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ABSTRACT
Gaining a better understanding on the mechanism of the interaction between the hydraulic fracture (HF) and the natural fracture (NF) is essential for increasing the stimulated reservoir volume (SRV) of shale gas fracturing. In this study, a two-dimensional (2D) numerical model for simulating the behavior of HF/NF interaction using particle flow code (PFC) method was established, and this model can consider the fluid-mechanical coupling effect, the fluid flow in permeable NFs, and the heterogeneity of particle size. The numerical model was verified by KGD analytical model and Gu and Weng’s analytical model. The input micro-parameters for PFC simulation were calibrated to match with the experimental macro-parameters of Longmaxi shale by trial-and-error method. The effects of various geologic and engineering parameters on the HF/NF interaction were investigated using PFC method. The modeling results show that there are six kinds of HF/NF interaction patterns observed from the results of PFC simulation. The HF will hardly cross the NF directly when the permeability of NF reaches a higher value of 100 mD. When the in-situ stress difference reaches 13 MPa, the HF will cross the NF even if the other factors are not favorable to the occurrence of “crossing”. The product of injection rate and fracturing fluid viscosity (Q·μ) is suggested to be used to study the HF/NF interaction, and the HF tends to cross the NF under a higher value of Q·μ. Moreover, the scenario of “crossing” is extremely likely to occur under orthogonal approach angle, and frictional coefficient of NF has little effect on orthogonal HF/NF interaction. The cases with the same HF/NF interaction pattern have a similar variation trend of borehole pressure history curve. Through analyzing the numerical results, the technical measures such as variable pump rate fracturing method and alternate injection method of slickwater-linear gel fluid were suggested to be applied to increase the complexity of fracture network.
Abbreviation
2D: Two-dimensional; 3D: Three-dimensional; PFC: Particle flow code; EIA: Energy Information Administration; SRV: Stimulated reservoir volume; BPM: Bonded particle model; PBM: Parallel bond model; FEM: Finite element method; BEM: Boundary element method; DEM: Discrete element method; XFEM: Extended finite element method; CZM: Cohesive zone model; UDEC: Universal distinct element code; 3DEC: Three-dimensional distinct element code; DDM: Displacement discontinuity method; SJM: Smooth joint model
Nomenclature
| = | Contact force vector between particle A and particle B | |
| = | Normal contact force between particle A and particle B | |
| = | Shear contact force between particle A and particle B | |
| = | Overlap displacement | |
| = | Contact normal stiffness | |
| = | Normal stiffness of particle A | |
| = | Normal stiffness of particle B | |
| = | Increment of shear force between particle A and particle B | |
| = | Increment of shear displacement | |
| = | Contact shear stiffness | |
| = | Shear stiffness of particle A | |
| = | Shear stiffness of particle B | |
| = | Friction coefficient of the particles | |
| = | Total force carried by the parallel bond | |
| = | Axial-directed force of parallel bond acting on particle B | |
| = | Shear-directed force of parallel bond acting on particle B | |
| = | Increment of axial-directed force of parallel bond | |
| = | Increment of shear-directed force of parallel bond | |
| = | Cross-sectional area of the parallel bond | |
| = | Total moment carried by the parallel bond | |
| = | Axial-directed moment of parallel bond acting on particle B | |
| = | Shear-directed moment of parallel bond acting on particle B | |
| = | Increment of axial-directed moment of parallel bond | |
| = | Increment of shear-directed moment of parallel bond | |
| = | Normal stiffness of the parallel bond | |
| = | Shear stiffness of the parallel bond | |
| = | Maximum tensile stress acting on the parallel bond | |
| = | Maximum shear stress acting on the parallel bond | |
| = | Polar moment of inertia | |
| = | Moment of inertia | |
| = | Rotation increment caused by polar moment of inertia | |
| = | Rotation increment caused by moment of inertia | |
| = | Parallel bond radius | |
| = | Radius of particle A | |
| = | Radius of particle B | |
| = | Radius multiplier of the parallel bond | |
| = | Thickness of each particle disk | |
| = | Normal strength of the parallel bond | |
| = | Shear strength of the parallel bond | |
| = | Volume flow rate through the plate per unit height | |
| = | Hydraulic aperture | |
| = | Fluid viscosity | |
| = | Increment of fluid pressure in the reservoir | |
| = | Flow pressure difference between two adjacent domains | |
| = | Pipe length | |
| = | Bulk modulus of fluid | |
| = | Domain volume | |
| = | Total volume flow rate | |
| = | Time step | |
| = | Change of domain volume | |
| = | Initial hydraulic aperture | |
| = | Hydraulic aperture under infinite normal stress | |
| = | Normal stress acting on the parallel bond | |
| = | Volume flow into the domain under disturbance | |
| = | Total number of the channels connected with a domain | |
| = | Average radius of particles around a domain | |
| = | Disturbance pressure | |
| = | Change of response pressure | |
| = | Relative displacement increment of two adjacent particles | |
| = | Normal relative displacement increment of two adjacent particles | |
| = | Shear relative displacement increment of two adjacent particles | |
| = | Smooth joint normal force at the beginning of the timestep | |
| = | Smooth joint shear force at the beginning of the timestep | |
| = | Updated smooth joint normal force | |
| = | Updated smooth joint shear force | |
| = | Area of smooth joint cross-section | |
| = | Dip angle | |
| = | Normal stiffness of SJM | |
| = | Shear stiffness of SJM | |
| = | Macro-Young’s modulus of reservoir | |
| = | Fracturing fluid viscosity | |
| = | Half fracture length | |
| = | Distance between a certain position of hydraulic fracture and bottom hole | |
| = | Poisson’s ratio of reservoir | |
| = | Injection rate of fracturing fluid | |
| = | Injection time |
Acknowledgments
The authors would like to thank the support of Dr Liuke Huang in providing the PFC2D software used in this work.
Additional information
Funding
Notes on contributors
Rui He
Rui He is a PhD student from Southwest Petroleum University with a research interest in mechanism of hydraulic fracturing and rock mechanics. He is a member of Society of Petroleum Engineers (SPE).
Zhaozhong Yang
Zhaozhong Yang is a professor from Southwest Petroleum University with a research interest in theory and technology of unconventional reservoir stimulation. He is an academic and technical leader in Sichuan Province. He holds a PhD from Southwest Petroleum University.
Xiaogang Li
Xiaogang Li is a professor from Southwest Petroleum University with a research interest in theory and technology of unconventional reservoir stimulation. He is a member of Society of Petroleum Engineers (SPE). He holds a PhD from Southwest Petroleum University.
Changyin Liu
Changyin Liu is a senior engineer from Sinopec Petroleum Exploration and Production Development Research Institute with a research interest in reservoir stimulation. He holds a PhD from Southwest Petroleum University.
Zhiyu Sun
Zhiyu Sun is a senior engineer from Sinopec Petroleum Exploration and Production Development Research Institute with a research interest in reservoir stimulation. He is a member of Society of Petroleum Engineers (SPE). He holds a PhD from East China University of Petroleum.
Wenhong Li
Wenhong Li is the vice President of Beijing Gepetto Petroleum Technology Co., Ltd with a research interest in application of hydraulic fracturing technique. He holds a bachelor's degree from Southwest Petroleum University.