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Driving Digital Rock towards Machine Learning: predicting permeability with Gradient Boosting and Deep Neural Networks
Oleg Sudakov, Evgeny Burnaev, Dmitry Koroteev
TL;DR
The paper asks whether machine learning can predict permeability from digitized rock images, addressing the need for fast surrogate models alongside physical modeling. It trains models on image-derived descriptors and simulated permeability, comparing engineered and deep-learning approaches. The study reports significant potential for data-driven image-based permeability prediction and describes the approach as fast and scalable, while cautioning that the results are limited to a given sandstone sample and depend on physics-based models.
Problem
The study addresses whether machine learning can provide fast surrogate models for predicting permeability from digitized rock images.
Method
The study trains permeability predictors from image-derived features, including deep-learning descriptors, using physical-modeling results as targets.
Results
The results demonstrate significant potential for data-driven image-based permeability prediction, with the approach described as fast and scalable.
Takeaways & Limitations
The study supports developing data-driven permeability-prediction models for Digital Rock technology.
Takeaways & Limitations
The reported predictive results correspond to a given sandstone sample and depend on physics-based models for the training targets.
Abstract
from arXiv · showhide
We present a research study aimed at testing of applicability of machine learning techniques for prediction of permeability of digitized rock samples. We prepare a training set containing 3D images of sandstone samples imaged with X-ray microtomography and corresponding permeability values simulated with Pore Network approach. We also use Minkowski functionals and Deep Learning-based descriptors of 3D images and 2D slices as input features for predictive model training and prediction. We compare predictive power of various feature sets and methods. The later include Gradient Boosting and various architectures of Deep Neural Networks (DNN). The results demonstrate applicability of machine learning for image-based permeability prediction and open a new area of Digital Rock research.
1. Introduction and Justification
The study applies machine learning to Digital Rock Physics to build fast surrogate models for image-based permeability prediction. It compares engineered descriptors and deep-learning approaches, finding that VGG-16-derived descriptors outperform Minkowski-functional features, while CNNs achieve equally accurate results without manual feature engineering.
- Motivation: Digital Rock Physics combines rock imaging and computation to estimate properties such as permeability from three-dimensional pore representations.Micro-scale X-ray computed tomography enables non-destructive imaging of internal rock structure.
- Motivation: The study aims to build fast surrogate models that predict permeability from physical-modeling results.The target is permeability prediction based on digitized rock images and corresponding physical simulations.
- Approach and findings: VGG-16 descriptors extracted from 2D layers and reduced to a low-dimensional representation outperform Minkowski functionals as input features.The descriptors are used to compute sample permeability from the slices composing each 3D image.
- Approach and findings: End-to-end convolutional neural networks simultaneously extract features and perform permeability regression without manual feature engineering.The paper reports that this approach provides equally accurate results.
2. Data Acquisition
The dataset consists of segmented Berea sandstone images divided into 9261 independent 100 × 100 × 100 voxel cubes. Each cube is paired with permeability computed using pore-scale network modeling under Stokes-flow assumptions.
- Sample and segmentation: A segmented Berea sandstone sample was represented as a 400 × 400 × 400 binary voxel image with 5.345 µm voxel size.Rock voxels were encoded as 0 and pore voxels as 1.
- Sample and segmentation: The sample was divided into smaller voxel cubes using a 15-voxel shift, producing 9261 samples that retain geometrical properties of the parent rock.Each smaller image was treated as an independent rock image.
- Permeability simulation: Pore-scale network modeling paired with OpenPNM was used to compute initial permeability values for the voxel cubes.The network model represents rock geometry with spherical pores and cylindrical throats.
- Permeability simulation: Permeability was computed using Darcy's law while assuming Stokes flow and negligible advective inertial forces relative to viscous forces.The network representation was used to calculate permeability for each cut sample.
- Permeability simulation: The resulting dataset contains 9261 100 × 100 × 100 voxel cubes with corresponding permeability values measured in millidarcies.The calculations also produced 9261 network models.
3. Regression on Generated Features
The paper evaluates regression from network, Minkowski-functional, rescaled-functional, and VGG-PCA descriptors using gradient boosting and deep neural networks. It also examines end-to-end neural approaches and reports that some feature groups are inferior to others for the studied sample.
