Non-Darcian Flow to a Partially Penetrating Pumping Well in a Leaky Aquifer Considering the Aquitard–Aquifer Interface Flow
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 12
Abstract
In this study, non-Darcian flow to a partially penetrating pumping well in a leaky aquifer was investigated. The aquifer system is composed of a main aquifer with an aquitard bounded on the top of the aquifer. The storage of the aquitard was considered in this study, which is the main contribution of this study. The horizontal flow in the main aquifer is assumed to be non-Darcian, while both the vertical flows in the main aquifer and the aquitard were assumed to be Darcian due to the relative low velocities. The non-Darcian flow was described by the Izbash equation. A linearization procedure associated with Laplace transform and separate variable method were used to solve the non-Darcian flow model. Semianalytical solutions (Laplace-domain solutions) were obtained then inverted to time domain by using the Stehfest method. The results indicated that the power index in the Izbash equation results in a smaller drawdown at late times, the flow approaches quasi steady state earlier, and the leakage has little impact on the drawdowns in the main aquifer when is larger. The drawdowns are quite different from each other for different positions even at the same radial distance. The sensitivity analysis indicated that the drawdown in the main aquifer is very sensitive to the power index , moderately sensitive to the parameters of the main aquifer, and relatively not sensitive to the parameters of the aquitard.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was partially supported by the Natural National Science Foundation of China (Grant Numbers: 41372253, 41521001), and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (Grant Numbers: CUG140503).
References
Barua, G., and Bora, S. N. (2010). “Hydraulics of a partially penetrating well with skin zone in a confined aquifer.” Adv. Water Resour., 33(12), 1575–1587.
Bordier, C., and Zimmer, D. (2000). “Drainage equations and non-Darcian modelling in coarse porous media or geosynthetic materials.” J. Hydrol., 228(3), 174–187.
Camacho, V. R. G., and Vasquez, C. M. (1992). “Comment on ‘Analytical Solution Incorporating Nonlinear Radial Flow in Confined Aquifers’ by Zekai Sen.” Water Resour. Res., 28(12), 3337–3338.
Cassiani, G., and Kabala, Z. J. (1998). “Hydraulics of a partially penetrating well: Solution to a mixed-type boundary value problem via dual integral equations.” J. Hydrol., 211(1–4), 100–111.
Chang, C. C., and Chen, C. S. (2003). “A flowing partially penetrating well in a finite-thickness aquifer: A mixed-type initial boundary value problem.” J. Hydrol., 271(1–4), 101–118.
Ewing, R. E., et al. (1999). “Numerical well model for non-Darcy flow through isotropic porous media.” Comp. Geosci., 3(3/4), 185–204.
Ewing, R. E., and Lin, Y. (2001). “A mathematical analysis for numerical well models for non-Darcy flows.” Appl. Numer. Math., 39(1), 17–30.
Feng, Q., and Zhan, H. (2015). “On the aquitard-aquifer interface flow and the drawdown sensitivity with a partially penetrating pumping well in an anisotropic leaky confined aquifer.” J. Hydrol., 521, 74–83.
Forchheimer, P. H. (1901). “Wasserbewegung durch Boden.” Z Ver Deutsch Ing, 45(1782), 1788.
Hantush, M. S. (1957). “Non-steady flow to a well partially penetrating an infinite leaky aquifer.” Proc. Iraqi. Sci. Soc., 1, 10–19.
Hantush, M. S. (1959). “Nonsteady flow to flowing wells in leaky aquifers.” J. Geophys. Res., 64(8), 1043–1052.
Hantush, M. S. (1960). “Modification of the theory of leaky aquifers.” J. Geophys. Res., 65(11), 3713–3725.
Hantush, M. S. (1961). “Drawdown around a partially penetrating well.” Proc. J. Hydrol. Div., 87(4), 83–98.
Hantush, M. S. (1964). “Hydraulics of wells.” Adv. Hydrosci., 1, 281–432.
Hantush, M. S. (1967). “Flow of groundwater in relatively thick leaky aquifers.” Water Resour. Res., 3(2), 583–590.
Hantush, M. S., and Jacob, C. E. (1955). “Non-steady radial flow in an infinite leaky aquifer.” Trans. Am. Geophys. Union, 36(1), 95–100.
Huang, Y. C., and Yeh, H. D. (2007). “The use of sensitivity analysis in on-line aquifer parameter estimation.” J. Hydrol., 335(3), 406–418.
Hunt, B. (2005). “Flow to vertical and nonvertical wells in leaky aquifers.” J. Hydrol. Eng., 477–484.
Hunt, B., and Scott, D. (2007). “Flow to a well in a two-aquifer system.” J. Hydrol. Eng., 146–155.
Izbash, S. V. (1931). “O filtracil V Kropnozemstom Maeriale.” USSR, Leningrad (in Russian).
