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Bulletin of Engineering Geology and the Environment
Published in: Bulletin of Engineering Geology and the Environment 3/2019

29-01-2018 | Original Paper

A predictive model correlating permeability to two-dimensional fracture network parameters

Authors: Richeng Liu, Tantan Zhu, Yujing Jiang, Bo Li, Liyuan Yu, Yan Du, Yingchao Wang

Published in: Bulletin of Engineering Geology and the Environment | Issue 3/2019

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Abstract

This study presents a predictive model of permeability with correlation to parameters of two-dimensional fracture networks, including mass density of fractures (dm), average number of intersections per meter at the inlet and outlet boundaries (din), and connectivity (Cr). The fracture networks were constructed by considering the influence of fracture number density, fracture length, orientation, and variance of fracture length. A total of 86 discrete fracture network (DFN) models were established using the Monte Carlo technique, and the relationships between permeability and dm, din, and Cr were analyzed. By fitting these calculated results, a multi-variable regression function was proposed for predicting permeability. The results show that the number density of fractures plays a more significant role in permeability than fracture length. Fracture orientation can change the connectivity of fracture networks robustly, and thereafter influence the permeability. Although variance of fracture length can affect the pattern of cumulative frequency – fracture length curves, the variance has negligible influence on the permeability of fracture networks. A necessary condition to form connected flow paths from inlet boundary to outlet boundary is: dm > 0.27 m/m2, din > 0.19 /m, and Cr > 1.20. The proposed regression function can predict permeability with a correlation coefficient larger than 0.87, and its validity is verified by comparisons with results reported in the literature. Finally, the potential future works that can facilitate the predictive models of permeability are pointed out as open questions.
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Literature
Alemdag S (2015) Assessment of bearing capacity and permeability of foundation rocks at the Gumustas waste dam site, (NE Turkey) using empirical and numerical analysis. Arab J Geosci 8:1099–1110
Baghbanan A, Jing L (2007) Hydraulic properties of fractured rock masses with correlated fracture length and aperture. Int J Rock Mech Min Sci 44(5):704–719
Baghbanan A, Jing L (2008) Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture. Int J Rock Mech Min Sci 45(8):1320–1334
Barton CC, Larsen E 1985 Fractal geometry of two-dimensional fracture networks at Yucca Mountain, southwestern Nevada. In: Proceedings of international symposium on fundamentals of rock joints conference. Bjorkliden, Sweden, 77–84
Barton N (1973) Review of a new shear-strength criterion for rock joints. Eng Geol 7(4):287–332
Black JH, Barker JA, Woodman ND (2007) An investigation of 'sparse channel networks’. Characteristic behaviours and their causes. Report R-07-35. Swedish Nuclear Fuel and Waste Management Co., Stockholm
Bogdanov II, Mourzenko VV, Thovert JF (2003) Effective permeability of fractured porous media in steady state flow. Water Resour Res 39(1):1023
Bour O, Davy P (1997) Connectivity of random fault networks following a power law fault length distribution. Water Res Res 33(7):1567–1583
Boutt DF, Grasselli G, Fredrich JT, Cook BK, Williams JR (2006) Trapping zones: the effect of fracture roughness on the directional anisotropy of fluid flow and colloid transport in a single fracture. Geophys Res Lett 33(21):L21402. https://​doi.​org/​10.​1029/​2006GL027275
Cacas MC, Ledoux E, Marsily G, Tillie B, Barbreau A, Durand E, Feuga B, Peaudecerf P (1990) Modeling fracture flow with a stochastic discrete fracture network: calibration and validation: 2. The transport model. Water Resour Res 26(3):491–500
