Numerical Modeling and Lattice Method for Characterizing Hydraulic Fracture Propagation: A Review of the Numerical, Experimental, and Field Studies

Abstract

In continuous formations, the rock properties and the state of in situ stresses control the propagation direction of an induced hydraulic fracture (HF) and its geometry. The present study succinctly reviews more than a hundred scientific papers that have deeply explored hydraulic fracture propagation from the rock mechanical perspective and summarizes the current state of knowledge on the propagation of hydraulic fractures. These studies fall into three major categories of field, experimental, and numerical studies. It was found that numerical simulations are the most common methods for studying hydraulic fracture propagation, while field and analytical studies are the least-used methods because of their technical complications and practical limitations. One of the most efficient methods for the numerical simulation that has been adopted by numerous researches from around the world in recent years is the Lattice simulation approach. This method is a particle-based model and uses the Distinct Element Method. Since the Lattice simulation presents higher accuracy and computational efficiency over the existing methods to simulate complex reservoir conditions, the current review particularly focuses on this method and also discusses the functionality of the recently introduced XSite simulation package. The results from this work demonstrate the superior ability of the Lattice simulation and XSite package in modeling different propagation regimes, geometry, and growth of the HF. Moreover, the authors simulated the interaction mode of hydraulic and natural fractures based on two significant parameters of the phenomenon, namely “angle of approach” and “in situ differential stress”, and verified the results with the Blanton criteria.

Appendix

The most important research studies on hydraulic fracturing since 1963 till 2020

Year	Author(s)	Main results	Method(s)
1963	Lamont and Jessen	A hydraulic fracture could expand across natural fractures with different width and orientation	Experimental
1974	Daneshy	Comparatively small flaws, whether open or closed, were a locally influenced induced hydraulic fracture and were unable to change their overall orientation	Experimental
1982	Blanton	Under high differential stresses and high angles of approach, hydraulic induced fractures would cross pre-existing fractures	Experimental
1983	Palmer and Carroll Jr	Analyzed the complexity of hydraulic fracturing propagation in the presence of different rock types and in situ stresses	Numerical
1986	Settari and Cleary	Analyzed the complexity of hydraulic fracturing propagation in the presence of different rock types and in situ stresses	Numerical
1988	Stevens	Compared FDM and FEM, and concluded using FDM would reduce the cost and computational time	Numerical
1989	Doe and Boyce	The significant importance of deviated stresses in fracture geometry was highlighted	Experimental
1989	El Rabaa	Fracture geometry near horizontal wells is controlled by well deviation and length of the perforated interval	Experimental
1990	Advani et al.	Developed the P3D model as an extension of the PKN model	Numerical
1991	Behrmann and Elbel	Bi-wings fractures occur in unsaturated blocks and multi-fractures occur in saturated blocks	Experimental
1991	Pucknell et al.	Investigated the damage caused by the perforation process	Experimental
1991	Thallak et al.	Used Flow-Coupled DEM/Simulated the two fractures initiated and propagated in a dense cohesionless granular medium under hydrostatic and non-hydrostatic stress fields	Numerical
1993	Warpinski, et al.	Higher pressure drops in fractures and shorter fracture lengths	Field
1993	Martha, et al.	Fracture reorientation modelling by FEM needs remeshing and was computationally expensive	Numerical
1994	Fast, et al.	Microfracture tests showed stress variations between reservoir layers were great enough to prevent fracture placement across an entire perforated interval	Field
1994	Warpinski, et al.	They showed only results and quantifiable comparisons	Field
1994	Halleck	Investigated the damage caused by the perforation process	Experimental
1994	Asadi, and Preston	Investigated the damage caused by the perforation process	Experimental
1994	De Pater, Weijers et al.	Studied nonlinear effects on hydraulic fracture propagation caused to multi fractures	Experimental
1995	Hopkins, et al.	Presence of contained fractures despite the lack of stress barriers and the lack of a low Young’s Modulus	Field
1995	Renshaw and Pollard	Derived a simple coefficient of friction criteria	Experimental Analytical
