Flow and transport through and deformation of rough fractures : theoretical and numerical modeling studies



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Understanding physical, chemical, and mechanical processes and properties of a single fracture is fundamental to many processes on Earth, particularly hydrogeological phenomena across many scales. However, classical and widely used theories governing flow and transport processes are founded on the parallel plates model; this ignores the complex morphology of natural fracture. To fill this gap, I have investigated the role of fracture morphology on flow (permeability), transport (dispersion coefficients and other surrogate parameters), and mechanical (stiffness) properties through complementary theoretical analysis and computational experiments. The collection of single fractures used in this dissertation included natural fractures mapped through high-resolution x-ray computed tomography and synthetic ones generated through a model which produces fractures with fractal properties. I developed a modified Local Cubic Law (MLCL) allowing for fracture roughness, tortuosity, and weak inertial force to improve the prediction of fluid flow process. The validation of the MLCL was tested by comparing volumetric flux from solving the Navier-Stokes equations to that from the MLCL. Secondly, the effect of fracture roughness on the non-Fickian or anomalous transport was studied through an ensemble of 2D direct transport simulations. Moreover, I was able to show, analyze, and predict the transition from non-Fickian to Fickian transport by developing a quasi-3D particle tracking algorithm. Finally, I developed a fracture deformation model. The co-evolving permeability and stiffness were then determined through the MLCL and strain-stress relationship based on the deformation model. Through my dissertation research, I confirm that the classical LCL fails to predict bulk permeability or volumetric flux (errors up to 41%). The MLCL performs better in characterizing local and effective fluid flow processes, with only 4% error. Moreover, I find out that fracture roughness leads to non-Fickian transport, and that the degree of non-Fickian behavior depends directly on the fracture roughness. Additionally, I theoretically derive asymptotic time and lengths scales for distinguishing non-Fickian from Fickian transport for the simplified Poiseuille and Hagan-Poiseuille flow fields. The increasing scales drives non-Fickian transitioning into Fickian transport even though the presence of persistent intermittent velocity structure. Lastly, I show that scaling between fracture permeability and normal stiffness depends on both fracture roughness and aperture correlation length, indicating a potentially universal model that can describe this behavior.