A model for hydraulic fracturing and proppant placement in unconsolidated sands




Lee, Dongkeun

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Hydraulic fracturing in unconsolidated or poorly consolidated formations has been used as a technique for well stimulation and for sand control. Although a large number of hydraulic fracturing operations have been performed in soft formations, the exact mechanisms of failure and fracture propagation remain an unresolved issue. Conventional hydraulic fracturing models based on the theory of linear elastic fracture mechanics (LEFM) consistently predict lower net fracturing pressure, smaller fracture widths and longer fracture lengths in soft formations than observed in the field. Operators who want to design and analyze frac-pack treatments routinely use a hard rock model and need to calibrate and often manipulate input parameters beyond a physically reasonable range to match the net fracturing pressure and well performance data. In this dissertation, we have developed a fully-coupled, three-dimensional hydraulic fracture model for poro-elasto-plastic materials and fluid flow coupled with proppant transport. A computational framework for fluid-structure interaction (FSI) based on finite volume method was developed for modeling of hydraulic fracturing and proppant placement in soft formations. Two separate domains, a fracture and a reservoir domain, are discretized individually, separate equations are solved in the two domains, and their interactions are modeled. The model includes the fully coupled process of power-law fluid flow inside the fracture with proppant transport, fluid leak-off from the fracture into the porous reservoir, pore pressure diffusion into the reservoir, inelastic deformation of the poro-elasto-plastic reservoir, and fracture propagation using a cohesive zone model along with a dynamic meshing procedure. Fully-coupled processes between the two domains, and pressure, flow and displacement coupling within each domain are modeled by an iterative and segregated solution procedure, where each component of the field variable is solved separately, consecutively, and iteratively. We verified the essential components of the model by comparing our simulation results with several well-known analytical solutions (elastoplastic deformation and failure problem, KGD model in a 2-D elastic domain, and KGD model in storage-toughness dominated regime). We applied the model to design and analyze frac-pack operations conducted in a Gulf of Mexico oilfield. Our model is capable of capturing the high net fracturing pressure commonly observed during frac-packing operations without adjusting any input parameters. The model shows quantitatively that plasticity causes lower stress concentration around the fracture tip which shields the tip of the propagating fracture from the fracturing pressure, and retards fracture growth. Our model predicts shorter fracture lengths and wider widths compared to a hard rock model. Shear failure around the fracture and ahead of the tip are modeled. Low cohesion sands tend to fail in shear first then in tension if sufficient pore pressure builds up. We investigated the effect of fluid viscosity, injection rate, and proppant diameter on fracture growth and proppant placement using sensitivity studies. Higher apparent fluid viscosity and injection rate results in wider fractures with better proppant placement, when the fracture is expected to be contained within the payzone. Utilizing larger diameter of proppant leads to settling-dominant proppant placement resulting in the formation of a proppant bank at the bottom of the induced fracture. The new frac-pack model for the first time allows operators to design and analyze hydraulic fracturing stimulations in soft, elastoplastic formations when complex fracturing fluids are used. Our results also provide guidelines for the selection of fracturing fluid rheology, proppant size, and injection rates.


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