Numerical Simulation Of Hydraulic Fracturing In Shale Gas Reservoirs Based On The Extended Finite Element Method

Shale gas trapped in shale formation is a kind of unconventional energy sources.It has gotten more and more attention with the increasingly serious energy crisis around the world.Because of the low or ultralow permeabilities and porosities,shale formations often need hydraulic fracturing treatments for economical production.Combining multistage hydraulic fracturing and horizontal drilling is a highly effective method of increasing the production rates of shale gas reservoirs.The simultaneous fracturing and consecutive fracturing are two commonly used fracturing sequences in the horizontal wells.The openings of propped transverse fractures in horizontal wells cause the reorientation of the stress in their neighborhood,which in turn affects the direction of propagation of the subsequent fractures.This phenomenon,often referred to as stress shadowing,can negatively impact the efficiency of each fracture stage.Increasing the fracture spacing can lower the impact of stress interference;however,excessive fracture spacing will also lower the conductivity of reservoir.It is desirable to minimize the fracture spacing while also ensuring the growth of transverse fractures in multi-fractured horizontal wells,in order to improve reservoir drainage.As a common feature of sedimentary rocks,shale shows different elastic properties in its vertical and horizontal planes.Thus,shale can often be regarded as an orthogonal anisotropic linear elastic body.The behavior of fracture propagation in orthotropic media is substantially different from that in isotropic media.The anisotropic properties of rock must be fully taken into consideration for the hydraulic fracturing design in shale formations.A large number of natural fractures exist in shale formations,which have a great influence on the hydraulic stimulation.The interactions between the hydraulic fractures and the pre-existing natural fractures often create complex fracture network.The natural fractures in rock formation usually can be divided into two types:frictional and cemented natural fractures.Due to their different mechanical properties,the processes of the interactions between the hydraulic fractures and the two types of natural fractures are substantially different.Both the frictional and cemented natural fractures can serve as weak paths for hydraulic fractures beginning and/or diversion and promote the formation of complex fracture network.As the production of the reservoir is directly related to the created fracture network,it is obliged to correctly predict the complex fracture network development during fracturing treatments to optimize stimulation design and completion strategy.Hydraulic fracturing is a complex multi-field coupling mechanics problem which contains the deformation of rock,fracture initiation and propagation,interaction of hydraulic fractures and natural fractures,fluid flow within fracture,fluid leak-off from the fracture surface and the diffusion of the fluid into the porous media.Because of the limitation of the theoretical and experimental investigations,many researchers have developed various numerical methods to study the hydraulic fracturing.The extended finite element method(XFEM),in which special enriched shape functions in conjunction with additional degrees of freedom are added to the standard finite element approximation with the framework of partition of unity,has been proposed for modeling cracks.This method allows cracks to be represented without requiring the explicit meshing of the crack surfaces.Hence,the crack geometry is completely independent of the mesh,and remeshing is not required.The XFEM has been widely utilized for modeling hydraulic fracture problems.In this paper,a two-dimensional fluid-solid coupled numerical model based on the XFEM is established to simulate the multistage hydraulic fracturing in a horizontal well,the hydraulic fracture initiation and propagation in orthotropic formations,the interactions of hydraulic fractures and natural fractures,and the creation of complex fracture network in formations.(1)The impact of stress interference on fracture propagation has been investigated for the consecutive fracturing method and alternate fracturing method in a horizontal well.The in-situ stress difference has a significant impact on the extent of the stress interference zone.To avoid fracture deviation from the desired orthogonal path,the fracture spacing needs to be increased with the decrease in the in-situ stress difference.The local in-situ stress in the near-tip region is redistributed during fracture propagation.The stress interference between a growing hydraulic fracture and one or more previous hydraulic fractures must be taken into account in the case of fracture propagation.The alternate fracturing technique can reduce the fracture spacing,owing to the propagation of a middle fracture in the stress reversal region between the previous two fractures.Thus,the optimal fracture spacing for the alternate fracturing technique is almost half of that for the consecutive fracturing technique.(2)The effects of the material angle and the Young's Modulus ratio on hydraulic fracture propagation have been investigated.The hydraulic fracture will deviate from its straight-ahead path if there is an angle(defined as the material angle a)between the initial fracture direction and the material axes of orthotropy.The hydraulic fracture significantly deviates from its initial direction at the first propagation step,and the initial deviation angle ? changes with the variation of the material angle ?The extent of fracture deviation increases with the Young's Modulus ratio.The hydraulic fracture tends to propagate along the material axis m2,along which the Young's Modulus approaches the minimum value.The in-situ stress also has a significant impact on the direction of hydraulic fracture propagation in orthotropic formations.When the stress difference is small,the direction of fracture propagation is mainly determined by the orthotropy of the material.However,when the stress difference is large,the direction of fracture propagation is mainly determined by the in-situ stress.(3)The interactions between hydraulic fractures and natural fractures,and further the formation of complex fracture network have been investigated.The effects of the frictional natural fractures and cemented natural fractures on the creation of complex fracture network are compared.When the hydraulic fracture intersects with the frictional natural fractures,the cross/arrest behavior mainly depends on the intersection angle,stress difference,friction coefficient of natural fractures,as well as rock tensile strength.When the hydraulic fracture intersects with the cemented natural fractures,the cross/arrest behavior mainly depends on the intersection angle,cement toughness of natural fractures and rock fracture toughness.A hydraulic fracture intersection with a cemented natural fracture is most likely to form an L-shaped fracture.However,a hydraulic fracture intersection with a frictional natural fracture is most likely to form a T-shaped fracture.For this reason,hydraulic fracturing often leads to more complex fracture network in the formation containing frictional natural fractures in comparison to the formation containing cemented natural fractures with the same initial geometrical configuration of natural fractures.(4)An XFEM-based 2D hydraulic fracturing program named "Matlab-XFEM"has been developed.It can simulate the propagation of hydraulic fracture in isotropic and anisotropic linear elastic rock formation,the propagation of multiple hydraulic fractures at the same time,the interactions of hydraulic fractures and natural fractures,and the creation of complex fracture network.The numerical model can be adopted to estimate the optimal fracture spacing in horizontal wells,the hydraulic fracture propagation behavior in the orthotropic formation,the intersection behavior between hydraulic fractures and natural fractures,and the formation of complex fracture network in shale formations containing a large number of pre-existing fractures.Furthermore,the simulation results can serve as a guide for the optimum design of hydraulic fracturing to enhance production.