Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

Feng, Qilin; Wen, Zhang

doi:10.1007/s10040-016-1389-8

Cited by 18 publications

(16 citation statements)

References 35 publications

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“…By employing the Izbash equation and a linearization procedure, Wen et al (2013) presented an approximate analytical solution, which can describe the non-Darcian flow toward a partially penetrating well in a confined aquifer. Feng and Wen (2016) proposed an analytical model describing non-Darcian flow toward a partially penetrating well in a confined aquifer, which considered the effects of the well skin. Table 1 summarizes and compares the available, above-mentioned analytical models.…”

Section: Water Resources Researchmentioning

confidence: 99%

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

Šimůnek

et al. 2020

Water Resources Research

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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.

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Section: Water Resources Researchmentioning

confidence: 99%

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

Šimůnek

et al. 2020

Water Resources Research

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“…Thank you for pointing out this problem. However, we would also like to point out that despite this known limitation, the Stehfest algorithm is still commonly used to carry out the sensitivity analysis and convert the analytical solutions obtained in the Laplace domain (e.g., Feng & Wen, 2016; Lin et al., 2016; Wen et al., 2013, etc. ).…”

Section: Reply To Additional Commentsmentioning

confidence: 99%

Reply to the 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.”

Šimůnek

et al. 2021

Water Resources Research

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We would like to thank Dr. Kabala for his interest in our work and his Comment on it and appreciate the opportunity to clarify and address his concerns. The idea of employing a single-well circulation groundwater heat-pump system (as shown in Figure 1) to provide heating or cooling of buildings was first presented by Sorensen and Reffstrup (1992). Our work is based on the conceptual model of Sorensen and Reffstrup (1992) and the analytical solution developed for this system by Ni et al. (2011). We have to admit that we were not aware of Kabala's (1993) work, partly because it did not appear in the literature with the geothermal exploitation background. Similarly, as Kabala (1993) and Kahler and Kabala (2018) apparently were not aware of the work of Sorensen and Reffstrup (1992), Ni et al. (2011), and related literature relevant to their works.In our study, we have rigorously derived the analytical solution for the governing equation for a single-well circulation system by employing a combination of the Laplace and Fourier cosine transforms, without using the superposition principle and adopting the analytical solution of a partially penetrating well obtained by Hantush (1961). More importantly, our approach provides an opportunity to be further extended to obtain analytical solutions for the governing equations for a single-well circulation system considering factors such as non-Darcian flow (Tu, Wu, Simunek, Zhu, et al., 2020), well skin (Tu et al., 2021), and wellbore storage (Tu et al., in preparation). This allows us to investigate further the effects of these factors on groundwater flow behavior in a single-well circulation system. It would not be possible to obtain such analytical solutions using the superposition principle (as used in Kabala, 1993) unless related analytical solutions already exist.While we admit that we did not sufficiently review the hydrogeological literature on single-well circulation systems, we disagree with Dr. Kabala's Comment that our work is a re-publication of his work (Kabala, 1993). We have clearly used in our work a different approach than Kabala (1993). A more detailed Reply to the original and revised Comment can be found in the following sections. Reply to Comments About the Derivation of the Analytical SolutionWe are certainly not the first to obtain an analytical solution for a single-well circulation groundwater heatpump system. Sorensen and Reffstrup (1992) were the first to present the concept of the single-well circulation groundwater heat-pump system (see Figure 1). This was a new engineering application for extracting

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“…The well skin is frequently induced by well construction or well clogging 9 and is usually represented as a skin factor either using an infinitesimally thin skin or a finite thickness skin. 4,[9][10][11][12][13][14][15] Fan and Parashar 16 considered the aquifer poroelastic deformation effect and presented analytical solutions to explore the wellbore storage and skin effect on drawdown behaviors in confined aquifers. Compared with a finite thickness skin, a smaller number of parameters are involved for an infinitesimally thin skin.…”

Section: Introductionmentioning

confidence: 99%

Two‐region flow caused by pumping at a partial penetration well in a leaky confined aquifer

Feng

2023

Num Anal Meth Geomechanics

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An analytical model for depicting two‐region flow caused by constant‐rate pumping at a partially penetrating well in a leaky confined aquifer is established. The two‐region flow is described by the radial Izbash non‐Darcy flow in the vicinity of the abstraction well and Darcy flow away from the abstraction well in the pumped aquifer. The model considers the effects of aquitard storage, wellbore storage, and wellbore skin. The semi‐analytical solutions of drawdown are developed by means of a linearization procedure combined with Laplace transform and separation of variables. The time‐domain drawdowns are then obtained by using the Stehfest method for numerical Laplace inversion. The solutions encompass previous solutions for one or two‐region flow to a partially penetrating well in a (non‐)leaky confined aquifer. The drawdown response in the abstraction well, non‐Darcy region, and Darcy region is investigated, and sensitivity analysis is made to assess the impact of various controlling parameters. The results demonstrate that the intermediate and late‐stage drawdowns in the abstraction well and non‐Darcy region for the two‐region flow model are larger than the corresponding values for the non‐Darcy flow model. The drawdown in the Darcy region for the two‐region flow model is larger than that for the Darcy flow model throughout the pumping duration. The results of sensitivity analysis show that the drawdowns in the abstraction well, non‐Darcy region, and Darcy region are most sensitive to the non‐Darcy constant n, and is very sensitive to the well configuration, and horizontal hydraulic conductivity of the Darcy region.

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Non-Darcian flow to a partially penetrating well in a confined aquifer with a finite-thickness skin

Cited by 18 publications

References 35 publications

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

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

Reply to the 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.”

Two‐region flow caused by pumping at a partial penetration well in a leaky confined aquifer

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