Effect of Density, Trace Length, Aperture, and Direction Angle on Permeability Performance of Fracture Networks
Publication: International Journal of Geomechanics
Volume 20, Issue 8
Abstract
A fractured rock mass was characterized by strong heterogeneity, discontinuity, and anisotropy. The study of flow in a fractured rock mass was a complex and challenging task. As the main seepage channels of a fractured rock mass, the fracture network was mainly affected by the fracture density, trace length, aperture, and direction angle. In this paper, the influence of fracture parameters on the permeability of the fracture network was studied by orthogonal experimental design and numerical modeling. A series of fracture networks were established to obtain seepage rules and permeability. The results showed that the increase in fracture density, trace length, and aperture increased the permeability of the model and that the fracture direction angle affected the pressure gradient and the anisotropy of the seepage in the model. The sensitivity of effective parameters on the discrete fracture network permeability performance was obtained. The influence factors of K1 were density, trace length, aperture, and direction angle in that order. The influence factors of K2 were direction angle, density, aperture, and trace length, in that order. The influence factors of K1/K2 were direction angle and density, aperture, and trace length in that order. These results could be used for parameter adjustment of fracture network modeling and determining the complex seepage characteristics in naturally fractured reservoirs.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
We would like to acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 51509147 and 51879153) and the Fundamental Research Funds of Shandong University (Grant Nos. 2017JC002 and 2017JC001).
References
Agosta, F., M. Alessandroni, M. Antonellini, E. Tondi, and M. Giorgioni. 2010. “From fractures to flow: A field-based quantitative analysis of an outcropping carbonate reservoir.” Tectonophysics 490 (3–4): 197–213. https://doi.org/10.1016/j.tecto.2010.05.005.
Andrews, B. J., J. J. Roberts, Z. K. Shipton, S. Bigi, M. C. Tartarello, and G. Johnson. 2019. “How do we see fractures? Quantifying subjective bias in fracture data collection.” Solid Earth 10 (2): 487–516. https://doi.org/10.5194/se-10-487-2019.
Baghbanan, A., and L. Jing. 2007. “Hydraulic properties of fractured rock masses with correlated fracture length and aperture.” Int. J. Rock Mech. Min. Sci. 44: 704–719. https://doi.org/10.1016/j.ijrmms.2006.11.001.
Baghbanan, A., and L. Jing. 2008. “Stress effects on permeability in a fractured rock mass with correlated fracture length and aperture.” Int. J. Rock Mech. Min. Sci. 45: 1320–1334. https://doi.org/10.1016/j.ijrmms.2008.01.015.
Barton, N. 1973. “Review of a new shear-strength criterion for rock joints.” Eng. Geol. 7 (4): 287–332. https://doi.org/10.1016/0013-7952(73)90013-6.
Barton, N., and V. Choubey. 1977. “The shear strength of rock joints in theory and practice.” Rock Mech. 10 (1–2): 1–54. https://doi.org/10.1007/BF01261801.
Bastian, P., Z. Chen, R. E. Ewing, R. Helmig, H. Jakobs, and V. Reichenberger. 2000. “Numerical simulation of multiphase flow in fractured porous media.” In Numerical treatment of multiphase flows in porous media, edited by Z. Chen, R. E. Ewing, and Z.-C. Shi, 50–68. Berlin: Springer.
Berkowitz, B. 2002. “Characterizing flow and transport in fractured geological media: A review.” Adv. Water Resour. 25 (8–12): 861–884. https://doi.org/10.1016/S0309-1708(02)00042-8.
Bigi, S., M. Marchese, M. Meda, S. Nardon, and M. Franceschi. 2015. “Discrete fracture network of the Latemar carbonate platform.” Ital. J. Geosci. 134 (3): 474–494. https://doi.org/10.3301/IJG.2014.34.
Bonnet, E., O. Bour, N. E. Odling, P. Davy, I. Main, P. Cowie, and B. Berkowitz. 2001. “Scaling of fracture systems in geological media.” Rev. Geophys. 39 (3): 347–383. https://doi.org/10.1029/1999RG000074.
