Abstract
Understanding the hydraulic fracturing (HF) characteristics of coral reef limestone (CRL) is of great significance for improving the mining efficiency of seabed energy (such as gas and oil) and ensuring the stability of rock masses in marine underground engineering. To investigate the crack evolution mechanism of CRL under hydraulic coupling, numerical simulations of HF on CRL are carried out using particle flow code (PFC). Firstly, a numerical model method based on two-dimensional particle flow code (PFC2D) is proposed to establish the random pore distribution model of CRL, and its effectiveness is verified through indoor experiments. Then, based on the random pore distribution method (RPDM), a numerical model of HF is created, and a calculation formula for breakdown pressure during HF of CRL is established. The breakdown pressure obtained by these two methods is relatively consistent. Finally, the influence mechanism of porosity and confining stress on the hydraulic behavior of CRL is studied. Results indicate that the propagation direction of hydraulic fracture is related to porosity and confining stress. The interactions between pores and hydraulic fractures primarily include penetration, deflection, and obstruction. The presence of pores hinders the transmission of pore pressure, reducing the seepage capacity. With increasing porosity, CRL is more likely to develop macroscopic fractures, leading to fluctuations in water injection pressure. The fluctuations are related to the number of pores involved in crack propagation, pore volume, number of propagation paths, and path length. The breakdown pressure of CRL is affected by the stress on hole walls and confining stress. A higher breakdown pressure on hole walls indicates a greater stability of the surrounding rock under high hydraulic pressures. As for the initiation stress, it is influenced by the confining stress. As the confining stress increases, the breakdown pressure on hole walls increases. For non-uniform confining stress conditions, the breakdown pressure can be determined by the minimum confining stress.
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References
Lyu Q, Tan JQ, Li L, Ju YW, Busch A, Wood DA, Ranjith PG, Middleton R, Shu B, Hu CE, Wang ZH, Hu RN (2021) The role of supercritical carbon dioxide for recovery of shale gas and sequestration in gas shale reservoirs. Energy Environ Sci 14:4203–4227. https://doi.org/10.1039/d0ee03648j
Zhang J, Li YW, Pan YS, Wang XY, Yan MS, Shi XD, Zhou XJ, Li HL (2021) Experiments and analysis on the influence of multiple closed cemented natural fractures on hydraulic fracture propagation in a tight sandstone reservoir. Eng Geol. https://doi.org/10.1016/j.enggeo.2020.105981
Xue Y, Liu J, Ranjith PG, Liang X, Wang SH (2021) Investigation of the influence of gas fracturing on fracturing characteristics of coal mass and gas extraction efficiency based on a multi-physical field model. J Pet Sci Eng. https://doi.org/10.1016/j.petrol.2021.109018
Guo TK, Tang SJ, Liu S, Liu XQ, Xu JC, Qi N, Rui ZH (2021) Physical simulation of hydraulic fracturing of large-sized tight sandstone outcrops. SPE J 26:372–393. https://doi.org/10.2118/204210-pa
Haimson BC, Cornet FH (2003) ISRM suggested methods for rock stress estimation—Part 3: hydraulic fracturing (HF) and/or hydraulic testing of pre-existing fractures (HTPF). Int J Rock Mech Min Sci 40:1011–1020. https://doi.org/10.1016/j.ijrmms.2003.08.002
Romanov D, Gabrovsek F, Dreybrodt W (2003) Dam sites in soluble rocks: a model of increasing leakage by dissolutional widening of fractures beneath a dam. Eng Geol 70:17–35. https://doi.org/10.1016/s0013-7952(03)00073-5
