Browsing by Author "Yeh, Hund-Der"

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A closed-form solution for a confined flow into a tunnel during progressive drilling in a multi-layer groundwater flow system
(2007-04-12)
Yang, Shaw-Yang
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Yeh, Hund-Der
;
環境工程研究所
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Institute of Environmental Engineering
A mathematical model is developed to describe the groundwater inflow into a tunnel in a multi-layer aquifer system. Based on the model, the closed-form solution is derived to estimate the groundwater flow rate entering the multi-layer tunnel during progressive drilling. The solution has an integrand not only consisting of the product and square of the Bessel functions but also having a singularity at the origin. A unified numerical approach is proposed to evaluate the solution with accuracy to five decimal places. This approach includes a singularity removal scheme, the Gaussian quadrature, and the Shanks method. For a multi-layer formation, the results obtained from the solution based on the equivalent hydraulic conductivity and the newly derived solution differ significantly. This solution is capable of estimating the maximum flow rate inside the horizontal tunnel, and thus can be used as a tool for designing the drainage tunnel system in a multi-layer formation.
A computer method based on simulated annealing to identify aquifer parameters using pumping-test data
(2008-02-25)
Huang, Yen-Chen
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Yeh, Hund-Der
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Lin, Yu-Chung
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環境工程研究所
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Institute of Environmental Engineering
Conventional graphical or computer methods for identifying aquifer parameters have their own inevitable limitations. This paper proposes a computer method based on a drawdown model and a heuristic approach of simulated annealing (SA) to determine the best-fit aquifer parameters of the confined and unconfined aquifer systems. The drawdown model for the confined aquifer is the Theis solution and the unconfined aquifer is the Neuman solution. The estimated results of proposed method have better accuracy than those of the graphical methods and agree well with those of the computer methods based on the extended Kalman filter and Newton's method. Finally, the sensitivity analyses for the control parameters of SA indicate that the proposed method is very robust and stable in parameter identification procedures. Copyright (c) 2007 John Wiley & Sons, Ltd.
A drawdown solution for constant-flux pumping in a confined anticline aquifer
(2011-08-05)
Chen, Yen-Ju
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Yeh, Hund-Der
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Kuo, Chia-Chen
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環境工程研究所
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Institute of Environmental Engineering
An An anticline, known as a convex-upward fold in layers of rock, commonly is formed during lateral compression, which may be elected as a potential site for carbon sequestration. A mathematical model is developed in this study for describing the steady-state drawdown distribution in an anticline aquifer in response to the constant-flux pumping. The topographical shape of the anticline is mimicked by three successive blocks. The solution is obtained by applying the infinite Fourier transform and the finite Fourier cosine transform in each blocks and acquiring the hydraulic continuities between the blocks. Simulated results reveal that the introduction of a thin-limbs or narrow-ridged anticline would produce a much greater head drop in the ridge zone. For a well of constant pumping rate, the dimensionless drawdown around the well increases with decreasing well screen length or/and aquifer anisotropy ratio. An examination of the effect of well location on the drawdown reveals that the partially penetrating well located at the top-middle of the ridge zone produces the largest drawdown. The simulation of the flow in an anticline aquifer based on MODFLOW results in slightly smaller drawdown values in most regions when compared with those predicted by the present solution. The present solution can also be used to simulate the flow in a slab-shaped aquifer or a hillslope aquifer. It can be applied to determine the aquifer parameters if coupled with an optimization scheme and to provide the basis for selecting a potential site for carbon sequestration in the future as well. (C) 2011 Elsevier B.V. All rights reserved.