Call, R. D., J. P. Savely, and D. E. Nicholas. 1976. “Estimation of joint set characteristics from surface mapping data.” In Proc., 17th US Symp. on Rock Mechanics, 2B2-1–2B2-9. Alexandria, VA: American Rock Mechanics Association.
Chaminé, H. I., M. J. Afonso, L. Ramos, and R. Pinheiro. 2015. “Scanline sampling techniques for rock engineering surveys: Insights from intrinsic geologic variability and uncertainty.” In Engineering geology for society and territory—Volume 6: Applied geology for major engineering projects, edited by G. Lollino, D. Giordan, K. Thuro, C. Carranza-Torres, F. Wu, P. Marinos, and C. Delgado, 357–361. Cham, Switzerland: Springer.
de Dreuzy, J. R., Y. Méheust, and G. Pichot. 2012. “Influence of fracture scale heterogeneity on the flow properties of three-dimensional discrete fracture networks (DFN).” J. Geophys. Res. Solid Earth 117 (B11): B11207. https://doi.org/10.1029/2012JB009461.
Earon, R., and B. Olofsson. 2018. “Hydraulic heterogeneity and its impact on kinematic porosity in Swedish coastal terrains.” Eng. Geol. 245: 61–71. https://doi.org/10.1016/j.enggeo.2018.08.008.
Fan, Z. Q., Z. H. Jin, and S. E. Johnson. 2012. “Modelling petroleum migration through microcrack propagation in transversely isotropic source rocks.” Geophys. J. Int. 190 (1): 179–187. https://doi.org/10.1111/j.1365-246X.2012.05516.x.
Fang, K. T., and Y. Wang. 1994. Number-theoretic methods in statistics. New York: Chapman & Hall.
Fisher, R. A. 1953. “Dispersion on a sphere.” Proc. R. Soc. London, Ser. A 217 (1130): 295–305. https://doi.org/10.1098/rspa.1953.0064.
Gale, J. F. W., S. E. Laubach, J. E. Olson, P. Eichhubl, and A. Fall. 2014. “Natural fractures in shale: A review and new observations.” AAPG Bull. 98 (11): 2165–2216. https://doi.org/10.1306/08121413151.
Gong, B., M. Karimi-Fard, and L. J. Durlofsky. 2008. “Upscaling discrete fracture characterizations to dual-porosity, dual-permeability models for efficient simulation of flow with strong gravitational effects.” SPE J. 13 (1): 58–67. https://doi.org/10.2118/102491-PA.
Guerriero, V., S. Vitale, S. Ciarcia, and S. Mazzoli. 2011. “Improved statistical multi-scale analysis of fractured reservoir analogues.” Tectonophysics 504 (1–4): 14–24. https://doi.org/10.1016/j.tecto.2011.01.003.
Guo, L., X. Hu, L. Wu, X. Li, and H. Ma. 2018. “Simulation of fluid flow in fractured rocks based on the discrete fracture network model optimized by measured information.” Int. J. Geomech. 18 (10): 05018008. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001270.
Hamdia, K. M., H. Ghasemi, X. Zhuang, N. Alajlan, and T. Rabczuk. 2018. “Sensitivity and uncertainty analysis for flexoelectric nanostructures.” Comput. Methods Appl. Mech. Eng. 337: 95–109. https://doi.org/10.1016/j.cma.2018.03.016.
Ho, S.-Y., H.-S. Lin, W.-H. Liauh, and S.-J. Ho. 2008. “OPSO: Orthogonal particle swarm optimization and its application to task assignment problems.” IEEE Trans. Syst. Man Cybern. Part A 38 (2): 288–298. https://doi.org/10.1109/TSMCA.2007.914796.
Hoteit, H., and A. Firoozabadi. 2006. “Compositional modeling by the combined discontinuous Galerkin and mixed methods.” SPE J. 11 (1): 19–34. https://doi.org/10.2118/90276-PA.
Indraratna, B., C. Kumara, S.-P. Zhu, and S. Sloan. 2014. “Mathematical modeling and experimental verification of fluid flow through deformable rough rock joints.” Int. J. Geomech. 15 (4): 04014065. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000413.
