Abstract
In recent years, convolutional neural networks (CNNs) have experienced an increasing interest in their ability to perform a fast approximation of effective hydrodynamic parameters in porous media research and applications. This paper presents a novel methodology for permeability prediction from micro-CT scans of geological rock samples. The training data set for CNNs dedicated to permeability prediction consists of permeability labels that are typically generated by classical lattice Boltzmann methods (LBM) that simulate the flow through the pore space of the segmented image data. We instead perform direct numerical simulation (DNS) by solving the stationary Stokes equation in an efficient and distributed-parallel manner. As such, we circumvent the convergence issues of LBM that frequently are observed on complex pore geometries, and therefore, improve the generality and accuracy of our training data set. Using the DNS-computed permeabilities, a physics-informed CNN (PhyCNN) is trained by additionally providing a tailored characteristic quantity of the pore space. More precisely, by exploiting the connection to flow problems on a graph representation of the pore space, additional information about confined structures is provided to the network in terms of the maximum flow value, which is the key innovative component of our workflow. The robustness of this approach is reflected by very high prediction accuracy, which is observed for a variety of sandstone samples from archetypal rock formations.
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Data Availability
The CNN code used in this paper is available as part of the porous media numerical toolkit RTSPHEM [17] on GitHub.
Change history
23 March 2023
A Correction to this paper has been published: https://doi.org/10.1007/s10596-023-10196-4
Abbreviations
- CNN:
-
Convolutional neural network
- DNS:
-
Direct numerical simulation
- DOF:
-
Degrees of freedom
- FFN:
-
Feed forward network
- LBM:
-
Lattice Boltzmann method
- μCT:
-
Microcomputed tomography
- MSE:
-
Mean squared error
- PhyCNN:
-
Physics-informed convolutional neural network
- ReLU:
-
Rectified linear unit
- REV:
-
Representative elementary volume
- SGD:
-
Stochastic gradient descent
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Acknowledgements
S. Gärttner and A. Meier were supported by the DFG Research Training Group 2339 Interfaces, Complex Structures, and Singular Limits. N. Ray was supported by the DFG Research Training Group 2339 Interfaces, Complex Structures, and Singular Limits and the DFG Research Unit 2179 MadSoil. F. Frank was supported by the Competence Network for Scientific High Performance Computing in Bavaria (KONWIHR). We further thank Martin Burger for insightful discussions and Fabian Woller for assisting with the MFEM implementation.
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Gärttner, S., Alpak, F.O., Meier, A. et al. Estimating permeability of 3D micro-CT images by physics-informed CNNs based on DNS. Comput Geosci 27, 245–262 (2023). https://doi.org/10.1007/s10596-022-10184-0
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DOI: https://doi.org/10.1007/s10596-022-10184-0