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

Abstract

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 ismore » 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.« less

Authors:

Wang, Kun  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-5000-3301"

Chen, Yu  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-2388-9143"

Mehana, Mohamed Zakaria Saad  ^[1];

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• Search DOE PAGES for ORCID "0000-0003-2472-2879"

Lubbers, Nicholas Edward  ^[1];

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Bennett, Kane  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-0822-6288"

Kang, Qinjun  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-4754-2240"

Viswanathan, Hari S.  ^[1];

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• Search DOE PAGES for ORCID "0000-0002-1178-9647"

Germann, Timothy Clark  ^[1]

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• Search DOE PAGES for ORCID "0000-0002-6813-238X"

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+ Show Author Affiliations

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

Publication Date:

Fri Oct 15 00:00:00 EDT 2021

Research Org.:

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

Sponsoring Org.:

USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:

1804349

Alternate Identifier(s):

OSTI ID: 1815191

Report Number(s):

LA-UR-20-27444
Journal ID: ISSN 0021-9991; TRN: US2212271

Grant/Contract Number:  

89233218CNA000001; 20190005DR

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Computational Physics

Additional Journal Information:

Journal Volume: 443; Journal ID: ISSN 0021-9991

Publisher:

Elsevier

Country of Publication:

United States

Language:

English

Subject:

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