Kirkham, D. (1959). “Exact theory of flow into a partially penetrating well.” J. Geophys. Res., 64(9), 1317–1327.
Liu, K., Wen, Z., and Liu, Z. (2013). “Approximate analytical solution for non-Darcian flow to a partially penetrating well in the first kind of leaky aquifer.” J. Hydraul. Eng., 46(8), 966–972 (in Chinese).
Mathias, S. A., Butler, A. P., and Zhan, H. (2008). “Approximate solutions for Forchheimer flow to a well.” J. Hydraul. Eng., 1318–1325.
Mathias, S. A., and Wen, Z. (2015). “Numerical simulation of forchheimer flow to a partially penetrating well with a mixed-type boundary condition.” J. Hydrol., 524, 53–61.
Mishra, P. K., Vesselinov, V. V., and Neuman, S. P. (2012). “Radial flow to a partially penetrating well with storage in an anisotropic confined aquifer.” J. Hydrol., 448(27), 255–259.
Neuman, S. P. (1974). “Effect of partial penetration on flow in unconfined aquifers considering delayed gravity response.” Water Resour. Res., 10(2), 303–312.
Perina, T., and Lee, T. C. (2006). “General well function for pumping from a confined, leaky, or unconfined aquifer.” J. Hydrol., 317(3–4), 239–260.
Sedghi-Asl, M., Rahimi, H., and Salehi, R. (2014). “Non-Darcy flow of water through a packed column test.” Trans. Porous Med., 101(2), 215–227.
Selim, M. S. and Kirkham, D. (1974). “Screen theory for wells and soil drainpipes.” Water Resour. Res., 10(5), 1019–1030.
Sen, Z. (1987). “Non-Darcian flow in fractured rocks with a linear flow pattern.” J. Hydrol., 92(1–2), 43–57.
Sen, Z. (1989). “Nonlinear flow toward wells.” J. Hydraul. Eng., 193–209.
Sen, Z. (1990). “Nonlinear radial flow in confined aquifers toward large-diameter wells.” Water Resour. Res., 26(5), 1103–1109.
Sen, Z. (1988a). “Analytical solution incorporating nonlinear radial flow in confined aquifers.” Water Resour. Res., 24(4), 601–606.
Sen, Z. (1988b). “Type curves for two-regime well flow.” J. Hydraul. Eng., 1461–1484.
Stehfest, H. (1970a). “Algorithm 368: Numerical inversion of Laplace transforms.” Commun. ACM, 13(1), 47–49.
Stehfest, H. (1970b). “Remark on algorithm 368: Numerical inversion of laplace transforms.” Commun. ACM, 13(10), 47–49.
Sun, D., and Zhan, H. (2006). “Flow to a horizontal well in an aquitard-aquifer system.” J. Hydrol., 321(1–4), 364–376.
Wang, Q., Zhan, H., and Wang, Y. (2015). “Non-Darcian effect on slug test in a leaky confined aquifer.” J. Hydrol., 527, 747–753.
Wen, Z., Huang, G., and Zhan, H. (2008a). “An analytical solution for non-Darcian flow in a confined aquifer using the power law function.” Adv. Water Resour., 31(1), 44–55.
Wen, Z., Huang, G., and Zhan, H. (2008b). “Non-Darcian flow to a well in an aquifer-aquitard system.” Adv. Water Resour., 31(12), 1754–1763.
Wen, Z., Huang, G., and Zhan, H. (2009). “A numerical solution for non-Darcian flow to a well in a confined aquifer using the power law function.” J. Hydrol., 364(1–2), 99–106.
Wen, Z., Huang, G., Zhan, H., and Li, J. (2008c). “Two-region non-Darcian flow toward a well in a confined aquifer.” Adv. Water Resour., 31(5), 818–827.
Wen, Z., Liu, K., and Chen, X. (2013). “Approximate analytical solution for non-Darcian flow toward a partially penetrating well in a confined aquifer.” J. Hydrol., 498, 124–131.
Wen, Z., Liu, K., and Zhan, H. (2014). “Non-Darcian flow toward a larger-diameter partially penetrating well in a confined aquifer.” Environ. Earth Sci., 72(11), 4617–4625.
Yu, C. C., Yang, S. Y., and Yeh, H. D. (2013). “Semi-analytical solution of groundwater flow in a leaky aquifer system subject to bending effect.” J. Hydrol., 486, 395–402.
Zhan, H., and Bian, A. (2006). “A method of calculating pumping induced leakage.” J. Hydrol., 328(3–4), 659–667.
Zhan, H., and Park, E. (2003). “Horizontal well hydraulics in leaky aquifers.” J. Hydrol., 281(1), 129–146.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 12 • December 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Apr 11, 2016
Accepted: Jun 22, 2016
Published online: Jul 22, 2016
Published in print: Dec 1, 2016
Discussion open until: Dec 22, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.