A numerical model to simulate fracture network induced by hydraulic fracturing for 3D shale gas reservoir with geo-stress interference

Qiang Wang, Yongquan Hu, Jinzhou Zhao, Lan Ren


In the two-dimensional (2D) stimulated reservoir volume (SRV) model, the positions of natural fractures are only determined by the approaching angle, and only the influence of horizontal principal stress is considered in its failure criterion. In the three-dimensional (3D) shale reservoir model, the positions of natural fractures must be determined by the dip and approaching angles, while considering the influences of the vertical and horizontal principal stresses on the failure criterion. In addition, the simultaneous opening of several hydraulic cracks will lead to a change in the geo-stress, thus causing a change in the conditions of the natural fracture and shear failure by the induced stress. To analyze the generation of 3D fracture networks, this study establishes a mathematical model based on elastic mechanics, 3D rock failure criterion, full permeability tensor, and material conservation equation. First, the finite element method model of geological stress caused by fracturing is established based on the crack propagation model, and the finite difference method module based on the 3D fluid diffusion control equation and full permeability tensor is used to solve the reservoir pressure distribution. Subsequently, the 3D tensile and shear failure criteria are used to determine whether any grid units are destroyed. Once a grid  has occurred in any form of rock failure criterion, the permeability of the corresponding grid unit will also change owing to the change in the natural fracture opening. Finally, the SRV is represented by the region of increased permeability. This work presents a sensitivity analysis of the multifactor after applying the microseismic data to validate the numerical model, including the influences of the injected fluid volume, natural fracture approaching angle, dip angle, and horizontal principal stress difference on the size of the SRV (such as shape, border width, and length). Our results show that, compared to the condition where no stress is induced, the tensile failure volume decreases and the shear failure volume increases, whereas the total SRV increases owing to the induced stress when the vertical principal stress is maximum among the three principal stress components. The length of the SRV increases with increasing approaching angle, dip angle, and horizontal principal stress difference of the natural fracture, but its width decreases. The width and length increase simultaneously only with increasing volume of injected fluid; the SRV size increases with increasing injection fluid volume and natural fracture dip, but decreases with increasing approaching angle and horizontal principal stress difference.



Shale gas; SRV; Tensile failure; Shear failure; Total permeability tensor; Stress interference

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Cipolla CL. Modeling production and evaluating fracture performance in unconventional gas reservoirs[J]. J Pet Technol61,2009,(09):84–90

Fanchi JR. Directional permeability[J]. SPE Reserv Eval Eng,2008,11(03):565–568

Fredd CN, McConnell SB, Boney CL, et al. Experimental study of fracture conductivity for water-fracturing and conventional fracturing applications[J]. SPE J,2001, 6(03):288–298

Ge J, Ghassemi A.Stimulated reservoir volume by hydraulic fracturing in naturally fractured shale gas reservoirs. In: 46th US rock mechanics/geomechanics symposium[J]. American RockMechanics Association, 24–27 June,2012, Chicago

Ghassemi A, Zhou XX, Rawal C. A three-dimensional poroelastic analysis of rock failure around a hydraulic fracture[J].J Pet Sci Eng,2013, 108:118–127

Guo J, Liu Y. A comprehensive model for simulating fracturing fluid leakoff in natural fractures[J]. J Nat Gas Sci Eng,2014, 21:977–985

Guo J, Liu Y. Opening of natural fracture and its effect on leakoff behavior in fractured gas reservoirs[J]. J Nat Gas Sci Eng,2014,18:324–328

Hossain MM, Rahman MK, Rahman SS. A shear dilation stimulation model for production enhancement from naturally fractured reservoirs. SPE J,2002, 7(02):183–195

Hu YQ, Li ZQ, Zhao JZ, et al. Optimization of hydraulic fracture-network parameters based on production simulation in shale gas reservoirs[J]. J Eng Res,2016, 4(04):159–180

Maulianda BT, Hareland G, Chen S. Geomechanical consideration in stimulated reservoir volume dimension models prediction during multi-stage hydraulic fractures in horizontal Wells–Glauconite tight formation in Hoadley field. In: 48th US rock mechanics/geomechanics symposium. 2014.American Rock Mechanics Association

Mayerhofer MJ, Lolon EP, Warpinski NR, et al, What is stimulated reservoir volume (SRV)? [J].SPE Prod Oper,2010, 15(4):473–485

Nassir M, Settari A, Wan RG. Prediction and optimization of fracturing in tight gas and shale using a coupled geomechanical model of combined tensile and shear fracturing. In: Paper SPE-152200-MS presented at the SPE hydraulic fracturing technology conference, 6–8 February, 2012,The Woodlands

Nassir M, Settari A, Wan RG. Prediction of stimulated reservoir volume and optimization of fracturing in tight gas and shale with a fully elasto-plastic coupled geomechanical model[J].SPE J,2014, 19(05):771–785