Javadi, M., M. Sharifzadeh, K. Shahriar, and Y. Mitani. 2014. “Critical Reynolds number for nonlinear flow through rough-walled fractures: The role of shear processes.” Water Resour. Res. 50 (2), 1789–1804. https://doi.org/10.1002/2013WR014610.
Jin, Z. H., S. E. Johnson, and Z. Q. Fan. 2010. “Subcritical propagation and coalescence of oil-filled cracks: Getting the oil out of low-permeability source rocks.” Geophys. Res. Lett. 37 (1): 1–5. https://doi.org/10.1029/2009GL041576.
Johnson, J., S. Brown, and H. Stockman. 2006. “Fluid flow and mixing in rough-walled fracture intersections.” J. Geophys. Res. Solid Earth 111: B12206. https://doi.org/10.1029/2005JB004087.
Karimi-Fard, M., L. J. Durlofsky, and K. Aziz. 2003. “An efficient discrete fracture model applicable for general purpose reservoir simulators.” In SPE Reservoir Simulation Symp. SPE 79699. Richardson, TX: SPE.
Keller, A. A., P. V. Roberts, and M. J. Blunt. 1999. “Effect of fracture aperture variations on the dispersion of contaminants.” Water Resour. Res. 35 (1): 55–63. https://doi.org/10.1029/1998WR900041.
Khan, S., Y. A. Khulief, and A. A. Al-Shuhail. 2017. “Numerical modeling of the geomechanical behavior of Biyadh reservoir undergoing CO2 injection.” Int. J. Geomech. 17 (8): 04017039. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000893.
Ki-Bok, M., J. Rutqvist, C. F. Tsang, and L. Jing. 2004. “Stress-dependent permeability of fractured rock masses: A numerical study.” Int. J. Rock Mech. Min. Sci. 41 (7): 1191–1210. https://doi.org/10.1016/j.ijrmms.2004.05.005.
Klimczak, C., R. A. Schultz, R. Parashar, and D. M. Reeves. 2010. “Cubic law with aperture-length correlation: Implications for network scale fluid flow.” Hydrogeol. J. 18: 851–862.
Kosakowski, G., and B. Berkowitz. 1999. “Flow pattern variability in natural fracture intersections.” Geophys. Res. Lett. 26 (12): 1765–1768. https://doi.org/10.1029/1999GL900344.
Kulatilake, P. H. S. W., J. Park, P. Balasingam, and R. Morgan. 2008. “Quantification of aperture and relations between aperture, normal stress and fluid flow for natural single rock fractures.” Geotech. Geol. Eng. 26 (3): 269–281. https://doi.org/10.1007/s10706-007-9163-2.
Latham, J. P., J. Xiang, M. Belayneh, H. M. Nick, C. F. Tsang, and M. J. Blunt. 2013. “Modelling stress-dependent permeability in fractured rock including effects of propagating and bending fractures.” Int. J. Rock Mech. Min. Sci. 57: 100–112. https://doi.org/10.1016/j.ijrmms.2012.08.002.
Li, W., Z. C. Wang, L. P. Bi, and J. Liu. 2019. “Representative elementary volume size for permeable property and equivalent permeability of fractured rock mass in radial flow configuration.” Rock Soil Mech. 40 (2): 720–727. https://doi.org/10.16285/j.rsm.2017.1394.
Liang, B., H. Jiang, J. Li, and C. Gong. 2016. “A systematic study of fracture parameters effect on fracture network permeability based on discrete-fracture model employing Finite Element Analyses.” J. Nat. Gas Sci. Eng. 28: 711–722. https://doi.org/10.1016/j.jngse.2015.12.011.
Lin, P., S. C. Li, Z. H. Xu, J. Wang, and X. Huang. 2019. “Water inflow prediction during heavy rain while tunneling through karst fissured zones.” Int. J. Geomech. 19 (8): 04019093. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001478.