Chen YF, Hong JM, Zheng HK, Li Y, Hu R, Zhou CB (2016) Evaluation of groundwater leakage into a drainage tunnel in Jinping-I arch dam foundation in Southwestern China: a case study. Rock Mech Rock Eng 49:961–979. https://doi.org/10.1007/s00603-015-0786-y
Ma D, Miao XX, Bai HB, Huang JH, Pu H, Wu Y, Zhang GM, Li JW (2016) Effect of mining on shear sidewall groundwater inrush hazard caused by seepage instability of the penetrated karst collapse pillar. Nat Hazards 82:73–93. https://doi.org/10.1007/s11069-016-2180-9
Huang Z, Zhao K, Li XZ, Zhong W, Wu Y (2021) Numerical characterization of groundwater flow and fracture-induced water inrush in tunnels. Tunn Undergr Space Technol. https://doi.org/10.1016/j.tust.2021.104119
Park BY, Kim KS, Kwon S, Kim C, Bae DS, Hartley LJ, Lee HK (2002) Determination of the hydraulic conductivity components using a three-dimensional fracture network model in volcanic rock. Eng Geol 66:127–141. https://doi.org/10.1016/s0013-7952(02)00037-6
Guo J, Luo B, Lu C, Lai J, Ren J (2017) Numerical investigation of hydraulic fracture propagation in a layered reservoir using the cohesive zone method. Eng Fract Mech 186:195–207. https://doi.org/10.1016/j.engfracmech.2017.10.013
Wei C, Li S, Yu L, Zhang B, Liu R, Pan D, Zhang F (2023) Study on mechanism of strength deterioration of rock-like specimen and fracture damage deterioration model under pulse hydraulic fracturing. Rock Mech Rock Eng 56:4959–4973. https://doi.org/10.1007/s00603-023-03313-3
Warpinski N, Teufel L (1987) Influence of geologic discontinuities on hydraulic fracture propagation (includes associated papers 17011 and 17074). J Pet Technol 39:209–220. https://doi.org/10.2118/13224-PA
Lei B, Zuo J, Coli M, Yu X, Li Y, Liu H (2024) Investigation on failure behavior and hydraulic fracturing mechanism of Longmaxi shale with different bedding properties. Comput Geotech 167:106081. https://doi.org/10.1016/j.compgeo.2024.106081
Zhou J, Chen M, Jin Y, Zhang GQ (2008) Analysis of fracture propagation behavior and fracture geometry using a tri-axial fracturing system in naturally fractured reservoirs. Int J Rock Mech Min Sci 45:1143–1152. https://doi.org/10.1016/j.ijrmms.2008.01.001
Doe TW, Boyce G (1989) Orientation of hydraulic fractures in salt under hydrostatic and non-hydrostatic stresses. Int J Rock Mech Min Sci Geomech Abstr 26:605–611. https://doi.org/10.1016/0148-9062(89)91441-1
Zhuang L, Kim KY, Jung SG, Diaz M, Min K-B (2019) Effect of water infiltration, injection rate and anisotropy on hydraulic fracturing behavior of granite. Rock Mech Rock Eng 52:575–589. https://doi.org/10.1007/s00603-018-1431-3
Duan K, Kwok CY, Zhang QY, Shang JL (2020) On the initiation, propagation and reorientation of simultaneously-induced multiple hydraulic fractures. Comput Geotech. https://doi.org/10.1016/j.compgeo.2019.103226
Yu D, Ye J, Yao L (2020) Prediction of the long-term settlement of the structures built on a reclaimed coral reef island: an aircraft runway. Bull Eng Geol Environ 79:4549–4564. https://doi.org/10.1007/s10064-020-01866-z
Wu K, Meng Q, Qin Q, Jiang X, Wang C (2022) Microscopic mechanisms of coral reef limestone crack propagation. Mar Geores Geotechnol. https://doi.org/10.1080/1064119x.2022.2143305
Wang X, Shan H, Wang X, Zhu C (2020) Strength characteristics of reef limestone for different cementation types. Geotech Geol Eng 38:79–89. https://doi.org/10.1007/s10706-019-01000-1
Li DJ, Shi C, Ruan HN, Li BY, Li WY, Yao XC (2022) Study on shear behavior of coral reef limestone-concrete interface. Mar Geores Geotechnol 40:438–447. https://doi.org/10.1080/1064119x.2021.1906365
Pei C, Li X, Ma R, Luo Y, Zhang C (2022) Research on the dynamic fracture toughness of reef limestone. Ocean Eng 264:112387. https://doi.org/10.1016/j.oceaneng.2022.112387
