A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

Journal Article · Fri Oct 15 00:00:00 EDT 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110526· OSTI ID:1804349

Wang, Kun ^[1]; Chen, Yu ^[1]; Mehana, Mohamed Zakaria Saad ^[1]; Lubbers, Nicholas Edward ^[1]; Bennett, Kane ^[1]; Kang, Qinjun ^[1]; Viswanathan, Hari S. ^[1]; Germann, Timothy Clark ^[1]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001
• OSTI ID: 1804349
• Alternate ID(s): OSTI ID: 1815191
• Report Number(s): LA-UR--20-27444
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 443; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CAE
Deep Learning
Lattice Boltzmann
Machine learning
Molecular dynamics
Permeability
Porous Media
Porous flow
Shale