Analytical solution for Non-Darcian effect on transient confined-unconfined flow in a confined aquifer

Peng-yu Shi; Jian-jun Liu; Yi-jie Zong; Kai-qing Teng; Yu-ming Huang; Liang Xiao

doi:10.26599/JGSE.2023.9280029

Volume 11 Issue 4

Dec. 2023

Turn off MathJax

Article Contents

Article Navigation > Journal of Groundwater Science and Engineering > 2023 > 11(4): 365-378

Shi PY, Liu JJ, Zong YJ, et al. 2023. Analytical solution for Non-Darcian effect on transient confined-unconfined flow in a confined aquifer. Journal of Groundwater Science and Engineering, 11(4): 365-378 doi: 10.26599/JGSE.2023.9280029

Citation:

PDF( 2117 KB)

Analytical solution for Non-Darcian effect on transient confined-unconfined flow in a confined aquifer

doi: 10.26599/JGSE.2023.9280029

Peng-yu Shi^{1, 2, 3
,},
Jian-jun Liu^{1, 2, 3},
Yi-jie Zong^{1, 2, 3},
Kai-qing Teng^{1, 2, 3},
Yu-ming Huang¹,
Liang Xiao^{1, 2, 3
,
,}

1.
College of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China
2.
Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, Guangxi University, Nanning 530004, China
3.
Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi University, Nanning 530004, China

More Information

Corresponding author: xiaoliang850425@sina.com
Received Date: 2022-12-25
Accepted Date: 2023-04-30

Available Online: 2023-12-10

Publish Date: 2023-12-31

Abstract

Abstract

This paper presents a new analytical solution to investigate the mechanism of transient confined-unconfined flow in a confined aquifer induced by pumping with a large rate during mine drainage. The study focuses on understanding the impact of non-Darcian effect on flow towards a fully penetrated pumping well. The nonlinear relationship between specific discharge and the hydraulic gradient is described using Izbash's equation. A novel approximate method is developed to linearize the mathematical model, and the solution is derived using the Boltzmann transform. The proposed solution is validated by comparing it with previous works. The findings indicate that increased non-Darcian index, quasi-hydraulic conductivity, and specific storage have negatively affect the development of the unconfined region and aquifer drawdown, as greater turbulence flow accelerates recharge to the pumping well. Drawdown is found to be sensitive to the non-Darcian index, quasi-hydraulic conductivity, while it is unaffected by specific yield and specific storage. The conclusions provide valuable insights for mine drainage and the application of geological and hydrological conditions.
- Non-Darcian flow,
- Izbash equation,
- Boltzmann transform,
- Sensitivity analysis

FullText(HTML)

References(47)

References

Basak P. 1976. Steady non-Darcian seepage through embankments. Journal of the Irrigation and Drainage Division, 102(4): 435−443. DOI: 10.1061/JRCEA4.0001256.

Bordier C, Zimmer D. 2000. Drainage equations and non-Darcian modeling in coarse porous media or geosynthetic materials. Journal of Hydrology, 228: 174−187. DOI: 10.1016/S0022-1694(00)00151-7.

Chen CX, Hu LT, Wang XS. 2006. Analysis of stead ground water flow toward wells in a confined-unconfined aquifer. Ground Water, 44(4): 609−612. DOI: 10.1111/j.1745-6584.2006.00170.x.

Chen CX, Wan JW, Zhan HB. 2003. Theoretical and experimental studies of coupled seepage-pipe flow to a horizontal well. Journal of Hydrology, 281(1-2): 159−171. DOI: 10.1016/S0022-1694(03)00207-5.

Elango K, Swaminathan K. 1980. A finite-element model for concurrent confined-unconfined zones in an aquifer. Journal of Hydrology, 46(3-4): 289−299. DOI: 10.1016/0022-1694(80)90082-7.

El-Hames AS. 2020. Development of a simple method for determining the influence radius of a pumping well in steady-state condition. Journal of Groundwater Science and Engineering, 8(2): 11. DOI: 10.19637/j.cnki.2305-7068.2020.02.001.

Feng Q, Wen Z. 2016. Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin. Hydrogeology Journal, 24(5): 1287−1296. DOI: 10.1007/s10040-016-1389-8.

Hao HB, Lv J, Chen YM, et al. 2021. Research advances in non-Darcian flow in low permeability media. Journal of Groundwater Science and Engineering, 9(1): 83−92. DOI: 10.19637/j.cnki.2305-7068.2021.01.008.

Houben GJ. 2015. Review: Hydraulics of water wells-flow laws and influence of geometry. Hydrogeology Journal, 23(8): 1633−1657. DOI: 10.1007/s10040-015-1312-8.

Hu LT, Chen CX. 2008. Analytical methods for transient flow to a well in a confined-unconfined aquifer. Ground water, 46(4): 642−646. DOI: 10.1111/j.1745-6584.2008.00436.x.

