Drawdown and Stream Depletion Produced by Pumping in the Vicinity of a Partially Penetrating Stream

Abstract

Commonly used analytical approaches for estimation of pumping-induced drawdown and stream depletion are based on a series of idealistic assumptions about the stream-aquifer system. A new solution has been developed for estimation of drawdown and stream depletion under conditions that are more representative of those in natural systems (finite width stream of shallow penetration adjoining an aquifer of limited lateral extent). This solution shows that the conventional assumption of a fully penetrating stream will lead to a significant overestimation of stream depletion (> 100%) in many practical applications. The degree of overestimation will depend on the value of the stream leakance parameter and the distance from the pumping well to the stream. Although leakance will increase with stream width, a very wide stream will not necessarily be well represented by a model of a fully penetrating stream. The impact of lateral boundaries depends upon the distance from the pumping well to the stream and the stream leakance parameter. In most cases, aquifer width must be on the order of hundreds of stream widths before the assumption of a laterally infinite aquifer is appropriate for stream-depletion calculations. An important assumption underlying this solution is that stream-channel penetration is negligible relative to aquifer thickness. However, an approximate extension to the case of nonnegligible penetration provides reasonable results for the range of relative penetrations found in most natural systems (up to 85 % ). Since this solution allows consideration of a much wider range of conditions than existing analytical approaches, it could prove to be a valuable new tool for water management design and water rights adjudication purposes.

Effects of Streambed Conductance on Stream Depletion

“…Analytical estimations of stream depletion were first proposed by Theis [4] and have since continued to be developed (e.g., [5][6][7][8][9][10]). However, Spalding and Khaleel [11] demonstrated that, despite their convenience, analytical approaches often fail to account for conditions that exist in natural steam-aquifer systems.…”

“…For a given change in the head difference, a higher C leads to a greater degree of stream depletion and a lower C leads to a lesser degree of stream depletion [13,14]. The correlation between C and the stream depletion makes it an important model parameter in numerical stream depletion simulations (e.g., [9][10][11][12]18,19]). …”

Evaluation of the streambed leakage concept in analytical models using data from three pumping tests

“…Therefore, three fitting parameters were used to reproduce the observed drawdown in the case of PT low and PT high : the hydraulic conductivity, K, the aquifer storativity, S, and streambed conductance, l, per unit stream length. In the case of the PT test in the absence of flow in Prairie Creek, the Theis (1935) model was used, and the number of fitting parameters reduces to two, namely K and S. The BZT model (Butler et al 2001) was used in the global cluster analysis for simulating a piecewise-homogeneous aquifer that accounts for the meandering stream architecture of the modern Prairie Creek deposits. In the BZT model, the aquifer consists of three parallel, infinite strips: one underneath the stream and one for each stream bank.…”

“…Model outline and hydrologic framework Hunt (1999) and Butler et al (2001) presented twodimensional models of stream-aquifer interactions as a correction to the two-dimensional Theis (1935) solution for drawdown in a homogeneous confined aquifer (in the following, these models will be referred to as Hunt and BZT models). This correction can be illustrated by the Hunt model for drawdown, s(x,y,t), as…”

“…Only recently, analytical models were improved to take into account partial stream penetration, a finite stream width, and also large-scale aquifer heterogeneity (Hunt 1999;Zlotnik et al 1999;Butler et al 2001). Yet, these two-dimensional models also rely on the application of the streambed conductance concept.…”