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Digital rocks obtained from high-resolution micro-computed tomography (micro-CT) imaging has quickly emerged as a powerful tool for studying pore-scale transport phenomena in petroleum engineering. In such frameworks, digital rock analysis usually carries the problematic aspect of segmenting greyscale images into different phases for quantifying many physical properties. Fine pore structures, such as small rock fissures, are usually lost during segmentation. In addition, user bias in this process can lead to significantly different results. An alternative approach based on deep learning is proposed. Convolutional Neural Networks (CNN) are utilized to rapidly predict several porous media properties from 2D greyscale micro-computed tomography images in a supervised learning frame. A dataset of greyscale micro-CT images of three different sandstones species is prepared for this study. The image dataset is segmented, and pore networks are extracted to compute porosity, coordination number, and average pore size for training and validating our model predictions. The greyscale images (input) and the computed properties (output) are uploaded to a deep neural network for training and validation in an end-to-end regression scheme. Overall, our model estimates porosity, coordination number, and average pore size with an average error of 0.05, 0.17, and 1.8μm, respectively. Training wall-time and prediction error analysis are also discussed. This is a first step to use artificial intelligence and machine learning methods for the robust prediction of porous media properties from unprocessed image-driven data.

Summary X-ray imaging of porous media has revolutionized the interpretation of various microscale phenomena in subsurface systems. The volumetric images acquired from this technology, known as digital rocks (DR), make it a suitable candidate for machine learning and computer-vision applications. The current routine DR frameworks involving image processing and modeling are susceptible to user bias and expensive computation requirements, especially for large domains. In comparison, the inference with trained machine-learning models can be significantly cheaper and computationally faster. Here we apply two popular convolutional neural network (ConvNet) architectures [residual network (ResNet) and ResNext] to learn the geometry of the pore space in 3D porous media images in a supervised learning scheme for flow-based characterization. The virtual permeability of the images to train the models is computed through a numerical simulation solver. Multiple ResNet variants are then trained to predict the continuous permeability value (regression). Our findings demonstrate the suitability of such networks to characterize volume images without having to resort to further ad-hoc and complex model adjustments. We show that training with richer representation of pore space improves the overall performance. We also compare the performance of the models statistically based on multiple metrics to assess the accuracy of the regression. The model inference of permeability from an unseen sandstone sample is executed on a standard workstation in less than 120 ms/sample and shows a score of 0.87 using explained variance score (EVS) metric, a mean absolute error (MAE) of 0.040 darcies, and 18.9% relative error in predicting the value of permeability compared to values acquired through simulation. Similar metrics are obtained when training with carbonate rock images. The training wall time and hyperparameters setting of the model are discussed. The findings of this study demonstrate the significant potential of machine learning for accurate DR analysis and rock typing while leveraging automation and scalability.

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Reliable quantitative analysis of digital rock images requires precise segmentation and identification of the macroporosity, sub-resolution porosity, and solid\mineral phases. This is highly emphasized in heterogeneous rocks with complex pore size distributions such as carbonates. Multi-label segmentation of carbonates using classic segmentation methods such as multi-thresholding is highly sensitive to user bias and often fails in identifying low-contrast sub-resolution porosity. In recent years, deep learning has introduced efficient and automated algorithms that are capable of handling hard tasks with precision comparable to human performance, with application to digital rocks super-resolution and segmentation emerging. Here, we present a framework for using convolutional neural networks (CNNs) to produce super-resolved segmentations of carbonates rock images for the objective of identifying sub-resolution porosity. The volumes used for training and testing are based on two different carbonates rocks imaged in-house at low and high resolutions. We experiment with various implementations of CNNs architectures where super-resolved segmentation is obtained in an end-to-end scheme and using two networks (super-resolution and segmentation) separately. We show the capability of the trained model of producing accurate segmentation by comparing multiple voxel-wise segmentation accuracy metrics, topological features, and measuring effective properties. The results underline the value of integrating deep learning frameworks in digital rock analysis.