Liu, R., Y. Jiang, B. Li, and X. Wang. 2015. “A fractal model for characterizing fluid flow in fractured rock masses based on randomly distributed rock fracture networks.” Comput. Geotech. 65: 45–55. https://doi.org/10.1016/j.compgeo.2014.11.004.
Liu, R., Y. Jiang, and Q. Yin. 2019. “Special Issue for CMES: “Modeling and Simulation of Fluid flows in Fracture Porous Media: Current Trends and Prospects.””
Liu, R., B. Li, and Y. Jiang. 2016a. “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. https://doi.org/10.1016/j.compgeo.2016.01.025.
Liu, R., B. Li, Y. Jiang, and L. Yu. 2018. “A numerical approach for assessing effects of shear on equivalent permeability and nonlinear flow characteristics of 2-D fracture networks.” Adv. Water Resour. 111: 289–300. https://doi.org/10.1016/j.advwatres.2017.11.022.
Liu, R., L. Yu, and Y. Jiang. 2016b. “Fractal analysis of directional permeability of gas shale fracture networks: A numerical study.” J. Nat. Gas Sci. Eng. 33: 1330–1341. https://doi.org/10.1016/j.jngse.2016.05.043.
Long, J. C. S., J. S. Remer, C. R. Wilson, and P. A. Witherspoon. 1982. “Porous media equivalents for networks of discontinuous fractures.” Water Resour. Res. 18 (3): 645–658. https://doi.org/10.1029/WR018i003p00645.
Ma, G., T. Li, Y. Wang, and Y. Chen. 2019. “The equivalent discrete fracture networks based on the correlation index in highly fractured rock masses.” Eng. Geol. 260: 105228. https://doi.org/10.1016/j.enggeo.2019.105228.
Manzocchi, T. 2002. “The connectivity of two-dimensional networks of spatially correlated fractures.” Water Resour. Res. 38 (9): 1-1–1-20. https://doi.org/10.1029/2000WR000180.
Marrett, R., O. J. Ortega, and C. M. Kelsey. 1999. “Extent of power-law scaling for natural fractures in rock.” Geology 27 (9): 799–802. https://doi.org/10.1130/0091-7613(1999)027%3C0799:EOPLSF%3E2.3.CO;2.
Matsuki, K., Y. Chida, K. Sakaguchi, and P. W. J. Glover. 2006. “Size effect on aperture and permeability of a fracture as estimated in large synthetic fractures.” Int. J. Rock Mech. Min. Sci. 43 (5): 726–755.
Mauldon, M. 1998. “Estimating mean fracture trace length and density from observations in convex windows.” Rock Mech. Rock Eng. 31 (4): 201–216. https://doi.org/10.1007/s006030050021.
Mauldon, M., W. M. Dunne, and M. B. Rohrbaugh. 2001. “Circular scanlines and circular windows: New tools for characterizing the geometry of fracture traces.” J. Struct. Geol. 23 (2–3): 247–258. https://doi.org/10.1016/S0191-8141(00)00094-8.
Mayerhofer, M. J., E. P. Lolon, J. E. Youngblood, and J. R. Heinze. 2006. “Integration of microseismic-fracture-mapping results with numerical fracture network production modeling in the Barnett Shale.” In SPE Annual Technical Conf. and Exhibition. SPE 102103. Richardson, TX: SPE.
McLaren, R. G., P. A. Forsyth, E. A. Sudicky, J. E. Vanderkwaak, F. W. Schwartz, and J. H. Kessler. 2000. “Flow and transport in fractured tuff at Yucca Mountain: Numerical experiments on fast preferential flow mechanisms.” J. Contam. Hydrol. 43 (3–4): 211–218. https://doi.org/10.1016/S0169-7722(00)00085-1.
Min, K. B., and L. Jing. 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. https://doi.org/10.1016/S1365-1609(03)00038-8.
Min, K. B., L. Jing, and O. Stephansson. 2004. “Determining the equivalent permeability tensor for fractured rock masses using a stochastic REV approach: Method and application to the field data from Sellafield, UK.” Hydrogeol. J. 12 (5): 497–510. https://doi.org/10.1007/s10040-004-0331-7.
