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

Abstract

Recent years have seen increased attention being given to stream-aquifer interaction, especially stream water filtration due to pumping (e.g.,

Resolving the Stream Depletion Model Paradox: Theory of Depletion with Stream Drawdown near a Pumping Well

“…4. The effects of streambed storage are neglected, with the focus being only on the effects of stream channel storage (Huang et al, 2020;Xiong et al, 2021). L] is the initial stream stage, which is set equal to the initial aquifer hydraulic head; the stream-aquifer system is assumed to be initially at equilibrium.…”

“…It is defined here as a dimensionless measure of the volume of water, Δ𝑉 -, which flows through a unit area of the streambed, Δ𝐴 % , per unit change in stream stage, Δℎ % (i.e., 𝐶 % = Δ𝑉 -/(Δ𝐴 % Δℎ % ) ). It is a measure of the volume contribution of water stored in the stream channel to aquifer flow, and is distinguished here from streambed elastic storage, which is neglected in the present study (Huang et al, 2020;Xiong et al, 2021). According to Huang et al (2020) and Xiong et al (2021) the effect of streambed specific storage, 𝑆 ' $ , may be neglected when the condition 𝑆 ' $ < (0.1𝑅/𝑏 $ )𝑆 ' is satisfied (Huang et al, 2020;Xiong, et al, 2021), where 𝑆 ' is aquifer specific storage, 𝑅 is the distance from the stream to the pumping well and 𝑏 $ is streambed thickness.…”

“…It is a measure of the volume contribution of water stored in the stream channel to aquifer flow, and is distinguished here from streambed elastic storage, which is neglected in the present study (Huang et al, 2020;Xiong et al, 2021). According to Huang et al (2020) and Xiong et al (2021) the effect of streambed specific storage, 𝑆 ' $ , may be neglected when the condition 𝑆 ' $ < (0.1𝑅/𝑏 $ )𝑆 ' is satisfied (Huang et al, 2020;Xiong, et al, 2021), where 𝑆 ' is aquifer specific storage, 𝑅 is the distance from the stream to the pumping well and 𝑏 $ is streambed thickness. In typical physical systems, 𝑅 ≫ 𝑏 $ , and if streambed sediment of similar composition as the aquifer material such that 𝑆 ' $ is of the same order of magnitude as 𝑆 ' , the above inequality is expected to hold.…”