Three-Dimensional Hydraulic Fracture Simulation with Hydromechanical Coupled-Element Partition Method
Publication: International Journal of Geomechanics
Volume 21, Issue 9
Abstract
The numerical simulation of a 3D complex reservoir has been an important but difficult problem. One of the biggest challenges is how to deal with the large number of natural fractures with consideration of hydromechanical coupling effect in those fractures. To address this problem, a 3D hydromechanical coupled element partition method (3D-EPM) is developed. The 3D-EPM allows a fracture to run through an element without any extra degree of freedom. It can embed any number of fractures in a background mesh without mesh modification. This brings great convenience to 3D reservoir simulation. To represent the permeability of a cracked element, the equivalent permeability of this cracked element is derived based on the cubic law. To account for the hydromechanical coupling effect in a fracture, the coupled equation of 3D-EPM is developed. It is verified by the analytical model. The simulation results suggest that this method can simulate the 3D hydraulic fracture propagation, its interaction with natural fractures and the impact of in-situ stresses. This paper provides an alternative method for the 3D hydraulic fracture simulation in a complex reservoir with consideration of hydromechanical coupling effect in a fracture.
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Acknowledgments
The present work is supported by Beijing Outstanding Young Scientist Program (No. BJJWZYJH01201911414038) and the National Natural Science Foundation of China (No. 11772190), which is gratefully acknowledged.
References
Adachi, J., E. Siebrits, A. Peirce, and J. Desroches. 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.
Bao, J. Q., E. Fathi, and S. Ameri. 2014. “A coupled finite element method for the numerical simulation of hydraulic fracturing with a condensation technique.” Eng. Fract. Mech. 131: 269–281. https://doi.org/10.1016/j.engfracmech.2014.08.002.
Belytschko, T., and T. Black. 1999. “Elastic crack growth in finite elements with minimal remeshing.” Int. J. Numer. Methods Eng. 45 (5): 601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5%3C601::AID-NME598%3E3.0.CO;2-S.
Boone, T. J., and A. R. Ingraffea. 1990. “A numerical procedure for simulation of hydraulically driven fracture propagation in poroelastic media.” Int. J. Numer. Anal. Methods Geomech. 14 (1): 27–47. https://doi.org/10.1002/nag.1610140103.
Chen, Y., and Z. Zhang. 2017. “Dynamic fracture simulation by using a discretized virtual internal bond with a regular hexagon cell.” Int. J. Comput. Methods 14 (6): 1750066. https://doi.org/10.1142/S0219876217500669.
Chen, Z. 2012. “Finite element modelling of viscosity-dominated hydraulic fractures.” J. Pet. Sci. Eng. 88–89: 136–144. https://doi.org/10.1016/j.petrol.2011.12.021.
Cheng, L., Z. Luo, Y. Yu, L. Zhao, and C. Zhou. 2019. “Study on the interaction mechanism between hydraulic fracture and natural karst cave with the extended finite element method.” Eng. Fract. Mech. 222: 106680. https://doi.org/10.1016/j.engfracmech.2019.106680.
Chong, Z., S. Karekal, X. Li, P. Hou, G. Yang, and S. Liang. 2017. “Numerical investigation of hydraulic fracturing in transversely isotropic shale reservoirs based on the discrete element method.” J. Nat. Gas Sci. Eng. 46: 398–420. https://doi.org/10.1016/j.jngse.2017.08.021.
Choo, L. Q., Z. Zhao, H. Chen, and Q. Tian. 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.
Deng, G., S. Wang, and B. Huang. 2004. “Research on behavior character of crack development induced by hydraulic fracturing in coal-rockmass.” [In Chinese.] Chin. J. Rock Mech. Rock Eng. 3 (20): 3489–3493.
Dong, W., Z. Wu, X. Tang, and X. Zhou. 2018. “A comparative study on stress intensity factor-based criteria for the prediction of mixed mode I-II crack propagation in concrete.” Eng. Fract. Mech. 197: 217–235. https://doi.org/10.1016/j.engfracmech.2018.05.009.
Emerman, S. H., D. L. Turcotte, and D. A. Spence. 1986. “Transport of magma and hydrothermal solutions by laminar and turbulent fluid fracture.” Phys. Earth Planet. Inter. 41 (4): 249–259. https://doi.org/10.1016/0031-9201(86)90004-X.
Francfort, G. A., and J. J. Marigo. 1998. “Revisiting brittle fracture as an energy minimization problem.” J. Mech. Phys. Solids 46 (8): 1319–1342. https://doi.org/10.1016/S0022-5096(98)00034-9.
