Abstract
A series of laboratory experiments on water flow through rough fractures was performed using self-designed experimental devices to investigate the effect of fracture roughness on the flow behavior. Nine models of single rough fractures—with three joint roughness coefficients (JRCs) of 0–2, 8–10 and 18–20, and three apertures for each JRC—were prepared using three-dimensional printing technology. In the flow experiments, the values of Reynolds numbers ranged widely from less than 10 to around 10,000. According to the experimental data, the fracture roughness has an obvious influence on the hydraulic properties of fractures. A parametric expression for the Forchheimer equation was proposed to quantitatively describe the influence of fracture roughness on the flow behaviour in the fractures. The relations between the parameters for nonlinear flow (such as critical Reynolds number, non-Darcy effect coefficient and friction factor) and the JRCs were obtained. It was found that the critical Reynolds number decreased significantly from 566 to 67 as the JRC increased from 2 to 20. The increase in fracture roughness causes more extra energy losses and enhances the degree of flow nonlinearity in single fractures.
Résumé
Une série d’expériences en laboratoire sur l’écoulement de l’eau à travers des fractures grossières a été réalisée à l’aide de dispositifs expérimentaux conçus par l’utilisateur pour étudier l’effet de la rugosité de la fracture sur le comportement de l’écoulement. Neuf modèles de fractures rugueuses uniques—avec trois coefficients de rugosité des joints (CRJs) de 0–2, 8–10 et 18–20, et trois ouvertures pour chaque CRJ—ont été préparés à l’aide de la technologie d’impression tridimensionnelle. Dans les expériences d’écoulement, les valeurs des nombres de Reynolds variaient largement de moins de 10 à environ 10′000. D’après les données expérimentales, la rugosité de la fracture a une influence évidente sur les propriétés hydrauliques des fractures. Une expression paramétrique de l’équation de Forchheimer a été proposée pour décrire quantitativement l’influence de la rugosité de fracture sur le comportement d’écoulement dans les fractures. Les relations entre les paramètres d’écoulement non linéaire (tels que le nombre de Reynolds critique, le coefficient d’effet non-Darcy et le facteur de frottement) et les CRJ ont été obtenues. Il a été constaté que le nombre critique de Reynolds diminuait de manière significative de 566 à 67 lorsque le CRJ augmentait de 2 à 20. L’augmentation de la rugosité de la fracture entraîne davantage de pertes d’énergie supplémentaires et augmente le degré de non-linéarité de l’écoulement dans les fractures simples.
Resumen
Una serie de experimentos de laboratorio sobre el flujo de agua a través de fracturas rugosas se llevó a cabo utilizando dispositivos experimentales de diseño propio para investigar el efecto de la rugosidad de las fracturas en el comportamiento del flujo. Se prepararon nueve modelos de fracturas rugosas simples—con tres coeficientes de rugosidad de la articulación (JRCs) de 0–2, 8–10 y 18–20, y tres aperturas para cada JRC—utilizando tecnología de impresión tridimensional. En los experimentos de flujo, los valores de los números de Reynolds variaron ampliamente desde menos de 10 hasta alrededor de 10.000. Según los datos experimentales, la rugosidad de las fracturas tiene una influencia obvia en sus propiedades hidráulicas. Se propuso una expresión paramétrica para la ecuación de Forchheimer a fin de describir cuantitativamente la influencia de la rugosidad en el comportamiento del flujo en las fracturas. Se obtuvieron las relaciones entre los parámetros del flujo no lineal (como el número crítico de Reynolds, el coeficiente de efecto no Darcy y el factor de fricción) y los JRC. Se encontró que el número crítico de Reynolds disminuyó significativamente de 566 a 67 a medida que el JRC aumentaba de 2 a 20. El aumento de la rugosidad de las fracturas causa más pérdidas de energía extra y aumenta el grado de no linealidad del flujo en las fracturas simples.
