Browsing by Author "Wang, Chih-Tse"

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A SEMIANALYTICAL SOLUTION FOR RESIDUAL DRAWDOWN AT A FINITE DIAMETER WELL IN A CONFINED AQUIFER
(2013-08-01)
Yeh, Hund-Der
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Wang, Chih-Tse
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環境工程研究所
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Institute of Environmental Engineering
After the end of pumping the water level in the observation well starts to recover and the reduced drawdown during the recovery period is named as the residual drawdown. Traditional approaches in analyzing the data of residual drawdown for estimating the aquifer hydraulic parameters are mostly based on the application of superposition principle and Theis equation. In addition, the effect of wellbore storage is commonly ignored in the evaluation even if the test well has a finite diameter. In this article, we develop a mathematical model for describing the residual drawdown with considering the wellbore storage effect and the existing drawdown distribution produced by the pumping part of the test. The Laplace-domain solution of the model is derived using the Laplace transform technique and the time-domain result is inverted based on the Stehfest algorithm. This new solution shows that the residual drawdown associated with the boundary and initial conditions are related to the well drawdown and the aquifer drawdown, respectively. The well residual drawdown will be overestimated by the Theis residual drawdown solution in the early recovery part if neglecting the wellbore storage. On the other hand, the Theis residual drawdown solution can be used to approximate the present residual drawdown solution in the late recovery part of the test.
Analysis of well residual drawdown after a constant-head test
(2009-07-15)
Yeh, Hund-Der
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Wang, Chih-Tse
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環境工程研究所
;
Institute of Environmental Engineering
A recovery test measures the residual drawdown after an aquifer pumping test has ended and analyzes the recovery data to determine hydrogeological parameters such as transmissivity and storage coefficient. To our knowledge, the solution for the distribution of residual drawdown following a constant-head test has never been presented. In this paper, we first develop a mathematical model that describes the residual drawdown taking into consideration the wellbore-storage effect and the drawdown distribution occurring at the end of a previous constant-head test. Then, the Laplace-domain solution of the model is developed using the Laplace transforms and its time-domain solution is obtained using the Stehfest algorithm. Numerical results show that the distribution of residual drawdown depends on the boundary condition related to the well drawdown and the initial condition related to the aquifer drawdown. The well residual drawdown (i.e., the residual drawdown at wellbore) during the early recovery period will be over-estimated by the approximate residual drawdown solution based on the Theis-type solution and superposition principle due to the neglect of wellbore storage. For a large recovery time, the effect of wellbore storage is negligible and the approximate residual drawdown solution is therefore applicable. (C) 2009 Elsevier B.V. All rights reserved.
Examining the large-time wellbore flux of constant head test
(2010-09-14)
Yeh, Hund-Der
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Wang, Chih-Tse
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Smith, Stefan G. Llewellyn
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環境工程研究所
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Institute of Environmental Engineering
The function 1/[p ln (p/lambda)] comes from the wellbore flux solution in the Laplace domain for a constant head aquifer test when the Laplace variable p is small. The resulting inverse Laplace transform v(lambda t), representing the large-time wellbore flux, grows exponentially with time, which does not agree with the physical behavior of the wellbore flux. Based on this result, Chen and Stone (1993) asserted that the well-known relationship of small p-large t may fail to yield the correct large-time asymptotic solution. Yeh and Wang (2007) pointed out that the large-time wellbore flux is not n(lambda t) if the inversion of 1/[p ln (p/lambda)] is subject to the constraint Re p > lambda. Chen (2009) subsequently questioned the necessity of imposing this constraint on the Laplace transform in the inversion of the large-time wellbore flux. Motived by Chen's comment, we reexamine the inversion of 1/[p ln (p/lambda)] and demonstrate that this contradictory issue originates from a spurious pole introduced when applying the small p-large t correspondence to the Laplace domain solution. We explain why this occurs and why the actual wellbore flux at large times is proportional to the function N(lambda t), known as Ramanujan's integral. The function N(lambda t) does decay at large time, which agrees with the steady state wellbore flux of the constant head test.
Large-time solutions for groundwater flow problems using the relationship of small p versus large t
(2007-06-21)
Yeh, Hund-Der
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Wang, Chih-Tse
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環境工程研究所
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Institute of Environmental Engineering
An approximate solution is useful if the corresponding analytical solution is complicated and difficult to accurately evaluate. In the past, the relationship of small p versus large t was commonly applied to the Laplace domain solution and could successfully obtain a large-time solution in the groundwater area. The large-time solution usually has a simpler form than the analytical solution and is much easier for estimating the transient behavior of the groundwater flow system. However, Chen and Stone (1993) pointed out that the use of this relationship might fail to yield the correct solution in calculating the wellbore flux for the constant head test problem. Later, Mathias and Zimmerman (2003) indicated that a poor result was obtained by Gerke and van Genuchten (1993) when using the relationship of small p versus large t to derive the water transfer coefficient for the dual-porosity media problem. This note is to show the detailed mathematical derivations involved in the issues that Chen and Stone (1993) and Gerke and van Genuchten (1993) addressed and to ensure that the relationship of small p versus large t is correct to obtain a large-time solution for transient groundwater flow problems.
Obtaining the steady-state drawdown solutions of constant-head and constant-flux tests
(2008-08-15)
Wang, Chih-Tse
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
The solutions of constant-head and sonstant-flux tests are commonly used to predict the temporal or spatial drawdown distribution or to determine aquifer parameters. Theis and Thiem equations, for instance, are well-known transient and steady-state drawdown solutions, respectively, of the constant-flux test. It is known that the Theis equation is not applicable to the case where the aquifer has a finite boundary or the pumping time tends to infinity. On the other hand, the Thiem equation does not apply to the case where the aquifer boundary is infinite. However. the issue of obtaining the Thiem equation from the transient drawdown solution has not previously been addressed. In this paper, the drawdown solutions for constant-head and constant-flux tests conducted in finite or infinite confined aquifers with or without consideration of the effect of the well radius are examined comprehensively. Mathematical verification and physical interpretation of the solutions to these two tests converging or not converging to the Thiem equation are presented. The result shows that there are some finite-domam solutions for these two tests that can converge to the Thiem equation when the time becomes infinitely large. In addition, the time criteria to give a good approximation to the finite-domain solution by the infinite-domain solution and the Thiem equation are investigated and presented. Copyright (C) 2008 John Wiley & Sons, Ltd.