Publications

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We generate a wide range of models of proppant-packed fractures using discrete element simulations, and measure fracture conductivity using finite element flow simulations. This allows for a controlled computational study of proppant structure and its relationship to fracture conductivity and stress in the proppant pack. For homogeneous multi-layered packings, we observe the expected increase in fracture conductivity with increasing fracture aperture, while the stress on the proppant pack remains nearly constant. This is consistent with the expected behavior in conventional proppant-packed fractures, but the present work offers a novel quantitative analysis with an explicit geometric representation of the proppant particles. In single-layered packings (i.e. proppant monolayers), there is a drastic increase in fracture conductivity as the proppant volume fraction decreases and open flow channels form. However, this also corresponds to a sharp increase in the mechanical stress on the proppant pack, as measured by the maximum normal stress relative to the side crushing strength of typical proppant particles. We also generate a variety of computational geometries that resemble highly heterogeneous proppant packings hypothesized to form during channel fracturing. In some cases, these heterogeneous packings show drastic improvements in conductivity with only moderate increase in the stress on the proppant particles, suggesting that in certain applications these structures are indeed optimal. We also compare our computer-generated structures to micro computed tomography imaging of a manually fractured laboratory-scale shale specimen, and find reasonable agreement in the geometric characteristics.

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Results of axisymmetric compression tests on weak, porous Castlegate Sandstone (Cretaceous, Utah, USA), covering a range of dilational and compactional behaviors, are examined for localization behavior. Assuming isotropy, bulk and shear moduli evolve as increasing functions of mean stress and Mises equivalent shear stress respectively, and as decreasing functions of work-conjugate plastic strains. Acoustic emissions events located during testing show onset of localization and permit calculation of observed shear and low-angle compaction localization zones, or bands, as localization commences. Total strain measured experimentally partitions into: A) elastic strain with constant moduli, B) elastic strain due to stress dependence of moduli, C) elastic strain due to moduli degradation with increasing plastic strain, and D) plastic strain. The third term is the elastic-plastic coupling strain, and though often ignored, contributes significantly to pre-failure total strain for brittle and transitional tests. Constitutive parameters and localization predictions derived from experiments are compared to theoretical predictions. In the brittle regime, predictions of band angles (angle between band normal and maximum compression) demonstrate good agreement with observed shear band angles. Compaction localization was observed in the transitional regime in between shear localization and spatially pervasive compaction, over a small range of mean stresses. In contrast with predictions, detailed acoustic emissions analyses in this regime show low angle, compaction-dominated but shear-enhanced, localization.

For assessing energy-related activities in the subsurface, it is important to investigate the impact of the spatial variability and anisotropy on the geomechanical behavior of shale. The Brazilian test, an indirect tensile-splitting method, is performed in this work, and the evolution of strain field is obtained using digital image correlation. Experimental results show the significant impact of local heterogeneity and lamination on the crack pattern characteristics. For numerical simulations, a phase field method is used to simulate the brittle fracture behavior under various Brazilian test conditions. In this study, shale is assumed to consist of two constituents including the stiff and soft layers to which the same toughness but different elastic moduli are assigned. Microstructural heterogeneity is simplified to represent mesoscale (e.g., millimeter scale) features such as layer orientation, thickness, volume fraction, and defects. The effect of these structural attributes on the onset, propagation, and coalescence of cracks is explored. The simulation results show that spatial heterogeneity and material anisotropy highly affect crack patterns and effective fracture toughness, and the elastic contrast of two constituents significantly alters the effective toughness. However, the complex crack patterns observed in the experiments cannot completely be accounted for by either an isotropic or transversely isotropic effective medium approach. This implies that cracks developed in the layered system may coalesce in complicated ways depending on the local heterogeneity, and the interaction mechanisms between the cracks using two-constituent systems may explain the wide range of effective toughness of shale reported in the literature.

