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Accounting for the morphology of shale formations, which represent highly heterogeneous porous media, is a difficult problem. Although two- or three-dimensional images of such formations may be obtained and analyzed, they either do not capture the nanoscale features of the porous media, or they are too small to be an accurate representative of the media, or both. Increasing the resolution of such images is also costly. While high-resolution images may be used to train a deep-learning network in order to increase the quality of low-resolution images, an important obstacle is the lack of a large number of images for the training, as the accuracy of the network's predictions depends on the extent of the training data. Generating a large number of high-resolution images by experimental means is, however, very time consuming and costly, hence limiting the application of deep-learning algorithms to such an important class of problems. To address the issue we propose a novel hybrid algorithm by which a stochastic reconstruction method is used to generate a large number of plausible images of a shale formation, using very few input images at very low cost, and then train a deep-learning convolutional network by the stochastic realizations. We refer to the method as hybrid stochastic deep-learning (HSDL) algorithm. The results indicate promising improvement in the quality of the images, the accuracy of which is confirmed by visual, as well as quantitative comparison between several of their statistical properties. The results are also compared with those obtained by the regular deep learning algorithm without using an enriched and large dataset for training, as well as with those generated by bicubic interpolation., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Although the morphology of porous membranes is the key factor in determining their flow, transport and separation properties, a general relation between the morphology and the physical properties has been difficult to identify. One promising approach to develop such a relation is through the application of a machine-learning (ML) algorithm to the problem. Over the last decade significant developments in the development of the ML approaches have led to many breakthroughs in various fields of science and engineering, but their application to porous media has been very limited. In this paper, we develop a deep network for predicting flow properties of porous membranes based on their morphology. The predicted properties include the spatial distributions of the fluid pressure and velocity throughout the entire membranes, provided that the deep network is properly trained by using high-resolution images of the membranes and the pressure and velocity distributions in their pore space at certain points in time. The network includes a residual U-net for developing a mapping between the input and output images, as well as a recurrent network for identifying physical correlations between the output data at various times. The results demonstrate that the deep network provides highly accurate predictions for the properties of interest. Thus, such a network may be used for predicting flow and transport properties of many other types of porous materials, as well as designing membranes for a specific application. Image 1 • A new machine learning method is proposed for modeling of flow in nano-membrane systems. • The Navier-Stokes equations are solved, and the flow properties are estimated. • The problem is considered as a dynamic system. • The flow properties are computed and compared at several time-steps. • The predictions are compared with the numerical results. [ABSTRACT FROM AUTHOR]

• The important methods of data mining and machine learning are reviewed and discussed. • The machine learning methods are reviewed for various applications in environmental science. • Deep learning methods for various problems and scales are discussed. • Several problems, the existing solutions, and potential directions are discussed. In recent years significant breakthroughs in exploring big data, recognition of complex patterns, and predicting intricate variables have been made. One efficient way of analyzing big data, recognizing complex patterns, and extracting trends is through machine-learning (ML) algorithms. The field of porous media, and more generally geoscience, have also witnessed much progress, and recent progress in developing various ML techniques have benefitted various problems in porous media and geoscience across disparate scales. Thus, it is becoming increasingly clear that it is imperative to adopt advanced ML methods for the problems in porous media and geoscience because they enable researchers to solve many difficult problems. At the same time, one can use the already existing extensive knowledge of porous media to endow ML algorithms and develop novel physics-guided methods. The goal of this review paper is to provide the first comprehensive review of the recently developed methods in the ML algorithms and describe their application to porous media and geoscience. Thus, we review the basic concept of the ML and describe more advanced methods, known as deep-learning algorithms. Then, the application of such methods to various problems in porous media and geoscience, such as hydrological modeling, fluid flow in porous media, and (sub)surface characterization, are reviewed. We also provide a discussion of future directions in this rapidly developing field. [ABSTRACT FROM AUTHOR]