1999	Moës, et al.	Used FEM for crack growth without remeshing/This method allows the entire crack to be represented independently by the mesh and, therefore no need for remeshing to model the crack growth	Numerical
2000	Sukumar, et al.	Used XFEM for improving computational efficiency	Numerical
2000	Sukumar, et al.	Used FEM/Concluded great flexibility of this method in modelling, applying varied boundary conditions and modelling of cracked environments with crack geometry was evident	Numerical
2001	Chudnovsky, et al.	Studied hydraulic fracturing process in layered formations/Concluded the fracture geometry could be elliptical even under uniform stress conditions and with a moderate fracture toughness ratio	Experimental Numerical
2002	Siebrits and Peirce	Developed a planar 3D (PL3D) model. Mentioned it is more accurate than P3D	Numerical
2002	Rahman, et al.	Studied the propagation of transverse hydraulic fracturing from horizontal wells/Resulted that the propagation of multiple fractures requires higher net pressures than a single fracture	Experimental Numerical Analytical
2007	Grieser, et al.	Via increasing access to microporosity or natural fractures as well as increasing surface area, enhanced shale production was possible	Field
2007	Gale, Reed et al.	Natural fractures distributed in a power-law size mode and the largest fracture stayed in an open state	Field
2007	Pursley, Penny et al.	By analyzing the production histories, showed microemulsion additive significantly enhanced the reservoir conductivity and effective fracture length compared to the historical completions	Field
2007	Adachi, Siebrits et al.	Developed a planar 3D (PL3D) model, which is more accurate than P3D	Numerical
2007	Zhang, Jeffrey et al.	Used 2D-BEM/Considered the importance of frictional behavior at the pre-existing fracture surfaces. Frictional energy loss influences the width of HF on the two pre-existing NFs	Numerical
2008	Kaufman, Penny et al.	The evolvement of fractures around the main fracture could increase the regional permeability, but it also could lead to significant leak-off, which in turn can limit the development of a hydraulic fracture	Field
2008	Zhang, Jeffrey et al.	Used 2D-BEM/Considered the importance of frictional behavior at the pre-existing fracture surfaces	Numerical
2008	Pak and Chan	Used FEM/Concluded that for uncemented porous medias, a single planar fracture was unlikely to occur and a fracture zone consisting of interconnected tiny cracks should be expected	Numerical Experimental
2009	Cipolla	Opening or closing of pre-existing micro cracks, played an important role in production because they could change the reservoir properties	Field
2009	Zhao and Young	Used DEM and PFC2D for simulating HF propagation	Numerical Experimental
2009	Taleghani and Olson	Used XFEM/Simulated fracture reorientation and interaction between HF and NFs	Numerical
2009	Dahi Taleghani	Used XFEM/Considered the effect of the cohesiveness of the sealed NFs and showed the main differences between hydraulic fracturing in NF reservoirs from non-fractured reservoirs	Numerical
2009	Chen, Bunger et al.	Used FEM to simulate HF in real time and avoid singularity problems in classical fracture mechanics	Numerical
2010	Jeffrey, Zhang et al.	The mapped fracture geometry and numerical modeling of it showed that opening mode hydraulic fractures could be effectively extended into the naturally fractured rock	Field Numerical
2010	Gu and Weng	Developed Renshaw and Pollard criterion	Experimental Analytical
2010	Damjanac, Gil et al.	Used a DFN to create a Synthetic Rock Mass and PFC2D for simulations/Resulted that by changing the fluid compressibility, the geometry of induced fractures was changed	Numerical
2010	Rahman, Aghighi et al.	Used FEM/Concluded the angle of approach, differential stress, opening pressure, and the type of the NFs had a significant effect on crossing or opening of HF	Numerical
2011	Zhou and Xue	Studied the effect of changing in situ stresses/Observed three types of fracture geometry	Experimental
2011	Rasouli, Sarmadivaleh et al.	Studied the effect of formation texture heterogeneity and interface properties on induced fracture propagation/Showed the fracture crossed strong interface and offset in the weak interface	Experimental
2011	Nagel, Gil et al.	Used 3DEC DEM/Increasing injection rate, strongly caused the increase of the tensile failure	Numerical
2011	Gil, Nagel et al.	Used DEM and 3DEC/Simulated the effect of injection rate and fluid viscosity on HF propagation	Numerical
2011	Sarmadivaleh, Rasouli et al.	Used PFC2D/Highlighted the role of interfaces’ filler materials and their effective role in the interaction mechanism	Numerical Experimental
2011	Rasouli, et al.	Used PFC/Studied the interaction mechanisms	Numerical