Gao, Q., and A. Ghassemi. 2020a. “Finite element simulations of 3D planar hydraulic fracture propagation using a coupled hydro-mechanical interface element.” Int. J. Numer. Anal. Methods Geomech. 44 (15): 1999–2024. https://doi.org/10.1002/nag.3116.
Gao, Q., and A. Ghassemi. 2020b. “Three dimensional finite element simulations of hydraulic fracture height growth in layered formations using a coupled hydro-mechanical model.” Int. J. Rock Mech. Min. Sci. 125: 104137. https://doi.org/10.1016/j.ijrmms.2019.104137.
Geertsma, J., and F. de Klerk. 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.
Guo, J., X. Zhao, H. Zhu, X. Zhang, and R. Pan. 2015. “Numerical simulation of interaction of hydraulic fracture and natural fracture based on the cohesive zone finite element method.” J. Nat. Gas Sci. Eng. 25: 180–188. https://doi.org/10.1016/j.jngse.2015.05.008.
Guo, T., S. Tang, S. Liu, X. Liu, W. Zhang, and G. Qu. 2020. “Numerical simulation of hydraulic fracturing of hot dry rock under thermal stress.” Eng. Fract. Mech. 240: 107350. https://doi.org/10.1016/j.engfracmech.2020.107350.
Gupta, P., and C. A. Duarte. 2014. “Simulation of non-planar three-dimensional hydraulic fracture propagation.” Int. J. Numer. Anal. Methods Geomech. 38 (13): 1397–1430. https://doi.org/10.1002/nag.2305.
Haddad, M., and K. Sepehrnoori. 2016. “XFEM-based CZM for the simulation of 3D multiple-cluster hydraulic fracturing in quasi-brittle shale formations.” Rock Mech. Rock Eng. 49 (12): 4731–4748. https://doi.org/10.1007/s00603-016-1057-2.
Hu, M., Y. Wang, and J. Rutqvist. 2017. “Fully coupled hydro-mechanical numerical manifold modeling of porous rock with dominant fractures.” Acta Geotech. 12 (2): 231–252. https://doi.org/10.1007/s11440-016-0495-z.
Huang, K., and Z. Zhang. 2010. “Three dimensional element partition method and numerical simulation of fractures subjected to compressive and shear stress.” [In Chinese.] Eng. Mech. 27 (12): 51–58.
Huang, K., Z. Zhang, and A. Ghassemi. 2013. “Modeling three-dimensional hydraulic fracture propagation using virtual multidimensional internal bonds.” Int. J. Numer. Anal. Methods Geomech. 37 (13): 2021–2038. https://doi.org/10.1002/nag.2119.
Huang, M., and O. C. Zienkiewicz. 1998. “New unconditionally stable staggered solution procedures for coupled soil-pore fluid dynamic problems.” Int. J. Numer. Methods Eng. 43 (6): 1029–1052. https://doi.org/10.1002/(SICI)1097-0207(19981130)43:6%3C1029::AID-NME459%3E3.0.CO;2-H.
Jiao, Y.-Y., H.-Q. Zhang, X.-L. Zhang, H.-B. Li, and Q.-H. Jiang. 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.
Katona, M. C., and O. C. Zienkiewicz. 1985. “A unified set of single step algorithms part 3: The beta-m method, a generalization of the Newmark scheme.” Int. J. Numer. Methods Eng. 21 (7): 1345–1359. https://doi.org/10.1002/nme.1620210713.
Khoei, A. R., S. Moallemi, and E. Haghighat. 2012. “Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique.” Eng. Fract. Mech. 96: 701–723. https://doi.org/10.1016/j.engfracmech.2012.10.003.
Khoei, A. R., M. Vahab, E. Haghighat, and S. Moallemi. 2014. “A mesh-independent finite element formulation for modeling crack growth in saturated porous media based on an enriched-FEM technique.” Int. J. Fract. 188 (1): 79–108. https://doi.org/10.1007/s10704-014-9948-2.
Khristianovic, S. A., and Y. P. Zheltov. 1955. “Formation of vertical fractures by means of highly viscous liquid.” In Proc., 4th World Petroleum Congress, 579–586. https://onepetro.org/WPCONGRESS/proceedings-abstract/WPC04/All-WPC04/WPC-6132/203824.
Kwok, C., K. Duan, and M. Pierce. 2020. “Modeling hydraulic fracturing in jointed shale formation with the use of fully coupled discrete element method.” Acta Geotech. 15 (1): 245–264. https://doi.org/10.1007/s11440-019-00858-y.
