CNN-PFVS: Integrating Neural Network and Finite Volume Models to Accelerate Flow Simulation on Pore Space Images

Super-Resolved Segmentation of X-ray Images of Carbonate Rocks Using Deep Learning

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.

Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media

The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains’ solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ($$>512^3$$ > 512 3 ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role.