Effects of geometrical feature on Forchheimer-flow behavior through rough-walled rock fractures

ZHOU Xin; SHENG Jian-long; YE Zu-yang; LUO Wang; HUANG Shi-bing; CHENG Ai-ping

doi:10.11779/CJGE202111014

Volume 43 Issue 11

Turn off MathJax

Article Contents

Abstract

References

Chinese Journal of Geotechnical Engineering > 2021 > 43(11): 2075-2083. > DOI: 10.11779/CJGE202111014

ZHOU Xin, SHENG Jian-long, YE Zu-yang, LUO Wang, HUANG Shi-bing, CHENG Ai-ping. Effects of geometrical feature on Forchheimer-flow behavior through rough-walled rock fractures[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(11): 2075-2083. DOI: 10.11779/CJGE202111014

Citation:

PDF (1829 KB)

Effects of geometrical feature on Forchheimer-flow behavior through rough-walled rock fractures

ZHOU Xin^{1, 2,},
SHENG Jian-long^{1, 2},
YE Zu-yang^{1, 2, ,},
LUO Wang^{1, 2},
HUANG Shi-bing^{1, 2},
CHENG Ai-ping^{1, 2}

1.
School of Resources and Environmental Engineering, Wuhan University of Science and Technology, Wuhan 430081, China
2.
Hubei Key Laboratory for Efficient Utilization and Agglomeration of Metallurgical Mineral Resources, Wuhan University of Science and Technology, Wuhan 430081, China

More Information

Received Date: November 03, 2020
Available Online: December 01, 2022

Graphical Abstract

Abstract

Abstract

In order to study the relationship between the geometrical feature and the nonlinear flow properties of rough-walled rock fractures, a numerical model based on the fractal behavior is proposed to characterize the three-dimensional geometry of rough-walled fractures. By solving the N-S (Navier-Stokes) equation directly, the effects of mean aperture, standard deviation of aperture and different fractal dimensions on the Forchheimer flow characteristics of fractures are investigated. The Forchheimer equation is validated to describe the nonlinear relationship between the flow rate and the pressure gradient. The results show that with the lower flow rate, the linear coefficient increases and the hydraulic aperture decreases with the decreasing mean aperture and increasing standard deviation of the aperture, thus the empirical relation for the hydraulic aperture, the mean aperture and the standard deviation of aperture is put forward, while the effects of the fractal dimension almost can be ignored. On the contrary, with larger flow rate, for the flow pattern changing from linear to nonlinear flow, as the mean aperture decreases and the standard deviation of aperture and the fractal dimension increase, the nonlinear coefficient increases, and the critical Reynolds number decreases, with the range of Re_c being 11.16~39.3.
- rock fracture,
- geometrical feature,
- flow property,
- fractal theory

FullText(HTML)

References (27)

