Simulation The Propagation Of Complex Hydraulic Fracture Network With XFEM For Volume Fracturing

Volume fracturing is a crucial technique for exploration and development of unconventional oil and gas resources.Making sufficient utilization of the effect of pre-existing natural fractures on the propagation path of hydraulic induced fracture,and the perturbation of propped hydraulic fractures on in-situ stresses,is the essential theories and countermeasures to generate intricate network fractures.However,simulation hydraulic fracturing in the presence of a natural fracture network is a challenging task,owing to the complex interactions between fracturing fluid,rock matrix,and rock interfaces,as well as the interactions between propagating fractures and pre-existing natural interfaces.All of this means that it is imperative to establish a theory and method for modeling the propagation process of complex fracture network,and then for scientifically guiding the hydraulic fracturing design.So,this investigation would establish a theoretical foundation and provide technical support for beneficial development of unconventional oil and gas reservoirs.This paper is aiming at the crucially scientific and technical issues in designing volume fracturing strategy for unconventional oil and gas reservoirs,and focusing on the propagation behaviors before,during and after the intersection of hydraulic fracture with pre-existing natural fractures,as well as on the non-planar,asymmetrical,and complicated reticular propagating pattern under the effect of stress shadow effects,and taking the coupled hydro-mechanical behavior during hydraulic fracturing as the main line.Taking fully advantages of extended finite element method(XFEM)when dealing with discontinuous problems,this dissertation proposes a systematic theory and numerical framework,which is a fully coupled model for rock deformation,single and multi-phase fluid flow,and crack propagation in fractured porous media with XFEM,to simulate the propagation of complex fracture network for volume fracturing.The major accomplished works and achievements are demonstrated as follows.(1)The XFEM theory for discontinuity problems is numerically implemented with MATLAB.According to the local enriched finite element displacement approximation for isolating,branching and intersecting cracks,the governing equations,including the strong form,the weak form,and the finite element discrete form were derived in detail.By characterizing and tracking crack,judging node enrichment-type,calculating and assembling the element stiffness matrix,determining numerical integral solution,and realizing crack surface contact,the XFEM theory is numerically implemented.The stress intensity factors(SIFs)of hydraulic crack were accurately calculated by interaction integral,which established a solid foundation for modeling the dynamic propagation of hydraulic fractures.(2)A local enriched finite element pore pressure approximation for isolating,branching and intersecting permeable fractured porous media is constructed.The pressure field is continuous across the geological permeable fractures,while its derivatives(i.e.seepage rate)are discontinuous.The absolute signed distance function,product of multiple absolute signed distance function,and appropriate asymptotic functions,are continuous but discontinuous in derivatives,which make them as suitable functions to improve the shape functions for a node whose support is bisected by a single crack,is slit by a singular fracture,and contain two intersecting discontinuities.The local enriched pore fluid pressure approximation is made to present a seepage theory with non-matching grid.(3)A XFEM model is derived for the single phase and multi-phase fluid flow in fractured porous media.According to the local enriched finite element pore pressure approximation,a XFEM model is proposed for fluid flow in fractured porous media,in which the fluid flow in fracture domain was intensively depicted only with a simple expression of fracture conductivity(i.e.cubic law)and an integral along lower-dimensional interface or line elements.The multi-phase fluid flow theory is used to analyze the effect of single pre-existing natural fracture on fracturing fluid leakoff behavior after careful verification.The investigation results show that the distance and the inclined angle would significantly affect the fracturing fluid leakoff behavior.The existence of permeable natural fracture will change the filtration pattern of the surrounding rock matrix.Accumulation fluid loss volume is linearly related to the exposure time.(4)A hydromechanical coupling model with XFEM(XFEM-HM)is established for fractured porous media.The directly coupled scheme for seepage field and stress field avoids the cumbersome process during calculating the fluid pressure in complicated fracture networks and translating into equivalent nodal force.Moreover,the XFEM-HM takes the effects of changes in pore fluid pressure surrounding porous media on fracture propagation into consideration.The coupled single phase fluid flow field and stress field model is used to analyze the deformation response and interaction mechanism between hydraulic induced fracture and non-intersected natural fractures at orthotropic and non-orthotropic angles.The analysis results imply that the induced hydraulic fracture tends to cross orthotropic natural fracture,while it is prior to being arrested by non-orthotropic natural fracture.(5)Mechanical criteria of propagating behavior during the intersection between hydraulic induced fracture and pre-existing natural fracture are improved.According to the mode I and mode II stress intensity factors calculated by interaction integral,a general intersection criterion between hydraulic induced fracture with arbitrary direction and pre-existing natural fractures with arbitrary approaching angles is developed.The underlying mechanisms of intersection behavior are revealed.Study results demonstrate that the probability of arresting increases at first then decreases with the increasing of the inclinded angle between hydraulic fracture and maximum horizontal principal stress,and the propagating behavior shift from crossing to be arrested with increasing of net fracture pressure.(6)A systematic theory and numerical framework for modeling the propagation of complex hydraulic fracture network during volume fracturing is formed.Integrating the coupled deformation and fluid flow model,maximum tensile circumferential stress theory,and general intersection criterion,a fully coupled rock deformation,single phase and multi-phase fluid flow,crack propagation model and numerical framework are established.The effects of porous medium permeability,injection rate and viscosity of fracturing fluid on the fracture dimensions,i.e.the fracture opening,the fracture length and the fracture width profile,and the injection pressure are investigated after carefully verified.Eventually,crack propagation paths for simultaneous multi-fracture treatments with properly using the stress shadow effects for horizontal wells are emulated.Simulating results show excellent agreement with laboratory scale experiments deliberately designed to produce field-representative results in literature.The analogue results display that the induced hydraulic flexural fracture deflecting to wellbore rather than transverse fracture would be formed during the progress of staged fracturing for horizontal well.Furthermore,the stress shadow effects decrease the horizontal stress difference,or even reverse the in-situ stress state,which is advantageous to increase the complexity of network fracture.