Connectivity of material constituents govern the transport, mechanical, chemical, thermal, and electromagnetic properties. Energy storage, recovery and conversion depends on connectivity of material constituents. High-resolution microscopy image of a material captures the microstructural aspects describing the distribution, topology and morphology of various material constituents. In this study, six metrics are developed and tested for quantifying the connectivity of material constituents as captured in the high-resolution microscopy images. The six metrics are as follows: geobody connectivity metric based on percolation theory, Euler number based on integral geometry, indicator variogram based on geostatistics, two-point cluster function, connectivity function, and travel-time histogram based on fast marching method. The performances of these metrics are tested on 3000 images representing six levels of connectivity. The metrics are also evaluated on the organic constituent captured in the scanning electron microscopy (SEM) images of organic-rich shale samples. The connectivity function and travel-time histogram based on fast-marching method are the most robust and reliable metrics. Material constituents exhibiting high connectivity result in large values of average travel time computed using fast-marching method and average connected distance computed using connectivity function. The proposed metrics will standardize and speed-up the analysis of connectivity to facilitate the characterization of properties and processes of energy-relevant materials.

1. Abstract Wave propagation and diffusive transport phenomena could work as evidence of the mechanical discontinuities in material. For the problem of poor efficiency of the existing fracture simulation methods, this paper proposes crack-bearing material characterization approach by processing wave travel-time using seven data-driven classification techniques. To that end, we perform classification models to predict discontinuities orientation, dispersion, and spatial distribution prediction by learning from the different-waves simulation model. The travel-time measured by multiple sensors placed around the material perform as our input data of machine learning method. As a result, this work found that machine learning models exhibit best classification performance on classifying crack dominant orientations. Combination of compressional wave and shear wave are enough to capture the crack information in the material, however, the pressure diffusion also able to optimize our algorithms. Voting classifier and gradient boosting classifier perform the best for purposes of characterization. When compare the performance of different mechanical discontinuities, embedded closed discontinuities shows high accuracy than open discontinuities on the classification models.

Machine learning has led to improvements in the efficiency and efficacy of subsurface engineering and characterization efforts that benefits the hydrocarbon and geothermal exploration and production as well as in carbon geo-sequestration. There have been rapid increases in sensor deployment, data acquisition, data storage, and data processing for purposes of geothermal/fossil energy development and exploration along with carbon geo-sequestration. This has promoted large-scale development of data-driven methods, machine learning and data analytics workflows to find and extract energy and material resources from the subsurface earth. Subsurface data ranges from nano-scale to kilometer-scale passive as well as active measurements in the form of physical fluid/solid samples, images, 3D scans, time-series data, waveforms, and depth-based multi-modal signals representing various physical phenomena, ranging from transport, chemical, mechanical, electrical, and thermal properties, to name a few. Integration of such varied multimodal, multipoint, time-varying data sources being acquired at varying scales, rates, resolutions, and volumes mandates robust machine learning methods to better characterize and engineer the subsurface earth. This review paper lays out popular machine learning applications in exploration, extraction, and recovery of subsurface energy resources, primarily in hydrocarbon exploration and production industry with potential applications in geothermal energy production and carbon geo-sequestration.

Mechanical wave transmission through a material is influenced by the mechanical discontinuity in the material. The propagation of embedded discontinuities can be monitored by analyzing the wave-transmission measurements recorded by a multipoint sensor system placed on the surface of the material. In our study, robust monitoring of the propagation of a mechanical discontinuity is achieved by using supervised learning followed by data-driven causal discovery to process the multipoint waveform measurements resulting from a single impulse source. The new data-driven causal-discovery workflow jointly processes the nine 25-µs waveforms measured by the multipoint sensor system comprising 9 sensors. The proposed workflow can monitor the propagation of mechanical discontinuity through three stages, namely initial, intermediate, and final stages. The workflow considers the wave attenuation, dispersion and multiple wave-propagation modes. Among various feature reduction techniques ranging from decomposition methods to manifold approximation methods, the features derived based on statistical parameterizations of the measured waveforms lead to reliable monitoring that is robust to changes in precision, resolution, and signal-to-noise ratio of the multipoint sensor measurements. Causal signatures have been successfully identified in the multipoint waveform measurements. The numbers of zero-crossing, negative-turning, and positive in the waveforms are the strongest causal signatures of crack propagation. Higher order moments of the waveforms, such as variance, skewness and kurtosis, are also strong causal signatures of crack propagation. The newly discovered causal signatures confirm that the statistical correlations and conventional feature rankings are not always statistically significant indicators of causality.