Deducing Optimal Classification Algorithm for Heterogeneous Fabric

For defining the optimal machine learning algorithm, the decision was not easy for which we shall choose. To help future researchers, we describe in this paper the optimal among the best of the algorithms. We built a synthetic data set and performed the supervised machine learning runs for five different algorithms. For heterogeneous rock fabric, we identified Random Forest, among others, to be the appropriate algorithm.

Morphology Decoder to Predict Heterogeneous Rock Permeability with Machine Learning Guided 3D Vision

<p><a></a><a>Permeability has a dominant influence on the flow behavior of a natural fluid, and without proper quantification, biological fluids (Hydrocarbons) and water resources become waste. During the first decades of the 21^st century, permeability quantification from nano-micro porous media images emerged, aided by 3D pore network flow simulation, primarily using the Lattice Boltzmann simulator. Earth scientists realized that the simulation process holds millions of flow dynamics calculations with accumulated errors and high computing power consumption. Therefore, accuracy and efficiency challenges obstruct planetary exploration. To effic­­­iently, consistently predict permeability with high quality, we propose the Morphology Decoder. It is a parallel and serial flow reconstruction of machine learning-driven semantically segmented heterogeneous rock texture images of 3D X-Ray Micro Computerized Tomography (μCT) and Nuclear Magnetic Resonance (MRI). For 3D vision, we introduce controllable-measurable-volume as new supervised semantic segmentation, in which a unique set of voxel intensity corresponds to grain and pore throat sizes. The morphology decoder demarks and aggregates the morphologies' boundaries in a novel way to quantify permeability. The morphology decoder method consists of five novel processes, which we describe in this paper, these novel processes are (1) Geometrical: 3D Permeability Governing Equation, (2) Machine Learning: Guided 3D Properties Recognition of Rock Morphology, (3) Analytical: 3D Image Properties Integration Model for Permeability, (4) Experimental: MRI Permeability Imager, and (5) Morphology Decoder (the process that integrates the other four novel processes).</a></p>

Morphology Decoder to Predict Heterogeneous Rock Permeability with Machine Learning Guided 3D Vision

<p><a></a><a>Permeability has a dominant influence on the flow behavior of a natural fluid, and without proper quantification, biological fluids (Hydrocarbons) and water resources become waste. During the first decades of the 21^st century, permeability quantification from nano-micro porous media images emerged, aided by 3D pore network flow simulation, primarily using the Lattice Boltzmann simulator. Earth scientists realized that the simulation process holds millions of flow dynamics calculations with accumulated errors and high computing power consumption. Therefore, accuracy and efficiency challenges obstruct planetary exploration. To effic­­­iently, consistently predict permeability with high quality, we propose the Morphology Decoder. It is a parallel and serial flow reconstruction of machine learning-driven semantically segmented heterogeneous rock texture images of 3D X-Ray Micro Computerized Tomography (μCT) and Nuclear Magnetic Resonance (MRI). For 3D vision, we introduce controllable-measurable-volume as new supervised semantic segmentation, in which a unique set of voxel intensity corresponds to grain and pore throat sizes. The morphology decoder demarks and aggregates the morphologies' boundaries in a novel way to quantify permeability. The morphology decoder method consists of five novel processes, which we describe in this paper, these novel processes are (1) Geometrical: 3D Permeability Governing Equation, (2) Machine Learning: Guided 3D Properties Recognition of Rock Morphology, (3) Analytical: 3D Image Properties Integration Model for Permeability, (4) Experimental: MRI Permeability Imager, and (5) Morphology Decoder (the process that integrates the other four novel processes).</a></p>

DDA Simulation Study on Mechanical Failure of Heterogenous Rock

Heterogeneity is an important characteristic that affects the mechanical behavior of rock. In the present work, a statistical rock mesoheterogeneity model based on the Weibull distribution function is introduced into the discontinuous deformation analysis (DDA) method to simulate the mechanical failure of heterogeneous rock, in which the general heterogeneity degree is controlled by a heterogeneity index and the mechanical property of each subblock element is randomly assigned. Brazilian disc and uniaxial compressive rectangular specimens are simulated as examples. Results show that it is more reasonable to consider the heterogeneity of elasticity properties (the elastic modulus and Poisson’s ratio) and strength properties (the tensile strength, cohesion, and friction angle) simultaneously in the heterogeneity model. It is also shown that with a larger heterogeneity index, which means a lower degree of heterogeneity, the reproducibility of the macroscopic response curves of a specimen gets better, while the exact cracking always differs but with less scattered cracks, and the global fracturing failure pattern and mode are weakly influenced by the heterogeneity. Moreover, with the increase in the heterogeneity index, the macroscopic equivalent modulus and strength get larger and approach those of a homogeneous specimen. This work indicates the importance of heterogeneity for rock mechanical behaviors including the macroscopic equivalent response and the fracturing failure. By the subblock DDA method to simulate fracturing realistically, the fracturing failure process of heterogeneous rock can be successfully reproduced, which builds good foundation for the simulation study of heterogeneous rock fracturing in practical problems, e.g., coal and rock fracturing in fluidization mining in the future.