摘要
使用自行设计的实验设备对流经粗糙裂隙的渗流进行了一系列室内实验,以研究裂隙粗糙度对渗流的影响。使用三维打印技术, 制作了9个粗糙单裂隙模型, 包括三个裂隙粗糙度系数(JRC)分别为0–2、8–10和18–20, 每个JRC有3个开度。在渗流实验中, 雷诺数范围从小于10到大约10,000。根据实验数据, 裂隙的粗糙度对裂隙的水力特性有明显的影响。提出了Forchheimer方程的参数表达式, 以定量描述裂隙粗糙度对裂隙渗流的影响。得到了非线性渗流参数(如临界雷诺数, 非达西效应系数和摩擦系数)与JRC之间的关系。发现随着JRC从2增加到20, 临界雷诺数从566显著降低到67。裂隙粗糙度的增加导致更多的额外能量损失, 并增强了单裂隙渗流的非线性程度。
Resumo
Uma série de experimentos de laboratório de fluxo de água através de fraturas rugosas foram realizados usando equipamentos experimentais de projeto próprio para investigar os efeitos da rugosidade da fratura no comportamento do fluxo. Nove modelos de uma única fratura rugosa—com três de coeficiente de rugosidade da junta (CRJ) de 0–2, 8–10, e 18–20, e três aberturas para cada CRJ—foram preparados usando tecnologia de impressão tridimensional. Nos experimentos de fluxo, os valores do número de Reynolds variaram bastante de menos que 10 a aproximadamente 10,000. De acordo com os dados experimentais, a rugosidade da fratura tem uma influência óbvia nas propriedades hidráulicas da fratura. Uma expressão paramétrica para a equação de Forchheimer foi proposta para descrever quantitativamente a influência da rugosidade da fratura no comportamento do fluxo nas fraturas. As relações entre os parâmetros para fluxo não linear (como número crítico de Reynolds, coeficiente do efeito não Darciniano e fator de fricção) e os CRJs foram obtidos. Foi observado que o número crítico de Reynolds diminui significativamente de 566 para 67 com o aumento do CRJ de 2 a 20. O aumento da rugosidade da fratura causa perdas adicionais de energia e aumento do grau de fluxo não linear um fraturas únicas.
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References
Barton N, Choubey V (1977) The shear strength of rock joints in theory and practice. Rock Mech 10:1–54. https://doi.org/10.1007/BF01261801
Bear J (1972) Dynamics of fluids in porous media. Elsevier, Amsterdam
Berkowitz B (2002) Characterizing flow and transport in fractured geological media: a review. Adv Water Resour 25(8):861–884. https://doi.org/10.1016/S0309-1708(02)00042-8
Brush DJ, Thomson NR (2003) Fluid flow in synthetic rough-walled fractures: Navier-Stokes, Stokes, and local cubic law simulations. Water Resour Res 39(4):1085. https://doi.org/10.1029/2002WR001346
Chen YF, Hu SH, Hu R, Zhou CB (2015a) 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. https://doi.org/10.1002/2014WR016458
Chen YF, Zhou JQ, Hu SH, Hu R, Zhou CB (2015b) Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures. J Hydrol 529:993–1006. https://doi.org/10.1016/j.jhydrol.2015.09.021
Chen YF, Hong JM, Tang SL, Zhou CB (2016) Characterization of transient groundwater flow through a high arch dam foundation during reservoir impounding. J Rock Mech Geotech Eng 8(4):462–471. https://doi.org/10.1016/j.jrmge.2016.03.004
Forchheimer PH (1901) Water movement through soil (in German). J Assoc Ger Eng 45:1782–1788
Iwai K (1976) Fundamental studies of fluid flow through a single fracture. Ph D thesis, California University, Berkeley. https://doi.org/10.1016/0148-9062(79)90543-6
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. https://doi.org/10.1002/2013WR014610
Jiang YJ, Li B, Wang G, Li SC (2008) New advances in an experimental study on seepage characteristics of rock fractures (in Chinese). Chin J Rock Mech Eng 27:2377–2386
Jing L, Stephansson O (2007) Fundamentals of discrete element methods for rock engineering: theory and applications. Elsevier, Amsterdam. p 111–138
Konzuk JS, Kueper BH (2004) Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture. Water Resour Res 40(2):W02402. https://doi.org/10.1029/2003WR002356
Liu RC, Jiang YJ, Li B, Yu LY, Du Y (2016a) Nonlinear seepage behaviors of fluid in fracture networks (in Chinese). Rock Soil Mech 37(10):2817–2824
Liu RC, Yu LY, Jiang YJ (2016b) Quantitative estimates of normalized transmissivity and the onset of nonlinear fluid flow through rough rock fractures. Rock Mech Rock Eng 50(4):1–9. https://doi.org/10.1007/s00603-016-1147-1
Liu RC, Jing HJ, He LX, Zhu TT, Yu LY, Su HJ (2017) An experimental study of the effect of fillings on hydraulic properties of single fractures. Environ Earth Sci 76:684. https://doi.org/10.1007/s12665-017-7024-8
Liu RC, Huang N, Jiang YJ, Jing HW, Yu LY (2020) A numerical study of shear-induced evolutions of geometric and hydraulic properties of self-affine rough-walled rock fractures. Int J Rock Mech Min Sci 127:1–17. https://doi.org/10.1016/j.ijrmms.2020.104211
