Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow

LIU Jian; YANG Qiaoyan; BAI Xue; SONG Kai; LUO Chengjie; SA Yongfang

doi:10.3969/j.issn.0258-2724.20180756

Volume 55 Issue 1

Jan. 2020

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Journal of Southwest Jiaotong University > 2020 > 55(1): 218-224.

LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756

Citation:

LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756

Citation:

LIU Jian, YANG Qiaoyan, BAI Xue, SONG Kai, LUO Chengjie, SA Yongfang. Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow[J]. Journal of Southwest Jiaotong University, 2020, 55(1): 218-224. doi: 10.3969/j.issn.0258-2724.20180756

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Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow

doi: 10.3969/j.issn.0258-2724.20180756

Received Date: 04 Sep 2018
Rev Recd Date: 08 Oct 2018

Available Online: 21 Dec 2018

Publish Date: 01 Feb 2020

Abstract

Abstract

In order to explore the movement law of water flow in rock mass fissures, a fracture seepage flow model was established with real rock mass materials to study the seepage flow state and parameters. The single-fracture seepage flow model was constructed using natural marble blocks, instead of the common non-stone materials such as cement, glass, acrylic, and steel. Based on the model, seepage experiments with different fissure widths (0.77, 1.18, 1.97, 2.73 mm) were conducted to investigate the relationship between pressure loss and flow rate, the critical point of transition from Darcian to non-Darcian flow, and the quantification of parameters in the Forchheimer equation. Results show that the relationship between pressure gradient and flow rate is governed by linear Darcy’s law when the fracture width is 0.77 mm, but obvious non-Darcy characteristics are observed with the increase of the fracture width and flow rate, which can be described by Forchheimer equation. The coefficient of viscosity and inertia term of the Forchheimer equation can be expressed as a power function of fracture width, and the error can be reduced by introducing Reynolds number to correct the inertia coefficient. Besides, the method of judging the critical point of transition from Darcian to non-Darcian flow via the slope characteristics of pressure gradient-flow curve proved feasible in this experiment.
- fracture,
- non-Darcy,
- Forchheimer equation,
- Reynolds number,
- critical point

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References(29)

References

闻德荪. 工程流体力学: 水力学[M]. 3版. 北京: 高等教育出版社, 2010: 225-228.

赵延林. 裂隙岩体流固耦合响应与工程应用[M]. 北京: 科学出版社, 2016: 14-21.

LOMIZE G M. Flow in fractured rocks[M]. Moscow: Gosenergoizdat, 1951: 27.

王媛,速宝玉. 单裂隙面渗流特性及等效水力隙宽[J]. 水科学进展,2002,13(1): 61-68. doi: 10.3321/j.issn:1001-6791.2002.01.011

WANG Yuan, SU Baoyu. Research on the behavior of fluid flow in a single fracture and its equivalent hydraulic apecture[J]. Advances in Water Science, 2002, 13(1): 61-68. doi: 10.3321/j.issn:1001-6791.2002.01.011

ZHANG Zhenyu, NEMCIK J, QIAO Qiuqiu, et al. A model for water flow through rock fractures based on friction factor[J]. Rock Mechanics & Rock Engineering, 2015, 48(2): 559-571.

QIAN Jiazhong, CHEN Zhou, ZHAN Hongbin, et al. Experimental study of the effect of roughness and Reynolds number on fluid flow in rough-walled single fractures:a check of local cubic law[J]. Hydrological Processes, 2011, 25(4): 614-622.

CHERUBINI C, GIASI C I, PASTORE N. Bench scale laboratory tests to analyze non-linear flow in fractured media[J]. Hydrology & Earth System Sciences, 2012, 9(4): 2511-2522.

SIDIROPOULOU M G, MOUTSOPOULOS K N, TSIHRINTZIS V A. Determination of Forchheimer equation coefficients a and b[J]. Hydrological Processes, 2007, 21(4): 534-554. doi: 10.1002/hyp.6264

JOHNSON J, BROWN S, STECKMAN H. Fluid flow and mixing in rough-walled fracture intersections[J]. Journal of Geophysical Research Solid Earth, 2006, 111: 1-16.

QIAN Jiazhong, ZHAN Hongbin, LUO Shaohe, 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): 206-215.

ZHANG Zhenyu, NEMCIK J. Fluid flow regimes and nonlinear flow characteristics in deformable rock fractures[J]. Journal of Hydrology, 2013, 477(1): 139-151.