Huang YC, Yeh HD. 2007. The use of sensitivity analysis in on-line aquifer parameter estimation. Journal of Hydrology, 335(3-4): 406−418. DOI: 10.1016/j.jhydrol.2006.12.007.

Ji SH, Koh YK. 2015. Nonlinear groundwater flow during a slug test in fractured rock. Journal of Hydrology, 520: 30−36. DOI: 10.1016/j.jhydrol.2014.11.039.

Li J, Xia XH, Zhan H, et al. 2021. Non-Darcian flow for an artificial recharge well in a confined aquifer with clogging-related permeability reduction. Advances in Water Resources, 147(8): 103820. DOI: 10.1016/j.advwatres.2020.103820.

Liu MM, Chen YF, Zhan HB, et al. 2017. A generalized Forchheimer radial flow model for constant-rate tests. Advances in Water Resources, 107(sep.): 317−325. DOI: 10.1016/j.advwatres.2017.07.004.

Marsily GD. 1986. Quantitative hydrogeology. Fontainebleau, France: Pairs School of Mines.

Mathias SA, Wen Z. 2015. Numerical simulation of Forchheimer flow to a partially penetrating well with a mixed-type boundary condition. Journal of Hydrology, 524: 53−61. DOI: 10.1016/j.jhydrol.2015.02.015.

Mathias SA, Moutsopoulos KN. 2016. Approximate solutions for Forchheimer flow during water injection and water production in an unconfined aquifer. Journal of Hydrology, 538: 13−21. DOI: 10.1016/j.jhydrol.2016.03.048.

Mawlood D, Mustafa J. 2016. Comparison between Neuman (1975) and Jacob (1946) application for analysing pumping test data of unconfined aquifer. Journal of Groundwater Science and Engineering, 4(3): 165−173. DOI: 10.21271/zjpas.32.2.2.

Moench AF, Prickett TA. 1972. Radial flow in an infinite aquifer undergoing conversion from artesian to water table conditions. Water Resource Research, 8(2): 494−499. DOI: 10.1029/WR008i002p00494.

Moench AF, Garabedian SP, LeBlanc DR. 2001. Estimation of hydraulic parameters from an unconfined aquifer test conducted in a glacial outwash deposit, Cape Cod, Massachusetts. US Geology Survey Professional Paper, (1629): 140.

Moutsopoulos KN, Tsihrintzis VA. 2005. Approximate analytical solutions of the Forchheimer equation. Journal of Hydrology, 309(1-4): 93−103. DOI: 10.1016/j.jhydrol.2004.11.014.

Moutsopoulos KN. 2007. One-dimensional unsteady inertial flow in phreatic aquifers, induced by a sudden change of the boundary head. Transport Porous Media, 70(1): 97−125. DOI: 10.1007/s11242-006-9086-z.

Moutsopoulos KN. 2009. Exact and approximate analytical solutions for unsteady fully developed turbulent flow in porous media and fractures for time dependent boundary conditions. Journal of Hydrology, 369(1-2): 78−89. DOI: 10.1016/j.jhydrol.2009.02.025.

Qian JZ, Zhan HB, Zhao WD. 2005. Experimental study of turbulent unconfined groundwater flow in a single fracture. Journal of Hydrology, 311(1-4): 134−142. DOI: 10.1016/j.jhydrol.2005.01.013.

Sen Z. 1987. Non-Darcian flow in fractured rocks with a linear flow pattern. Journal of Hydrology, 92(1-2): 43−57. DOI: 10.1016/0022-1694(87)90088-6.

Sen Z. 1989. Non-linear flow toward wells. Journal of Hydrology Engineering, 115(2): 193−209. DOI: 10.1061/(ASCE)0733-9429(1989)115:2(193).

Sen Z. 1990. Nonliear radical flow in confined aquifers toward large-dsameter wells. Water Resource Research, 26(5): 1103−1109. DOI: 10.1016/0148-9062(90)91166-5.

Soni JP, Islam N, Basak P. 1978. An experimental evaluation of non-Darcian flow in porous media. Jounal of Hydrology, 38(3-4): 231−241. DOI: 10.1016/0022-1694(78)90070-7.

Wang QR, Zhan HB, Wang YX. 2015. Non-Darcian effect on slug test in a leaky confined aquifer. Journal of Hydrology, 527: 747−753. DOI: 10.1016/j.jhydrol.2015.05.038.

Wang XF. 2011. Fundamentals of hydrogeology. Hydrogeology & Engineering Geology, 38 (03): 1. (in Chinese)

Wang XS, Wan L, Hu B. 2009. New approximate solutions of horizontal confined–unconfined flow. Journal of Hydrology (Amsterdam), 376(3-4): 417−427. DOI: 10.1016/j.jhydrol.2009.07.050.

