Abstract
The Silurian Longmaxi formation in the Sichuan Basin, which is the most important gas-producing shale reservoir in China, is characterized by relatively small effective thickness, large in-situ stress difference and highly-developed natural fracture (NF) system. Microseismic monitoring shows that complex hydraulic fracture (HF) networks with relatively small height could be stimulated in the Longmaxi shale reservoirs. Traditional two-dimensional (2D) numerical models cannot capture the three-dimensional (3D) nature of the limited-height HFs, which is not suitable for investigating the fracturing of Longmaxi shale reservoirs. This work develops a fully coupled hydro-mechanical model for HF network propagation based on the discontinuous deformation analysis (DDA) method. A new efficient method is proposed to consider the 3D effect in 2D DDA-based fracturing simulations. Hence an approximate 3D solution of fracture-induced stress and deformation could be obtained. This method is verified against previous works. Then, a series of simulations is performed to investigate the influence of reservoir thickness, in-situ stress difference and NF pattern on the hydraulic stimulation of Longmaxi shale reservoirs. Modeling results show that limited reservoir thickness is favorable to the formation of HF network. Complex and dense fracture network is easily to be formed in thin reservoirs. Large in-situ stress difference will impede the hydraulic stimulation. However, when the reservoir thickness is small, dense fracture network is still likely to be formed under large stress differences. Besides, the NF system is essential for the formation of HF network. The modeling results indicate that as a result of the limited thickness and highly-developed NF system, complex and dense fracture networks could be stimulated in the Longmaxi shale reservoirs. This work partly accounts for the initial success of gas recovery in the Longmaxi shale reservoirs. It also provides a feasible numerical method and theoretical supports for further optimization of shale gas exploitation in China.
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Abbreviations
- [Di]:
-
Deformation matrix of the ith block
- u0, v0 :
-
Rigid body translation components (m)
- r 0 :
-
Rigid body rotation (°)
- εx, εy, εxy :
-
Strain components
- x0, y0 :
-
Coordinates of block centroid (m)
- u, v :
-
Displacement components (m)
- [Ti]:
-
Displacement transformation matrix of the ith block
- [K]:
-
Global stiffness matrix
- [D]:
-
Global deformation matrix
- [F]:
-
Global force matrix
- n :
-
Number of blocks
- σn, στ :
-
Normal and shear stress of the bock interface (MPa)
- T 0 :
-
Tensile strength (MPa)
- c :
-
Cohesive strength (MPa)
- φ :
-
Friction angle (°)
- F c :
-
3D constraint force (N)
- Fcx, Fcy :
-
Components of 3D constraint force (N)
- k :
-
Stiffness of constraint spring (MPa)
- ∆d :
-
Displacement vector (m)
- S 0 :
-
Area of block element (m2)
- E :
-
Young’s modulus (MPa)
- G:
-
Coefficient, representing the influence of fracture height on the constraint spring stiffness
- H :
-
Fracture height (m)
- α :
-
Empirically determined constant
- [Fi]:
-
Force matrix of ith block
- q :
-
Volumetric flow rate (m3/s)
- ω :
-
Fracture aperture (m)
- μ :
-
Dynamic viscosity of fluid (mPa·s)
- p :
-
Fluid pressure (MPa)
- p x , p y :
-
Fluid pressure components (MPa)
- c 0 :
-
Fluid injection or leak-off rate (m3/s)
- e m :
-
Average fracture aperture (m)
- r :
-
Fluid pressure ratio
- m :
-
Length of block interface (m)
- σ1, σ2,σ3 :
-
Maximum, intermediate and minimum principal stress (MPa)
- ∆σ :
-
In-situ stress difference (MPa)
References
Adachi J, Siebrits E, Peirce A, Desroches J (2007) Computer simulation of hydraulic fractures. Int J Rock Mech Min Sci 44(5):739–757. https://doi.org/10.1016/j.ijrmms.2006.11.006