Multi-Dimensional Nuclear Magnetic Resonance Methods in the Inhomogeneous Magnetic Field

<p>This thesis introduces new NMR techniques which use the inhomogeneous internal magnetic fields present in the pore space of a porous medium exposed to an external magnetic field to obtain information about the pore size and heterogeneities of the the sample. Typically internal field inhomogeneities are regarded as unwanted due to their effect on various material properties such as relaxation and diffusion. However, in the experiments presented here, we choose samples specifically for their inhomogeneous internal fields and use multi-dimensional NMR methods and simulations to obtain our pore space and heterogeneity information. We first describe software developed to specifically simulate the internal magnetic field and diffusion through the pore space of a simple sphere pack system. This software generates a sphere pack and calculates the internal magnetic field generated by z-aligned magnetic dipoles placed at the center of each sphere. The internal magnetic field gradient is also calculated in the pore space. From there, a random walk method is developed and a realistic reflection off a sphere is introduced. We work through the development of this software and the mathematics behind the algorithms used. This simulation is used in all subsequent experimental chapters. We then use a two-dimensional exchange experiment to separate the susceptibility induced line broadening with the broadening caused by diffusion through the inhomogeneous field. We observe off-diagonal line broadening as the mixing time increases. We attempt to quantify this off-diagonal growth by selecting points on either side of the off-diagonal maximum and plotting their average as a function of mixing time. A biexponential fit to the average intensities with respect to mixing time results in a characteristic time and from that a characteristic length as a fraction of bead diameter. This experiment is simulated and a biexponential growth is also observed in the simulated off-diagonal with characteristic lengths comparable to experiment. To obtain a correlation length directly from experiment and not deduce one from a characteristic time, we add a spatial dimension to our exchange experiment in the form of a propagator dimension. This dimension allows us to select 2D spectra based on their Z-displacement. We observe off-diagonal growth due to both an increase in Z-displacement and an increase in mixing time. We move away from the biexponential fit and move to a relationship based on mixing time, effective diffusion, and Z-displacement to directly calculate a characteristic length. We see these same traits in the simulated data which agrees well with experiment. Lastly, we move away from exchange experiments and move to correlating the transverse relaxation time with the internal field offset. We find that there is correlation at large magnetic field offsets and small T2 times which appear to be indicative of sample heterogeneities. To confirm this we use a highly heterogeneous rock core sample which increases the correlations seen at the previous offsets and times. This experiment is more qualitative than the previous two as we do not have a concrete value for the heterogeneity of our samples. The simulation used throughout the thesis, while showing a definite correlation between field offset and T2 relaxation, is unable to accurately simulate the experiment and requires more development.</p>

Multi-Dimensional Nuclear Magnetic Resonance Methods in the Inhomogeneous Magnetic Field

<p>This thesis introduces new NMR techniques which use the inhomogeneous internal magnetic fields present in the pore space of a porous medium exposed to an external magnetic field to obtain information about the pore size and heterogeneities of the the sample. Typically internal field inhomogeneities are regarded as unwanted due to their effect on various material properties such as relaxation and diffusion. However, in the experiments presented here, we choose samples specifically for their inhomogeneous internal fields and use multi-dimensional NMR methods and simulations to obtain our pore space and heterogeneity information. We first describe software developed to specifically simulate the internal magnetic field and diffusion through the pore space of a simple sphere pack system. This software generates a sphere pack and calculates the internal magnetic field generated by z-aligned magnetic dipoles placed at the center of each sphere. The internal magnetic field gradient is also calculated in the pore space. From there, a random walk method is developed and a realistic reflection off a sphere is introduced. We work through the development of this software and the mathematics behind the algorithms used. This simulation is used in all subsequent experimental chapters. We then use a two-dimensional exchange experiment to separate the susceptibility induced line broadening with the broadening caused by diffusion through the inhomogeneous field. We observe off-diagonal line broadening as the mixing time increases. We attempt to quantify this off-diagonal growth by selecting points on either side of the off-diagonal maximum and plotting their average as a function of mixing time. A biexponential fit to the average intensities with respect to mixing time results in a characteristic time and from that a characteristic length as a fraction of bead diameter. This experiment is simulated and a biexponential growth is also observed in the simulated off-diagonal with characteristic lengths comparable to experiment. To obtain a correlation length directly from experiment and not deduce one from a characteristic time, we add a spatial dimension to our exchange experiment in the form of a propagator dimension. This dimension allows us to select 2D spectra based on their Z-displacement. We observe off-diagonal growth due to both an increase in Z-displacement and an increase in mixing time. We move away from the biexponential fit and move to a relationship based on mixing time, effective diffusion, and Z-displacement to directly calculate a characteristic length. We see these same traits in the simulated data which agrees well with experiment. Lastly, we move away from exchange experiments and move to correlating the transverse relaxation time with the internal field offset. We find that there is correlation at large magnetic field offsets and small T2 times which appear to be indicative of sample heterogeneities. To confirm this we use a highly heterogeneous rock core sample which increases the correlations seen at the previous offsets and times. This experiment is more qualitative than the previous two as we do not have a concrete value for the heterogeneity of our samples. The simulation used throughout the thesis, while showing a definite correlation between field offset and T2 relaxation, is unable to accurately simulate the experiment and requires more development.</p>