Cai J, Hu X, Standnes DC, You L (2012) An analytical model for spontaneous imbibition in fractal porous media including gravity. Colloids Surf A Physicochem Eng Asp 414:228–233
Cai J, Luo L, Ye R, Zeng X, Hu X (2015) Recent advances on fractal modeling of permeability for fibrous porous media. Fractals 23(01):1540006
Cai J, Perfect E, Cheng CL, Hu X (2014) Generalized modeling of spontaneous imbibition based on Hagen–Poiseuille flow in tortuous capillaries with variably shaped apertures. Langmuir 30(18):5142–5151
Cai J, Hu X, Xiao B, Zhou Y, Wei W (2017) Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation. Int J Heat Mass Tran. 05:23–637
Cappa F, Guglielmi Y, Fénart P, Merrien-Soukatchoff V, Thoraval A (2005) Hydromechanical interactions in a fractured carbonate reservoir inferred from hydraulic and mechanical measurements. Int J Rock Mech Min Sci 42(2):287–306
Charlaix E, Guyon E, Roux S (1987) Permeability of a random array of fractures of widely varying apertures. Transport Porous Med. 2(1):31–43
Chen Y, Zhou C, Sheng Y (2007) Formulation of strain-dependent hydraulic conductivity for a fractured rock mass. Int J Rock Mech Min Sci 44(7):981–996
Chen YF, Hu SH, Hu R, Zhou CB (2015) Estimating hydraulic conductivity of fractured rocks from high-pressure packer tests with an Izbash's law-based empirical model. Water Resour Res 51(4):2096–2118
Clauser C (1992) Permeability of crystalline rocks. Eos Trans Am Geophys Union 73(21):233–238
Cvetkovic, V., Painter, S., Outters, N., Selroos, J.O., 2004. Stochastic simulation of radionuclide migration in discretely fractured rock near the Äspö Hard Rock Laboratory. Water Resour Res. 40(2)
De Dreuzy JR, Davy P, Bour O (2001b) Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 2. Permeability of networks based on lognormal distribution of apertures. Water Resour Res 37:2079–2095
De Dreuzy JR, Davy P, Bour O (2001a) Hydraulic properties of two-dimensional random fracture networks following a power law length distribution: 1. Effective connectivity. Water Resour Res 37(8):2065–2078
De Dreuzy JR, Davy P, Bour O (2002) Hydraulic properties of two-dimensional random fracture networks following power law distributions of length and aperture. Water Resour Res 38(12):12-1–12-9
Dershowitz WS, Fidelibus C (1999) Derivation of equivalent pipe network analogues for three-dimensional discrete fracture networks by the boundary element method. Water Resour Res 35(9):2685–2691
Dershowitz WS (1988) Einstein H H. Characterizing rock joint geometry with joint system models. Rock Mech Rock Eng 21(1):21–51
Dverstorp B, Andersson J (1989) Application of the discrete fracture network concept with field data: possibilities of model calibration and validation. Water Resour Res 25(3):540–550
Esaki T, Du S, Mitani Y, Ikusada, Jing L (1999) Development of a shear-flow test apparatus and determination of coupled properties for a single rock joint. Int J Rock Mech Min Sci 36(5):641–650
Esmaieli K, Hadjigeorgiou J, Grenon M (2010) Estimating geometrical and mechanical REV based on synthetic rock mass models at Brunswick mine. Int J Rock Mech Min Sci 47(6):915–926
Figueiredo B, Tsang CF, Rutqvist J, Niemi A (2015) A study of changes in deep fractured rock permeability due to coupled hydro-mechanical effects. Int J Rock Mech Min Sci 79:70–85
Follin S (2008) Bedrock hydrogeology Forsmark. Site descriptive modelling, SDM-Site Forsmark. Report R-08-95. Swedish Nuclear Fuel and Waste Management Co., Stockholm
Grassberger P (1999) Conductivity exponent and backbone dimension in 2-d percolation. Phys Stat Mech Appl 262(3):251–263
Gurocak Z, Alemdag S (2012) Assessment of permeability and injection depth at the Atasu dam site (Turkey) based on experimental and numerical analyses. Bull Eng Geol Environ 71:221–229
Hans J, Boulon M (2003) A new device for investigating the hydro-mechanical properties of rock joints. Int J Numer Anal Met 27(6):513–548