Wen Z, Huang GH, Zhan HB. 2006. Non-Darcian flow in a single confined vertical fracture toward a well. Journal of Hydrology, 330(3): 698−708. DOI: 10.1016/j.jhydrol.2006.05.001.

Wen Z, Huang GH. Zhan HB. 2008a. Non-Darcian flow to a well in an aquifer–aquitard system. Advances in Water Resources, 31(12): 1754−1763. DOI: 10.1016/j.advwatres.2008.09.002.

Wen Z, Huang GH, Zhan HB. 2008b. Two-region non-Darcian flow toward a well in a confined aquifer. Advances in Water Resources, 31(5): 818−827. DOI: 10.1016/j.advwatres.2008.01.014.

Wen Z, Huang GH, Zhan HB. 2008c. An analytical solution for non-Darcian flow in a confined aquifer using the power law function. Advances in Water Resources, 31(1): 44−55. DOI: 10.1016/j.advwatres.2007.06.002.

Wen Z, Huang GH, Zhan HB. 2009. A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function. Journal of Hydrology, 364(1/2): 99−106. DOI: 10.1016/j.jhydrol.2008.10.009.

Wen Z, Huang GH, Zhan HB. 2011. Non-Darcian flow to a well in a leaky aquifer using the Forchheimer equation. Hydrogeology Journal, 19(3): 563−572. DOI: 10.1007/s10040-011-0709-2.

Wen Z, Wang QR. 2013. Approximate analytical and numerical solutions for radial non-Darcian flow to a well in a leaky aquifer with wellbore storage and skin effect. International Journal for Numerical & Analytical Methods in Geomechanics, 37(11): 1453−1469. DOI: 10.1002/nag.2091.

Wen Z, Liu K, Chen XL. 2013. Approximate analytical solution for non-Darcian flow toward a partially penetrating well in a confined aquifer. Journal of Hydrology, 498: 124−131. DOI: 10.1016/j.jhydrol.2013.06.027.

Wu YS. 2001. Non-Darcy displacement of immiscible fluids in porous media. Water Resource Research, 37(12): 2943−2950. DOI: 10.1029/2001WR000389.

Wu YS. 2002a. An approximate analytical solution for non-Darcy flow toward a well in fractured media. Water Resource Research, 38(3): 5−1. DOI: 10.1029/2001WR000713.

Wu YS. 2002b. Numerical simulation of single-phase and multi-phase non-Darcy flow in porous and fractured reservoirs. Transport Porous Media, 49(2): 209−240. DOI: 10.1023/A:1016018020180.

Xiao L, Guo GH, Chen LH, et al. 2022. Theory of transient confined-unconfined flow in a confined aquifer considering delayed responses of water table. Journal of Hydrology, 2022(608): 127644. DOI: 10.1016/j.jhydrol.2022.127644.

Xiao L, Liu JJ, Gan FW, et al. 2023. A semi-analytical solution for transient confined–unconfined flow with non-Darcian effect. Journal of Hydrologic Engineering, 28(5): 04023012. DOI: 10.1061/JHYEFF.HEENG-5845.

Xiao L, Ye M, Xu YX. 2018. A new solution for confined-unconfined flow toward a fully penetrating well in a confined aquifer. Groundwater, 56(6): 959−968. DOI: 10.1111/gwat.12642.

Zhao RJ, Mao DQ, Liu ZB, et al. 2021. An analysis of sequential water releasing tests of the confined aquifers in a coal mine based on hydraulic tomography. Hydrogeology & Engineering Geology, 48(1): 1−9. (in Chinese) DOI: 10.16030/j.cnki.issn.1000-3665.202003024.

Zong YJ, Chen LH, Liu JJ, et al. 2022. Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect. Journal of Groundwater Science and Engineering, 10(4): 311−321. DOI: 10.19637/j.cnki.2305-7068.2022.04.001.

2305-7068/© Journal of Groundwater Science and Engineering Editorial Office. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0)

