictions.

Highlights

Fluid flow and transport in heterogeneous porous media are of fundamental importance to the working of a wide variety of systems of scientific interest, as well as applications[1,2]
We propose an approach based on an machine learning (ML) method that incorporates in its training the governing equations for fluid flow in porous media, i.e., the mass conservation (MC) and the Navier–Stokes equations (NS)
We present and discuss calculations for the polymeric membrane

Summary

Introduction

Fluid flow and transport in heterogeneous porous media are of fundamental importance to the working of a wide variety of systems of scientific interest, as well as applications[1,2] Examples of such porous media include catalysts, membranes, filters, adsorbents, print paper, wood, nanostructured materials, and biological tissues, as well as soil and pavement, and oil, gas, and geothermal reservoirs. Such porous media are typically heterogeneous, with the heterogeneity manifesting itself in the shape, size, connectivity, and surface structure of the pores at small scales, and in the spatial variations of the porosity, permeability, and the elastic moduli at large length scales. Developing efficient predictive algorithms has always been an active area of research

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