Hartley L, Hunter F, Jackson P, McCarthy R (2006) Regional hydrogeological simulations using CONNECTFLOW. Preliminary site description–Laxemar subarea, version 1.2. Report R-06-23. Swedish Nuclear Fuel and Waste Management Co., Stockholm
Hartley L, Roberts D (2012) Summary of discrete fracture network modelling as applied to hydrogeology of the Forsmark and Laxemar sites. Report R-12-04. Swedish Nuclear Fuel and Waste Management Co., Stockholm
Huang N, Jiang Y, Li B, Liu R (2016) A numerical method for simulating fluid flow through 3-D fracture networks. J Nat Gas Sci Eng. 33:1271–1281
Hudson JA, Priest SD (1983) Discontinuity frequency in rock masses. Int J Rock Mech Min Sci 20(2):73–89
Hyman JD, Karra S, Makedonska N, Gable CW, Painter SL, Viswanathan HS (2015) dfnWorks: a discrete fracture network framework for modeling subsurface flow and transport. Comput Geosci 84:10–19
Indraratna B, Thirukumaran S, Brown ET, Zhu SP (2015) Modelling the shear behaviour of rock joints with asperity damage under constant normal stiffness. Rock Mech Rock Eng 48(1):179–195
Ivanova VM, Sousa R, Murrihy B, Einstein HH (2014) Mathematical algorithm development and parametric studies with the GEOFRAC three-dimensional stochastic model of natural rock fracture systems. Comput Geosci 67:100–109
Jafari A, Babadagli T (2012) Estimation of equivalent fracture network permeability using fractal and statistical network properties. J Pet Sci Eng 92:110–123
Jafari A, Babadagli T (2013) Relationship between percolation–fractal properties and permeability of 2-D fracture networks. Int J Rock Mech Min Sci 60:353–362
Javadi M, Sharifzadeh M, Shahriar K, Mitani Y (2014) Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes. Water Resour Res 50(2):1789–1804
Khaleel R (1989) Scale dependence of continuum models for fractured basalts. Water Resour Res 25(8):1847–1855
Kirkpatrick S (1971) Classical transport in disordered media: scaling and effective-medium theories. Phys Rev Lett 27(25):1722
Klimczak C, Schultz RA, Parashar R, Reeves DM (2010) Cubic law with aperture-length correlation: implications for network scale fluid flow. Hydrogeol J 18(4):851–862
Lang PS, Paluszny A, Zimmerman RW (2014) Permeability tensor of three-dimensional fractured porous rock and a comparison to trace map predictions. J Geophys Res 119(8):6288–6307
Latham JP, Xiang J, Belayneh M, Nick HM, Tsang CF, Blunt MJ (2013) Modelling stress-dependent permeability in fractured rock including effects of propagating and bending fractures. Int J Rock Mech Min Sci 57:100–112
Lei Q, Latham JP, Tsang CF, Xiang J, Lang P (2015) A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics. J Geophys Res 120(7):4784–4807
Lei Q, Latham JP, Tsang CF (2017) The use of discrete fracture networks for modelling coupled geomechanical and hydrological behaviour of fractured rocks. Comput Geotech 85:151–176
Leung CTO, Zimmerman RW (2012) Estimating the hydraulic conductivity of two-dimensional fracture networks using network geometric properties. Transport Porous Med 93(3):777–797
Li B, Liu R, Jiang Y (2016a) A multiple fractal model for estimating permeability of dual-porosity media. J Hydrol 540:659–669
Li B, Liu R, Jiang Y (2016b) Influences of hydraulic gradient, surface roughness, intersecting angle, and scale effect on nonlinear flow behavior at single fracture intersections. J Hydrol 538:440–453
Li JH, Zhang LM (2010) Geometric parameters and REV of a crack network in soil. Comput Geotech 37(4):466–475
Li LP, Zhou ZQ, Li SC, Xue YG, Xu ZH, Shi SS (2015) An attribute synthetic evaluation system for risk assessment of floor water inrush in coal mines. Mine Water Environ 34(3):288–294
Li SJ, Liu YX (2008) Permeability estimation of jointed rock mass using fractal network model. J Phys Conf Ser 96(1):012131