A general analytical model for head response to oscillatory pumping in unconfined aquifers: effects of delayed gravity drainage and initial condition
(2019-03-08)
Huang, Ching-Sheng
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Tsai, Ya-Hsin
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Yeh, Hund-Der
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Yang, Tao
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環境工程研究所
Oscillatory pumping tests (OPTs) provide an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters when OPT data are analyzed based on an associated analytical model coupled with an optimization approach. There are a large number of analytical models presented for the analysis of the OPT. The combined effects of delayed gravity drainage (DGD) and the initial condition regarding the hydraulic head are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by the OPT in an unconfined aquifer. The model contains a groundwater flow equation with the initial condition of a static water table, Neumann boundary condition specified at the rim of a partially screened well, and a free surface equation describing water table motion with the DGD effect. The solution is derived using the Laplace, finite-integral, and Weber transforms. Sensitivity analysis is carried out for exploring head response to the change in each hydraulic parameter. Results suggest that the DGD reduces to instantaneous gravity drainage in predicting transient head fluctuation when the dimensionless parameter a(1) = epsilon S(y)b/K-z exceeds 500 with empirical constant epsilon, specific yield S-y, aquifer thickness b, and vertical hydraulic conductivity K-z. The water table can be regarded as a no-flow boundary when a(1) < 10(-2) and P < 10(4) s, with P being the period of the oscillatory pumping rate. A pseudo-steady-state model without the initial condition causes a time-shift from the actual transient model in predicting simple harmonic motion of head fluctuation during a late pumping period. In addition, the present solution agrees well with head fluctuation data observed at the Savannah River site. Highlights. An analytical model of the hydraulic head due to oscillatory pumping in unconfined aquifers is presented. Head fluctuations affected by instantaneous and delayed gravity drainages are discussed. The effect of the initial condition on the phase of head fluctuation is analyzed. The present solution agrees well with head fluctuation data taken from field oscillatory pumping.
A general analytical model for pumping tests in radial finite two-zone confined aquifers with Robin-type outer boundary
(2016-09)
Lin, Ye-Chen
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Yang, Shaw-Yang
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Fen, Chiu-Shia
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Yeh, Hund-Der
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環境工程研究所
This study develops a general analytical model for describing transient drawdown distribution induced by pumping at a finite-radius well in a radial two-zone confined aquifer of finite areal extent with Robin-type condition at both inner and outer boundaries. This model is also applicable to heat conduction problems for a composite hollow cylinder on the basis of the analogy between heat flow and groundwater flow. The time-domain solution of the model is derived by the methods of Laplace transform, Bromwich integral, and residue theorem. This new solution can reduce to the solution for constant-head test (CHT) or constant-rate test (CRT) problem by specifying appropriate coefficients at the Robin inner boundary condition. The solution describing the flow rate across the wellbore due to CHT is further developed by applying Darcy\'s law to the new solution. In addition, steady-state solutions for both CHT and CRT are also developed based on the approximation for Bessel functions with very small argument values. Many existing solutions for transient flow in homogeneous or two-zone finite aquifers with Dirichlet or no-flow condition at the outer boundary are shown to be special cases of the present solution. Furthermore, the sensitivity analysis is also performed to investigate the behaviors of the wellbore flow due to CHT and the aquifer drawdown induced by CRT in response to the change in each of aquifer parameters. (C) 2016 Elsevier B.V. All rights reserved.
A general analytical solution for flow to a single horizontal well by Fourier and Laplace transforms
(2011-05-01)
Huang, Ching-Sheng
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Chen, Yu-Lin
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
The objective of this paper is to present an analytical solution for describing the head distribution in an unconfined aquifer with a single pumping horizontal well parallel to a fully penetrating stream. The Laplace-domain solution is developed by applying Fourier sine, Fourier and Laplace transforms to the governing equation as well as the associated initial and boundary conditions. The time-domain solution is obtained after taking the inverse Laplace transform along with the Bromwich integral method and inverse Fourier and Fourier sine transforms. The upper boundary condition of the aquifer is represented by the free surface equation in which the second-order slope terms are neglected. Based on the solution and Darcy's law, the equation representing the stream depletion rate is then derived. The solution can simulate head distributions in an aquifer infinitely extending in horizontal direction if the well is located far away from the stream. In addition, the solution can also simulate head distributions in confined aquifers if specific yield is set zero. It is shown that the solution can be applied practically to evaluate flow to a horizontal well. (C) 2011 Elsevier Ltd. All rights reserved.
