Vertical Flux in a Two-Layer Aquifer System Absent of Aquitard
Publication: Journal of Hydrologic Engineering
Volume 28, Issue 4
Abstract
Heterogeneously layered river-basin or reservoir-bank aquifers are widely distributed, and the two-layer aquifer system is a simple representative of such aquifers. In this research, a conceptual model of vertical groundwater flux induced by a rising prescribed head boundary in a two-layer aquifer system (without an aquitard in between) is developed. A semianalytical solution is derived using Green’s function method (GFM) and compared with finite-element numerical solutions. The result indicates that differences of hydraulic parameters have profound effects on the hydraulic head distribution in both layers and dynamics of vertical mass exchange between the layers. A larger media anisotropy () leads to a smaller buildup contrast between the two layers and a greater peak value of vertical groundwater flux across the interface of two layers. The buildup in the upper layer is insensitive to [which is the permeability ratio of the lower (less permeable) layer to the upper (more permeable) layer], whereas the buildup in the lower layer is sensitive to . A greater permeability contrast between the two layers causes a larger groundwater flux across the interface and a greater peak flux. A larger specific storage contrast leads to smaller buildups, and a smaller specific storage contrast leads to a greater peak vertical groundwater flux. Among many applications, the proposed solutions have profound chemical, biological, and thermal transport implications because tracer elements or heat of different layers can dynamically interact with each other, driven by the vertical groundwater flux of different layers.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This research was supported by Program of the Natural Science Foundation of China (No. 42272296); The authors would like to thank the Associate Editor and the anonymous reviewers for their constructive comments which help us improve the quality of the manuscript.
References
Bakker, M. 2006. “An analytic element approach for modeling polygonal inhomogeneities in multi-aquifer systems.” Adv. Water Resour. 29 (10): 1546–1555. https://doi.org/10.1016/j.advwatres.2005.11.005.
Ba Rlow, P. M., L. A. Desimone, and A. F. Moench. 2000. “Aquifer response to stream-stage and recharge variations. II. Convolution method and applications.” J. Hydrol. 230 (3–4): 211–229. https://doi.org/10.1016/S0022-1694(00)00176-1.
Battin, T. J., K. Besemer, M. M. Bengtsson, A. M. Romani, and A. I. Packmann. 2016. “The ecology and biogeochemistry of stream biofilms.” Nat. Rev. Microbiol. 14 (4): 251. https://doi.org/10.1038/nrmicro.2016.15.
Bear, J. 1972. Dynamics of fluids in porous media. Amsterdam, Netherlands: Elsevier.
Bhandari, A. D., V. Pradhan, and R. K. Bansal. 2018. “New analytical solution for stream–aquifer interaction under constant replenishment.” Appl. Water Sci. 8 (6): 1–8. https://doi.org/10.1007/s13201-018-0814-7.
Carslaw, H. S., and J. C. Jaeger. 1992. Conduction of heat in solids. Oxford, UK: Clarendon Press.
Chen, K., H. Zhan, and Q. Wang. 2018. “An innovative solution of diurnal heat transport in streambeds with arbitrary initial condition and implications to the estimation of water flux and thermal diffusivity under transient condition.” J. Hydrol. 567 (Dec): 361–369. https://doi.org/10.1016/j.jhydrol.2018.10.008.
Cordey, J., et al. 1996. “A review of the dimensionless parameter scaling studies.” Plasma Phys. Controlled Fusion 38 (12): A67. https://doi.org/10.1088/0741-3335/38/12A/006.
Dagan, G., A. Fiori, and I. Janković. 2003. “Flow and transport in highly heterogeneous formations: 1. Conceptual framework and validity of first-order approximations.” Water Resour. Res. 39 (9): 3. https://doi.org/10.1029/2002WR001717.
Feng, Q., X. Yuan, and H. Zhan. 2019. “Flow to a partially penetrating well with variable discharge in an anisotropic two-layer aquifer system.” J. Hydrol. 578 (Nov): 124027. https://doi.org/10.1016/j.jhydrol.2019.124027.
Fetter, C. W. 2018. Applied hydrogeology. Long Grove, IL: Waveland Press.
Fox, G. A., P. DuChateau, and D. S. Dumford. 2002. “Analytical model for aquifer response incorporating distributed stream leakage.” Ground Water 40 (4): 378–384. https://doi.org/10.1111/j.1745-6584.2002.tb02516.x.
Fukada, T., K. M. Hiscock, P. F. Dennis, and T. Grischek. 2003. “A dual isotope approach to identify denitrification in groundwater at a river-bank infiltration site.” Water Res. 37 (13): 3070–3078. https://doi.org/10.1016/S0043-1354(03)00176-3.
Guo, Q., Z. Zhou, G. Huang, and Z. Dou. 2019. “Variations of groundwater quality in the multi-layered aquifer system near the Luanhe River, China.” Sustainability 11 (4): 994. https://doi.org/10.3390/su11040994.
Gutiérrez, J. P., D. van Halem, W. S. Uijttewaal, E. Del Risco, and L. C. Rietveld. 2018. “Natural recovery of infiltration capacity in simulated bank filtration of highly turbid waters.” Water Res. 147 (Dec): 299–310. https://doi.org/10.1016/j.watres.2018.10.009.
Huang, D., D. M. Gu, Y. X. Song, D. F. Cen, and B. Zeng. 2018. “Towards a complete understanding of the triggering mechanism of a large reactivated landslide in the Three Gorges Reservoir.” Eng. Geol. 238 (May): 36–51. https://doi.org/10.1016/j.enggeo.2018.03.008.