Percolation and fracture propagation in disordered solids represent two important problems in science and engineering that are characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold pc and formation of a macroscopic fracture network at the incipient fracture point (IFP). Percolation also represents the fracture problem in the limit of very strong disorder. An important unsolved problem is accurate prediction of physical properties of systems undergoing such transitions, given limited data far from the transition point. There is currently no theoretical method that can use limited data for a region far from a transition point pc or the IFP and predict the physical properties all the way to that point, including their location. We present a deep neural network (DNN) for predicting such properties of two- and three-dimensional systems and in particular their percolation probability, the threshold pc, the elastic moduli, and the universal Poisson ratio at pc. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly pc, even though the training data were for the state of the systems far from pc. This opens up the possibility of using the DNN for predicting physical properties of many types of disordered materials that undergo phase transformation, for which limited data are available for only far from the transition point. [ABSTRACT FROM AUTHOR]

Time and cost are two main hurdles to acquiring a large number of digital image I of the microstructure of materials. Thus, use of stochastic methods for producing plausible realizations of materials' morphology based on one or very few images has become an increasingly common practice in their modeling. The accuracy of the realizations is often evaluated using two-point microstructural descriptors or physics-based modeling of certain phenomena in the materials, such as transport processes or fluid flow. In many cases, however, two-point correlation functions do not provide accurate evaluation of the realizations, as they are usually unable to distinguish between high- and low-quality reconstructed models. Calculating flow and transport properties of the realization is an accurate way of checking the quality of the realizations, but it is computationally expensive. In this paper a method based on machine learning is proposed for evaluating stochastic approaches for reconstruction of materials, which is applicable to any of such methods. The method reduces the dimensionality of the realizations using an unsupervised deep-learning algorithm by compressing images and realizations of materials. Two criteria for evaluating the accuracy of a reconstruction algorithm are then introduced. One, referred to as the internal uncertainty space, is based on the recognition that for a reconstruction method to be effective, the differences between the realizations that it produces must be reasonably wide, so that they faithfully represent all the possible spatial variations in the materials' microstructure. The second criterion recognizes that the realizations must be close to the original I and, thus, it quantifies the similarity based on an external uncertainty space. Finally, the ratio of two uncertainty indices associated with the two criteria is considered as the final score of the accuracy of a stochastic algorithm, which provides a quantitative basis for comparing various realizations and the approaches that produce them. The proposed method is tested with images of three types of heterogeneous materials in order to evaluate four stochastic reconstruction algorithms. [ABSTRACT FROM AUTHOR]

[Display omitted] • A hybrid method is proposed to reconstruct large and high-resolution digital rocks. • CycleGAN is presented to fuse multiresolution structures into the final model. • The hybrid method is validated based on heterogeneous samples. Digital rock physics (DRP) has become an effective tool to predict the petrophysical properties of rocks and reveal the mass transport mechanisms in porous media. Accurate prediction of the physical properties of heterogeneous rocks based on DRP requires 3D high-resolution (HR) and large-view images. It is, however, extremely challenging to acquire such images since the current imaging technologies cannot resolve the dilemma between the high resolution and large field of view and we often end up with low-resolution (LR) images but with a large field of view or HR images with a small field of view. Moreover, available HR images are limited and always unpaired with accessible LR images, so it is of great difficulty to train a deep learning model based on the limited unpaired images. To address these issues, we used a fast and stabilized generative adversarial network (FastGAN) to synthesize thousands of plausible LR and HR images based on ∼100 unpaired images. Taking the synthetic images as training images, we then utilized a cycle-consistent GAN (CycleGAN) to reconstruct the 3D HR large-scale digital rocks by assimilating the fine-scale structures from 2D HR images into 3D LR images. The accuracy of the proposed method (FastGAN-CycleGAN) is validated by comparing the porosity, pore size distribution, multiple-point correlation, and permeability of the reconstructed digital rocks of shale and carbonate samples with laboratory measurements. The proposed unsupervised approach does not require prior image processing knowledge. Furthermore, it can be also applied to other types of images such as magnetic resonance and fluorescence microscopy images in the future. [ABSTRACT FROM AUTHOR]