2012	Rasouli	Used PFC2D/Studied the effect of stress anisotropy on hydraulic fracturing propagation.	Experimental Numerical
2012	Sarmadivaleh	Used PFC/Studied the interaction mechanisms	Numerical
2012	Sanchez-Nagel et al.	Used DEM/Considered the critical impact of an induced HF on the shear of the NF system	Numerical
2013	Ben, Wang et al.	Used DDA and a pipe network model/Concluded the in situ stresses and joint properties were the main effective parameters on HF propagation	Numerical
2014	Huang, Safari et al.	Their sensitivity analysis showed geomechanical models that involve complex fracture networks could be calibrated against synthetic microseismic data and helped predict reservoir response to stimulation	Field
2014	Marji	Used DDM/The method allows fracture reorientation under certain stress conditions	Numerical
2014	Bao, Fathi et al.	Used FEM/Condensation technique had a strong influence on computation costs, especially in the viscose-dominated propagation regime	Numerical
2015	Sun and Schechter	Because of the existence of natural fractures, the stimulated volume was increased. Also, the capability of developed meshing algorithms to accurately model fracture width and fracture geometry increased too	Field
2015	Lee, et al.	Showed the importance of interface filling material properties on the interaction mechanism	Experimental
2015	Fallahzadeh, et al.	Investigated the effect of stress anisotropy and geometry of the fracture near the wellbore	Experimental
2015	Guo, Zhang et al.	Used 2D-FEM/Resulted permeability and mechanical properties of natural fractures, angle of approach, the difference between horizontal stresses and flow rate were the main factors affecting HF propagation	Numerical
2015	Wang	Used XFEM/Simulated fracture reorientation and interaction between HF and NFs	Numerical
2015	Marji	Used DDM/The method allows fracture reorientation under certain stress conditions	Numerical
2015	Zhang, Li et al.	Used DDM/Considered the necessary conditions for stable HF propagation in unconventional resources	Numerical
2015	Guo, Zhang et al.	Used 2D fracture propagation Method/Demonstrated the mechanical properties and permeability of NFs, angle of approach, horizontal stress difference, viscosity, and fluid flow rates were the main parameters affecting the fracture network geometry and fracture propagation in shale gas reservoirs	Numerical
2016	Alabbad and Olson	Reviewed the geomechanical factors controlling interaction mechanism/Found crossing mode was largely dictated by the preexisting fractures cement fill type relative to the matrix of the host rock	Experimental
2016	Abdollahipour, et al.	Used DEM/Simulated the confining pressure effects on the crack opening displacement in HF process	Numerical
2016	Yushi, Xinfang et al.	Used DEM/Simulate HF propagation in layered shale formations/Revealed that the presence of bedding plane interfaces increased the injection pressure during fracturing	Numerical
2016	Damjanac and Cundall	Used DEM/Considered the SRM had an ability to solve the HF propagation/Mentioned their model could deliver a pattern of HF in intact rock or sliding and opening of pre-existing joints	Numerical
2016	Zou, Zhang et al.	Used 3D-DEM/The interaction between induced and NFs might change before and after plugging	Numerical
2016	Zeng and Yao	Used DDM/Fracture spacing and stress anisotropy were two important parameters that had a considerable effect on fracture geometry and propagation	Numerical
2016	Damjanac and Cundall	Used 3D-DEM HF simulator/Indicated HF simulator was a powerful 3D simulator for representing hydraulic fracturing in the jointed rock mass	Numerical
2017	Masoomi and Viktorovich	Used Pseudo 3D HF model (P3D) and 2D modelling of PKN, KGD and Radial models for investigating the main effective parameters on HF propagation	Numerical
2017	Zhou, Zhang et al.	Used PFC/Studied the interaction mechanisms	Numerical
2017	Dehghan, et al.	Used XFEM and ABAQUS/3D simulated HF propagation and its interaction with pre-existing NFs	Numerical
2017	Shi, Wang et al.	Used XFEM with reduction technique/Concluded this method could speed up the simulation considerably without decreasing the convergence or computational accuracy in iterations	Numerical
2017	Fatahi, Hossain et al.	Used PFC/By increasing the angle between NF and maximum horizontal stress, the possibility of crossing mode was increased. The strength of filling materials affects the possibility of cross mode.	Numerical Experimental
2018	Kumari, Ranjith et al.	Breakdown pressure and temperature had an opposite relationship	Experimental
2018	Li, Xiao et al.	Simulated HF propagation in radial well/Investigated changing in situ stress field distribution during the radial well fracturing and forming the induced stress field along the radial well at the same time	Experimental Numerical