Palmer I, Cameron J, Moschovidis Z, et al. Natural fractures influence shear stimulation direction[J]. Oil Gas J,2009, 107(12):37–43

Palmer ID, Moschovidis ZA, Cameron JR . Modeling shear failure and stimulation of the Barnett shale after hydraulic fracturing. In: Paper SPE-106113-MS presented at the hydraulic fracturing technology conference, 29–31 January, 2007,College Station

Palmer ID, Moschovidis ZA, Schaefer A. Microseismic clouds: modeling and implications[J]. SPE Prod Oper,2013, 28(02):181–190

Ren L, Lin R, Zhao J, et al. Simultaneous hydraulic fracturing of ultra-low permeability sandstone reservoirs in China: mechanism and its field test[J]. J Cent South Univ,2015,22:1427–1436

Ren L, Lin R, Zhao J, et al. Cluster spacing optimal design for staged fracturing in horizontal shale gas wells based on optimal SRV[J]. Natural Gas Industry, 2017, 47(4): 69-79.

Ren L, Lin R, Zhao J, et al. Stimulated reservoir volume estimation for shale gas fracturing: Mechanism and modeling approaching [J]. J Pet Sci Eng,2017,166:290-304

Ren L, Su Y, Zhan S, et al. Modeling and simulation of complex fracture network propagation with SRV fracturing in unconventional shale reservoirs [J]. J Nat Gas Sci Eng,2016, 28:132–141

Ren Lan, Lin Ran, Zhao Jinzhou, Yang kewen, Hu Yongquan & Wang Xiujuan. Simultaneous hydraulic fracturing of ultra-low permeability sandstone reservoirs in China: Mechanism and its field test[J]. Journal of Central South University,2015,22(4):1427-1436.

Shahid ASA, Wassing BBT, Fokker PA ,et al. Natural-fracture reactivation in shale gas reservoir and resulting microseismicity[J]. J Can Pet Technol ,2015,54(06):450–459

Sun RZ (2016) The research on the calculation method of stimulated reservoir volume for shale gas reservoir in Fuling area of China. Master Degree Thesis, Southwest Petroleum University

Wang Y, Li X, Zhou RQ, et al. Numerical evaluation of the shear stimulation effect in naturally fractured formations[J]. Sci China Earth Sci,2016, 59(2):371–383

Warpinski NR & Teufel LW. Influence of geologic discontinuities on hydraulic fracture propagation[J]. JPT,1987,39(2):209-220.

Warpinski NR, Wolhart SL, Wright CA. Analysis and prediction of microseismicity induced by hydraulic fracturing.In: Paper SPE 71649-MS presented at the SPE annual technical conference and exhibition, 30 September–3 October, 2001,New Orleans

Weng X, Kresse O, Cohen CE, et al. Modeling of hydraulic fracture-network propagation in a naturally fractured formation[J].SPE Prod Oper,2011, 26(04):368–380

Xu W, Thiercelin M, Ganguly U, et al. Wiremesh: a novel shale fracturing simulator. In: Paper SPE 132218 presented at CPS/SPE international oil and gas conference and exhibitiion, 8–10 June,2010, Beijing

Xu W, Thiercelin MJ, Walton IC. Characterization of hydraulically-induced shale fracture network using an analytical/semi-analytical model. In: Paper SPE 124697-MS presented at the SPE annual technical conference and exhibition, 4–7 October, 2009,New Orleans

Yu G, Aguilera R. 3D analytical modeling of hydraulic fracturing stimulated reservoir volume. In: Paper SPE-153468 presented at SPE Latin America and Caribbean petroleum engineering conference, 16–18 April,2012, Mexico City

Zhang J, Kamenov A, Zhu D, et al. Laboratory measurement ofhydraulic fracture conductivities in the Barnett shale. In: Paper IPTC-16444-MS presented at the international petroleum technology conference, 26–28 March, 2013, Beijing

Zhou L, Hou MZ. A new numerical 3D-model for simulation of hydraulic fracturing in consideration of hydro-mechanical coupling effects. Int. J. Rock Mech. Min.Sci.,2013,60:370–380.

Zhou L, Hou MZ, Gou Y, et al. Numerical investigation of a low-efficient hydraulic fracturing operation in a tight gas reservoir in the North German Basin [J]. Journal of Petroleum Science and Engineering, 2014, 120:119-129

Zimmerman RW, Kumar S, Bodvarsson GS. Lubrication theory analysis of the permeability of rough-walled fractures[J].Int.J.RockMech.Min.Sci.,1991,28, 325–331

Zou Y, Zhang S, Ma X, et al. Numerical investigation of hydraulic fracture network propagation in naturally fractured shale formations[J]. J Struct Geol,2016, 84:1–13


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