Open Access

ARTICLE

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

by Jiangxia Han^1,2, Liang Xue^1,2,*, Ying Jia³, Mpoki Sam Mwasamwasa^1,2, Felix Nanguka⁴, Charles Sangweni⁵, Hailong Liu³, Qian Li³

1 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing, 102249, China
2 Department of Oil-Gas Field Development Engineering, College of Petroleum Engineering, China University of Petroleum, Beijing, 102249, China
3 Exploration Production Research Institute, Sinopec, Beijing, 102249, China
4 Ministry of Energy, Tanzania Petroleum Development Corporation, Tower, Dar es Salaam, 2774, Tanzania
5 Ministry of Energy Building, Petroleum Upstream Regulatory Authority in Tanzania (PURA), Dar es Salaam, 11439, Tanzania

* Corresponding Author: Liang Xue. Email:

(This article belongs to the Special Issue: Modeling of Fluids Flow in Unconventional Reservoirs)

Computer Modeling in Engineering & Sciences 2024, 138(2), 1323-1340. https://doi.org/10.32604/cmes.2023.031093

Received 13 May 2023; Accepted 10 July 2023; Issue published 17 November 2023

Abstract

Recent advances in deep neural networks have shed new light on physics, engineering, and scientific computing. Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots. The physics-informed neural network (PINN) is currently the most general framework, which is more popular due to the convenience of constructing NNs and excellent generalization ability. The automatic differentiation (AD)-based PINN model is suitable for the homogeneous scientific problem; however, it is unclear how AD can enforce flux continuity across boundaries between cells of different properties where spatial heterogeneity is represented by grid cells with different physical properties. In this work, we propose a criss-cross physics-informed convolutional neural network (CC-PINN) learning architecture, aiming to learn the solution of parametric PDEs with spatial heterogeneity of physical properties. To achieve the seamless enforcement of flux continuity and integration of physical meaning into CNN, a predefined 2D convolutional layer is proposed to accurately express transmissibility between adjacent cells. The efficacy of the proposed method was evaluated through predictions of several petroleum reservoir problems with spatial heterogeneity and compared against state-of-the-art (PINN) through numerical analysis as a benchmark, which demonstrated the superiority of the proposed method over the PINN.

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Keywords

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