References

[1]	SNOW D T. A parallel plate model of fractured permeable media[D]. Berkeley: University of California of Berkeley, 1965.
[2]	ZIMMERMAN R W, AL-YAARUBI A, PAIN C C, et al. Non-linear regimes of fluid flow in rock fractures[J]. International Journal of Rock Mechanics & Mining Sciences, 2004, 41(3): 163-169.
[3]	ZHANG Z Y, NEMCIK J. Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J]. Journal of Hydrology, 2013, 477(16): 139-151.
[4]	姚池, 邵玉龙, 杨建华, 等. 非线性渗流对裂隙岩体渗流传热过程的影响[J]. 岩土工程学报, 2020, 42(6): 1050-1058. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202006011.htm YAO Chi, SHAO Yu-long, YANG Jian-hua, et al. Effect of nonlinear seepage on flow and heat transfer process of fractured rocks[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(6): 1050-1058. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC202006011.htm
[5]	张戈, 田园, 李英骏. 不同JRC粗糙单裂隙的渗流机理数值模拟研究[J]. 中国科学：物理学力学天文学, 2019, 49(1): 30-39. https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201901003.htm ZHANG Ge, TIAN Yuan, LI Ying-jun. Numerical study on the mechanism of fluid flow through single rough fractures with different JRC[J]. Scientia Sinica (Physica, Mechanica & Astronomica), 2019, 49(1): 30-39. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201901003.htm
[6]	CHEN Y F, ZHOU J Q, HU S H, et al. Evaluation of Forchheimer equation coefficients for non-Darcy flow in deformable rough-walled fractures[J]. Journal of Hydrology, 2015, 529: 993-1006. doi: 10.1016/j.jhydrol.2015.09.021
[7]	YIN Q, MA G W, JING H W, et al. Hydraulic properties of 3D rough-walled fractures during shearing: an experimental study[J]. Journal of Hydrology, 2017, 555: 169-184. doi: 10.1016/j.jhydrol.2017.10.019
[8]	肖维民, 夏才初, 王伟, 等. 考虑接触面积影响的粗糙节理渗流分析[J]. 岩土力学, 2013, 34(7): 1913-1922. doi: 10.16285/j.rsm.2013.07.022 XIAO Wei-min, XIA Cai-chu, WANG Wei, et al. Analysis of fluid flow through a rough joint considering effect of contact area[J]. Rock and Soil Mechanics, 2013, 34(7): 1913-1922. (in Chinese) doi: 10.16285/j.rsm.2013.07.022
[9]	TSANG Y W. The effect of tortuosity on fluid flow through a single fracture[J]. Water Resources Research, 1984, 20(9): 1209-1215. doi: 10.1029/WR020i009p01209
[10]	熊峰, 孙昊, 姜清辉, 等. 粗糙岩石裂隙低速非线性渗流模型及试验验证[J]. 岩土力学, 2018, 39(9): 3294-3302, 3312. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201809025.htm XIONG Feng, SUN Hao, JIANG Qing-hui, et al. Theoretical model and experimental verification on non-linear flow at low velocity through rough-walled rock fracture[J]. Rock and Soil Mechanics, 2018, 39(9): 3294-3302, 3312. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201809025.htm
[11]	CHEN Y D, LIAN H J, LIANG W G, et al. The influence of fracture geometry variation on non-Darcy flow in fractures under confining stresses[J]. International Journal of Rock Mechanics and Mining Sciences, 2019, 113: 59-71. doi: 10.1016/j.ijrmms.2018.11.017
[12]	WANG C S, JIANG Y J, LIU R C, et al. Experimental study of the nonlinear flow characteristics of fluid in 3D rough-walled fractures during shear process[J]. Rock Mechanics and Rock Engineering, 2020, 53(6): 2581-2604. doi: 10.1007/s00603-020-02068-5
[13]	谢和平. 分形几何及其在岩土力学中的应用[J]. 岩土工程学报, 1992, 14(1): 14-24. doi: 10.3321/j.issn:1000-4548.1992.01.002 XIE He-ping. Fractal geometry and its application to rock and soil materials[J]. Chinese Journal of Geotechnical Engineering, 1992, 14(1): 14-24. (in Chinese) doi: 10.3321/j.issn:1000-4548.1992.01.002
[14]	BROWN S R. Fluid flow through rock joints: The effect of surface roughness[J]. Journal of Geophysical Research: Solid Earth, 1987, 92(B2): 1337-1347. doi: 10.1029/JB092iB02p01337
[15]	LIU R C, HE M, HUANG N, et al. Three-dimensional double-rough-walled modeling of fluid flow through self-affine shear fractures[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2020, 12(1): 41-49. doi: 10.1016/j.jrmge.2019.09.002
[16]	李毅. 岩石裂隙的非饱和渗透特性及其演化规律研究[J]. 岩土力学, 2016, 37(8): 2254-2262. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201608017.htm LI Yi. Unsaturated hydraulic properties of rock fractures and their variation law[J]. Rock and Soil Mechanics, 2016, 37(8): 2254-2262. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201608017.htm
[17]	YE Z Y, LIU H H, JIANG Q H, et al. Two-phase flow properties in aperture-based fractures under normal deformation conditions: analytical approach and numerical simulation[J]. Journal of Hydrology, 2017, 545: 72-87. doi: 10.1016/j.jhydrol.2016.12.017
[18]	WANG J, NARASIMHAN T, SCHOLZ C. Aperture correlation of a fractal fracture[J]. Journal of Geophysical Research, 1988, 93: 2216-2224. doi: 10.1029/JB093iB03p02216
[19]	ZENG Z W, GRIGG R. A criterion for non-darcy flow in porous media[J]. Transport in Porous Media, 2006, 63(1): 57-69. doi: 10.1007/s11242-005-2720-3
[20]	JAVADI M, SHARIFZADEH M, SHAHRIAR K, et al. Critical Reynolds number for nonlinear flow through rough-walled fractures: the role of shear processes[J]. Water Resources Research, 2014, 50(2): 1789-1804. doi: 10.1002/2013WR014610
[21]	ZOU L C, JING L R, CVETKOVIC V. Shear-enhanced nonlinear flow in rough-walled rock fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 97: 33-45. doi: 10.1016/j.ijrmms.2017.06.001
[22]	WANG Z H, XU C S, DOWD P, et al. A nonlinear version of the Reynolds equation for flow in rock fractures with complex void geometries[J]. Water Resources Research, 2020, 56(2): 1-12.
[23]	王志良, 申林方, 徐则民, 等. 岩体裂隙面粗糙度对其渗流特性的影响研究[J]. 岩土工程学报, 2016, 38(7): 1262-1268. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201607013.htm WANG Zhi-liang, SHEN Lin-fang, XU Ze-min, et al. Influence of roughness of rock fracture on seepage characteristics[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(7): 1262-1268. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201607013.htm
[24]	KONZUK J S, KUEPER B H. Evaluation of cubic law based models describing single-phase flow through a rough-walled fracture[J]. Water Resources Research, 2004, 40(2): W02402.
[25]	CHEN Y F, HU S H, HU R, et al. Estimating hydraulic conductivity of fractured rocks from high-pressure packer tests with an Izbash's law-based empirical model[J]. Water Resources Research, 2015, 51(4): 2096-2118. doi: 10.1002/2014WR016458
[26]	QIAN J Z, ZHAN H B, LUO S H, et al. Experimental evidence of scale-dependent hydraulic conductivity for fully developed turbulent flow in a single fracture[J]. Journal of Hydrology, 2007, 339(3/4): 206-215.
[27]	RONG G, YANG J, CHENG L, et al. Laboratory investigation of nonlinear flow characteristics in rough fractures during shear process[J]. Journal of Hydrology, 2016, 541: 1385-1394. doi: 10.1016/j.jhydrol.2016.08.043