Neuman, S. P. 2005. “Trends, prospects and challenges in quantifying flow and transport through fractured rocks.” Hydrogeol. J. 13 (1): 124–147. https://doi.org/10.1007/s10040-004-0397-2.
Ni, X., W. Chen, Z. Li, and X. Gao. 2017. “Reconstruction of different scales of pore-fractures network of coal reservoir and its permeability prediction with Monte Carlo method.” Int. J. Min. Sci. Technol. 27 (4): 693–699. https://doi.org/10.1016/j.ijmst.2017.05.021.
Niven, E. B., and C. V. Deutsch. 2009. A sensitivity analysis for equivalent permeability tensors calculated from 2D discrete fracture networks. CCG Annual Rep. 11. Canada: University of Alberta, Canada.
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.
Olson, J. E. 2003. “Sublinear scaling of fracture aperture versus length: An exception or the rule?” J. Geophys. Res. Solid Earth 108 (B9): 2413. https://doi.org/10.1029/2001JB000419.
Olson, J. E., S. E. Laubach, and R. H. Lander. 2007. “Combining diagenesis and mechanics to quantity fracture aperture distributions an fracture pattern permeability.” Geol. Soc. Spec. Publ. 270 (1): 101–116. https://doi.org/10.1144/GSL.SP.2007.270.01.08.
Parashar, R., and D. M. Reeves. 2012. “On iterative techniques for computing flow in large two-dimensional discrete fracture networks.” J. Comput. Appl. Math. 236 (18): 4712–4724. https://doi.org/10.1016/j.cam.2012.02.038.
Park, G.-J. 2007. Analytic methods for design practice. Berlin: Springer Science & Business Media.
Phadke, M. S. 1995. Quality engineering using robust design. Upper Saddle River, NJ: Prentice Hall.
Pinheiro, R., L. Ramos, J. Teixeira, M. J. Afonso, and H. I. Chaminé. 2014. “MGC-RocDesignCALC: A geomechanical calculator tool for rock design.” In Rock Engineering and Rock Mechanics: Structures in and on Rock Masses—Proc., EUROCK 2014, ISRM European Regional Symp., 655–660. Balkema: CRC Press.
Pollard, D. D., and A. Aydin. 1990. “Progress in understanding jointing over the past century.” GSA Bull. 100 (8): 1181–1204. https://doi.org/10.1130/0016-7606(1988)100%3C1181:PIUJOT%3E2.3.CO;2.
Pollard, D. D., and P. Segall. 1987. “Theoretical displacements and stresses near fractures in rock: With applications to faults, joints, veins, dikes, and solution surfaces.” In Fracture mechanics of rock, edited by B. K. Atkinson, 277–347. Amsterdam, Netherlands: Elsevier.
Priest, S. D. 1993. Discontinuity analysis for rock engineering. Berlin: Springer.
Priest, S. D. 2004. “Determination of discontinuity size distributions from scanline data.” Rock Mech. Rock Eng. 37 (5): 347–368. https://doi.org/10.1007/s00603-004-0035-2.
Priest, S. D., and J. A. Hudson. 1981. “Estimation of discontinuity spacing and trace length using scanline surveys.” Int. J. Rock Mech. Min. Sci. Geomech. Abs. 18 (3): 183–197. https://doi.org/10.1016/0148-9062(81)90973-6.
Pyrak-Nolte, L. J., and J. P. Morris. 2000. “Single fractures under normal stress: The relation between fracture specific stiffness and fluid flow.” Int. J. Rock Mech. Min. Sci. 37 (1–2): 245–262. https://doi.org/10.1016/S1365-1609(99)00104-5.
Rahman, M. M., and S. S. Rahman. 2013. “Studies of hydraulic fracture-propagation behavior in presence of natural fractures: Fully coupled fractured-reservoir modeling in poroelastic environments.” Int. J. Geomech. 13 (6): 809–826. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000274.
Rasouli, V., and A. Hosseinian. 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. https://doi.org/10.1007/s00603-011-0148-3.