Liu R, Jiang Y, Li B, Wang X (2015) A fractal model for charactering fluid flow in fractured rock masses on randomly distributed rock fracture networks. Comput Geotech 65:45–55
Liu R, Jiang Y, Li B (2016f) Effects of intersection and dead-end of fractures on nonlinear flow and particle transport in rock fracture networks. Geosci J 20:415–426
Liu R, Li B, Jiang Y, Huang N (2016a) Review: mathematical expressions for estimating equivalent permeability of rock fracture networks. Hydrogeol J 24:1623–1649
Liu R, Jiang Y, Li B, Yu B (2016b) Estimating permeability of porous media based on modified Hagen–Poiseuille flow in tortuous capillaries with variable lengths. Microfluid Nanofluid 20(8):120
Liu R, Li B, Jiang Y (2016c) A fractal model based on a new governing equation of fluid flow in fractures for characterizing hydraulic properties of rock fracture networks. Comput Geotech 75:57–68
Liu R, Li B, Jiang Y (2016e) Critical hydraulic gradient for nonlinear flow through rock fracture networks: the roles of aperture, surface roughness, and number of intersections. Adv Water Resour 88:53–65
Liu R, Yu L, Jiang Y (2016d) Fractal analysis of directional permeability of gas shale fracture networks: a numerical study. J Nat Gas Sci Eng 33:1271–1281
Lomize G (1951) Fluid flow in fissured formation. Moskva, Leninggrad (in Russian)
Long JCS, Remer JS, Wilson CR, Witherspoon PA (1982) Porous media equivalents for networks of discontinuous fractures. Water Resour Res 18(3):645–658
Long J, Billaux DM (1987) From field data to fracture network modeling: an example incorporating spatial structure. Water Resour Res 23(7):1201–1216
Long J, Witherspoon PA (1985) The relationship of the degree of interconnection to permeability in fracture networks. J Geophys Res 90(B4):3087–3098
MacMinn CW, Szulczewski ML, Juanes R (2010) CO2 migration in saline aquifers. Part 1. Capillary trapping under slope and groundwater flow. J. Fluid Mech 662:329–351
MacQuarrie KTB, Mayer KU (2005) Reactive transport modeling in fractured rock: a state-of-the-science review. Earth-Sci Rev 72(3):189–227
Margolin G, Berkowitz B, Scher H (1998) Structure, flow, and generalized conductivity scaling in fracture networks. Water Resour Res 34(9):2103–2121
Masihi M, King PR, Nurafza PR (2008) Connectivity prediction in fractured reservoirs with variable fracture size: analysis and validation. SPE J 13(01):88–98
Miao T, Yu B, Duan Y, Fang Q (2015) A fractal analysis of permeability for fractured rocks. Int J Heat Mass Tran. 81:75–80
Min KB, Jing L (2003) Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method. Int J Rock Mech Min Sci 40(6):795–816
Min KB, Rutqvist J, Tsang CF, Jing L (2004) Stress-dependent permeability of fractured rock masses: a numerical study. Int J Rock Mech Min Sci 41(7):1191–1210
Myers NO (1962) Characterization of surface roughness. Wear 5(3):182–189
Neretnieks, I., 1987. Channeling effects in flow and transport in fractured rocks-Some recent observations and models. Proceedings of GEOVAL-87, International Symposium, Stockholm, Sweden, 315–335
Nolte DD, Pyrak-Nolte LJ, Cook NGW (1989) The fractal geometry of flow paths in natural fractures in rock and the approach to percolation. Pure Appl Geophys 131(1–2):111–138
Oda M (1985) Permeability tensor for discontinuous rock masses. Geotechnique 35(4):483–495
Olsson R, Barton N (2001) An improved model for hydromechanical coupling during shearing of rock joints. Int J Rock Mech Min Sci 38(3):317–329
Parashar R, Reeves DM (2012) On iterative techniques for computing flow in large two-dimensional discrete fracture networks. J Comput Appl Math 236(18):4712–4724
Rasouli V, Hosseinian A (2011) Correlations developed for estimation of hydraulic parameters of rough fractures through the simulation of JRC flow channels. Rock Mech Rock Eng 44(4):447–461
Renshaw CE (1998) Sample bias and the scaling of hydraulic conductivity in fractured rock. Geophys Res Let 25(1):121–124
Roman A, Ahmadi G, Issen KA, Smith DH (2012) Permeability of fractured media under confining pressure: a simplified model. Open Petrol Eng J 5:36–41