Luo Y, Gong H, Wei X, Zheng S, Pei C, Li X (2023) Dynamic compressive characteristics and damage constitutive model of coral reef limestone with different cementation degrees. Constr Build Mater. https://doi.org/10.1016/j.conbuildmat.2022.129783
Liu H, Zhu C, Zheng K, Ma C, Yi M (2021) Crack initiation and damage evolution of micritized framework reef limestone in the South China Sea. Rock Mech Rock Eng 54:5591–5601. https://doi.org/10.1007/s00603-021-02570-4
Zhou Z, Li S, Li X, Duan Z, Liu S (2022) Investigating progressive failure characteristics of reef limestone based on X-ray micro-CT: take S Reef as an example. Arab J Geosci 15:1379. https://doi.org/10.1007/s12517-022-10628-y
Wu K, Meng QS, Wang C, Qin QL, Dong ZW (2023) Investigation of damage characteristics of coral reef limestone under uniaxial compression based on pore structure. Eng Geol. https://doi.org/10.1016/j.enggeo.2022.106976
Wu K, Meng QS, Wang C, Qin QL, Li CS (2023) Experimental investigation of damage evolution characteristics of coral reef limestone based on acoustic emission and digital volume correlation techniques. Rock Mech Rock Eng 56:2357–2374. https://doi.org/10.1007/s00603-022-03186-y
Ma L, Wu J, Wang M, Dong L, Wei H (2020) Dynamic compressive properties of dry and saturated coral rocks at high strain rates. Eng Geol. https://doi.org/10.1016/j.enggeo.2020.105615
Pei CH, Li XP, Ma RQ, Luo Y, Zhang C (2022) Research on the dynamic fracture toughness of reef limestone. Ocean Eng. https://doi.org/10.1016/j.oceaneng.2022.112387
Wei H, Ma L, Wu J, Yu J, Li Z, Xu R (2022) Dynamic mechanical behavior of coral rock subjected to high strain rate loading. Mar Geophys Res. https://doi.org/10.1007/s11001-022-09493-x
Zhang H, Ren HQ, Mu CM, Wu XY, Huang K, Zhang HE, Wang F (2023) Experimental study on dynamic mechanical properties and damage characteristics of coral reef limestone. Constr Build Mater. https://doi.org/10.1016/j.conbuildmat.2023.131007
Yuan W, Min M (2023) Investigation on the scale dependence of shear mechanical behavior of rock joints using DEM simulation. Comput Part Mech 10:1613–1627. https://doi.org/10.1007/s40571-023-00577-y
Ma D, Wu Y, Hu X, Li D, Geng H, Hao Y (2023) DEM simulation of injection-induced micro-cracks behaviors in the heterogeneous glutenite by fluid-solid coupling. Comput Part Mech. https://doi.org/10.1007/s40571-023-00662-2
Shi C, Wang L, Zhang C, Zhang Y, Zhang W (2023) A pipe domain seepage model based on outsourcing Voronoi network with particle flow code. Comput Part Mech. https://doi.org/10.1007/s40571-023-00620-y
Cai W, Li Y, Wang K (2022) Crack propagation mechanism of rock-like specimens containing non-parallel flaws subjected to internal hydraulic pressure and shear loading. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2022.103350
Lu Y, Huang S, Ge Z, Zhou Z, Song Z (2023) Fluid-driven cracking behavior of coal with prefabricated plane: a particle-based hydro-mechanical coupled numerical investigation. Theor Appl Fract Mech. https://doi.org/10.1016/j.tafmec.2023.103825
Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41:1329–1364. https://doi.org/10.1016/j.ijrmms.2004.09.011
Potyondy DO (2007) Simulating stress corrosion with a bonded-particle model for rock. Int J Rock Mech Min Sci 44:677–691. https://doi.org/10.1016/j.ijrmms.2006.10.002
Zhang XP, Wong LNY (2013) Crack initiation, propagation and coalescence in rock-like material containing two flaws: a numerical study based on bonded-particle model approach. Rock Mech Rock Eng 46:1001–1021. https://doi.org/10.1007/s00603-012-0323-1
Cundall PA (1971) A computer model for simulating progressive, large-scale movement in blocky rock system. In: Proceedings of the international symposium on rock mechanics, 129–136.
