Source-linked AI summary
Seeing Permeability From Images: Fast Prediction with Convolutional Neural Networks
Jin-Long Wu, Xiao-Long Yin, Heng Xiao
TL;DR
Computing permeability from pore-scale images is accurate but expensive, motivating a faster surrogate model for geometry-dependent transport. The paper generates synthetic media, obtains simulation-based training data, and trains a physics-informed CNN using images plus physical quantities. Across varied synthetic porosities and dilated-pore geometries, most predictions have less than 10% error, while real-rock applicability remains unresolved.
Problem
Direct pore-scale simulations provide accurate transport properties but are computationally very costly, creating a need for fast permeability prediction from pore geometry.
Method
The framework generates porous-media images, computes permeability with fluid-dynamics simulations, trains a physics-informed CNN, and predicts permeability for new images.
Results
Most predicted permeabilities for synthetic samples have less than 10% error compared with lattice Boltzmann simulations across varied porosities and dilated-pore fractions.
Takeaways & Limitations
Including porosity and specific surface area generally improves CNN permeability predictions, especially where dilated pores make Kozeny–Carman estimates unreliable.
Takeaways & Limitations
The study uses synthetic images, so its CNN performance cannot yet be projected to real rock geometries; different rock types may require separate training data.
Abstract
from arXiv · showhide
Fast prediction of permeability directly from images enabled by image recognition neural networks is a novel pore-scale modeling method that has a great potential. This article presents a framework that includes (1) generation of porous media samples, (2) computation of permeability via fluid dynamics simulations, (3) training of convolutional neural networks (CNN) with simulated data, and (4) validations against simulations. Comparison of machine learning results and the ground truths suggests excellent predictive performance across a wide range of porosities and pore geometries, especially for those with dilated pores. Owning to such heterogeneity, the permeability cannot be estimated using the conventional Kozeny-Carman approach. Computational time was reduced by several orders of magnitude compared to fluid dynamic simulations. We found that, by including physical parameters that are known to affect permeability into the neural network, the physics-informed CNN generated better results than regular CNN, however improvements vary with implemented heterogeneity.
1. Introduction
Image-based pore-scale studies need efficient ways to compute transport properties: direct simulations are accurate but costly, while neural networks offer a surrogate route for geometry-dependent permeability. The paper proposes a physics-informed CNN that combines images with porosity and specific surface area to improve prediction across varied porous media.
- Motivation: Direct pore-scale simulations solve microscopic transport equations on image-derived geometries but have very high computational costs.They can address single- and multiphase flow as well as reactive and non-reactive transport.
- Motivation: Permeability depends solely on pore geometry, motivating surrogate models that map pore images directly to physical properties.Such models could avoid direct simulations or network calculations when predicting permeability.
- Related work: Convolutional neural networks have been applied successfully to image classification and diverse science and engineering problems, including surrogate modeling.This prior use supports applying CNNs to image-based porous-media prediction.
- Contribution: The proposed physics-informed architecture combines image information with porosity and specific surface area in one neural network.The paper reports generally superior predictive performance to conventional CNNs, although improvements vary by case.
- Contribution: The physics-informed CNN predicts permeability to 10% accuracy for synthetic two-dimensional media across varied porosities, dilated-pore fractions, and dataset similarities.The evaluation covers a wide range of scenarios rather than a single pore geometry.
2. Methodology
The framework generates synthetic porous-media images, computes their permeabilities with lattice Boltzmann simulations, and trains CNN surrogates to predict permeability for new images. It combines image information with geometric properties and uses synthetic two-dimensional parameterized media, while extending the architecture toward three-dimensional applications.
- Framework overview: The workflow generates porous-media images, simulates their permeabilities, trains a physics-informed CNN, and predicts permeability for new samples.The training database consists of image–permeability pairs produced from synthetic samples and direct lattice Boltzmann simulations.
- Generation of training data: Synthetic two-dimensional images cover porosity and dilated-pore variability using Voronoi tessellations controlled by parameters N and λ.N controls polygon size and porosity, while λ removes cells to create larger pore spaces and increase porosity with specific surface area nearly unchanged.
- Generation of training data: λ > 0 produces permeability–porosity relations that are not well predicted by the Kozeny–Carman equation.The synthetic geometries span porosities from 0.08 to 0.39, and dilated pores create scattering in the φ–k relation.
