Frac-pack completions have been used as a technique for well stimulation and sand control. Conventional hydraulic fracturing models based on linear elastic fracture mechanics often lead to inaccurate predictions of fracture geometry and fracturing pressure response due to large inelastic deformations and strong fluid-solid coupling. We present a fully-coupled, three-dimensional hydraulic fracture model in poro-elasto-plastic materials using a finite volume cohesive zone model for frac-pack applications.

Our model is capable of capturing the high net fracturing pressure commonly observed during frac-packing operations. The 3-D model simulates both shear and tensile failure around the fracture and computes the stresses and displacements around the fracture. We observe that plasticity causes lower stress concentration around the fracture tip which shields the tip of the propagating fracture from the fracturing pressure. High leak-off can also lead to shear failure around the fracture and ahead of the tip due to pore pressure diffusion. The low cohesion sands tend to fail in shear first then in tension if sufficient pore pressure and poroelastic backstress build up. We use a three-dimensional numerical computation of fluid leak-off using a fracture-reservoir domain coupling in this model to overcome the limitation of linear, one-dimensional leak-off models. Higher pressure gradients due to lower permeability, higher viscosity and injection rate results in a faster fracture propagation rate.

LEFM models inherently predict lower net fracturing pressure, smaller fracture widths and longer lengths in soft formations than observed in the field. In many instances, such models are used to fit the net pressure data by manipulating input parameters beyond physically reasonable values. The model presented here provides a much more physically realistic approach to model fracture growth in unconsolidated reservoirs with lab measured mechanical properties. The model has allowed us to design and analyze hydraulic fracturing stimulations much more accurately than LEFM models used in the past.

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