An Analytical Solution of Groundwater Flow in a Confined Aquifer With a Single‐Well Circulation System

Abstract

In this study, a general analytical model for the single‐well circulation system is developed to analyze transient drawdown in a confined aquifer. The analytical solution of transient drawdown in the Laplace domain, which is numerically inverted into the time domain using the Stehfest method, is derived by employing a combination of the Laplace and Fourier cosine transforms. The characteristics of transient drawdown and the effects of different parameters related to the single‐well circulation system on drawdown are investigated. Furthermore, the analytical solution under steady‐state conditions is obtained using the Fourier cosine transform. The results show that steady drawdown contours are symmetric around a horizontal midplane of an aquifer and vary tremendously with distance from the well axis. The contours of drawdown around the sealed section are dense, meaning that the hydraulic gradient in this area is relatively large. The sensitivity analysis, performed to evaluate the characteristics of drawdown to changes in each parameter, indicates that the radial hydraulic conductivity and the length of the sealed section have a large impact on the drawdown and that each parameter has its influence period on the drawdown.

Comment on “Tu et al., An Analytical Solution of Groundwater Flow in a Confined Aquifer With a Single Well Circulation System, Water Resources Research, First Published: 12 June 2020.”

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Although renewed interest in flow around groundwater circulation wells is a positive development, the multiple and unacknowledged republication of previously published results is not. This is what has happened in a recent paper published in Water Resources Research by Tu et al (2020). The study repeats results that appeared in Ni et al (2011) as well as in the lead authors' own earlier work: Tu et al (2019).

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“…Since it was missed by Tu et al (2020), their reviewers, and their associate editor, I demonstrate the spuriousness of this claim in two ways in the next two subsections.…”

“…Contrary to their claim, we will see here that the direct solution of Tu et al (2020, Equation 7) is actually identical to one derived by the superposition of two solutions obtained by Hantush (1964) for a partially penetrating well. We start with the Hantush notation and then switch to that of Tu et al (2020). Hantush (1964) presents a schematic of a partially penetrating well in a homogeneous, anisotropic, leaky aquifer reproduced in Figure 1.…”

“…Another Google Scholar (and Web of Science) search for this phrase and its singular variant opens the floodgates to relevant hydrologic literature. Citing only three germane studies, Tu et al (2020) obviously made no effort to conduct a literature search for their central subject of flow around groundwater circulation wells. And neither did Tu et al (2019) nor Ni et al (2011).…”

“…Let me note that I notified the authors (and the Journal) of the problem with the study in July 2020, and I postponed the writing and submission of this note until mid-October when it became clear that a self-retraction was not forthcoming. What follows represents the report that I would have submitted had I been asked to review Tu et al (2020).…”