A fully implicit stochastic model for hydraulic fracturing based on the discontinuous deformation analysis

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Morgan, William Edmund
Aral, Mustafa M.
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In recent years, hydraulic fracturing has led to a dramatic increase in the worldwide production of natural gas. In a typical hydraulic fracturing treatment, millions of gallons of water, sand and chemicals are injected into a reservoir to generate fractures in the reservoir that serve as pathways for fluid flow. Recent research has shown that both the effectiveness of fracturing treatments and the productivity of fractured reservoirs can be heavily influenced by the presence of pre-existing natural fracture networks. This work presents a fully implicit hydro-mechanical algorithm for modeling hydraulic fracturing in complex fracture networks using the two-dimensional discontinuous deformation analysis (DDA). Building upon previous studies coupling the DDA to fracture network flow, this work emphasizes various improvements made to stabilize the existing algorithms and facilitate their convergence. Additional emphasis is placed on validation of the model and on extending the model to the stochastic characterization of hydraulic fracturing in naturally fractured systems. To validate the coupled algorithm, the model was tested against two analytical solutions for hydraulic fracturing, one for the growth of a fixed-length fracture subject to constant fluid pressure, and the other for the growth of a viscosity-storage dominated fracture subject to a constant rate of fluid injection. Additionally, the model was used to reproduce the results of a hydraulic fracturing experiment performed using high-viscosity fracturing fluid in a homogeneous medium. Very good agreement was displayed in all cases, suggesting that the algorithm is suitable for simulating hydraulic fracturing in homogeneous media. Next, this work explores the relationship between the maximum tensile stress and Mohr-Coulomb fracture criteria used in the DDA and the critical stress intensity factor criteria from linear elastic fracture mechanics (LEFM). The relationship between the criteria is derived, and the ability of the model to capture the relationship is examined for both Mode I and Mode II fracturing. The model was then used to simulate the LEFM solution for a toughness-storage dominated bi-wing hydraulic fracture. Good agreement was found between the numerical and theoretical results, suggesting that the simpler maximum tensile stress criteria can serve as an acceptable substitute for the more rigorous LEFM criteria in studies of hydraulic fracturing. Finally, this work presents a method for modeling hydraulic fracturing in reservoirs characterized by pre-existing fracture networks. The ability of the algorithm to correctly model the interaction mechanism of intersecting fractures is demonstrated through comparison with experimental results, and the method is extended to the stochastic analysis of hydraulic fracturing in probabilistically characterized reservoirs. Ultimately, the method is applied to a case study of hydraulic fracturing in the Marcellus Shale, and the sensitivity of fracture propagation to variations in rock and fluid parameters is analyzed.
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