Neuman SP (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
Nigon B, Englert A, Pascal C (2019) Three-dimensional flow characterization in a joint with plumose pattern. Hydrogeol J 27(1):87–99. https://doi.org/10.1007/s10040-018-1847-6
Qian JZ, Zhan HB, Chen Z, Ye H (2011) Experimental study of solute transport under non-Darcian flow in a single fracture. J Hydrol 399(3):246–254. https://doi.org/10.1016/j.jhydrol.2011.01.003
Qian X, Xia CC, Gui Y (2018) Quantitative estimates of non-Darcy groundwater flow properties and normalized hydraulic aperture through discrete open rough-walled joints. Int J Geomech 18(9):04018099. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001228
Qiao LP, Wang ZC, Li SC, Bi LP, Xu ZH (2017) Assessing containment properties of underground oil storage caverns: methods and a case study. Geosci J 21(4):579–593. https://doi.org/10.1007/s12303-016-0063-4
Scesi L, Gattinoni P (2007) Roughness control on hydraulic conductivity in fractured rocks. Hydrogeol J 15(2):201–211. https://doi.org/10.1007/s10040-006-0076-6
Skjetne E, Hansen A, Gudmundsson JS (1999) High-velocity flow in a rough fracture. J Fluid Mech 383:1–28. https://doi.org/10.1017/S0022112098002444
Tse R, Cruden DM (1979) Estimating joint roughness coefficients. Int J Rock Mech Min Sci Geomech Abstr 16(5):303–307. https://doi.org/10.1016/0148-9062(79)90241-9
Tzelepis V, Moutsopoulos KN, Papaspyros JNE, Tsihrintzis VA (2015) Experimental investigation of flow behavior in smooth and rough artificial fractures. J Hydrol 521(2):108–118. https://doi.org/10.1016/j.jhydrol.2014.11.054
Wang ZC, Li SC, Qiao LP, Zhang QS (2015) Finite element analysis of hydromechanical 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. https://doi.org/10.1016/j.ijrmms.2014.09.018
Wang M, Chen YF, Ma GW, Zhou JQ, Zhou CB (2016) Influence of surface roughness on nonlinear flow behaviors in 3D self-affine rough fractures: lattice Boltzmann simulations. Adv Water Resour 96:373–388. https://doi.org/10.1016/j.advwatres.2016.08.006
White FM (2003) Fluid mechanics, 5th edn. McGraw-Hill, New York. p 304–314
Xu K, Lei XW, Meng QS, Zhou XB (2012) Study of inertial coefficient of non-Darcy seepage flow (in Chinese). Chin J Rock Mech Eng 31(1):164–170
Yu LY, Liu RC, Jiang YJ (2017) A review of critical conditions for the onset of nonlinear fluid flow in rock fractures. Geofluids 2017:1–17. https://doi.org/10.1155/2019/9273968
Zeng Z, Grigg R (2006) A criterion for non-Darcy flow in porous media. Transp Porous Media 63(1):57–59. https://doi.org/10.1007/s11242-005-2720-3
Zhang Z, Nemcik J (2013a) Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures. J Hydrol 477(1):139–151. https://doi.org/10.1016/j.jhydrol.2012.11.024
Zhang Z, Nemcik J (2013b) Friction factor of water flow through rough rock fractures. Rock Mech Rock Eng 46(5):1125–1134. https://doi.org/10.1007/s00603-012-0328-9
Zhou JQ, Hu SH, Chen YF, Wang M, Zhou CB (2016) The friction factor in the Forchheimer equation for rock fractures. Rock Mech Rock Eng 49(8):3055–3068. https://doi.org/10.1007/s00603-016-0960-x
Zhou JQ, Wang M, Wang LC, Chen YF, Zhou CB (2018) Emergence of nonlinear laminar flow in fractures during shear. Rock Mech Rock Eng 51:3635–3643. https://doi.org/10.1007/s00603-018-1545-7
Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transp Porous Media 23(1):1–30. https://doi.org/10.1007/bf00145263
Zimmerman RW, Al-Yaarubi A, Pain CC, Grattoni CA (2004) Nonlinear regimes of fluid flow in rock fractures. Int J Rock Mech Min Sci 41(3):163–169. https://doi.org/10.1016/j.ijrmms.2004.03.036
Funding
This study was financially supported by the National Natural Science Foundation of China under contract Nos. 51779045 and 51579141, the Fundamental Research Funds for the Central Universities under contract Nos. N180104022 and N2001026, Liao Ning Revitalization Talents Program under contract No. XLYC1807029 and Liaoning Natural Science Foundation under contract No. 2019-YQ-02.
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Liu, J., Wang, Z., Qiao, L. et al. Transition from linear to nonlinear flow in single rough fractures: effect of fracture roughness. Hydrogeol J 29, 1343–1353 (2021). https://doi.org/10.1007/s10040-020-02297-6
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DOI: https://doi.org/10.1007/s10040-020-02297-6