Study on the Effect of Amygdales on Mechanical Characteristics of Basalt Using the Combined Finite-Discrete Element Method

Amygdaloidal basalt, as a heterogeneous rock, is widely exposed at Baihetan hydropower station, China. The geometric effect of amygdales needs further studies and quantifying the shape, orientation, and statistical distribution of amygdales plays an important role in the laboratory and numerical experiments. Therefore, digital image processing (DIP) was first utilized to build a heterogeneous model (HM) to calibrate against the laboratory test results. Then, the heterogeneous models (HMs) with prescribed geometric features were generated by the inverse Monte-Carlo (IMC) algorithm. The uniaxial compression experiments based on HMs were conducted to study the mechanism of the crack initiation and propagation in the amygdaloidal basalt. The tensile fractures were mainly occurred in the matrix, and the shear fractures were mainly occurred in the amygdales. With the increase in the elliptic coefficient of amygdales, the uniaxial compressive strength (UCS) showed a linear growth trend. With the increase in the orientation of amygdales, the UCS exhibited a “V-shaped” distribution characteristic. This paper provides a numerical method for studying the mechanical properties of rocks with flaws.

Experimental and Numerical Investigation of Characteristics of Highly Heterogeneous Rock Mechanical Responses in Tight Sandy Conglomerate Reservoir Rock Under Tri-axial Compression

Due to the use of horizontal wells and hydraulic fracturing, commercial tight oil production from some tight sandy conglomerate reservoirs has been achieved. Since the widely distributed gravels in the sandy matrix in conglomerate reservoir rocks are harder than the matrix, the rock mechanical response in conglomerates under compression is highly heterogeneous. This increases the complexity of understanding the hydraulic fracturing behaviors in conglomerate reservoirs. Previous tri-axial compression tests provided the stress-strain relationships of conglomerate samples as a whole, and the stress and strain in the gravels and in the sandy matrix were not investigated due to the limitation of the compression test lab. This study presents tri-axial test results for a conglomerate sample cored from a reservoir that has been economically developed. Lab results are then used to calibrate the numerical model for the simulation of the tri-axial compression process. Numerical results indicate that the elastic modulus and size of gravels have significant impacts on the axial stresses and axial strains in the conglomerate. Stress concentrations are observed in gravels due to the heterogeneous mechanical properties in the conglomerate. The reorientation of the maximum horizontal principal stress is quantified to study the mechanisms of the interaction types between hydraulic fractures and gravels embedded in the tight sandy matrix.

Quantitative Geomorphological Parameters Analysis for the Aynalem- Illala Streams, Tigray, Northern Ethiopia

Morphometric analysis is the measurement and mathematical analysis of the configuration of the surface, shape, and dimension of landforms. The objective of this study is to characterize the Aynalem and Illala streams using the morphometric parameter. The topographic map at a scale of 1:50,000 taken from the Ethiopian National Mapping Agency was used to characterize the linear and areal aspects. ASTER Digital Elevation Model with 10m resolution was used to characterize the relief aspect. The Arc GIS 10.4.1 was used during the morphometric analysis. The analysis result of the streams is summarized based on the linear, areal, and relief aspects. The area is characterized by a dendritic drainage pattern which is characteristics of massive hard rock terrain. The Aynalem and Illala streams are 4th and 5th order streams. Considering the number of streams in the Aynalem (75.81%) and Illala (74.66%) is composed of first-order streams that indicate a flashy flood and the mean bifurcation value of Aynalem (6.8) and Illala (4.7) shows that the Aynalem area is more structurally affected than Illala but both show less stream integration. The analysis of areal aspects such as elongation ratio, circularity ratio, and form factor has indicated that both streams are characterized as elongated streams, this implies that both streams are flowing in heterogeneous rock material, presences of structural effect, and slow runoff discharge. The other areal aspect such as drainage density, stream frequency, infiltration number, and length of overland flow all show smaller values in both streams. This implies that the streams are characterized by a relatively permeable rock material with a higher infiltration capacity. The relief aspect of the Aynalem and Illala was also analyzed using basin relief, relief ratio, ruggedness number, hypsometric curves, and Hypsometric integral. The streams are characterized by a lower relief ratio and ruggedness number which implies a relatively flat slope and lower relief. The hypsometric curves and the Hypsometric Integral of the streams indicate that the Aynalem and Illala are at the maturity stage. This shows the area is characterized by higher erosion but less affected by recent structures. Based on the morphometric parameter analysis result it is possible to conclude that the stream development is dependent on the topography and geology of the study area and both streams show similar morphometric character.