No abstract

No abstract

No abstract

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.

Summary Direct simulation of flow on microcomputed-tomography (micro-CT) images of rocks is widely used for the calculation of permeability. However, direct numerical methods are computationally demanding. A rapid and robust method is proposed to solve the elliptic flow equation. Segmented micro-CT images are used for the calculation of local conductivity in each voxel. The elliptic flow equation is then solved on the images using the finite-volume method. The numerical method is optimized in terms of memory usage using sparse matrix modules to eliminate memory overhead associated with both the inherent sparsity of the finite-volume two-point flux-approximation (TPFA) method, and the presence of zero conductivity for impermeable grain cells. The estimated permeabilities for a number of sandstone and carbonate micro-CT images are compared against estimation of other solvers, and results show a difference of approximately 11%. However, the computational time is 80% lower. Local conductivity can furthermore be assigned directly into matrix voxels without a loss in generality, hence allowing the pore-scale finite-volume solver (PFVS) to be able to solve for flow in a permeable matrix as well as open pore space. This has been developed to include the effect of microporosity in flow simulation.