How long does it take for aquifer recharge or aquifer discharge processes to reach steady state?

Simpson, Matthew, Jazaei, Farhad, & Clement, Prabhakar (2013) How long does it take for aquifer recharge or aquifer discharge processes to reach steady state? Journal of Hydrology, 501, pp. 241-248.

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Groundwater flow models are usually characterized as being either transient flow models or steady state flow models. Given that steady state groundwater flow conditions arise as a long time asymptotic limit of a particular transient response, it is natural for us to seek a finite estimate of the amount of time required for a particular transient flow problem to effectively reach steady state. Here, we introduce the concept of mean action time (MAT) to address a fundamental question: How long does it take for a groundwater recharge process or discharge processes to effectively reach steady state? This concept relies on identifying a cumulative distribution function, $F(t;x)$, which varies from $F(0;x)=0$ to $F(t;x) \to \infty$ as $t\to \infty$, thereby providing us with a measurement of the progress of the system towards steady state. The MAT corresponds to the mean of the associated probability density function $f(t;x) = \dfrac{dF}{dt}$, and we demonstrate that this framework provides useful analytical insight by explicitly showing how the MAT depends on the parameters in the model and the geometry of the problem.

Additional theoretical results relating to the variance of $f(t;x)$, known as the variance of action time (VAT), are also presented. To test our theoretical predictions we include measurements from a laboratory–scale experiment describing flow through a homogeneous porous medium. The laboratory data confirms that the theoretical MAT predictions are in good agreement with measurements from the physical model.

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ID Code: 61707
Item Type: Journal Article
Refereed: Yes
Keywords: Aquifer recharge, Aquifer discharge, Mean Action Time, Variance of Action Time, steady state, time to steady state
DOI: 10.1016/j.jhydrol.2013.08.005
ISSN: 0022-1694
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Approximation Theory and Asymptotic Methods (010201)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > CIVIL ENGINEERING (090500) > Water Resources Engineering (090509)
Divisions: Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Elsevier
Copyright Statement: This is the author’s version of a work that was accepted for publication in Journal of Hydrology. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Hydrology, [VOL 501, (2013)] DOI:10.1016/j.jhydrol.2013.08.005
Deposited On: 06 Aug 2013 22:44
Last Modified: 11 Oct 2015 08:18

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