- Feature generation: Three feature-generation approaches were considered: network-model characteristics, Minkowski functionals, and descriptors extracted from 2D image slices.The generated features are used for regression-based permeability prediction.
- Results: The network-characteristic approach proved inferior to the other approaches for the evaluated permeability-prediction setting.The reported comparison concerns the studied sandstone sample and XgBoost model.
- Feature generation: Minkowski functionals encode volume, area, mean breadth, and Euler-Poincaré characteristic as additive morphological measures.For voxel images, their computation can be reduced to enumerating local open voxels, faces, and edges.
- Regression methods: Gradient boosting and deep neural networks were used to assess the predictive power of the generated feature groups.XgBoost hyperparameters were selected by grid search using a hold-out validation subset and the ABSq metric.
4. End-to-End Regression
The section describes CNN-based end-to-end regression for permeability prediction from 2D slices and 3D rock samples. It contrasts 2D and 3D convolutions, emphasizing how filters capture spatial structure and neighboring-layer information.
- The study assesses end-to-end convolutional neural networks for permeability regression using individual 2D slices and whole 3D rock samples.
- CNNs use convolutional and pooling layers whose filters learn patterns from local receptive fields while preserving spatial relationships.A filter computes weighted products over an input subset, then passes on their sum.
- Spatial structure matters because porosity depends strongly on pore number and shape, making distance-sensitive voxel processing valuable for local and global rock structure.
- 2D convolutional neural networks: The 2D CNN treats the 100 layers of a 3D sample as input channels, then applies convolutions, max-pooling, and fully connected layers to calculate permeability.
- 3D convolutional neural networks: 3D CNNs use 3D filters that integrate local information across all three dimensions, including neighboring layers, matching the three-dimensional nature of rock pores.
5. Model Evaluation and Results
The study evaluates feature sets and machine-learning approaches for permeability prediction, including XgBoost, MLPs, and 2D and 3D CNNs. Logarithmic permeability, feature combinations, and the ABSq error metric are examined, with 3D CNNs performing best overall.
- Evaluation criteria: ABSq compares prediction error with the variability of true permeability values, providing more information than conventional mean squared error.The metric uses true and predicted permeability values together with percentile-based normalization.
- XgBoost evaluation: XgBoost models were evaluated across selected feature groups, with the best combination reported as the final row for each method.The evaluated descriptors include VGG-PCA, network features, and Minkowski functionals for an X-rescaled cube.
- XgBoost evaluation: Logarithmic permeability improved some prediction results, while VGG-PCA features performed much better with logarithmic than usual permeability.The cause of VGG-PCA's poorer performance for usual permeability was not examined because it would require discussion of VGG-16 specifics beyond the article's scope.
- Deep neural networks: MLP experiments compared three restricted feature-group combinations and selected the best architecture for each combination.The combinations included VGG-PCA, selected Minkowski functionals, and their combination; the search was restricted to reduce neural-network training time.
- Deep neural networks: Minkowski functionals appeared to benefit from batch normalization, whereas adding VGG-PCA descriptors reduced prediction error but the best result used them separately.The authors attribute the additional error from combined features to insufficient training time to eliminate excess information from the Minkowski functionals.
6. Conclusions and Discussion
The study demonstrates potential for fast, scalable machine-learning prediction of rock permeability and related petrophysical properties. Future progress depends on richer inputs, physics-driven pore-scale modeling, and improved training-data and model-design strategies.
- Machine learning shows significant potential for image-based permeability prediction in Digital Rock applications.
- The data-driven approach is described as extremely fast, scalable, and potentially transformative for Digital Rock technology.
- Prediction may extend beyond single-phase permeability to relative phase permeabilities and other properties relevant to petrophysics, geology, and field development.
- Higher predictive power may require input information on mineral distribution, wettability, intergrain contacts, and pore fluids.
- Deep Learning may support prediction of fluid-displacement dynamics, not only static characteristics of digitized rock samples.
- Physics-driven pore-scale modeling remains necessary because machine learning for image-based permeability prediction requires physics-based models and training data.
- Future work includes more efficient DNNs, regression ensembles, improved parameter initialization, multi-fidelity modeling, and adaptive experimental design for training-sample generation.