A general analytical solution for groundwater fluctuations due to dual tide in long but narrow islands
(2012-05-04)
Huang, Ching-Sheng
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Yeh, Hund-Der
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Chang, Chia-Hao
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環境工程研究所
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Institute of Environmental Engineering
This paper develops a general mathematical model for describing head fluctuations in an aquifer of long but narrow islands subject to a dual tide effect. The upper boundary condition of the aquifer is represented by an equation combining the simplified free surface equation with a leakage term. Such an equation is considered as a general expression representing the upper boundary condition of a confined, unconfined, or leaky confined aquifer. The closed-form solution of the model represented by two series terms is developed by the direct Fourier method and finite Fourier sine transform. One of the series can reduce to a closed-form expression by means of contour integral and residue theorem. If the width of the island is very large, this solution gives the predicted head almost the same as that of the solution for an aquifer subject to a single tide effect. It is found that the presence of an upper aquitard produces significant vertical flow in the lower leaky confined aquifer even if the aquitard permeability is low. Neglecting such vertical flow may result in an overestimate of hydraulic head in the leaky confined aquifer. The attenuation factor and phase lag predicted from the present solution subject to the dual tide effect agree well with those estimated from 57 day head fluctuation data observed at Garden Island, Australia.
A General Semi-Analytical Solution for Three Types of Well Tests in Confined Aquifers with a Partially Penetrating Well
(2012-10-01)
Yang, Shaw-Yang
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Yeh, Hund-Der
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環境工程研究所
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應用化學系
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Institute of Environmental Engineering
This note develops a general mathematical model for describing the transient hydraulic head response for constant-head test, constant-flux test, and slug test in a radial confined aquifer system with a partially penetrating well. The Laplace-domain solution for the model is derived by applying the Laplace transform with respect to time and finite Fourier cosine transform with respect to the z-direction. This new solution has been shown to reduce to the constant-head test when discounting the wellbore storage and maintaining a constant well water level. This solution can also be reduced to the constant-flux test solution when discounting the wellbore storage and keeping a constant pumping rate in the well. Moreover, the solution becomes the slug test solution when there is no pumping in the well. This general solution can be used to develop a single computer code to estimate aquifer parameters if coupled with an optimization algorithm or to assess the effect of well partial penetration on hydraulic head distribution for three types of aquifer tests.
A generalized solution for groundwater head fluctuation in a tidal leaky aquifer system
(2011-12-01)
Chuang, Mo-Hsiung
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
A new analytical solution is developed for describing groundwater level fluctuations in a coupled leaky confined aquifer system which consists of an unconfined aquifer, confined aquifer, and an aquitard in between. The aquifer system has a tidal boundary at the seashore, a no flow boundary at remote inland side, and a confined aquifer extending under the sea and terminated with an outlet-capping. This new solution has shown to be a generalisation of most existing analytical solutions for a tidal aquifer system which includes single confined and leaky confined aquifers. In addition, the solution is used to explore the influences of the dimensionless leakance of the outlet-capping, the dimensionless hydraulic diffusivities, and the leakages of the inland and offshore aquitards on the head responses in the leaky confined aquifer.
A Lagging Model for Describing Drawdown Induced by a Constant-Rate Pumping in a Leaky Confined Aquifer
(2017-10-01)
Lin, Ye-Chen
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Yeh, Hund-Der
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環境工程研究所
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Institute of Environmental Engineering
This study proposes a generalized Darcy's law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant-rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual-porosity model. The Laplace-domain solution of the model with the effect of well bore storage is derived by the Laplace transform method. The time-domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the dravvdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer.
A mathematical solution and analysis of contaminant transport in a radial two-zone confined aquifer
(2012-09-01)
Chen, Yen-Ju
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Yeh, Hund-Der
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Chang, Kai-Ju
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環境工程研究所
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Institute of Environmental Engineering
An aquifer with a wellbore surrounded by a finite-thickness skin, such as a gravel pack, can be regarded as a radial two-zone system. In this study, a mathematical model is developed to describe contaminant transport in a radial two-zone confined aquifer system. The solution of the model equations can be used to delineate contaminant transport in such a two-zone aquifer system and to investigate the skin effect on the temporal and spatial concentration distribution. The present solution is shown to reduce to an existing solution for transport in a homogeneous aquifer in the case when there is no wellbore skin. The results predicted from the solution indicate that the skin effect has a significant impact on the concentration distribution at early time. But an abrupt change in the spatial concentration distribution may occur at the interface of the skin zone and aquifer formation zone. The results from a sensitivity analysis reveal that dispersivity in the formation zone has a more significant effect on the concentration distribution than do the effects of skin thickness and dispersivity in the skin zone. (c) 2012 Elsevier B.V. All rights reserved.