Advani SH, Lee TS, Lee JK (1990) Three-dimensional modeling of hydraulic fractures in layered media: Part I—finite element formulations. J Energy Resour Technol 112(1):1–9. https://doi.org/10.1115/1.2905706
Ben Y, Xue J, Miao Q, Wang Y, Shi GH (2012) Simulating hydraulic fracturing with discontinuous deformation analysis. In: 46th U.S. Rock Mechanics/Geomechanics Symposium, Chicago, IL, 24–27 June
Carrier B, Granet S (2012) Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng Fract Mech 79:312–328. https://doi.org/10.1016/j.engfracmech.2011.11.012
Chen X (2018) Fracture propagation law for shale gas well in strip-curvature-crack development area: a case study of Southwest Jiaoshiba Block in Fuling shale gas field. Fault-Block Oil Gas Field 25(6):742–746 (in Chinese)
Chen S, Zhu Y, Wang H, Liu H, Wei W, Fang J (2011) Shale gas reservoir characterisation: A typical case in the southern Sichuan Basin of China. Energy 36(11):6609–6616. https://doi.org/10.1016/j.energy.2011.09.001
Chen Z, Cheng X, Huang X, Bai W, Jin Z (2014) Three-dimensional numerical analysis of magma transport through a pre-existing fracture in the crust. J Geodyn 76:46–55. https://doi.org/10.1016/j.jog.2014.03.002
Choo LQ, Zhao Z, Chen H, Tian Q (2016) Hydraulic fracturing modeling using the discontinuous deformation analysis (DDA) method. Comput Geotech 76:12–22. https://doi.org/10.1016/j.compgeo.2016.02.011
Damjanac B, Cundall P (2016) Application of distinct element methods to simulation of hydraulic fracturing in naturally fractured reservoirs. Comput Geotech 71:283–294. https://doi.org/10.1016/j.compgeo.2015.06.007
Danko G, Jobbik A, Baracza MK, Varga G, Kovacs I, Wittig V (2020) Energy potential of a single-fracture, robust, engineered geothermal system. Geomech Geophys Geo-Energy Geo-Resour 6:26. https://doi.org/10.1007/s40948-020-00149-x
Dong D, Wang Y, Li X, Zou C, Guan Q, Zhang C, Huang J, Wang S, Wang H, Liu H, Bai W, Liang F, Lin W, Zhao Q, Liu D, Qiu Z (2016) Breakthrough and prospect of shale gas exploration and development in China. Nat Gas Ind B 3(1):12–26. https://doi.org/10.1016/j.ngib.2016.02.002
Dong D, Shi Z, Guan Q, Jiang S, Zhang M, Zhang C, Wang S, Sun S, Yu R, Liu D, Peng P, Wang S (2018) Progress, challenges and prospects of shale gas exploration in the Wufeng–Longmaxi reservoirs in the Sichuan Basin. Nat Gas Ind B 5(5):415–424. https://doi.org/10.1016/j.ngib.2018.04.011
Fan C, Zhong C, Zhang Y, Qin Q, HE S (2019) Geological factors controlling the accumulation and high yield of marine-facies shale gas: case study of the Wufeng-Longmaxi formation in the Dingshan Area of Southeast Sichuan, China. Acta Geol Sin 93(3):536–560. https://doi.org/10.1111/1755-6724.13857
Figueiredo B, Tsang CF, Rutqvist J, Niemi A (2017) Study of hydraulic fracturing processes in shale formations with complex geological settings. J Pet Sci Eng 152:361–374. https://doi.org/10.1016/j.petrol.2017.03.011
Fisher MK, Warpinski NR (2012) Hydraulic-fracture-height growth: Real data. SPE Prod Oper 27(1):8–19. https://doi.org/10.2118/145949-PA
Gao D, Zhao Z, Zhang H, Li T (2018) Micro-seismic real-time monitoring technology for staged fracturing wells in Jiaoshiba Block. Well Test 27(5):42–49 (in Chinese)
Geertsma J, De Klerk F (1969) A Rapid method of predicting width and extent of hydraulically induced fractures. J Pet Technol 21(12):1571–1581. https://doi.org/10.2118/2458-PA
Gordeliy E, Peirce A (2013) Coupling schemes for modeling hydraulic fracture propagation using the XFEM. Comput Methods Appl Mech Eng 253:305–322. https://doi.org/10.1016/j.cma.2012.08.017
Guo T, Zhang H (2014) Formation and enrichment mode of Jiaoshiba shale gas field, Sichuan Basin. Pet Explor Dev 41(1):31–40. https://doi.org/10.1016/S1876-3804(14)60003-3
