Peridynamic Simulation On Hydraulic Fracture Propagation In Shale Formation

Hydraulic fracturing is currently an effective volumetric treatment technique for shale gas extraction,aiming at creating fracture networks for gas seepage paths.The effectiveness of this technique is influenced by many factors such as the inhomogeneity of shale reservoirs,bedding properties,and in-situ stress.These factors make fracture propagation paths complex and diverse.But how do these factors affect the initiation and propagation of a fracture network through hydraulic fracturing has been unclear so far.An effective numerical simulation method can help us understand the roles of these factors in fracture initiation and propagation.As a non-local numerical method,peridynamic theory can well describe the discontinuous deformation in terms of spatial integration form.It provides a new theoretical approach to investigate the initiation and propagation of fracture in hydraulic fracturing.In this study,a peridynamic fluid-solid coupling model was developed for the numerical simulation on hydraulic fracturing process in bedding shale and its numerical performances were evaluated through numerical simulations.From these investigations,following main research results are obtained.(1)A peridynamic fluid-solid coupling model was established.In this model,both normal bond and tangential bond were introduced to replace the force density function in the bond-based peridynamic theory.This replacement can describe the deformation characteristics of the "bonds" and avoid the "Poisson self-locking" phenomenon in the bond-based peridynamic theory.Further,a pressure bond was introduced to describe the transport properties of fluids in porous media.Finally,the poroelastic theory was combined with the non-local theory to establish a nonlocal equivalent model of deformation-seepage coupling in porous media.This model provided the theoretical basis for the numerical simulation on hydraulic fracturing.(2)A peridynamic fracture criterion was derived with normal bond and tangential bond.From the perspective of strain energy density and energy release rate,the energy transformation during crack extension was quantitatively characterized,and the correspondence between crack opening displacement and energy release rate was derived by combining the J-integral principle and non-local theory,thus a peridynamic fracture criterion was establish with normal bond and tangential bond.This fracture criterion was verified by the relationship between the damage accumulation curve and the displacement loading curve in three-point bending beam tests on the crack propagation in shale specimens with different laminar dip angles.This criterion provided a peridynamic fracture criterion for the simulation of initiation and propagation of hydraulic fractures.(3)The formation law of fracture networks in bedding shale during hydraulic fracturing was revealed under complex stress conditions.The numerical discretization of proposed peridynamic fluid-solid coupling model was established and verified by comparing the results of shale three-point bending test.The accuracy of the seepage diffusion equation and the fluid-solid coupling equation were verified by five-spot well model and the Terzaghi’s problem,respectively.The hydraulic fracturing simulation results showed that the change of laminar surface dip angle had a salient effect on damage when the local stress difference was larger.An increase in horizontal in-situ stress would result in an increase in the extensional pressure of the reservoir.When the horizontal in-situ stress was low,the influence of laminar dip angle on reservoir fracture extension was significant;when the horizontal in-situ stress was high,the reservoir fracture propagation became difficult,and the fracture initiation near the wellhead and extended radially in the bedding direction.