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In view of fluid flow in cracks and rock deformation, the mathematical model for shale hydraulic crack propagation was established. The crack flow field and the rock stress field were solved with the finite element method and the extended finite element method respectively, and the two fields were coupled through the Picard iteration. The presented model gave results consistent with those of the classic model, which verified correctness of the former. Based on the model, the effects of the rock elasticity modulus, Poisson's ratio and injection rate on the crack geometry, and the dynamic process of a hydraulic crack approaching a natural crack at an arbitrary angle, were simulated. The numerical results show that the elasticity modulus and injection rate have significant influence on the crack geometry, while the Poisson's ratio has little effect; the more brittle the shale is, the longer and narrower the hydraulic crack will grow; the greater the principal stress difference and the approaching angle are, the easier the hydraulic crack crosses the natural crack; there is a relatively large decrease in the crack width at the intersection between a hydraulic crack and a natural crack; the extended finite element method avoids mesh reconstruction and refinement during computation, and reduces the computing time. The presented model provides an effective theoretical tool for the shale fracturing design. [ABSTRACT FROM AUTHOR]

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]

In this study, we present an efficient numerical solution for studying hydraulic fracturing under coupled thermal–hydraulic conditions in an elastic–plastic porous medium. The propagation of macroscopic fracture is described by using an extended finite element method. Both the fluid flow through the porous medium and the exchange between the medium and fracture are taken into account. It is the same for the heat transfer. An efficient iterative scheme is then proposed to deal with the coupling between material deformation with fracture growth, fluid flow and heat transfer. The proposed method is assessed through comparisons with analytical solutions for a number of well-established problems. A series of numerical calculations are further performed in order to investigate the effect of plastic deformation and temperature change on the process of hydraulic fracture propagation. [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]