- Permeability computation: Lattice Boltzmann simulations model strictly Stokes-regime flow through each generated geometry to obtain permeability.The simulations use a two-dimensional D2Q9 scheme with a multi-relaxation-time collision operator.
- CNN architecture: The physics-informed CNN combines image-derived features with porosity and specific surface area before producing permeability.The architecture uses convolutional and pooling layers followed by fully connected layers, with physical quantities introduced into a fully connected layer.
- Scope and extension: Applying the architecture to three-dimensional porous media would require 3-D convolution kernels, more coefficients, and more training data and computational cost.The study uses two-dimensional synthetic binary images; three-dimensional real-rock images are left for future work.
3. Numerical Experiments
Three numerical cases test permeability prediction across varying pore geometries and training conditions. Physics-informed CNN predictions generally outperform standard CNN and Kozeny–Carman when dilated pores create heterogeneous geometries.
- Case 1: Case 1 evaluates regular and physics-informed CNN predictions across samples with varying numbers of seeds and no dilated pores.Most regular-CNN predictions fall within ±10% error, while the physics-informed CNN improves agreement and approaches Kozeny–Carman predictions.
- Case 2: Case 2 tests generalization to λ = 0.05 samples using training data with λ = 0 and 0.1.The physics-informed CNN predicts within ±10% error, whereas Kozeny–Carman has relative errors over 200%.
- Case 3: Case 3 uses different seed counts between training and testing and compares physics-informed CNN predictions with Kozeny–Carman.Physics-informed CNN predictions mostly fall within ±10% of lattice Boltzmann ground truth, while Kozeny–Carman overestimates permeability for all testing samples.
- Quantitative evaluation: Across all three cases, physics-informed CNN has better prediction performance than standard CNN, although its improvement in case 2 is relatively marginal.R2 scores and mean squared errors provide the quantitative evaluation.
- Quantitative evaluation: Case 3 is more difficult than cases 1 and 2, and physics-informed CNN improves more over standard CNN than in case 2.Its lower R2 scores indicate larger prediction differences relative to the variation in ground-truth permeability.
4. Discussion
The CNN learns distinct image patterns associated with channels and dilated pores, helping explain its permeability predictions and advantage over Kozeny–Carman. However, the visualized features are qualitative, and performance cannot yet be projected to real-rock geometries.
- 4. Discussion: CNN filtered features separately represent pore paths and dilated pores, helping explain its better permeability prediction than Kozeny–Carman.Kozeny–Carman treats dilated-pore porosity like channel porosity and therefore significantly overestimates permeability.
- 4. Discussion: The learned features shown in Figure 8 provide only a qualitative visualization of CNN pattern recognition.CNN parameters are instead determined by minimizing training prediction error while using techniques such as dropout or sparsity to prevent overfitting.
- 4. Discussion: The study’s synthetic images do not correspond to real rocks, so CNN performance on real-rock geometries cannot yet be projected.Real porous media span several permeability orders of magnitude, whereas this study varied permeability by only one order of magnitude.
- 4. Discussion: Predicting different rock types may require realistic geometry-specific training data, potentially augmented with real images of known permeability.The paper suggests validating extrapolation with real-rock images when most training samples are synthetic.
5. Conclusion
The study proposes a physics-informed CNN framework that predicts permeability from pore-scale images using simulation-generated training data. It performs well across varied synthetic pore geometries, especially dilated pores, while operating much faster than direct simulations.
- 5. Conclusion: The framework generates porous-media images, computes training permeabilities with fluid-dynamics simulations, trains a physics-informed CNN, and predicts unseen images.The workflow uses simulated data to train and validate image-based permeability prediction.
- 5. Conclusion: Most predicted permeabilities have less than 10% error relative to lattice Boltzmann simulation results across synthetic images with varied porosity and dilated-pore fractions.The evaluation covers a wide range of porosities and micro-scale heterogeneity.
- 5. Conclusion: For images with dilated pores, the proposed model predicts permeability much better than the Kozeny–Carman estimate.The paper identifies these geometries as cases where Kozeny–Carman cannot be applied effectively.
- 5. Conclusion: CNN-based permeability prediction is orders of magnitude faster than direct lattice Boltzmann simulations.This supports fast prediction of porous-media physical properties within the demonstrated synthetic setting.