Ren, F., G. Ma, L. Fan, Y. Wang, and H. Zhu. 2017. “Equivalent discrete fracture networks for modelling fluid flow in highly fractured rock mass.” Eng. Geol. 229: 21–30. https://doi.org/10.1016/j.enggeo.2017.09.013.
Rohrbaugh, J. B., W. M. Dunne, and M. Mauldon. 2002. “Estimating fracture trace intensity, density, and mean length using circular scan lines and windows.” AAPG Bull. 86 (12): 2089–2104. https://doi.org/10.1306/61EEDE0E-173E-11D7-8645000102C1865D.
Roy, G. D., and T. N. Singh. 2015. “Fluid flow through rough rock fractures: Parametric study.” Int. J. Geomech. 16 (3): 04015067. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000522.
Rutqvist, J., and O. Stephansson. 2003. “The role of hydrochemical coupling in fractured rock engineering.” Hydrogeol. J. 11 (1): 7–40. https://doi.org/10.1007/s10040-002-0241-5.
Samardzioska, T., and V. Popov. 2005. “Numerical comparison of the equivalent continuum, non-homogeneous and dual porosity models for flow and transport in fractured porous media.” Adv. Water Resour. 28 (3): 235–255. https://doi.org/10.1016/j.advwatres.2004.11.002.
Sanaee, R., G. F. Oluyemi, M. Hossain, and M. B. Oyeneyin. 2012. “Fracture-Matrix flow partitioning and cross flow: Numerical modeling of laboratory fractured core flood.” In COMSOL Conf. Bengaluru, India: COMSOL.
Sanderson, D. J., and C. W. Nixon. 2018. “Topology, connectivity and percolation in fracture networks.” J. Struct. Geol. 115: 167–177. https://doi.org/10.1016/j.jsg.2018.07.011.
Sanderson, D. J., and X. Zhang. 1999. “Critical stress localization of flow associated with deformation of well-fractured rock masses, with implications for mineral deposits.” Geol. Soc. Spec. Publ. 155: 69–81. https://doi.org/10.1144/GSL.SP.1999.155.01.07.
Schultz, R. A. 2000. “Growth of geologic fractures into large-strain populations: Review of nomenclature, subcritical crack growth, and some implications for rock engineering.” Int. J. Rock Mech. Min. Sci. 37 (1–2): 403–411. https://doi.org/10.1016/S1365-1609(99)00115-X.
Snow, D. T. 1966. “Three-hole pressure test for anisotropic foundation permeability.” Rock Mech. Eng. Geol. 4 (4): 298–316.
Song, J. J., and C. I. Lee. 2001. “Estimation of joint length distribution using window sampling.” Int. J. Rock Mech. Min. Sci. 38 (4): 519–528. https://doi.org/10.1016/S1365-1609(01)00018-1.
Stalker, R., G. M. Graham, and G. Oluyemi. 2009. “Modelling staged diversion treatments and chemical placement in the presence of near-wellbore fractures.” In Proc., SPE Int. Symp. on Oilfield Chemistry, 745–757. Richardson, TX: SPE.
Sudicky, E. A., and R. G. McLaren. 1992. “The Laplace transform Galerkin technique for large-scale simulation of mass transport in discretely fractured porous formations.” Water Resour. Res. 28 (2): 499–514. https://doi.org/10.1029/91WR02560.
Sultan, M. A., C. P. Fonte, M. M. Dias, J. C. B. Lopes, and R. J. Santos. 2012. “Experimental study of flow regime and mixing in T-jets mixers.” Chem. Eng. Sci. 73: 388–399. https://doi.org/10.1016/j.ces.2012.02.010.
Swanson, S. K., J. M. Bahr, K. R. Bradbury, and K. M. Anderson. 2006. “Evidence for preferential flow through sandstone aquifers in Southern Wisconsin.” Sediment. Geol. 184 (3–4): 331–342. https://doi.org/10.1016/j.sedgeo.2005.11.008.
Tamagawa, T., and D. D. Pollard. 2008. “Fracture permeability created by perturbed tress fieldsaround active faults in a fractured basement reservoir.” AAPG Bull. 92 (6): 743–764. https://doi.org/10.1306/02050807013.