Heng S, Guo Y, Yang C, Daemen JJK, Li Z (2015) Experimental and theoretical study of the anisotropic properties of shale. Int J Rock Mech Min Sci 74:58–68. https://doi.org/10.1016/J.IJRMMS.2015.01.003
Itasca Consulting Group Inc (2014) UDEC (universal distinct element code), version 6.0 ICG. Itasca, Minneapolis
Jiao YY, Zhao J, Ge XR (2004) New formulation and validation of the three-dimensional extension of a static relaxation method. Adv Eng Softw 35(6):317–323. https://doi.org/10.1016/j.advengsoft.2004.04.004
Jiao YY, Zhang HQ, Zhang XL, Li HB, Jiang QH (2015) A two-dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing. Int J Numer Anal Methods Geomech 39(5):457–481. https://doi.org/10.1002/nag.2314
Jing L, Ma Y, Fang Z (2001) Modeling of fluid flow and solid deformation for fractured rocks with discontinuous deformation analysis (DDA) method. Int J Rock Mech Min Sci 38(3):343–355. https://doi.org/10.1016/S1365-1609(01)00005-3
Kresse O, Weng X, Gu H, Wu R (2013) Numerical modeling of hydraulic fractures interaction in complex naturally fractured formations. Rock Mech Rock Eng 46:555–568. https://doi.org/10.1007/s00603-012-0359-2
Li Z, Li L, Huang B, Zhang L, Li M, Zuo J, Li A, Yu Q (2017) Numerical investigation on the propagation behavior of hydraulic fractures in shale reservoir based on the DIP technique. J Pet Sci Eng 154:302–314. https://doi.org/10.1016/j.petrol.2017.04.034
Li F, Yang Y, Fan X, Xu B, Ju Y, Wang Y, Li Y, Chen J (2018) Numerical analysis of the hydrofracturing behaviours and mechanisms of heterogeneous reservoir rock using the continuum-based discrete element method considering pre-existing fractures. Geomech Geophys Geo-Energy Geo-Resour 4:383–401. https://doi.org/10.1007/s40948-018-0095-5
Liang C, Jiang Z, Yang Y, Wei X (2012) Shale lithofacies and reservoir space of the Wufeng-Longmaxi Formation, Sichuan Basin, China. Pet Explor Dev 39(6):736–743. https://doi.org/10.1016/S1876-3804(12)60098-6
Liao Z, Ren M, Tang C, Zhu J (2020) A three-dimensional damage-based contact element model for simulating the interfacial behaviors of rocks and its validation and applications. Geomech Geophys Geo-Energy Geo-Resour 6:45. https://doi.org/10.1007/s40948-020-00171-z
Lin C, He J, Li X, Wan X, Zheng B (2017) An experimental investigation into the effects of the anisotropy of shale on hydraulic fracture propagation. Rock Mech Rock Eng 50:543–554. https://doi.org/10.1007/s00603-016-1136-4
Lisjak A, Kaifosh P, He L, Tatone BSA, Mahabadi OK, Grasselli G (2017) A 2D, fully-coupled, hydro-mechanical, FDEM formulation for modelling fracturing processes in discontinuous, porous rock masses. Comput Geotech 81:1–18. https://doi.org/10.1016/j.compgeo.2016.07.009
Liu S, Ma W, Jansa L, Huang W, Zeng X, Zhang C (2013) Characteristics of the Shale Gas Reservoir Rocks in the Lower Silurian Longmaxi Formation, East Sichuan Basin, China. Energy Explor Exploit 31(2):187–219. https://doi.org/10.1260/0144-5987.31.2.187
Liu Y, Liao R, Zhang Y, Gao D, Zhang H, Li T, Zhang C (2017) Application of surface–downhole combined microseismic monitoring technology in the Fuling shale gas field and its enlightenment. Nat Gas Ind B 4(1):62–67. https://doi.org/10.1016/j.ngib.2017.07.009
Liu HH, Chen H, An C (2019) A criterion for evaluating the effect of shale-matrix dual-continuum flow on gas production. Geomech Geophys Geo-Energy Geo-Resour 5:87–102. https://doi.org/10.1007/s40948-018-0100-z
Ma X, Li N, Yin C, Li Y, Zou Y, Wu S, He F, Wang X, Zhou T (2017) Hydraulic fracture propagation geometry and acoustic emission interpretation: A case study of Silurian Longmaxi Formation shale in Sichuan Basin, SW China. Pet Explor Dev 44(6):1030–1037. https://doi.org/10.1016/s1876-3804(17)30116-7