Selroos JO, Walker DD, Ström A, Gylling B, Follin S (2002) Comparison of alternative modelling approaches for groundwater flow in fractured rock. J Hydrol 257(1):174–188
Snow DT (1969) Anisotropic permeability of fractured media. Water Resour Res 5(6):1273–1289
Stauffer D, Aharony A (1992) Introduction to percolation theory, 2nd edn. Taylor and Francis, Philadelphia
Tsang CF (2005) Is current hydrogeologic research addressing long-term predictions? Ground Water 43(3):296–300
Tsang YW, Tsang CF, Hale FV, Dverstorp B (1996) Tracer transport in a stochastic continuum model of fractured media. Water Resour Res 32(10):3077–3092
Van Golf-Racht TD (1982) Fundamentals of fractured reservoir engineering. Elsevier, Amsterdam
Waite ME, Ge S, Spetzler H (1999) A new conceptual model for fluid flow in discrete fractures: an experimental and numerical study. J Geophys Res 104(B6):13049–13059
Walsh JB (1981) Effect of pore pressure and confining pressure on fracture permeability. Int J Rock Mech Min Sci 18(5):429–435
Wang M, Kulatilake P, Um J, Narvaiz J (2002) Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling. Int J Rock Mech Min Sci 39(7):887–904
Wang Z, Li S, Qiao L, Zhang Q (2015) Finite element analysis of the hydro-mechanical behavior of an underground crude oil storage facility in granite subject to cyclic loading during operation. Int J Rock Mech Min Sci 73:70–81
Wei W, Cai J, Hu X, Han Q (2015) An electrical conductivity model for fractal porous media. Geophys Res Lett 42(12):4833–4840
Wei W, Xia Y (2017) Geometrical, fractal and hydraulic properties of fractured reservoirs: a mini-review. Adv Geo-energ Res 1(1):31–38
Wu Q, Kulatilake P (2012) REV and its properties on fracture system and mechanical properties, and an orthotropic constitutive model for a jointed rock mass in a dam site in China. Comput Geotech 43:124–142
Zhang X, Powrie W, Harkness R, Wang S (1999) Estimation of permeability for the rock mass around the shiplocks of the three gorges project, China. Int J Rock Mech Min Sci 36(3):381–397
Zhang X, Sanderson DJ (1996) Effects of stress on the two-dimensional permeability tensor of natural fracture networks. Geophys J Int 125(3):912–924
Zhang Z, Nemcik J (2013) Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J Hydrol 477:139–151
Zhao Z, Jing L, Neretnieks I, Moreno L (2011) Analytical solution of coupled stress-flow-transport processes in a single rock fracture. Comput Geosci 37(9):1437–1449
Zhao Z, Jing L, Neretnieks I (2010) Evaluation of hydrodynamic dispersion parameters in fractured rocks. J Rock Mech Geotech Eng 2(3):243–254
Zhao Z (2013) Gouge particle evolution in a rock fracture undergoing shear: a microscopic DEM study. Rock Mech Rock Eng 46(6):1461–1479
Zhou CB, Sharma RS, Chen YF, Rong G (2008) Flow–stress coupled permeability tensor for fractured rock masses. Int J Numer Anal Met 32(11):1289–1309
Zhou JQ, Hu SH, Fang S, Chen YF, Zhou CB (2015) Nonlinear flow behavior at low Reynolds numbers through rough-walled fractures subjected to normal compressive loading. Int J Rock Mech Min Sci 80:202–218
Zhuang YJ, Yu HZ, Zhu QY (2016) Experimental and numerical investigations on the flow around and through the fractal soft rocks with water vapor absorption. Int J Heat Mass Tran 96:413–429
Zimmerman RW, Al-Yaarubi A, Pain CC, Grattoni CA (2004) Non-linear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41:163–169
Metadata
Title
A predictive model correlating permeability to two-dimensional fracture network parameters
Authors
Richeng Liu
Tantan Zhu
Yujing Jiang
Bo Li
Liyuan Yu
Yan Du
Yingchao Wang
Publication date
29-01-2018
Publisher
Springer Berlin Heidelberg
Published in
Bulletin of Engineering Geology and the Environment / Issue 3/2019
Print ISSN: 1435-9529
Electronic ISSN: 1435-9537
DOI
https://doi.org/10.1007/s10064-018-1231-8

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