Effective permeability of three-dimensional fractured rock with low fracture densities

HE Chen; YAO Chi; SHAO Yulong; HUANG Fan; ZHOU Chuangbing

doi:10.16511/j.cnki.qhdxxb.2021.25.014

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Journal of Tsinghua University(Science and Technology) ›› 2021, Vol. 61 ›› Issue (8) : 827-832. DOI: 10.16511/j.cnki.qhdxxb.2021.25.014

Numerical Simulation

Effective permeability of three-dimensional fractured rock with low fracture densities

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Abstract

The permeability of fractured rock is an important parameter in many underground projects, but the permeability characteristics are normally not well known and differ significantly from the effective permeability of rocks with high fracture densities that have been widely studied in previous research. This paper presents a numerical method to model the flows in three-dimensional fractured porous media based on the equivalent discrete fracture network model. This method uses two-dimensional triangular elements to simulate the flows in the fractures and the permeable matrix in the rock which predicts the fluid exchange between the fractures and the matrix. The results are used to derive an analytical expression for the conductivity coefficient of the equivalent element. Then, the Monte-Carlo method is used to analyze the permeability of fractured rock with various fracture densities and scales. The results show that the presence of a fracture network in the study area greatly influences the effective permeability and that the effective permeability of fractured rock has a unique scale effect for low fracture densities. After classifying the effective permeabilities with and without fracture networks in the domain, the average effective permeabilities for the two types show regular variations depending on the scale of the domain. This rule can be used to establish a relationship between the effective permeability of various size rock masses.

Key words

rock mechanics / fractured rock / equivalent discrete fracture network / seepage / low fracture density

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HE Chen, YAO Chi, SHAO Yulong, HUANG Fan, ZHOU Chuangbing. Effective permeability of three-dimensional fractured rock with low fracture densities[J]. Journal of Tsinghua University(Science and Technology). 2021, 61(8): 827-832 https://doi.org/10.16511/j.cnki.qhdxxb.2021.25.014