Mayerhofer MJ, Lolon EP, Rightmire C, Walser D, Cipolla CL, Warplnskl NR (2010) What is stimulated reservoir volume? SPE Prod Oper 25(1):89–98. https://doi.org/10.2118/119890-PA
McClure M, Horne R (2014) Characterizing hydraulic fracturing with a tendency-for-shear-stimulation test. SPE Reserv Eval Eng 17(2):233–243. https://doi.org/10.2118/166332-PA
Morgan WE, Aral MM (2015) An implicitly coupled hydro-geomechanical model for hydraulic fracture simulation with the discontinuous deformation analysis. Int J Rock Mech Min Sci 73:82–94. https://doi.org/10.1016/j.ijrmms.2014.09.021
Nagel NB, Sanchez-Nagel MA, Zhang F, Garcia X, Lee B (2013) Coupled numerical evaluations of the geomechanical interactions between a hydraulic fracture stimulation and a natural fracture system in shale formations. Rock Mech Rock Eng 46:581–609. https://doi.org/10.1007/s00603-013-0391-x
Nordgren RP (1972) Propagation of a vertical hydraulic fracture. Soc Pet Eng J 12(4):306–314. https://doi.org/10.2118/3009-PA
Olson JE (2004) Predicting fracture swarms — the influence of subcritical crack growth and the crack-tip process zone on joint spacing in rock. Geol Soc London Spec Publ 231(1):73–88. https://doi.org/10.1144/GSL.SP.2004.231.01.05
Riahi A, Damjanac B (2013) Numerical study of interaction between hydraulic fracture and discrete fracture network. In: ISRM international conference for effective and sustainable hydraulic fracturing, Brisbane, Australia, 20–22 May
Rongved M, Holt RM, Larsen I (2019) The effect of heterogeneity on multiple fracture interaction and on the effect of a non-uniform perforation cluster distribution. Geomech Geophys Geo-Energy Geo-Resour 5:315–332. https://doi.org/10.1007/s40948-019-00113-4
Shi GH (1988) Discontinuous deformation analysis—a new model for the statics and dynamics of block systems. PhD Dissertation, University of California, Berkeley, CA
Siebrits E, Peirce AP (2002) An efficient multi-layer planar 3D fracture growth algorithm using a fixed mesh approach. Int J Numer Methods Eng 53(3):691–717. https://doi.org/10.1002/nme.308
Wang YM, Dong DZ, Yang H, He L, Wang SQ, Huang JL, Pu BL, Wang SF (2014) Quantitative characterization of reservoir space in the Lower Silurian Longmaxi Shale, southern Sichuan, China. Sci China Earth Sci 57:313–322. https://doi.org/10.1007/s11430-013-4645-y
Wang Y, Li X, Zhang YX, Wu YS, Zheng B (2016a) Gas shale hydraulic fracturing: a numerical investigation of the fracturing network evolution in the Silurian Longmaxi formation in the southeast of Sichuan Basin, China, using a coupled FSD approach. Environ Earth Sci 75:1093. https://doi.org/10.1007/s12665-016-5696-0
Wang Y, Li X, Zhou RQ, Zheng B, Zhang B, Wu YF (2016b) Numerical evaluation of the effect of fracture network connectivity in naturally fractured shale based on FSD model. Sci China Earth Sci 59(3):626–639. https://doi.org/10.1007/s11430-015-5164-9
Weng X (2015) Modeling of complex hydraulic fractures in naturally fractured formation. J Unconv Oil Gas Resour 9:114–135. https://doi.org/10.1016/j.juogr.2014.07.001
Wu K, Olson JE (2015) Numerical investigation of complex hydraulic fracture development in naturally fractured reservoirs. In: SPE paper 173326 presented at hydraulic fracturing technology conference, Woodlands, TX, 3–5 Feb. https://doi.org/10.2118/173326-ms
Wu Y, Li X, He J, Zheng B (2016) Mechanical properties of Longmaxi black organic-Rich shale samples from South China under uniaxial and triaxial compression states. Energies 9(12):1088. https://doi.org/10.3390/en9121088
Xu S, Gou Q, Hao F, Zhang B, Shu Z, Zhang Y (2020) Multiscale faults and fractures characterization and their effects on shale gas accumulation in the Jiaoshiba area, Sichuan Basin, China. J Pet Sci Eng 189:107026. https://doi.org/10.1016/j.petrol.2020.107026