Lecampion, B., and E. Detournay. 2007. “An implicit algorithm for the propagation of a hydraulic fracture with a fluid lag.” Comput. Methods Appl. Mech. Eng. 196 (49–52): 4863–4880. https://doi.org/10.1016/j.cma.2007.06.011.
Li, S., X. Li, and D. Zhang. 2016. “A fully coupled thermo-hydro-mechanical, three-dimensional model for hydraulic stimulation treatments.” J. Nat. Gas Sci. Eng. 34: 64–84. https://doi.org/10.1016/j.jngse.2016.06.046.
Lisjak, A., P. Kaifosh, L. He, B. S. A. Tatone, O. K. Mahabadi, and G. Grasselli. 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, F., P. A. Gordon, and D. M. Valiveti. 2018. “Modeling competing hydraulic fracture propagation with the extended finite element method.” Acta Geotech. 13 (2): 243–265. https://doi.org/10.1007/s11440-017-0569-6.
Liu, Y., and S. Mahadevan. 2007. “Threshold stress intensity factor and crack growth rate prediction under mixed-mode loading.” Eng. Fract. Mech. 74 (3): 332–345. https://doi.org/10.1016/j.engfracmech.2006.06.003.
Meng, Q., S. Zhang, X. Guo, X. Chen, and Y. Zhang. 2010. “A primary investigation on propagation mechanism for hydraulic fracture in glutenite formation.” [In Chinese.] J. Oil Gas Technol. 32 (4): 119–123.
Mohammadnejad, T., and A. R. Khoei. 2013. “An extended finite element method for hydraulic fracture propagation in deformable porous media with the cohesive crack model.” Finite Elem. Anal. Des. 73: 77–95. https://doi.org/10.1016/j.finel.2013.05.005.
Morgan, W. E., and M. M. Aral. 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.
Morita, N., D. L. Whitfill, and H. A. Wahl. 1988. “Stress-intensity factor and fracture cross-sectional shape predictions from a three-dimensional model for hydraulically induced fractures.” J. Pet. Technol. 40 (10): 1–329. https://doi.org/10.2118/14262-PA.
Nordgren, R. P. 1972. “Propagation of a vertical hydraulic fracture.” Soc. Pet. Eng. J. 12 (4): 306–314. https://doi.org/10.2118/3009-PA.
Oda, M. 1986. “An equivalent continuum model for coupled stress and fluid flow analysis in jointed rock masses.” Water Resour. Res. 22 (13): 1845–1856. https://doi.org/10.1029/WR022i013p01845.
Paul, B., M. Faivre, P. Massin, R. Giot, D. Colombo, F. Golfier, and A. Martin. 2018. “3D coupled HM-XFEM modeling with cohesive zone model and applications to non planar hydraulic fracture propagation and multiple hydraulic fractures interference.” Comput. Methods Appl. Mech. Eng. 342: 321–353. https://doi.org/10.1016/j.cma.2018.08.009.
Peirce, A. P., and E. Siebrits. 2001. “Uniform asymptotic approximations for accurate modeling of cracks in layered elastic media.” Int. J. Fract. 110 (3): 205–239. https://doi.org/10.1023/A:1010861821959.
Peirce, A. P., and E. Siebrits. 2005. “A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problems.” Int. J. Numer. Methods Eng. 63 (13): 1797–1823. https://doi.org/10.1002/nme.1330.
Perkins, T. K., and L. R. Kern. 1961. “Widths of hydraulic fractures.” J. Pet. Technol. 13 (9): 937–949. https://doi.org/10.2118/89-PA.
Roche, V., M. van Der Baan, and G. Preisig. 2018. “A study of 3D modeling of hydraulic fracturing and stress perturbations during fluid injection.” J. Pet. Sci. Eng. 170: 829–843. https://doi.org/10.1016/j.petrol.2018.06.037.
Roth, S.-N., P. Léger, and A. Soulaïmani. 2020a. “Strongly coupled XFEM formulation for non-planar three-dimensional simulation of hydraulic fracturing with emphasis on concrete dams.” Comput. Methods Appl. Mech. Eng. 363: 112899. https://doi.org/10.1016/j.cma.2020.112899.
Roth, S.-N., P. Léger, and A. Soulaïmani. 2020b. “Fully-coupled hydro-mechanical cracking using XFEM in 3D for application to complex flow in discontinuities including drainage system.” Comput. Methods Appl. Mech. Eng. 370: 113282. https://doi.org/10.1016/j.cma.2020.113282.
