Uncertainty quantification and inverse modeling for subsurface flow in 3D heterogeneous formations using a theory-guided convolutional encoder-decoder network

•TgCNN is used for surrogate modeling of 3D subsurface flow problems.•Dynamic pressure estimation can be obtained given stochastic permeability fields.•Uncertainty quantification and inverse modeling tasks are studied.•TgCNN-based surrogate models show improved efficiency with high accuracy. We buil...

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Bibliographic Details
Published in:Journal of hydrology (Amsterdam) Vol. 613; p. 128321
Main Authors: Xu, Rui, Zhang, Dongxiao, Wang, Nanzhe
Format: Journal Article
Language:English
Published: Elsevier B.V 01.10.2022
Subjects:
Convolutional neural network
equations
Inverse problem
mathematical models
permeability
Subsurface flow
Surrogate modeling
Theory-guided machine learning
uncertainty
Uncertainty quantification
Uncertainty quantification
Subsurface flow
Surrogate modeling
Convolutional neural network
Theory-guided machine learning
Inverse problem
ISSN:0022-1694, 1879-2707
Online Access:Get full text
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Summary:•TgCNN is used for surrogate modeling of 3D subsurface flow problems.•Dynamic pressure estimation can be obtained given stochastic permeability fields.•Uncertainty quantification and inverse modeling tasks are studied.•TgCNN-based surrogate models show improved efficiency with high accuracy. We build surrogate models for dynamic 3D subsurface single-phase flow problems with multiple vertical producing wells. The surrogate model provides efficient pressure estimation of the entire formation at any timestep given a stochastic permeability field, arbitrary well locations and penetration lengths, and a timestep matrix as inputs. The well production rate or bottom hole pressure can then be determined based on Peaceman’s formula. The original surrogate modeling task is transformed into an image-to-image regression problem using a convolutional encoder-decoder neural network architecture. The residual of the governing flow equation in its discretized form is incorporated into the loss function to impose theoretical guidance on the model training process. As a result, the accuracy and generalization ability of the trained surrogate models are significantly improved compared to those of fully data-driven models. They are also shown to possess flexible extrapolation ability to permeability fields with different statistics. The surrogate models are used to conduct uncertainty quantification considering a stochastic permeability field, as well as to infer unknown permeability information based on limited well production data and observation data of formation properties. Results are shown to be in close accordance with those of traditional numerical simulation tools, but computational efficiency is dramatically improved.
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ISSN:0022-1694
1879-2707
DOI:10.1016/j.jhydrol.2022.128321