Kong L, Ranjith PG, Li BQ (2021) Fluid-driven micro-cracking behaviour of crystalline rock using a coupled hydro-grain-based discrete element method. Int J Rock Mech Min Sci 144:104766. https://doi.org/10.1016/j.ijrmms.2021.104766
Al-Busaidi A, Hazzard J, Young R (2005) Distinct element modeling of hydraulically fractured Lac du Bonnet granite. J Geophys Res-Solid Earth. https://doi.org/10.1029/2004JB003297
Zhou J, Zhang L, Pan Z, Han Z (2016) Numerical investigation of fluid-driven near-borehole fracture propagation in laminated reservoir rock using PFC2D. J Nat Gas Sci Eng 36:719–733. https://doi.org/10.1016/j.jngse.2016.11.010
Wang S, Zhou J, Zhang L, Nagel T, Han Z, Kong Y (2023) Modeling injection-induced fracture propagation in crystalline rocks by a fluid-solid coupling grain-based model. Rock Mech Rock Eng 56:5781–5814. https://doi.org/10.1007/s00603-023-03374-4
Li M, Zhang F, Wang S, Dontsov E, Li P (2023) DEM modeling of simultaneous propagation of multiple hydraulic fractures across different regimes, from toughness- to viscosity-dominated. Rock Mech Rock Eng. https://doi.org/10.1007/s00603-023-03554-2
Hökmark H, Lönnqvist M, Fälth B (2010) THM-issues in repository rock. Thermal, mechanical, thermo-mechanical and hydro-mechanical evolution of the rock at the Forsmark and Laxemar sites.
Yoon JS, Zang A, Stephansson O (2014) Numerical investigation on optimized stimulation of intact and naturally fractured deep geothermal reservoirs using hydro-mechanical coupled discrete particles joints model. Geothermics 52:165–184. https://doi.org/10.1016/j.geothermics.2014.01.009
Haimson B, Fairhurst C (1967) Initiation and extension of hydraulic fractures in rocks. SPE J 7:310–318. https://doi.org/10.2118/1710-PA
Daneshy AA (2003) Off-balance growth: a new concept in hydraulic fracturing. J Pet Technol 55:78–85. https://doi.org/10.2118/80992-JPT
Liu D, Lecampion B (2019) Growth of a radial hydraulic fracture accounting for the viscous fluid flow in a rough cohesive zone. In: ARMA-CUPB Geothermal International Conference, Beijing, ARMA-CUPB-19-4210
Ma XF, Zou YS, Li N, Chen M, Zhang Y, Liu ZZ (2017) Experimental study on the mechanism of hydraulic fracture growth in a glutenite reservoir. J Struct Geol 97:37–47. https://doi.org/10.1016/j.jsg.2017.02.012
Shimizu H, Murata S, Ishida T (2011) The distinct element analysis for hydraulic fracturing in hard rock considering fluid viscosity and particle size distribution. Int J Rock Mech Min Sci 48:712–727. https://doi.org/10.1016/j.ijrmms.2011.04.013
Wang Y, Hu YZ, Li CH (2018) Optimization and evaluation of multiple hydraulically fractured parameters in random naturally fractured model blocks: an experimental investigation. Geotech Geol Eng 36:3411–3423. https://doi.org/10.1007/s10706-018-0543-6
Zhao Y, Cao SG, Shang DL, Yang HW, Yu YJ, Li Y, Liu JQ, Wang H, Pan RK, Yang HY, Zhang B, Tu HJ (2019) Crack propagation and crack direction changes during the hydraulic fracturing of coalbed. Comput Geotech 111:229–242. https://doi.org/10.1016/j.compgeo.2019.03.018
Acknowledgements
The research was financially supported by the National Key R&D Program of China (No.2021YFC3100801), National Natural Science Foundation of China (Project Nos. 52079102, 52279108), the Knowledge Innovation Program of Wuhan-Shuguang Project (No.2022010801020186), and the PhD Scientific Research and Innovation Foundation of Sanya Yazhou Bay Science and Technology City (HSPHDSRF-2022-03-009). Thanks also go to Dr Ruiqiu Ma and Dr Chenhao Pei for their helpful discussion. Two anonymous reviewers have given constructive comments, which have helped substantially improve the paper.
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Liu, T., Shao, Y., Zhang, C. et al. Analysis of crack propagation and hydraulic fracturing behavior of coral reef limestone. Comp. Part. Mech. (2024). https://doi.org/10.1007/s40571-024-00759-2
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DOI: https://doi.org/10.1007/s40571-024-00759-2