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In this paper, a hydro-mechanical model for non-planar hydraulic fracture propagation in ductile formations is developed based on the Drucker-Prager plasticity theory, Biot's theory and cohesive zone model (CZM). A hybrid extended finite element method (XFEM)-finite volume method (FVM)-embedded discrete fracture model (EDFM) method is proposed for numerical implementation. The XFEM and return-mapping method are used to simulate the deformation of inelastic media with strong discontinuities. The discontinuous pressure field is modelled by the EDFM and FVM. In addition, a dual-layer iterative algorithm is proposed to solve the strong nonlinear systems by a combination of the fixed-stress iteration, Picard iteration and Newton-Raphson iterative method. Then, the accuracy and ability of the proposed model are demonstrated through several reference cases. Finally, the proposed model are applied to two numerical cases and the influences of the plastic deformation on the simultaneous propagation of multi-fractures are investigated. • A poro-elasto-plastic model for non-planar hydraulic fracture propagation in ductile formations was developed. • A hybrid XFEM-FVM-EDFM method was proposed to conduct numerical implementation. • A dual-layer iterative algorithm was constructed to solve the strong nonlinear equation systems. • The effects of rock plasticity on multi-fractures propagation in the ductile formations were investigated. [ABSTRACT FROM AUTHOR]

Abstract With the increasing demand of oil and gas resource, the development of deep reservoir has become an inevitable trend. To investigate the coupled effects of rock elasto-plastic deformation, fluid flow and heat transfer in the process of hydraulic fracturing of deep reservoir, the mathematical model of elasto-plastic hydraulic fracture propagation is established based on cohesive zone model (CZM) and embedded discrete fracture model (EDFM). The constitutive equation incorporating thermal stress is derived by using Drucker-Prager yield condition and the associated flow law. Fluid flow in the fracture is modeled with lubrication theory. The thermal non-equilibrium theory is employed to describe the heat exchange between rock matrix and fluid in the fracture based on EDFM. The CZM is used as fracture propagation criterion. The rock deformation equation is solved by finite element method. The temperature field and fluid flow in the fracture are discretized by finite volume method. Due to the non-linearity of flow equation, the iterative method is used to solve the coupled problem of stress, pressure and temperature fields. A Triangular-PEBI (Perpendicular Bisector) dual mesh system is presented for numerical implementation. The numerical model is validated against with analytical solution and other methods in the literature. The results show the significance of accounting for elasto-plastic deformation and heat transfer when simulating hydraulic fracture propagation in deep reservoir. Highlights • Developed model involves plastic deformation, fluid flow and temperature field. • Heat exchange between matrix and fracturing fluid is modeled based on EDFM. • A Triangle-PEBI dual mesh system is presented for numerical implementation. • An efficient algorithm for thermal-elasto-plastic fracture propagating is proposed. • Result shows that plastic zone moves forward and expands during propagating. [ABSTRACT FROM AUTHOR]

Rock yielding may well take place during hydraulic fracturing in deep reservoirs. The prevailing models based on the linear elastic fracture mechanics (LEFM) are incapable of describing the evolution process of hydraulic fractures accurately. In this paper, a hydro-elasto-plastic model is proposed to investigate the hydraulic fracture propagation in deep reservoirs. The Drucker–Prager plasticity model, Darcy's law, cubic law and cohesive zone model are employed to describe the plastic deformation, matrix flow, fracture flow and evolution of hydraulic fractures, respectively. Combining the embedded discrete fracture model (EDFM), extended finite element method (XFEM) and finite volume method, a hybrid numerical scheme is presented to carry out simulations. A dual-layer iterative procedure is developed based on the fixed-stress split method, Picard iterative method and Newton–Raphson iterative method. The iterative procedure is used to deal with the coupling between nonlinear deformation with fracture extension and fluid flow. The proposed model is verified against analytical solutions and other numerical simulation results. A series of numerical cases are performed to investigate the influences of rock plasticity, internal friction angle, dilatancy angle and permeability on hydraulic fracture propagation. Finally, the proposed model is extended to simulate multiple hydraulic fracture propagation. The result shows that plastic deformation can enhance the stress-shadowing effect. [ABSTRACT FROM AUTHOR]

Nonuniform proppant distribution is fairly common in hydraulic fractures, and different closure behaviors of the propped and unpropped fractures have been observed in lots of physical experiments. However, the modeling of partially propped fracture closure is rarely performed, and its effect on gas production is not well understood as a result of previous studies. In this paper, a fully coupled fluid flow and geomechanics model is developed to simulate partially propped fracture closure, and to examine its effect on gas production in fractured shale reservoirs. Specifically, an efficient hybrid model, which consists of a single porosity model, a multiple porosity model and the embedded discrete fracture model (EDFM), is adopted to model the hydro-mechanical coupling process in fractured shale reservoirs. In flow equations, the Klinkenberg effect is considered in gas apparent permeability, and adsorption/desorption is treated as an additional source term. In the geomechanical domain, the closure behaviors of propped and unpropped fractures are described through two different constitutive models. Then, a stabilized extended finite element method (XFEM) iterative formulation, which is based on the polynomial pressure projection (PPP) technique, is developed to simulate a partially propped fracture closure with the consideration of displacement discontinuity at the fracture interfaces. After that, the sequential implicit method is applied to solve the coupled problem, in which the finite volume method (FVM) and stabilized XFEM are applied to discretize the flow and geomechanics equations, respectively. Finally, the proposed method is validated through some numerical examples, and then it is further used to study the effect of partially propped fracture closures on gas production in 3D fractured shale reservoir simulation models. This work will contribute to a better understanding of the dynamic behaviors of fractured shale reservoirs during gas production, and will provide more realistic production forecasts. [ABSTRACT FROM AUTHOR]