An analytical study on artesian flow conditions in unconfined‐aquifer drainage basins

Abstract

Although it has been reported that flowing artesian wells could be topographically controlled, there is no quantitative research on artesian flow conditions in unconfined aquifers. In this study, the water table, which has a lower amplitude than the land surface, is damped from the topography and used as the boundary condition to obtain the analytical solution of hydraulic head of a unit basin with a single flow system. The term artesian head is defined to characterize the condition of flowing artesian wells. The zone with positive artesian head is called artesian zone while with negative artesian head is nonartesian zone. The maximum artesian head and the size of artesian zones are found to increase with the damping factor and the anisotropy ratio, and decrease with the ratio of basin width to depth and the depth‐decay exponent of hydraulic conductivity. Moreover, the artesian head increases with depth nearby the valley and decreases with depth near by the divide, and the variation rates are influenced by the decay exponent and the anisotropy ratio. Finally, the distribution of flowing artesian wells and the artesian head measurements in different depths of a borehole in a small catchment in the Ordos Plateau, Northwestern China is used to illustrate the theoretical findings. The change in artesian head with depth was used to estimate the anisotropy ratio and the decay exponent. This study opens up a new door to analyze basin‐scale groundwater flow.

A numerical study on the occurrence of flowing wells in the discharge area of basins due to the upward hydraulic gradient induced wellbore flow

“…The unit basin model has been widely applied to study regional groundwater flow induced by the undulating water table (Gleeson, Befus, Jasechko, Luijendijk, & Cardenas, ; Vandenberg, ; Zlotnik, Toundykov, & Cardenas, ), including the possible occurrence of flowing wells in the discharge area (J. Z. Wang, Jiang, Wan, Wörman, et al, ). To study the flow field influenced by a well, a 3D basin should be adopted.…”

“…J. Z. Wang, Jiang, Wan, Wörman, et al () introduced the ratio of water table undulation to topography undulation, α , to obtain a series of water table undulations based on the known undulating topography. In the 3D case, the undulating water table, z wt ( x , y , α ), can be written as Note that α is dependent on the geology and climate of a specific basin and ranges between 0 and 1.…”

“…In a recent study, J. Z. Wang, Jiang, Wan, Wörman, et al () quantitatively examined the primary controls on occurrence of flowing wells by using Tóth's () classic unit basin model and found that the undulating water table largely controls the size of the zone with the potential of occurrence of flowing wells, which is within the discharge area of a unit basin. However, there is no research on the exchange of groundwater between a flowing well and the surrounding aquifer, which restricts hydrogeologists' understanding on the mechanism of occurrence of flowing wells.…”

“…Based on J. Z. Wang, Jiang, Wan, Wörman, et al's () study on the control of undulating water table on occurrence of flowing wells, the current study aims to identify the mechanism of occurrence of flowing wells in discharge areas and find out the provenance of the water at the outlets of flowing wells by examining the vertical profiles of flow rates in flowing wells, the approach of which had been applied in numerous studies on wellbore flow induced by vertical gradients in the aquifer (e.g., Bomana, Molz, & Boonec, ; Crisman, Molz, Dunn, & Sappington, ; Martin‐Hayden, Plummer, & Britt, ; Varljen, Barcelona, Obereiner, & Kaminski, ).…”

An analytical study on three‐dimensional versus two‐dimensional water table‐induced flow patterns in a Tóthian basin

“…For a two‐dimensional (2‐D) cross section, a one‐wave water table undulation leads to a single flow system, whereas a multiple‐wave water table undulation results in hierarchically nested flow systems (Tóth, , ). In the following decades, 2‐D cross‐sectional models with a prescribed‐head boundary condition at the water table have been widely used to explain a variety of geologic, hydrologic, chemical, and biologic processes associated with groundwater (e.g., Cardenas, ; Domenico & Palciauskas, ; Garven, ; Gleeson, Befus, Jasechko, Luijendijk, & Cardenas, ; Gomez & Wilson, ; Wang et al, ; Winter, ). Moreover, it has been claimed that the nested flow structure in 2‐D cross sections can also be applied to delineate hyporheic flow driven by the spatially varying head distribution at the water–sediment interface in the form of ripples or dunes (e.g., Cardenas, Wilson, & Zlotnik, ; Gomez & Wilson, ; Sawyer & Cardenas, ; Zlotnik, Cardenas, & Toundykov, ).…”