Mult-scale Modeling of the Coupled Fluid Transport and Permeability Alteration in Naturally Fractured Porous Media

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The injection of a high pressure fluid in a porous medium to activate pre-existing fractures is commonly used in the development of stimulated shale gas formations and engineered geothermal systems (EGS). Understanding the coupling between fluid transport and the activation of the fractures is essential in optimizing the stimulation process and modeling convective transport in hydraulically stimulated reservoirs. Based on the assumption that a fracture slips and activates when the fluid pressure is larger than a critical value that depends on the fracture's orientation with respect to the principal stress field, the effects of stress anisotropy, injection conditions, and the connectivity of the pre-existing fractures on the morphology of the cluster of activated fractures are analyzed. Depending on the importance of the viscous pressure drop, three growth regimes denoted as the homogenous, fractal, and intermediate regimes are identified. In the fractal and intermediate regimes, the injected fluid propagates in a preferred direction when the pre-existing fractures are well-connected and the tendency of stress anisotropy to activate favorably oriented fractures becomes pronounced. In the homogeneous regime, the viscous pressure drop is negligible over the correlation length of the pre-existing fractures but is important over the size of the stimulated reservoir. In this regime, the effects of stress anisotropy are overcome by the viscous forces and a homogeneous cluster is formed whose growth follows an isotropic linear diffusion equation. In the fractal regime, the viscous pressure drop is negligible over the size of the stimulated region. Thus, the injected fluid activates and flows through the least resistance accessible fractures forming a fractal network. For poorly connected pre-existing fractures, the activation process belongs to the same universality class as random percolation. Using large-cell Monte Carlo renormalization group, a cross-over that does not change the universality class is identified as the radius of cluster exceeds the correlation length of the pre-existing fractures. An interesting intermediate regime develops when the viscous pressure drop is negligible over length scales that are larger than the pre-existing fractures' correlation length but is important over the stimulated reservoir. In this regime, the network is fractal at small length scales but is heterogeneous at larger scales. For poorly connected pre-existing fractures where the effects of stress anisotropy are negligible, a continuum model of fluid transport in the cluster of activated fractures is developed where percolation theory is used to relate the effective porosity and permeability of the network to the local fluid pressure. The model is tested using a discrete fracture network simulations. Finally, these insights about the connectivity of activated fractures are applied to analyze the thermal draw-down of EGS systems. It is shown that the properties of the shortest path such as its average residence time and the frequency of exchanging fluid flowing through it with other intersecting paths control the thermal drawdown. A homogeneous network performs the best followed by a fractal cluster; an intermediate network has the poorest performance.

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Statistical physics; Fluid Mechanics; Natural Fractures; percolation theory; Fractal Dimension; Invasion Percolation; Porous media; Self-Similar; Petroleum engineering


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Koch, Donald L.

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Escobedo, Fernando
Zehnder, Alan Taylor

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Chemical Engineering

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Ph. D., Chemical Engineering

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Doctor of Philosophy

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Government Document




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dissertation or thesis

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