Yan C, Jiao YY (2018) A 2D fully coupled hydro-mechanical finite-discrete element model with real pore seepage for simulating the deformation and fracture of porous medium driven by fluid. Comput Struct 196:311–326. https://doi.org/10.1016/j.compstruc.2017.10.005
Yan C, Zheng H, Sun G, Ge X (2015) Combined finite-discrete element method for simulation of hydraulic fracturing. Rock Mech Rock Eng 49:1389–1410. https://doi.org/10.1007/s00603-015-0816-9
Yang SQ, Yin PF, Ranjith PG (2020a) Experimental study on mechanical behavior and brittleness characteristics of Longmaxi Formation shale in Changning, Sichuan Basin, China. Rock Mech Rock Eng 53:2461–2483. https://doi.org/10.1007/s00603-020-02057-8
Yang W, Geng Y, Zhou Z, Li L, Gao C, Wang M, Zhang D (2020b) DEM numerical simulation study on fracture propagation of synchronous fracturing in a double fracture rock mass. Geomech Geophys Geo-Energy Geo-Resour 6:39. https://doi.org/10.1007/s40948-020-00162-0
Yasin Q, Du Q, Sohail GM, Ismail A (2018) Fracturing index-based brittleness prediction from geophysical logging data: application to Longmaxi shale. Geomech Geophys Geo-Energy Geo-Resour 4:301–325. https://doi.org/10.1007/s40948-018-0088-4
Zhang Z, Li X, Yuan W, He J, Li G, Wu Y (2015) Numerical analysis on the optimization of hydraulic fracture networks. Energies 8(10):12061–12079. https://doi.org/10.3390/en81012061
Zhang H, Xu C, Xiao H, Zhang X, Zhong Z (2019) Evaluation of fracturing effect of B201–7H1 Well in Fengdu Block. J Chongq Univ Sci Technol (Nat Sci Edit) 21(5):18–22 (in Chinese)
Zhao X, Yang Y (2015) The current situation of shale gas in Sichuan, China. Renew Sust Energ Rev 50:653–664. https://doi.org/10.1016/j.rser.2015.05.023
Zhao W, Ge J, Wang T, Zhang H, Li Y (2020) Study on catastrophe mechanism of hydraulic fracturing fracks initiation in radial boreholes. Geomech Geophys Geo-Energy Geo-Resour 6:47. https://doi.org/10.1007/s40948-020-00169-7
Zou C, Dong D, Wang S, Li J, Li X, Wang Y, Li D, Cheng K (2010) Geological characteristics and resource potential of shale gas in China. Pet Explor Dev 37(6):641–653. https://doi.org/10.1016/S1876-3804(11)60001-3
Zou C, Dong D, Wang Y, Li X, Huang J, Wang S, Guan Q, Zhang C, Wang H, Liu H, Bai W, Liang F, Lin W, Zhao Q, Liu D, Yang Z, Liang P, Sun S, Qiu Z (2016a) Shale gas in China: Characteristics, challenges and prospects (II). Pet Explor Dev 43(2):182–196. https://doi.org/10.1016/S1876-3804(16)30022-2
Zou C, Yang Z, Pan S, Chen Y, Lin S, Huang J, Wu S, Dong D, Wang S, Liang F, Sun S, Huang Y, Weng D (2016b) Shale gas formation and occurrence in China: An overview of the current status and future potential. Acta Geol Sin-English Ed 90(4):1249–1283. https://doi.org/10.1111/1755-6724.12769
Zou C, Pan S, Jing Z, Gao J, Yang Z, Wu S, Zhao Q (2020) Shale oil and gas revolution and its impact. Acta Pet Sin 41(1):1–12 (in Chinese)
Acknowledgements
The authors would like to thank the Editor and the anonymous reviewers for their helpful and constructive comments. This work was supported by the National Natural Science Foundation of China (No. 51734009), the Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (No. 2019QZKK0904), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB10030000), Science Foundation of Key Laboratory of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences (No.KLSG201708) and the Joint PhD Training Program of University of Chinese Academy of Sciences (UCAS).
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Hu, Y., Li, X., Zhang, Z. et al. Numerical investigation on the hydraulic stimulation of naturally fractured Longmaxi shale reservoirs using an extended discontinuous deformation analysis (DDA) method. Geomech. Geophys. Geo-energ. Geo-resour. 6, 73 (2020). https://doi.org/10.1007/s40948-020-00195-5
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DOI: https://doi.org/10.1007/s40948-020-00195-5