ZOU Liangchao, JING Lanru, CVETKOVIC V. Roughness decomposition and nonlinear fluid flow in a single rock fracture[J]. International Journal of Rock Mechanics & Mining Sciences, 2015, 75: 102-118.

QIAN Jiazhong, WANG Mu, ZHANG Yong, et al. Experimental study of the transition from non-Darcian to Darcy behavior for flow through a single fracture[J]. Journal of Hydrodynamics, 2015, 27(5): 679-688. doi: 10.1016/S1001-6058(15)60530-3

QUINN P M, CHERRY J A, PARKER B L. Quantification of non-Darcian flow observed during packer testing in fractured sedimentary rock[J]. Water Resources Research, 2011, 47(9): 1-15.

刘日成,李博,蒋宇静,等. 等效水力隙宽和水力梯度对岩体裂隙网络非线性渗流特性的影响[J]. 岩土力学,2016,37(11): 3165-3174.

LIU Richeng, LI Bo, JIANG Yujing, et al. Effects of equivalent hydraulic aperture and hydraulic gradient on nonlinear seepage properties of rock mass fracture networks[J]. Rock and Soil Mechanics, 2016, 37(11): 3165-3174.

CHEN Yifeng, ZHOU Jiaqing, HU Shaohua, 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

刘咏, 钱家忠, 赵卫东. 窄缝裂隙水流雷诺数的实验研究[C]//第七届全国水动力学学术会议暨第十九届全国水动力学研讨会文集（上册）. 上海: 海洋出版社, 2005: 475-480

刘丽红,吴潇潇,颜冰. 岩块尺度达西流非达西流流态转化研究[J]. 科技通报,2017,33(1): 32-38.

LIU Lihong, WU Xiaoxiao, YAN Bing. Research of transition between the Darcian and non-Darcian flow of rock block scale[J]. Bulletin of Science and Technology, 2017, 33(1): 32-38.

郭建春,庄园,刘超. 考虑非达西效应的酸蚀裂缝流场数值模拟[J]. 岩土力学,2015,36(11): 3315-3321.

GUO Jianchun, ZHUANG Yuan, LIU Chao. Numerical simulation of flow field of acid etched fractures considering non-Darcy effect[J]. Rock and Soil Mechanics, 2015, 36(11): 3315-3321.

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): 384-384.

FORCHHEIMER P H. FORCHHEIMER P H. Wasserbewegung durch Boden[J]. Zeitschrift des Vereines Deutscher Ingeneieure, 1901, 45: 1782-1788.

李加武,崔欣,张宏杰,等. 粗糙度对雷诺数效应的影响[J]. 长安大学学报(自然科学版),2009,29(2): 56-59.

LI Jiawu, CUI Xin, ZHANG Hongjie, et al. Influence of surface roughness on Reynolds number effects[J]. Journal of Chang ’an University ( Natural Science Edition), 2009, 29(2): 56-59.

SCHRAUF T W, EVANS D D. Laboratory studies of gas flow through a single natural fracture[J]. Water Resour. Res., 1986, 22(7): 1038-1050. doi: 10.1029/WR022i007p01038

ZIMMERMAN R W, BODVARSSON G S. Hydraulic conductivity of rock fractures[J]. Transport in Porous Media, 1996, 23(1): 1-30.

NOWAMOOZ A, RADILLA G, FOURAR M. Non-Darcian two-phase flow in a transparent replica of a rough-walled rock fracture[J]. Water Resources Research, 2009, 45(7): W07406.

TZELEPIS V, MOUTSOPOULOS K N, PAPASPYROS J N E, et al. Experimental investigation of flow behavior in smooth and rough artificialfractures[J]. Journal of Hydrology, 2015, 521: 108-118. doi: 10.1016/j.jhydrol.2014.11.054

王潇. 单裂隙中粗糙元及其疏密度对水流特性影响模拟研究[D]. 合肥: 合肥工业大学, 2014.

ZENG Zhengwen, 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

MACINI P, MESINI E, VIOLA R. Laboratory measurements of non-Darcy flow coefficients in natural and artificial unconsolidated porous media[J]. Journal of Petroleum Science and Engineering, 2011, 77(3): 365-374.

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Parameters Quantification of Forchheimer Equation and Critical Point of Transition from Darcian to Non-Darcian Flow

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