Schrefler, B. A., S. Secchi, and L. Simoni. 2006. “On adaptive refinement techniques in multi-field problems including cohesive fracture.” Comput. Methods Appl. Mech. Eng. 195 (4–6): 444–461. https://doi.org/10.1016/j.cma.2004.10.014.
Settari, A., and M. P. Cleary. 1986. “Development and testing of a pseudo-three-dimensional model of hydraulic fracture geometry.” SPE Prod. Eng. 1 (6): 449–466. https://doi.org/10.2118/10505-PA.
Settgast, R. R., P. Fu, S. D. C. Walsh, J. A. White, C. Annavarapu, and F. J. Ryerson. 2017. “A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions.” Int. J. Numer. Anal. Methods Geomech. 41 (5): 627–653. https://doi.org/10.1002/nag.2557.
Seweryn, A. 1994. “Brittle fracture criterion for structures with sharp notches.” Eng. Fract. Mech. 47 (5): 673–681. https://doi.org/10.1016/0013-7944(94)90158-9.
Shimizu, H., T. Ito, T. Tamagawa, and K. Tezuka. 2018. “A study of the effect of brittleness on hydraulic fracture complexity using a flow-coupled discrete element method.” J. Pet. Sci. Eng. 160: 372–383. https://doi.org/10.1016/j.petrol.2017.10.064.
Siebrits, E., and A. P. Peirce. 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.
Simonson, E. R., A. S. Abou-Sayed, and R. J. Clifton. 1978. “Containment of massive hydraulic fractures.” Soc. Pet. Eng. J. 18 (1): 27–32. https://doi.org/10.2118/6089-PA.
Spence, D. A., and P. Sharp. 1985. “Self-similar solutions for elastohydrodynamic cavity flow.” Proc. R. Soc. London, Ser. A 400 (1819): 289–313. https://doi.org/10.1098/rspa.1985.0081.
Taleghani, A. D., M. Gonzalez-Chavez, H. Yu, and H. Asala. 2018. “Numerical simulation of hydraulic fracture propagation in naturally fractured formations using the cohesive zone model.” J. Pet. Sci. Eng. 165: 42–57. https://doi.org/10.1016/j.petrol.2018.01.063.
Vahab, M., and N. Khalili. 2020. “Empirical and conceptual challenges in hydraulic fracturing with special reference to the inflow.” Int. J. Geomech. 20 (3): 04019182. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001545.
Wangen, M. 2013. “Finite element modeling of hydraulic fracturing in 3D.” Comput. Geosci. 17 (4): 647–659. https://doi.org/10.1007/s10596-013-9346-2.
Wu, M., D. Zhang, W. Wang, M. Li, S. Liu, J. Lu, and H. Gao. 2020a. “Numerical simulation of hydraulic fracturing based on two-dimensional surface fracture morphology reconstruction and combined finite-discrete element method.” J. Nat. Gas Sci. Eng. 82: 103479. https://doi.org/10.1016/j.jngse.2020.103479.
Wu, W., Y. Yang, and H. Zheng. 2020b. “Hydro-mechanical simulation of the saturated and semi-saturated porous soil-rock mixtures using the numerical manifold method.” Comput. Methods Appl. Mech. Eng. 370: 113238. https://doi.org/10.1016/j.cma.2020.113238.
Wu, Z., H. Sun, and L. N. Y. Wong. 2019. “A cohesive element-based numerical manifold method for hydraulic fracturing modelling with voronoi grains.” Rock Mech. Rock Eng. 52 (7): 2335–2359. https://doi.org/10.1007/s00603-018-1717-5.
Xia, L., J. Yvonnet, and S. Ghabezloo. 2017. “Phase field modeling of hydraulic fracturing with interfacial damage in highly heterogeneous fluid-saturated porous media.” Eng. Fract. Mech. 186: 158–180. https://doi.org/10.1016/j.engfracmech.2017.10.005.
Xie, L., K. Min, and B. Shen. 2016. “Simulation of hydraulic fracturing and its interactions with a pre-existing fracture using displacement discontinuity method.” J. Nat. Gas Sci. Eng. 36: 1284–1294. https://doi.org/10.1016/j.jngse.2016.03.050.
Yan, C., and Y.-Y. Jiao. 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., Y.-Y. Jiao, and H. Zheng. 2018. “A fully coupled three-dimensional hydro-mechanical finite discrete element approach with real porous seepage for simulating 3D hydraulic fracturing.” Comput. Geotech. 96: 73–89. https://doi.org/10.1016/j.compgeo.2017.10.008.