References

[1] XU T F, APPS J A, PRUESS K. Numerical simulation of CO₂ disposal by mineral trapping in deep aquifers[J]. Applied Geochemistry, 2004, 19(6):917-936.
[2] TSANG C F, BERNIER F, DAVIES C. Geohydromechanical processes in the excavation damaged zone in crystalline rock, rock salt, and indurated and plastic clays[J]. International Journal of Rock Mechanics and Mining Sciences, 2005, 42(1):109-125.
[3] ZHANG H, FALCONE G, TEODORIU C. Modeling fully transient two-phase flow in the near-wellbore region during liquid loading in gas wells[J]. Journal of Natural Gas Science and Engineering, 2010, 2(2-3):122-131.
[4] 汪小刚, 贾志欣, 张发明, 等. 岩体结构面网络模拟原理及其工程应用[M]. 北京:中国水利水电出版社, 2010. WANG X G, JIA Z X, ZHANG F M, et al. Rock mass structural plane network simulation principle and its engineering application[M]. Beijing:China Water Conservancy and Hydropower Press, 2010. (in Chinese)
[5] LIU R C, LI B, JIANG Y J, et al. Review:Mathematical expressions for estimating equivalent permeability of rock fracture networks[J]. Hydrogeology Journal, 2016, 24(7):1623-1649.
[6] 叶祖洋, 姜清辉, 姚池, 等. 岩体裂隙网络非稳定渗流分析与数值模拟[J]. 岩土力学, 2013, 34(4):1171-1178. YE Z Y, JIANG Q H, YAO C, et al. Formulation and simulation of non-steady seepage flow through fracture network in rock masses[J]. Rock and Soil Mechanics, 2013, 34(4):1171-1178. (in Chinese)
[7] 姚池, 姜清辉, 叶祖洋, 等. 裂隙网络无压渗流分析的初流量法[J]. 岩土力学, 2012, 33(6):1896-1903. YAO C, JIANG Q H, YE Z Y, et al. Initial flow method for unconfined seepage problems of fracture networks[J]. Rock and Soil Mechanics, 2012, 33(6):1896-1903. (in Chinese)
[8] BOGDANOV I I, MOURZENKO V V, THOVERT J F, et al. Effective permeability of fractured porous media in steady state flow[J]. Water Resources Research, 2003, 39(1):257-263.
[9] VU M N, POUYA A, SEYEDI D M. Effective permeability of three-dimensional porous media containing anisotropic distributions of oriented elliptical disc-shaped fractures with uniform aperture[J]. Advances in Water Resources, 2018, 118:1-11.
[10] HYMAN J D, KARRA S, CAREY J W, et al. Discontinuities in effective permeability due to fracture percolation[J]. Mechanics of Materials, 2018, 119:25-33.
[11] ADLER P M, THOVERT J F, MOURZENKO V V. Fractured porous media[M]. Oxford:Oxford University Press, 2013.
[12] YAO C, HE C, YANG J H, et al. A novel numerical model for fluid flow in 3D fractured porous media based on an equivalent matrix-fracture network[J]. Geofluids, 2019, 2019:9736729.
[13] LANG P S, PALUSZNY A, ZIMMERMAN R W. Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions[J]. Journal of Geophysical Research:Solid Earth, 2014, 119(8):6288-6307.
[14] MOURZENKO V V, THOVERT J F, ADLER P M. Permeability of isotropic and anisotropic fracture networks, from the percolation threshold to very large densities[J]. Physical Review E, 2011, 84(3):036307.
[15] REN F, MA G W, WANG Y, et al. Unified pipe network method for simulation of water flow in fractured porous rock[J]. Journal of Hydrology, 2017, 547:80-96.
[16] REN F, MA G W, WANG Y, et al. Pipe network model for unconfined seepage analysis in fractured rock masses[J]. International Journal of Rock Mechanics and Mining Sciences, 2016, 88:183-196.
[17] 何忱, 姚池, 杨建华, 等. 基于等效离散裂隙网络的三维裂隙岩体渗流模型[J]. 岩石力学与工程学报, 2019, 38(S1):2748-2759. HE C, YAO C, YANG J H, et al. A 3D model for flow in fractured rock mass based on the equivalent discrete fracture network[J]. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(S1):2748-2759. (in Chinese)
[18] KOUDINA N, GARCIA R G, THOVERT J F, et al. Permeability of three-dimensional fracture networks[J]. Physical Review E, 1998, 57(4):4466-4479.
[19] KHAMFOROUSH M, SHAMS K, THOVERT J F, et al. Permeability and percolation of anisotropic three-dimensional fracture networks[J]. Physical Review E, 2008, 77(5):056307.
[20] BOGDANOV I I, MOURZENKO V V, THOVERT J F, et al. Effective permeability of fractured porous media with power-law distribution of fracture sizes[J]. Physical Review E, 2007, 76(3):036309.
[21] SHAFIRO B, KACHANOV M. Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes[J]. Journal of Applied Physics, 2000, 87(12):8561-8569.
[22] 周创兵, 熊文林. 双场耦合条件下裂隙岩体的渗透张量[J]. 岩石力学与工程学报, 1996, 15(4):338-344. ZHOU C B, XIONG W L. Permeability tensor for jointed rock masses in coupled seepage and stress field[J]. Chinese Journal of Rock Mechanics and Engineering, 1996, 15(4):338-344. (in Chinese)
[23] 陈益峰, 周创兵, 胡冉, 等. 大型水电工程渗流分析的若干关键问题研究[J]. 岩土工程学报, 2010, 32(9):1448-1454. CHEN Y F, ZHOU C B, HU R, et al. Key issues on seepage flow analysis in large scale hydropower projects[J]. Chinese Journal of Geotechnical Engineering, 2010, 32(9):1448-1454. (in Chinese)