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Erschienen in: Hydrogeology Journal 1/2019

21.08.2018 | Paper

Review: Revisiting the Theis solution derivation to enhance understanding and application

verfasst von: Luke Flores, Ryan T. Bailey

Erschienen in: Hydrogeology Journal | Ausgabe 1/2019

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Abstract

The Theis solution is perhaps the most influential and frequently used analytical model in groundwater hydrology. Its publication in 1935 led to immediate and continued use for simulating hydraulic head drawdown, in both confined and unconfined aquifers, as a tool in aquifer parameter estimation. For educational purposes, the Theis solution and the related Jacob’s approximation often serve as the backbone for teaching pumping-well theory, including topics such as boundary conditions in aquifers, image well theory, linear superposition, and pumping-induced streamflow depletion. Clearly, a thorough understanding of the Theis solution is critical for groundwater engineers and hydrologists. However, the solution often is presented as a “black box”, neglecting the actual origins of its derivation and accompanying physical context. This can lead to misconceptions about the model and its inherent limitations. In this paper, a physically based detailed derivation of the Theis solution is presented, along with a method of calculating drawdown from a pumping well without resorting to the final Theis equation. Examples of both constant-rate pumping and variable-rate pumping are presented and compared to results using the original Theis solution. In particular, variable pumping rates are accounted for by direct numerical integration of an earlier form in the original Theis derivation, removing the need for linear superposition of solutions in time. In this way, it is hoped the paper will provide a method of calculation that ties the model user to the physical meaning of the solution, including its assumptions.

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Literatur
Zurück zum Zitat Barlow PM (2000) Documentation of computer program STRMDEPL: a program to calculate streamflow depletion by wells using analytical solutions. In: Zarriello PJ, Ries KG III (eds) A precipitation-runoff model for analysis of the effects of water withdrawals on streamflow, Ipswich River Basin, Massachusetts. US Geol Surv Water Resour Invest Rep 00-4029, pp 77–89 Barlow PM (2000) Documentation of computer program STRMDEPL: a program to calculate streamflow depletion by wells using analytical solutions. In: Zarriello PJ, Ries KG III (eds) A precipitation-runoff model for analysis of the effects of water withdrawals on streamflow, Ipswich River Basin, Massachusetts. US Geol Surv Water Resour Invest Rep 00-4029, pp 77–89
Zurück zum Zitat Carslaw HS (1921) Introduction to the mathematical theory of the conduction of heat in solids, 2nd edn. MacMillan, London Carslaw HS (1921) Introduction to the mathematical theory of the conduction of heat in solids, 2nd edn. MacMillan, London
Zurück zum Zitat Chin DA (2013) Water-resources engineering. Pearson, Upper Saddle River, NJ Chin DA (2013) Water-resources engineering. Pearson, Upper Saddle River, NJ
Zurück zum Zitat Fetter CW (2001) Applied hydrogeology. Prentice-Hall, Upper Saddle River, NJ Fetter CW (2001) Applied hydrogeology. Prentice-Hall, Upper Saddle River, NJ
Zurück zum Zitat Glover RE, Balmer CG (1954) River depletion resulting from pumping a well near a river. Am Geophys Union Trans 35(3):468–470CrossRef Glover RE, Balmer CG (1954) River depletion resulting from pumping a well near a river. Am Geophys Union Trans 35(3):468–470CrossRef
Zurück zum Zitat Hantush MS (1965) Wells near streams with semipervious beds. J Geophys Res 70(12):2829–2838CrossRef Hantush MS (1965) Wells near streams with semipervious beds. J Geophys Res 70(12):2829–2838CrossRef
Zurück zum Zitat Hiscock KM, Bense VF (2014) Hydrogeology: principles and practice. Wiley, Chichester, UK Hiscock KM, Bense VF (2014) Hydrogeology: principles and practice. Wiley, Chichester, UK
Zurück zum Zitat Hunt B (1999) Unsteady stream depletion from ground water pumping. Groundwater 37(1):98–102CrossRef Hunt B (1999) Unsteady stream depletion from ground water pumping. Groundwater 37(1):98–102CrossRef
Zurück zum Zitat Olsthorrn TN (2008) Do a bit more with convolution. Ground Water 46:13–22CrossRef Olsthorrn TN (2008) Do a bit more with convolution. Ground Water 46:13–22CrossRef
Zurück zum Zitat Renard P, Glez D, Mejias M (2009) Understanding diagnostic plots for well-test interpretation. Hydrogeol J 17:589–600CrossRef Renard P, Glez D, Mejias M (2009) Understanding diagnostic plots for well-test interpretation. Hydrogeol J 17:589–600CrossRef
Zurück zum Zitat Schwartz FW, Zhang H (2003), Fundamentals of ground water. Wiley, New York Schwartz FW, Zhang H (2003), Fundamentals of ground water. Wiley, New York
Zurück zum Zitat Theis CV (1935) The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Trans Am Geophys Union 16:519–524CrossRef Theis CV (1935) The relation between the lowering of the piezometric surface and the rate and duration of discharge of a well using groundwater storage. Trans Am Geophys Union 16:519–524CrossRef
Zurück zum Zitat Todd DK, Mays LW (2005) Groundwater hydrology. Wiley, Hoboken, NJ Todd DK, Mays LW (2005) Groundwater hydrology. Wiley, Hoboken, NJ
Zurück zum Zitat Wurbs RA, James WP (2002) Water resources engineering. Prentice Hall, Upper Saddle River, NJ Wurbs RA, James WP (2002) Water resources engineering. Prentice Hall, Upper Saddle River, NJ
Zurück zum Zitat Zech A, Mueller S, Mai J, Hesse F, Attinger S (2016) Extending Theis’ solution using transient pumping tests to estimate parameters to aquifer heterogeneity. Water Resour Res 52(8):6156–6170CrossRef Zech A, Mueller S, Mai J, Hesse F, Attinger S (2016) Extending Theis’ solution using transient pumping tests to estimate parameters to aquifer heterogeneity. Water Resour Res 52(8):6156–6170CrossRef
Metadaten
Titel
Review: Revisiting the Theis solution derivation to enhance understanding and application
verfasst von
Luke Flores
Ryan T. Bailey
Publikationsdatum
21.08.2018
Verlag
Springer Berlin Heidelberg
Erschienen in
Hydrogeology Journal / Ausgabe 1/2019
Print ISSN: 1431-2174
Elektronische ISSN: 1435-0157
DOI
https://doi.org/10.1007/s10040-018-1843-x

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