Relative Articles

[1]	Xiang Gao, Tai-lu Li, Yu-wen Qiao, Yao Zhang, Ze-yu Wang, 2024: A combined method using Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM) to simulate geothermal reservoirs in Enhanced Geothermal System (EGS), Journal of Groundwater Science and Engineering, 12, 132-146. doi: 10.26599/JGSE.2024.9280011
[2]	Masoud H Hamed, Rebwar N Dara, Marios C Kirlas, 2024: Groundwater vulnerability assessment using a GIS-based DRASTIC method in the Erbil Dumpsite area (Kani Qirzhala), Central Erbil Basin, North Iraq, Journal of Groundwater Science and Engineering, 12, 16-33. doi: 10.26599/JGSE.2024.9280003
[3]	Shima Nasiri, Hossein Ansari, Ali Naghi Ziaei, 2022: Determination of water balance equation components in irrigated agricultural watersheds using SWAT and MODFLOW models : A case study of Samalqan plain in Iran, Journal of Groundwater Science and Engineering, 10, 44-56. doi: 10.19637/j.cnki.2305-7068.2022.01.005
[4]	Yi-jie Zong, Li-hua Chen, Jian-jun Liu, Yue-hui Liu, Yong-xin Xu, Fu-wan Gan, Liang Xiao, 2022: Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect, Journal of Groundwater Science and Engineering, 10, 311-321. doi: 10.19637/j.cnki.2305-7068.2022.04.001
[5]	Zhao-xian Zheng, Xiao-shun Cui, Pu-cheng Zhu, Si-jia Guo, 2021: Sensitivity assessment of strontium isotope as indicator of polluted groundwater for hydraulic fracturing flowback fluids produced in the Dameigou Shale of Qaidam Basin, Journal of Groundwater Science and Engineering, 9, 93-101. doi: 10.19637/j.cnki.2305-7068.2021.02.001
[6]	Hong-bo HAO, Jie LV, Yan-mei CHEN, Chuan-zi WANG, Xiao-rui HUANG, 2021: Research advances in non-Darcy flow in low permeability media, Journal of Groundwater Science and Engineering, 9, 83-92. doi: 10.19637/j.cnki.2305-7068.2021.01.008
[7]	ZHANG Han-xiong, HU Xiao-nong, 2018: Simulation and analysis of Chloride concentration in Zhoushan reclamation area, Journal of Groundwater Science and Engineering, 6, 150-160. doi: 10.19637/j.cnki.2305-7068.2018.02.008
[8]	ZHU Wei, TANG Wen, LIU Qiang, ZHANG Mei-gui, 2017: Analysis on variation characteristics of geothermal response in Liaoning Province, Journal of Groundwater Science and Engineering, 5, 336-342.
[9]	WU Jian-qiang, WU Xia-yi, 2016: Geological environment impact analysis of a landfill by the Yangtze River, Journal of Groundwater Science and Engineering, 4, 96-102.
[10]	ZHOU Xun, WANG Xiao-cui, CAO Qin, LONG Mi, ZHENG Yu-hui, GUO Juan, SHEN Xiao-wei, ZHANG Yu-qi, TA Ming-ming, CUI Xiang-fei, 2016: A discussion of up-flow springs, Journal of Groundwater Science and Engineering, 4, 279-283.
[11]	DAI Wen-Bin, ZHANG Wei-Jun, COWEN Taha, 2015: An analysis of River Derwent pollution and its impacts, Journal of Groundwater Science and Engineering, 3, 39-44.
[12]	YANG Yun, WU Jian-feng, LIU De-peng, 2015: Numerical modeling of water yield of mine in Yangzhuang Iron Mine, Anhui Province of China, Journal of Groundwater Science and Engineering, 3, 352-362.
[13]	CUI Qiu-ping, LIU Zhi-gang, LIU Li-jun, ZHANG Shao-cai, CHEN Yun-qian, 2014: Emergency water supply capacity analysis of major cities in Hebei, Journal of Groundwater Science and Engineering, 2, 76-86.
[14]	HE Hong, GUO Hong-bin, LIU Hong-yun, 2014: Analysis of effect of water construction in different phases on groundwater environment, Journal of Groundwater Science and Engineering, 2, 54-59.
[15]	SHI Jian-sheng, LIU Chang-li, DONG Hua, YAN Zhen-peng, WANG Yan-jun, LIU Xin-hao, GUO Xiu-yan, JIAO Hong-jun, YIN Mi-ying, HOU Huai-ren, 2014: Stability assessment and risk analysis of aboveground river in lower Yellow River, Journal of Groundwater Science and Engineering, 2, 1-18.
[16]	GU Ming-xu, LIU Yu, HAN Chong, SHANG Lin-qun, JIANG Xian-qiao, WANG Lin-ying, 2014: Analysis of impact of outfalls on surrounding soil and groundwater environment, Journal of Groundwater Science and Engineering, 2, 54-60.
[17]	BAI Xi-qing, LIU Yan, 2014: Feasibility Analysis on Resuming Flow of Large Karst Spring in Heilongdong, Journal of Groundwater Science and Engineering, 2, 80-87.
[18]	, 2013: Analysis of Groundwater Environmental Conditions and Influencing Factors in Typical City in Northwest China, Journal of Groundwater Science and Engineering, 1, 60-73.
[19]	Cheng Yanpei, Ma Renhui, 2013: Analysis of Water Resource Demands: Based on the Hydrological Unit, Journal of Groundwater Science and Engineering, 1, 48-59.
[20]	Zong-jun Gao, Yong-gui Liu, 2013: Groundwater Flow Driven by Heat, Journal of Groundwater Science and Engineering, 1, 22-27.