A new analytical solution solved by triple series equations method for constant-head tests in confined aquifers
(2010-06-01)
Chang, Ya-Chi
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Yeh, Hund-Der
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環境工程研究所
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Institute of Environmental Engineering
The constant-head pumping tests are usually employed to determine the aquifer parameters and they can be performed in fully or partially penetrating wells. 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 mathematical model describing the aquifer response to a constant-head test performed in a fully penetrating well can be easily solved by the conventional integral transform technique under the uniform Dirichlet-type condition along the rim of wellbore. However, the boundary condition for a test well with partial penetration should be considered as a mixed-type condition. This mixed boundary value problem in a confined aquifer system of infinite radial extent and finite vertical extent is solved by the Laplace and finite Fourier transforms in conjunction with the triple series equations method. This approach provides analytical results for the drawdown in a partially penetrating well for arbitrary location of the well screen in a finite thickness aquifer. The semi-analytical solutions are particularly useful for the practical applications from the computational point of view. (C) 2010 Elsevier Ltd. All rights reserved.
A new approximate solution for chlorine concentration decay in pipes
(2008-05-01)
Yeh, Hund-Der
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Wen, Shi-Bin
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Chang, Ya-Chi
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Lu, Chung-Sying
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環境工程研究所
Biswas et al. (1993. A model for chlorine concentration decay in pipes. Water Res. 27(12), 1715-1724) presented an analytical solution of a two-dimensional (2-D) steady-state chlorine transport equation in a pipe under the turbulent condition and employed fractional error function and regression technique to develop an approximate solution. However, their approximate solution may not give a good result if the wall decay parameter is large. This paper provides a more accurate approximate solution of the 2-D steady-state chlorine transport equation under the turbulent condition. This new approximate solution has advantages of easy evaluation and good accuracy when compared with the approximate solution given by Biswas et al. (1993). In addition, this paper also develops a methodology that combines simulated annealing (SA) with this new approximate solution to determine the wall decay parameter. Two cases are chosen to demonstrate the application of the present approximate solution and methodology. The first case is to use this new approximate solution in simulating chlorine decay in pipes with the experiment-observed data given by Rossman (2006. The effect of advanced treatment on chlorine decay in metallic pipes. Water Res. 40(13), 2493-2502), while the second case presents the determination of the wall consumption at the end of the pipe network. (c) 2008 Elsevier Ltd. All rights reserved.
A New Method for Laboratory Estimation of the Transverse Dispersion Coefficient - Discussion
(2010-01-01)
Yeh, Hund-Der
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Yang, Shaw-
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環境工程研究所
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Institute of Environmental Engineering
A new solution for a partially penetrating constant-rate pumping well with a finite-thickness skin
(2007-12-25)
Chiu, Pin-Yuan
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Yeh, Hund-Der
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Yang, Shaw-Yang
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環境工程研究所
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Institute of Environmental Engineering
A mathematical model describing the constant pumping is developed for a partially penetrating well in a heterogeneous aquifer system. The Laplace-domain solution for the model is derived by applying the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to vertical co-ordinates. This solution is used to produce the curves of dimensionless drawdawn versus dimensionless time to investigate the influences of the patch zone and well partial penetration on the drawdown distributions. The results show that the dimensionless drawdown depends on the hydraulic properties of the patch and formation zones. The effect of a partially penetrating well on the drawdown with a negative patch zone is larger than that with a positive patch zone. For a single-zone aquifer case, neglecting the effect of a well radius will give significant error in estimating dimensionless drawdown, especially when dimensionless distance is small. The dimensionless drawdown curves for cases with and without considering the well radius approach the Hantush equation (Advances in Hydroscience. Academic Press: New York, 1964) at large time and/or large distance away from a test well. Copyright (C) 2007 John Wiley & Sons, Ltd.