2018	Xing, Yoshioka et al.	Investigated the effect of three principal stresses/Height, growth, containment, and growth along the horizontal weak interface determined the distinct regions in parametric space	Experimental Numerical
2018	Dharmendra K.	Used 3D-DDM/Concluded that the mechanical interactions between the fractures are the main parameters which affect the fracture network geometries	Numerical
2018	Li, Xiao et al.	Used 3D-XFEM/Fracture spacing is a key parameter that controlls the multiple fractures geometries	Numerical
2019	Ning, Shicheng et al.	Studied the temperature-dependency of mechanical properties of an HF surface and fracture conductivity	Experimental
2019	R Feng	Unstable initiation & propagation of HF due to extension of HF aligned to the minimum horizontal stress	Experimental
2019	Zheng, Liu et al.	Used DEM/Concluded the fracture height was limited by the weak joints and was controlled by parameters such as the angle between the hydraulic fractures, the interface, and the stress state	Numerical
2019	Zou, Ma et al.	Used 3D-DEM/Did sensitivity analysis on fluid injection pressure and horizontal differential stresses and resulted that changing injection pressure could strongly affect the HF propagation behavior	Numerical
2019	Li, Dong et al.	Used 2D-FEM based on the Pore Pressure Cohesive Zone (PPCZ)/Concluded that the horizontal differential stress is the most important factor for controlling the HF propagation network	Numerical
2019	Tian, Li et al.	Used XFEM/By comparing Sequential Fracturing, Alternate Fracturing, and the Modified Zipper Fracturing methods concluded that the effect of induced stresses on fracture propagation is lower. Also, indicated the in situ stress difference was the main controller parameter of fracture deviation	Numerical
2019	Janiszewski, Shen et al.	Used 2D-FRACOD/By increasing angle of approach, the crossing happened, and by decreasing the angle of approach, the crossing was reduced, and opening happened	Numerical
2019	Wu, Sun et al.	Used Cohesive Element-Based/Natural fracture friction coefficient affected HF propagation strongly	Numerical
2019	Tang, Zuo et al.	Used 3D-DDM for simulating rock deformation and FDM for modelling fluid flow along vertical fractures/Mentioned the 3D-DDM could describe the pressure gradient around fracture tips accurately	Numerical
2019	Zheng, Liu et al.	Used 3D-DEM/By increasing the angle of approach, crossing mode was more likely to happen	Numerical Experimental
2019	Huang, Liu et al.	Used 2D-DEM/Despite the weak effect of inherent heterogeneity on the HF process in the viscose dominated regime it had a stronger effect on hydraulic fracturing propagating in toughness dominated	Numerical
2019	Garagash	Studied cohesive-zone effects in HF propagation/In the real field, fluid lag is embedded in the fracture	Numerical
2019	Badrouchi, Wan et al.	Used XSite/After initiating HF at the center of the Middle Bakken, it could penetrate both the Upper and Lower Bakken Formation because of their high Young’s modulus	Numerical
2019	Djabelkhir, Song et al.	Used XSite)/A predefined crack led to better conditions for fracture initiation and rock breakdown	Numerical
2019	Wan, Rasouli et al.	Used XSite and FLAC3D/Fracture propagation caused a stress reversal regime near the HF	Numerical
2019	Bakhshi. E	Used XSite and compared results with lab data/The larger angle of intersection and stronger filling material will promote the crossing mode	Numerical
2019	Liu, Qu et al.	Used Lattice Method/In-situ stress difference and cluster spacing are the most important parameters which affect the length and geometry of HF	Numerical
2019	Akash, Rasouli et al.	Used XSite/Indicated that in case of orienting perforations perpendicular to the direction of minimum horizontal stress, a single wide fracture was observed	Numerical
1990	Blair, Thorpe et al.	Used FEM/After running true triaxial test, a single-wing fracture, propagating in a plane perpendicular to the interface was obtained	Experimental Numerical
2019	Bakhshi, Rasouli et al.	Used XSite/Analytical solutions were just suitable for simple cases (samples without any fractures)	Numerical
2019	Bakhshi, Rasouli et al.	Used XSite/By increasing the angle of approach and the strength of filling materials, the possibility of crossing mode was increased	Numerical
2019	Bakhshi, Rasouli et al.	Used XSite/Shear strength and stress anisotropy were the main factors affecting the interaction mechanism	Numerical
2020	Wan, Rasouli et al.	Used XSite/Decreasing the rock brittleness prevents fracture propagation. Also, the lower minimum horizontal stress contrast led to the fracture containment	Numerical

1. ** HF: Hydraulic Fracturing/NFs: Natural Fractures