Yan, C., and H. Zheng. 2016. “A two-dimensional coupled hydro-mechanical finite-discrete model considering porous media flow for simulating hydraulic fracturing.” Int. J. Rock Mech. Min. Sci. 88: 115–128. https://doi.org/10.1016/j.ijrmms.2016.07.019.
Yan, C., and H. Zheng. 2017. “Three-dimensional hydromechanical model of hydraulic fracturing with arbitrarily discrete fracture networks using finite-discrete element method.” Int. J. Geomech. 17 (6): 04016133. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000819.
Yew, C. H., and G. F. Liu. 1993. “The fracture tip and critical stress intensity factor of a hydraulically induced fracture.” SPE Prod. Facil. 8 (3): 171–177. https://doi.org/10.2118/22875-PA.
Yin, Z., H. Huang, F. Zhang, L. Zhang, and S. Maxwell. 2020. “Three-dimensional distinct element modeling of fault reactivation and induced seismicity due to hydraulic fracturing injection and backflow.” J. Rock Mech. Geotech. Eng. 12 (4): 752–767. https://doi.org/10.1016/j.jrmge.2019.12.009.
Zeng, Q., J. Yao, and J. Shao. 2020. “An extended finite element solution for hydraulic fracturing with thermo-hydro-elastic–plastic coupling.” Comput. Methods Appl. Mech. Eng. 364: 112967. https://doi.org/10.1016/j.cma.2020.112967.
Zhang, F., B. Damjanac, and S. Maxwell. 2019. “Investigating hydraulic fracturing complexity in naturally fractured rock masses using fully coupled multiscale numerical modeling.” Rock Mech. Rock Eng. 52 (12): 5137–5160. https://doi.org/10.1007/s00603-019-01851-3.
Zhang, H., and J. J. Sheng. 2020. “Numerical simulation and optimization study of the complex fracture network in naturally fractured reservoirs.” J. Pet. Sci. Eng. 195: 107726. https://doi.org/10.1016/j.petrol.2020.107726.
Zhang, Z. 2013. “Discretized virtual internal bond model for nonlinear elasticity.” Int. J. Solids Struct. 50 (22–23): 3618–3625. https://doi.org/10.1016/j.ijsolstr.2013.07.003.
Zhang, Z., and Y. Chen. 2009a. “Simulation of fracture propagation subjected to compressive and shear stress field using virtual multidimensional internal bonds.” Int. J. Rock Mech. Min. Sci. 46 (6): 1010–1022. https://doi.org/10.1016/j.ijrmms.2009.01.003.
Zhang, Z., and Y. Chen. 2009b. “Novel numerical approach to jointed rock mass simulation: Element partition method.” [In Chinese.] Chin. J. Geotech. Eng. 31 (12): 1858–1865.
Zhang, Z., and A. Ghassemi. 2011. “Simulation of hydraulic fracture propagation near a natural fracture using virtual multidimensional internal bonds.” Int. J. Numer. Anal. Methods Geomech. 35 (4): 480–495. https://doi.org/10.1002/nag.905.
Zhang, Z., X. Li, J. He, Y. Wu, and G. Li. 2017. “Numerical study on the propagation of tensile and shear fracture network in naturally fractured shale reservoirs.” J. Nat. Gas Sci. Eng. 37: 1–14. https://doi.org/10.1016/j.jngse.2016.11.031.
Zhang, Z., D. Wang, and X. Ge. 2013. “A novel triangular finite element partition method for fracture simulation without enrichment of interpolation.” Int. J. Comput. Methods 10 (4): 1350015. https://doi.org/10.1142/S0219876213500151.
Zhang, Z., D. Wang, X. Ge, and H. Zheng. 2016. “Three-dimensional element partition method for fracture simulation.” Int. J. Geomech. 16 (3): 04015074. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000597.
Zheng, H., C. Pu, and C. Sun. 2020. “Study on the interaction between hydraulic fracture and natural fracture based on extended finite element method.” Eng. Fract. Mech. 230: 106981. https://doi.org/10.1016/j.engfracmech.2020.106981.
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International Journal of Geomechanics
Volume 21 • Issue 9 • September 2021
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© 2021 American Society of Civil Engineers.
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Received: May 18, 2020
Accepted: May 1, 2021
Published online: Jun 21, 2021
Published in print: Sep 1, 2021
Discussion open until: Nov 21, 2021
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