Analytical solutions for constant-rate test in bounded confined aquifers with non-Darcian effect
-
Abstract:
This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries. The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle, of which the non-Darcian effect is characterized by Izbash’s equation. The solutions are derived by Boltzmann and dimensionless transformations. Then, the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution. The results show that the aquifer boundaries have non-negligible effects on pumping, and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping. The higher the degree of non-Darcian, the smaller the drawdown.
-
Key words:
- Non-Darcian effect /
- Bounded aquifer /
- Wellbore storage /
- Izbash’s equation /
- Analytical solution
-
-
Table 2. Parameter values in dimensionless format
Parameters Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 
0.1 0.02 0.02 0.2 0.2 0.2 
0.02 0.02 0.02 0 0.02 0, 0, 0.02 
0.1 0.05 0.05 0 0.03 0, 0, 0.05 
0.2 0.1, 1, 10 0.2 0.1, 1, 10 0.1, 1, 10 0.2 
0.001 0.001 0.001 0.001 0.001 0.001 
1.2 1.2 1, 1.3, 1.5 1.2 1.2 1, 1.5, 1.5 
下载: 导出CSV
-
Asadi-Aghbolaghi M, Seyyedian H. 2010. An analytical solution for groundwater flow to a vertical well in a triangle-shaped aquifer. Journal of Hydrology, 393(3−4): 341−348. doi: 10.1016/j.jhydrol.2010.08.034
Chan YK. 1976. Improved image-well technique for aquifer analysis. Journal of Hydrology, 29: 149−164. doi: 10.1016/0022-1694(76)90011-1
Chen YJ, Yeh HD, Yang SY. 2009. Analytical solutions for constant-flux and constant-head tests at a Finite-Diameter well in a wedge-shaped aquifer. Journal of Hydraulic Engineering, 135: 333−337. doi: 10.1061/(ASCE)0733-9429(2009)135:4(333
Cherry GS. 2001. Simulation of flow in the upper north coast limestone aquifer, Manati-Vega Baja area, Puerto Rico. Water-Resources Investigations Report: 2000−4266. doi: 10.3133/wri20004266
Corapcioglu MY, Borekci O, Haridas A. 1983. Analytical solutions for rectangular aquifers with third-kind (Cauchy) boundary conditions. Water Resources Research, 19: 523−528. doi: 10.1029/WR019i002p00523
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
Gavin L. 2004. Pre-Darcian flow: A missing piece of the improved oil recovery puzzle? The SPE/DOE Symposium on Improved Oil Recovery, Tulsa, Oklahoma.SPE-89433-MS.
Guadagnini A, Riva M, Neuman SP. 2003. Three-dimensional steady state flow to a well in a randomly heterogeneous bounded aquifer. Water Resources Research, 39(3): 53−62. doi: 10.1029/2002WR001443
Hao HB, Jie LV, 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
Holzbecher E. 2005. Analytical solution for two-dimensional groundwater flow in presence of two isopotential lines. Water Resources Research, 41(12): W12502. doi: 10.1029/2005WR004583
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
Jafari F, Javadi S, Golmohammadi G, et al. 2016. Numerical simulation of groundwater flow and aquifer-system compaction using simulation and InSAR technique: Saveh basin, Iran. Environmental Earth Sciences, 75(9): 833. doi: 10.1007/s12665-016-5654-x
Kacimov AR, Kayumov IR, Al-Maktoumi A. 2016a. Rainfall induced groundwater mound in wedge-shaped promontories: The Strack-Chernyshov model revisited. Advances in Water Resources, 97: 110−119. doi: 10.1016/j.advwatres.2016.08.011
Kacimov AR, Maklakov DV, Kayumov IR, et al. 2016b. Free surface flow in a microfluidic corner and in an unconfined aquifer with accretion: The signorini and Saint-Venant analytical techniques revisited. Transport in Porous Media, 116(1): 1−28. doi: 10.1007/s11242-016-0767-y
Kihm JH, Kim JM, Song SH, et al. 2007. Three-dimensional numerical simulation of fully coupled groundwater flow and land deformation due to groundwater pumping in an unsaturated fluvial aquifer system. Journal of Hydrology, 335(1−2): 1−14. doi: 10.1016/j.jhydrol.2006.09.031
Kim JM. 2005. Three-dimensional numerical simulation of fully coupled groundwater flow and land deformation in unsaturated true anisotropic aquifers due to groundwater pumping. Water Resources Research, 41(1): 1003. doi: 10.1029/2003wr002941
Kruseman GP, Ridderna NAD. 1990. Analysis and evaluation of pumping test data, 2nd ed. International Institute for Land Reclamation and Improvement: 21-30.