[1]	ZHU Sheng, YE Hua-yang, XU Jin, FENG Shu-rong. Research and application of relative density test method for large coarse-grained soil[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(6): 1087-1095. DOI: 10.11779/CJGE202206013
[2]	ZHANG Lin, LI Tong-lu, CHEN Cun-li. Soil-water characteristics and permeability of compacted loess considering effects of dry density[J]. Chinese Journal of Geotechnical Engineering, 2022, 44(5): 945-953. DOI: 10.11779/CJGE202205018
[3]	WU Er-lu, ZHU Jun-gao, GUO Wan-li, CHEN Ge. Experimental study on effect of scaling on compact density of coarse-grained soils[J]. Chinese Journal of Geotechnical Engineering, 2019, 41(9): 1767-1772. DOI: 10.11779/CJGE201909023
[4]	ZHU Jun-gao, SHI Jiang-wei, LUO Xue-hao, XU Jia-cheng. Experimental study on stress-strain-strength behavior of sand with different densities[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(2): 336-341. DOI: 10.11779/CJGE201602018
[5]	XING Hai-ling, JIANG Tong, YAO Dong-sheng, GENG Chuan-zhi. Calculation of free field response spectrum from bed rock response spectrum directly for horizontally-layered site using equivalent linear method[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(12): 2337-2344.
[6]	NIE Ru-song, LENG Wu-ming, WEI Wei. Equivalent conversion method for self-balanced tests[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(sup2): 188-191.
[7]	SHAO Shengjun, WANG Ting, YU Qinggao. Equivalent consolidation deformation properties and one-dimensional analysis method of unsaturated soils[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(7): 1037-1045.
[8]	ZHANG Yujun. Equivalent model and numerical analysis and laboratory test for jointed rockmasses[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(1): 29-32.
[9]	Zhang Zaiming. Analysis of Nonlinear Behavior of Equivalent Deformation Modulus[J]. Chinese Journal of Geotechnical Engineering, 1997, 19(5): 58-61.
[10]	He Yupei, Jiang Qian. Pressuremeter Test of Soft Rock[J]. Chinese Journal of Geotechnical Engineering, 1994, 16(2): 58-63.