Hunt, B. 2009. “Stream depletion in a two-layer leaky aquifer system.” J. Hydrol. Eng. 14 (9): 895–903. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000063.
Intaraprasong, T., and H. Zhan. 2009. “A general framework of stream-aquifer interaction caused by variable stream stages.” J. Hydrol. 373 (1–2): 112–121. https://doi.org/10.1016/j.jhydrol.2009.04.016.
Liang, X., H. Zhan, Y.-K. Zhang, and K. Schilling. 2017. “Base flow recession from unsaturated-saturated porous media considering lateral unsaturated discharge and aquifer compressibility.” Water Resour. Res. 53 (9): 7832–7852. https://doi.org/10.1002/2017WR020938.
Liang, X., Y. K. Zhang, J. Liu, E. Ma, and C. Zheng. 2019. “Solute transport with linear reactions in porous media with layered structure: A semianalytical model.” Water Resour. Res. 55 (6): 5102–5118. https://doi.org/10.1029/2019WR024778.
Liu, Y., L. Ma, Q. Yang, G. Li, and F. Zhang. 2018. “Occurrence and spatial distribution of perfluorinated compounds in groundwater receiving reclaimed water through river bank infiltration.” Chemosphere 211 (Nov): 1203–1211. https://doi.org/10.1016/j.chemosphere.2018.08.028.
Martinez, A. R., D. Roubinet, and D. Tartakovsky. 2014. “Analytical models of heat conduction in fractured rocks.” J. Geophys. Res. Solid Earth 119 (1): 83–98. https://doi.org/10.1002/2012JB010016.
Newcomer, M. E., et al. 2016. “Simulating bioclogging effects on dynamic riverbed permeability and infiltration.” Water Resour. Res. 52 (4): 2883–2900. https://doi.org/10.1002/2015WR018351.
O’Reilly, A. M., R. M. Holt, G. R. Davidson, A. C. Patton, and J. R. Rigby. 2020. “A dynamic water balance/nonlinear reservoir model of a perched phreatic aquifer–river system with hydrogeologic threshold effects.” Water Resour. Res. 56 (6): e2019WR025382. https://doi.org/10.1029/2019WR025382.
Paronuzzi, P., et al. 2013. “Influence of filling-drawdown cycles of the Vajont Reservoir on Mt. Toc slope stability.” Geomorphology 191 (Jun): 75–93. https://doi.org/10.1016/j.geomorph.2013.03.004.
Pavelic, P., et al. 2011. “Laboratory assessment of factors affecting soil clogging of soil aquifer treatment systems.” Water Res. 45 (10): 3153–3163. https://doi.org/10.1016/j.watres.2011.03.027.
Qi, C., H. Zhan, X. Liang, and C. Ma. 2020. “Influence of time-dependent ground surface flux on aquifer recharge with a vadose zone injection well.” J. Hydrol. 584 (May): 124739. https://doi.org/10.1016/j.jhydrol.2020.124739.
Roubinet, D., J. R. de Dreuzy, and D. M. Tartakovsky. 2012. “Semi-analytical solutions for solute transport and exchange in fractured porous media.” Water Resour. Res. 48 (1): 11168. https://doi.org/10.1029/2011WR011168.
Sedghi, M. M., and H. Zhan. 2016. “Hydraulic response of an unconfine d-fracture d two-aquifer system driven by dual tidal or stream fluctuations.” J. Hydrol. 97 (Apr): 266–278. https://doi.org/10.1016/j.advwatres.2016.10.005.
Wang, J., et al. 2021. “A semi-analytical approach to simulate cross-flow effect on the flow behavior of partially penetrating well in two-layer confined aquifer by Green function method.” J. Hydrol. 597 (Jun): 126141. https://doi.org/10.1016/j.jhydrol.2021.126141.
Workman, S. R., S. E. Serrano, and K. Liberty. 1997. “Development and application of an analytical model of stream/aquifer interaction.” J. Hydrol. 200 (1–4): 149–163. https://doi.org/10.1016/S0022-1694(97)00014-0.
Xian, Y., M. Jin, H. Zhan, and Y. Liu. 2019. “Reactive transport of nutrients and bioclogging during dynamic disconnection process of stream and groundwater.” Water Resour. Res. 55 (5): 3882–3903. https://doi.org/10.1029/2019WR024826.
Xu, Y.-S., S.-L. Shen, Y.-J. Du, J.-C. Chai, and S. Horpibulsuk. 2013. “Modelling the cutoff behavior of underground structure in multi-aquifer-aquitard groundwater system.” Nat. Hazards 66 (2): 731–748. https://doi.org/10.1007/s11069-012-0512-y.
Zaadnoordijk, W. 1988. “Analytic elements for transient groundwater flow.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Minnesota.
Zhang, L., B. Shi, D. Zhang, Y. Sun, and H. I. Inyang. 2020. “Kinematics, triggers and mechanism of Majiagou landslide based on FBG real-time monitoring.” Environ. Earth Sci. 79 (9): 200. https://doi.org/10.1007/s12665-020-08940-5.
Zhu, Q., Z. Wen, H. Zhan, and S. Yuan. 2020. “Optimization strategies for in situ groundwater remediation by a vertical circulation well based on particle-tracking and node-dependent finite difference methods.” Water Resour. Res. 56 (11): e2020WR027396. https://doi.org/10.1029/2020WR027396.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 28 • Issue 4 • April 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: May 19, 2022
Accepted: Nov 16, 2022
Published online: Feb 11, 2023
Published in print: Apr 1, 2023
Discussion open until: Jul 11, 2023
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.