CNN-powered micro- to macro-scale flow modeling in deformable porous media

TL;DR

This study transfers micro-CT geometry to macroscopic transport by learning the deformation-dependent intrinsic permeability tensor $\mathbf{K}^S$ from Bentheimer sandstone images, using LBM-ground-truth data for supervision. It introduces three CNN architectures, including a physics-informed and a data-augmented transfer-learning variant, to predict $\mathbf{K}^S$ and $n^F$ across deformation states within the TPM framework. The results show high accuracy (≈0.98–0.99 $R^2$) on unseen data and demonstrate that synthetic data plus transfer learning can markedly improve training efficiency. The work paves the way for rapid, image-driven multiscale modeling of flow in deformable porous media with potential applications in geotechnical engineering, hydrology, and materials science.

Abstract

This work introduces a novel application for predicting the macroscopic intrinsic permeability tensor in deformable porous media, using a limited set of micro-CT images of real microgeometries. The primary goal is to develop an efficient, machine-learning (ML)-based method that overcomes the limitations of traditional permeability estimation techniques, which often rely on time-consuming experiments or computationally expensive fluid dynamics simulations. The novelty of this work lies in leveraging Convolutional Neural Networks (CNN) to predict pore-fluid flow behavior under deformation and anisotropic flow conditions. Particularly, the described approach employs binarized CT images of porous micro-structure as inputs to predict the symmetric second-order permeability tensor, a critical parameter in continuum porous media flow modeling. The methodology comprises four key steps: (1) constructing a dataset of CT images from Bentheim sandstone at different volumetric strain levels; (2) performing pore-scale simulations of single-phase flow using the lattice Boltzmann method (LBM) to generate permeability data; (3) training the CNN model with the processed CT images as inputs and permeability tensors as outputs; and (4) exploring techniques to improve model generalization, including data augmentation and alternative CNN architectures. Examples are provided to demonstrate the CNN's capability to accurately predict the permeability tensor, a crucial parameter in various disciplines such as geotechnical engineering, hydrology, and material science. An exemplary source code is made available for interested readers.

Figures (12)

• Figure 1: Overview of the major steps of the 2D CNN model to predict porous media effective properties (mainly the permeability) based on CT images. This includes the input, the output, dataset preparation, and model training.
• Figure 2: Illustration of data sampling (left). Mean and standard deviation of the porosity $n^F$ for each strain level $\varepsilon^V$ showing the deformation-dependency, while the 448 samples are considered (right).
• Figure 3: Illustration of data generation using LBM with prescribed pressure difference and no-slip/natural slip BCs (left). Mean and standard deviation of the intrinsic permeability components $K^S_{ii}$ for each strain level $\varepsilon^V$ showing the deformation-dependency and anisotropy (right).
• Figure 4: Architecture of the 3D CNN illustrating the flow of information from the input image through multiple convolutional layers, max pooling layers, and fully connected layers. The input image is a 3D volume with dimensions $256 \times 256 \times 32$, which passes through four convolutional layers (Conv1 to Conv4), each followed by max pooling to reduce spatial dimensions. After flattening, the feature maps are processed by two fully connected (FC) layers before generating the final output predictions ($n^F$, $K^S_{11}$, $K^S_{22}$, $K^S_{33}$).
• Figure 5: Model (1): Loss function value over the number of weight updates (Epoch).