A novel analytical solution for a slug test conducted in a well with a finite-thickness skin
(2006-10-01)
Yeh, Hund-Der
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Yang, Shaw-Yang
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環境工程研究所
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Institute of Environmental Engineering
An aquifer containing a skin zone is considered as a two-zone system. A mathematical model describing the head distribution is presented for a slug test performed in a two-zone confined aquifer system. A closed-form solution for the model is derived by Laplace transforms and Bromwich integral. This new solution is used to investigate the effects of skin type, skin thickness, and the contrast of skin transmissivity to formation transmissivity on the distributions of dimensionless hydraulic head. The results indicate that the effect of skin type is marked if the slug-test data is obtained from a radial two-zone aquifer system. The dimensionless well water level increases with the dimensionless positive skin thickness and decreases as the dimensionless negative skin thickness increases. In addition, the distribution of dimensionless well water level due to the slug test depends on the hydraulic properties of both the wellbore skin and formation zones. (C) 2005 Published by Elsevier Ltd.
A novel analytical solution for constant-head test in a patchy aquifer
(2006-10-01)
Yang, Shaw-Yang
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Yeh, Hund-Der
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環境工程研究所
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Institute of Environmental Engineering
A mathematical model describing the hydraulic head distribution for a constant-head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer-region transmissivity to patch-region transmissivity as alpha. The dimensionless hydraulic head for alpha = 0.1 case is about 2.72 times to that for alpha = 10 case at dimensionless large time (e.g. tau >= 10(6)) when the dimensionless distance (rho) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two-zone formations. Copyright (C) 2006 John Wiley & Sons, Ltd.
A perturbation solution for head fluctuations in a coastal leaky aquifer system considering water table over-height
(2012)
Chuang, Mo-Hsiung
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Mahdi, Asadi-Aghbolaghi
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Yeh, Hund-Der
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環境工程研究所
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Institute of Environmental Engineering
This paper develops a new analytical solution for the aquifer system, which comprises an unconfined aquifer on the top, a semi-confined aquifer at the bottom and an aquitard between them. This new solution is derived from the Boussinesq equation for the unconfined aquifer and one-dimensional leaky confined flow equation for the lower aquifer using the perturbation method, considering the water table over-height at the remote boundary. The head fluctuation predicted from this solution is generally greater than the one solved from the linearized Boussinesq equation when the ratio of the tidal amplitude to the thickness of unconfined aquifer is large. It is found that both submarine groundwater discharges from upper and lower aquifers increase with tidal amplitude-aquifer thickness ratio and may be underestimated if the discharge is calculated based on the average head fluctuation. The effects of the aquifer parameters and linearization of the Boussinesq equation on the normalized head fluctuation are also investigated.
A reduced-order based CE-QUAL-W2 model for simulation of nitrate concentration in dam reservoirs
(2015-11-01)
Noori, Roohollah
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Yeh, Hund-Der
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Ashrafi, Khosro
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Rezazadeh, Najmeh
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Bateni, Sayed M.
When the number of computational grids increases, water quality simulation complexities arise. Therefore, using a reduced order framework to express the variations of the objective parameter may facilitate the simulation task and also the interpretation of computational results. In this regard, a new reduced-order approach was proposed to link a water quality simulator model (CE-QUAL-W2, W2) with a data reduction technique (proper orthogonal decomposition, POD). The W2 model simulated spatio-temporal variations of nitrate in the Karkheh Reservoir, Iran. Thereafter, the POD model reduced the dimensions of simulated nitrate in the computational grids. The performance of the developed reduced-order model (ROM) results was evaluated through the comparison of the regenerated nitrate data by the model, and the simulated ones by W2. Findings indicated that the first four modes among 1825 computed ones by ROM conserved approximately over 91% of the nitrate variations. It means that the ROM was capable of showing the spatio-temporal variations of nitrate in the reservoir using the first few modes. Finally, confirmation of ROM indicated that the error of order of magnitude was less than 0.001, for nitrate ROM to regenerate nitrate data using 100 basis functions. (C) 2015 Elsevier B.V. All rights reserved.
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.