Tang, Y. B., M. Li, and X. F. Li. 2017. “Connectivity, formation factor and permeability of 2D fracture network.” Physica A 483: 319–329. https://doi.org/10.1016/j.physa.2017.04.116.
Tsai, J.-T., T.-K. Liu, and J.-H. Chou. 2004. “Hybrid Taguchi-genetic algorithm for global numerical optimization.” IEEE Trans. Evol. Comput. 8 (4): 365–377. https://doi.org/10.1109/TEVC.2004.826895.
Usmani, A., G. Kannan, A. Nanda, and S. K. Jain. 2015. “Seepage behavior and grouting effects for large rock caverns.” Int. J. Geomech. 15 (3): 06014023. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000449.
Van Stappen, J. F., R. Meftah, M. A. Boone, T. Bultreys, T. De Kock, B. K. Blykers, K. Senger, S. Olaussen, and V. Cnudde. 2018. “In situ triaxial testing to determine fracture permeability and aperture distribution for CO2 sequestration in Svalbard, Norway.” Environ. Sci. Technol. 52 (8): 4546–4554. https://doi.org/10.1021/acs.est.8b00861.
Vermilye, J. M., and C. H. Scholz. 1995. “Relation between vein length and aperture.” J. Struct. Geol. 17 (3): 423–434. https://doi.org/10.1016/0191-8141(94)00058-8.
Wang, Z., and A. Krupnick. 2013. “A retrospective review of shale Gas development in the United States: What led to the boom?” SSRN Electron. J. 4 (1). https://doi.org/10.2139/ssrn.2286239.
Wang, Z., W. Li, L. Bi, L. Qiao, R. Liu, and J. Liu. 2018a. “Estimation of the REV size and equivalent permeability coefficient of fractured rock masses with an emphasis on comparing the radial and unidirectional flow configurations.” Rock Mech. Rock Eng. 51 (5): 1457–1471. https://doi.org/10.1007/s00603-018-1422-4.
Wang, Z., W. Li, L. Qiao, J. Liu, and J. Yang. 2018b. “Hydraulic properties of fractured rock mass with correlated fracture length and aperture in both radial and unidirectional flow configurations.” Comput. Geotech. 104: 167–184. https://doi.org/10.1016/j.compgeo.2018.08.017.
Wilson, C. R., and P. A. Witherspoon. 1976. “Flow interference effects at fracture intersections.” Water Resour. Res. 12 (1): 102–104. https://doi.org/10.1029/WR012i001p00102.
Wittke, W. 1990. Rock mechanics, theory and applications with case histories. Berlin: Springer-Verlag.
Wu, Q., P. H. S. W. Kulatilake, and H.-m. Tang. 2011. “Comparison of rock discontinuity mean trace length and density estimation methods using discontinuity data from an outcrop in Wenchuan area, China.” Comput. Geotech. 38 (2): 258–268. https://doi.org/10.1016/j.compgeo.2010.12.003.
Ye, Z., Q. Jiang, C. Zhou, and Y. Liu. 2017. “Numerical analysis of unsaturated seepage flow in two-dimensional fracture networks.” Int. J. Geomech. 17 (5): 04016118. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000826.
Zhang, Q., Q. Wang, J. Chen, Y. Li, and Y. Ruan. 2016. “Estimation of mean trace length by setting scanlines in rectangular sampling window.” Int. J. Rock Mech. Min. Sci. 84: 74–79. https://doi.org/10.1016/j.ijrmms.2016.02.002.
Zhang, S., S. Yin, F. Wang, and H. Zhao. 2017. “Characterization of in situ stress state and joint properties from extended leak-off tests in fractured reservoirs.” Int. J. Geomech. 17 (3): 04016074. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000757.
Zimmerman, R. W., and I. G. Main. 2004. “Chapter 7 hydromechanical behavior of fractured rocks.” Int. Geophys. 89: 363–421. https://doi.org/10.1016/S0074-6142(03)80023-2.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 20 • Issue 8 • August 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Mar 25, 2019
Accepted: Jan 16, 2020
Published online: May 22, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 22, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.