Browsing by Author "Yeh, H. D."

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An analytical solution for tidal fluctuations in unconfined aquifers with a vertical beach
(2010-10-22)
Yeh, H. D.
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Huang, C. S.
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Chang, Y. C.
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Jeng, D. S.
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環境工程研究所
The perturbation technique has been commonly used to develop analytical solutions for simulating the dynamic response of tidal fluctuations in unconfined aquifers. However, the solutions obtained from the perturbation method might result in poor accuracy for the case of the perturbation parameter being not small enough. In this paper, we develop a new analytical model for describing the water table fluctuations in unconfined aquifers, based on Laplace and Fourier transforms. In the new approach, the mean sea level is used as the initial condition and a free surface equation, neglecting the second-order slope terms, as the upper boundary condition. Numerical results show that the present solution agrees well with the finite different model with the second-order surface terms. Unlike Teo et al.'s (2003) approximation which restricts on the case of shallow aquifers, the present model can be applied to most of the tidal aquifers except for the very shallow one. In addition, a large-time solution in terms of sine function is provided and examined graphically with four different tidal periods.
Improvement on the estimation of constant-rate drawdown in large-diameter wells
(2013-04-01)
Chang, Y. C.
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Yeh, H. D.
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Wang, C. T.
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環境工程研究所
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Institute of Environmental Engineering
Papadopulos and Cooper's (PC) solution can be used to describe the drawdown resulting from pumping with a constant rate at a large-diameter well. However, this solution is too complicated to be accurately evaluated due to the oscillatory nature of the Bessel functions. The PC approach resulted in tabulated values of dimensionless drawdown at the well with an accuracy of four or fewer digits for selected values of dimensionless storage coefficient versus dimensionless time. Some researchers have fitted the tabulated values with interpolation formulas that are easy to use in engineering applications. Those formulas may be more accurate if the tabulated values are computed with greater accuracy. In this study, we propose an efficient numerical procedure, including a root search scheme, to find the roots of the integrand, Gaussian quadrature for numerical integration, and Shanks transform to accelerate convergence of infinite series. The proposed procedure can evaluate the dimensionless drawdown with greater accuracy and is useful in practice if there is a need for high accuracy for the observation either at the well or in the aquifer at some distance from the pumping well Editor D. Koutsoyiannis Citation Chang, Y.C., Yeh, H.D., and Wang, C.T., 2013. Improvement on the estimation of constant-rate drawdown in large-diameter wells. Hydrological Sciences Journal, 58 (3), 716727.
New solutions to the constant-head test performed at a partially penetrating well
(2009-05-05)
Chang, Y. C.
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Yeh, H. D.
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環境工程研究所
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Institute of Environmental Engineering
The mathematical model describing the aquifer response to a constant-head test performed at a fully penetrating well can be easily solved by the conventional integral transform technique. In addition, the Dirichlet-type condition should be chosen as the boundary condition along the rim of wellbore for such a test well. However, the boundary condition for a test well with partial penetration must be considered as a mixed-type condition. Generally, the Dirichlet condition is prescribed along the well screen and the Neumann type no-flow condition is specified over the unscreened part of the test well. The model for such a mixed boundary problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the dual series equations and perturbation method. This approach provides analytical results for the drawdown in the partially penetrating well and the well discharge along the screen. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view. (C) 2009 Elsevier B.V. All rights reserved.
Transient solution for radial two-zone flow in unconfined aquifers under constant-head tests
(2010-05-30)
Chang, Y. C.
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Yeh, H. D.
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Chen, G. Y.
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環境工程研究所
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Institute of Environmental Engineering
The constant-head test (CHT) is commonly employed to determine the aquifer parameters. This test is also applied to many environmental problems such as recovering light nonaqueous phase liquids (LNAPL) and controlling off-site migration of contaminated groundwater in low-transmissivity aquifers. A well skin near the wellbore may be produced due to the well construction or development and its formation properties are significantly different from the original ones. A more appropriate description for the skin effect on the aquifer system should treat the well skin as a different formation instead of using a skin factor. Thus, the aquifer system becomes a two-zone formation including the skin and formation zones. This study presents a mathematical model developed for analyzing a two-zone unconfined aquifer system and the associated solution for CHTs at partially penetrating wells under transient state. The solution of the model may be used either to identify the in situ aquifer parameters or to investigate the effects of the wellbore storage and well skin on the head changes in unconfined aquifers under constant-head pumping. Copyright (C) 2010 John Wiley & Sons, Ltd.