A series of constant mean stress (CMS) and constant shear stress (CSS) tests were performed to investigate the evolution of permeability and Biot coefficient at high mean stresses in a high porosity reservoir analog (Castlegate sandstone). Permeability decreases as expected with increasing mean stress, from about 20 Darcy at the beginning of the tests to between 1.5 and 0.3 Darcy at the end of the tests (mean stresses up to 275 MPa). The application of shear stress causes permeability to drop below that of a hydrostatic test at the same mean stress. Results show a nearly constant rate decrease in the Biot coefficient as the mean stress increases during hydrostatic loading, and as the shear stress increases during CMS loading. CSS tests show a stabilization of the Biot coefficient after the application of shear stress.

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A series of tests have been performed on Sierra White granite subjected to general (true triaxial) states of stress. Tests were performed under constant Lode angle conditions at Lode angles of 23.4, 16.1 and 0°. The constant Lode angle condition was maintained by holding the minimum principal stress constant while increasing the maximum and intermediate principal stress at a predetermined ratio. Tests were performed at minimum principal stresses of 5, 17 and 30 MPa. All of the specimens failed in a brittle manner, with significant dilatant volume strain accumulated, and failure showed a strong dependence on Lode angle. Specimens behaved in a nearly linear elastic manner until approximately 75% of the peak stress was reached. The angle of the failure feature (shear band) was compared to predictions developed by using the Rudnicki and Rice (1975) localization criterion. It was found that there was good agreement (within 7°) between the experimental results and theoretical predictions.

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The recent boom in the oil and natural gas industry of hydraulic fracture of source rocks has caused a new era in oil and gas production worldwide. However, there are many parts of this process that are poorly understood and thus hard to control. One of the few things that can be controlled is the process of injection to create the fractures in the subsurface and the subsequent injection of proppants to maintain the permeability of the fractured formation, allowing hydrocarbons to be extracted. The goal of this work was to better understand the injection process and resulting proppant distribution in the fracture through a combination of lab-scale experiments and computational models.

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The present study results are focused on laboratory testing of surrogate materials representing Waste Isolation Pilot Plant (WIPP) waste. The surrogate wastes correspond to a conservative estimate of the containers and transuranic waste materials emplaced at the WIPP. Testing consists of hydrostatic, triaxial, and uniaxial tests performed on surrogate waste recipes based on those previously developed by Hansen et al. (1997). These recipes represent actual waste by weight percent of each constituent and total density. Testing was performed on full-scale and 1/4-scale containers. Axial, lateral, and volumetric strain and axial and lateral stress measurements were made. Unique testing techniques were developed during the course of the experimental program. The first involves the use of a spirometer or precision flow meter to measure sample volumetric strain under the various stress conditions. Since the manner in which the waste containers deformed when compressed was not even, the volumetric and axial strains were used to determine the lateral strains. The second technique involved the development of unique coating procedures that also acted as jackets during hydrostatic, triaxial, and full-scale uniaxial testing; 1/4-scale uniaxial tests were not coated but wrapped with clay to maintain an airtight seal for volumetric strain measurement. During all testing methods, the coatings allowed the use of either a spirometer or precision flow meter to estimate the amount of air driven from the container as it crushed down since the jacket adhered to the container and yet was flexible enough to remain airtight during deformation.

Performing experiments in the laboratory that mimic conditions in the field is challenging. In an attempt to understand hydraulic fracture in the field, and provide laboratory flow results for model verification, an effort to duplicate the typical fracture pattern for long horizontal wells has been made. The typical "disks on a string" fracture formation is caused by properly orienting the long horizontal well such that it is parallel to the minimum principal stress direction, then fracturing the rock. In order to replicate this feature in the laboratory with a traditional cylindrical specimen the test must be performed under extensile stress conditions and the specimen must have been cored parallel to bedding in order to avoid failure along a bedding plane, and replicate bedding orientation in the field. Testing has shown that it is possible to form failure features of this type in the laboratory. A novel method for jacketing is employed to allow fluid to flow out of the fracture and leave the specimen without risking the integrity of the jacket; this allows proppant to be injected into the fracture, simulating loss of fracturing fluids to the formation, and allowing a solid proppant pack to be developed.