Estimating stream filtration from a meandering stream under the Robin condition

Abstract

This study applies image well theory to estimate the stream depletion rate (SDR) due to pumping near a meandering stream with a clogged streambed treated as the Robin condition. The stream is considered as an irregular boundary represented by discrete nodes. Image wells are arranged along the stream and near those nodes. On the basis of the Theis (1935) solution and the principle of superposition, the solution for the aquifer drawdown subject to the stream can then be expressed as the sum of the Theis solution and a simple series representing the effect of those image wells. The discharge rates of the image wells are determined by solving a system of equations obtained by substituting the drawdown solution into the Robin condition. Quantitative criteria for assessing the applicability of the image well theory are provided. On the basis of the drawdown solution and Darcy's law, the analytical solution for SDR can then be obtained. A finite element solution is also developed to verify the SDR solution. Temporal SDR distributions predicted by both the analytical solution and finite element solution agree well over the entire period except at late time when the stream filtration rate approaches the pumping rate (i.e., SDR ffi 1). It is found that a meandering stream has a significant effect on SDR compared with a rectilinear one and the effect should be taken into account in estimating SDR.

New Analytical Models for Flow Induced by Pumping in a Stream‐Aquifer System: A New Robin Boundary Condition Reflecting Joint Effect of Streambed Width and Storage

“…In recent years, there is a large amount of research interest in dealing with the problems of stream-aquifer interaction (e.g., Frei & Gilfedder, 2015;Ghasemizade et al, 2019;Grinevskiy et al, 2018;Huang & Yeh, 2015;Lamontagne et al, 2015;Liang et al, 2018;Xian et al, 2019;Zipper et al, 2018Zipper et al, , 2019. Groundwater extraction from wells in an aquifer induces water filtration from an adjacent stream and may influence ecosystems due to a drop in the stream water level (Foglia et al, 2013).…”

Analytical study of dual‐porosity coastal aquifer with generalized nonlinear water transfer term

“…According to Huang and Yeh (2015), the intrusion distance is defined as the location where A h = A h,f = 0.25% A . In this subsection, the effect of λ on the intrusion distance is first explored herein.…”

“…In this subsection, the effect of λ on the intrusion distance is first explored herein. For convenience, the length of the tidal propagation, L p [L], can be defined as (Huang & Yeh, 2015) $$$$ {L}_p=\sqrt{\frac{2T}{\omega S}} $$$$ …”

A New Approach to Three‐Dimensional Flow in a Pumped Confined Aquifer Connected to a Shallow Stream: Near‐Stream and Far‐From‐Stream Groundwater Extractions

“…The Dupuit assumption of no vertical flow has commonly been applied in estimating SDR and aquifer drawdown for pumped stream‐aquifer systems (e.g., Butler et al., 2001; Glover & Balmer, 1954; Huang & Yeh, 2015; Hunt 1999). Bouwer (1969, p. 126) concluded the Dupuit assumption is applicable in predicting aquifer drawdown under two conditions.…”