Latinopoulos P. 1984. Periodic recharge to finite aquifiers from rectangular areas. Advances in Water Resources, 7: 137−140. doi: 10.1016/0309-1708(84)90043-5
Latinopoulos P. 1985. Analytical solutions for periodic well recharge in rectangular aquifers with third-kind boundary conditions. Journal of Hydrology, 77: 296−306. doi: 10.1016/0022-1694(85)90213-6
Li Y, Zhou Z, Zhuang C. et al. 2020. Non-Darcian effect on a variable-rate pumping test in a confined aquifer. Hydrogeology Journal, 28: 2853−2863. doi: 10.1007/s10040-020-02223-w
Lin CC, Chang YC, Yeh HD. 2018. Analysis of groundwater flow and stream depletion in L-shaped fluvial aquifers. Hydrology and Earth System Sciences, 22(4): 2359−2375. doi: 10.5194/hess-22-2359-2018
Liu MM, Chen YF, Zhan H, et al. 2017. A generalized Forchheimer radial flow model for constant-rate tests. Advances in Water Resources, 107: 317−325. doi: 10.1016/j.advwatres.2017.07.004
Loudyi D, Falconer RA, Lin B. 2006. Mathematical development and verification of a non-orthogonal finite volume model for groundwater flow applications. Advances in Water Resources, 30(1): 29−42. doi: 10.1016/j.advwatres.2006.02.010
Lu C, Xin P, Li L, et al. 2015. Steady state analytical solutions for pumping in a fully bounded rectangular aquifer. Water Resource Research, 51: 8294−8302. doi: 10.1002/2015WR017019
Mahdavi A, Seyyedian H. 2014. Steady-state groundwater recharge in trapezoidal-shaped aquifers: A semi-analytical approach based on variational calculus. Journal of Hydrology, 512: 457−462. doi: 10.1016/j.jhydrol.2014.03.014
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
Samani N, Sedghi MM. 2015. Semi-analytical solutions of groundwater flow in multi-zone (patchy) wedge-shaped aquifers. Advances in Water Resources, 77: 1−16. doi: 10.1016/j.advwatres.2015.01.003
Samani N, Zarei-Doudeji S. 2012. Capture zone of a multi-well System in wedge-shaped aquifers for remediation purposes. Advances in Water Resources, 39: 71−84. doi: 10.1016/j.advwatres.2012.01.004
Sen. 1990. Nonlinear radial flow in confined aquifers toward large-diameter wells. Water Resources Research, 26(5): 1103−1109. doi: 10.1029/WR026i005p01103
Sergio E, Serrano. 2013. A simple approach to groundwater modelling with decomposition. Hydrological Sciences Journal, 58: 177−185. doi: 10.1080/02626667.2012.745938
Stallman RW, Brown RH. 1951. Nonequilibrium type curves modified for two-well systems. Open-File Report: 51-150.
Taigbenu AE. 2003. Green element simulations of multiaquifer flows with a time-dependent Green’s function. Journal of Hydrology, 284(1-4): 131−150. doi: 10.1016/j.jhydrol.2003.07.002
Wen Z, Huang G, Zhan H. 2011. Solutions for Non-Darcian flow to an extended well in fractured rock. Ground water, 49(2): 280−285. doi: 10.1111/j.1745-6584.2010.00728.x
Wen Z, Huang G, Zhan H, et al. 2008a. Two-region non-Darcian flow toward a well in a confined aquifer. Advances in Water Resources, 31: 818−827. doi: 10.1016/j.advwatres.2008.01.014
Wen Z, Huang G, Zhan H. 2008b. An analytical solution for non-Darcian flow in a confined aquifer using the power law function. Advances in Water Resources, 364(1): 99−106. doi: 10.1016/j.jhydrol.2008.10.009
Wen Z, Liu K, Zhan H. 2014. Non-Darcian flow toward a larger-diameter partially penetrating well in a confined aquifer. Environmental Earth Sciences, 72(11): 4617−4625. doi: 10.1007/s12665-014-3359-6
Xiao L, Ye M, Xu Y, et al. 2019. A simplified solution using Izbash’s equation for non-Darcian flow in a constant rate pumping test. Ground water, 57(6): 962−968. doi: 10.1111/gwat.12886
Xiong Y, Yu J, Sun H, et al. 2016. A new Non-Darcian flow model for low-velocity multiphase flow in tight reservoirs. Transport in Porous Media, 117: 367−383. doi: 10.1007/s11242-017-0838-8
Younger, PAUL. 2007. Groundwater in the environment: An introduction. Fems Microbiology Letters, 291(2): 169−174. doi: 10.1111/j.1574-6968.2008.01448.x
Zhang M, Lai Y, Li S, et al. 2007. Laboratory study on cooling effect of crushedrock embankment with impermeable boundary in cold regions. Proceedings of the seventh International Symposium on Permafrost Engineering: 239−247. doi: 10.1061/40836(210)31
-
图(8)
表(2)
计量
- 文章访问数: 1123
- PDF下载数: 17
- 施引文献: 0