Browsing by Author "Yeh, HD"

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A closed form solution for constant flux pumping in a well under partial penetration condition
(2006-05-19)
Yang, SY
;
Yeh, HD
;
Chiu, PY
;
環境工程研究所
;
Institute of Environmental Engineering
[ 1] An analytical model for the constant flux pumping test is developed in a radial confined aquifer system with a partially penetrating well. The Laplace domain solution is derived by the application of the Laplace transforms with respect to time and the finite Fourier cosine transforms with respect to the vertical coordinates. A time domain solution is obtained using the inverse Laplace transforms, convolution theorem, and Bromwich integral method. The effect of partial penetration is apparent if the test well is completed with a short screen. An aquifer thickness 100 times larger than the screen length of the well can be considered as infinite. This solution can be used to investigate the effects of screen length and location on the drawdown distribution in a radial confined aquifer system and to produce type curves for the estimation of aquifer parameters with field pumping drawdown data.
A Laplace transform solution for tracer tests in a radially convergent flow field with upstream dispersion
(1996-09-01)
Chen, JS
;
Liu, CW
;
Chen, CS
;
Yeh, HD
;
環境工程研究所
When tracers are introduced into an injection borehole, noticeable concentration gradients at the injection well may cause a backward spreading of the initial plume during radially convergent tracer tests. Based on this concept a non-rigorous mathematical model is developed to estimate the effect of backward spreading. The injection well with an instantaneous slug input is treated as a mathematical source and the initial plume at the injection well is allowed to move upstream. The model assumes that advection and longitudinal dispersion are the transport mechanisms in a radially converging how field. The Laplace transform solution for solute concentration in an infinite porous medium is obtained using the method of Green's function. Breakthrough curves are computed by numerically inverting the Laplace transform solution. As compared with the solution of Moench, it is concluded that the presence of backward movement of initial plume yields a decrease of peak concentration and spreading out of breakthrough curve tails. This effect is significant for small Peclet numbers and can be neglected for large Peclet numbers. A field tracer test is carried out to demonstrate the applicability of the model. The experimental data are fitted with the type curves of this study, and those of Moench's study, to determine dispersivity and aquifer porosity. The results show that dispersivity values estimated by matching the two type curves are different. Because it neglects backward dispersion, Moench's solution overestimates the dispersivity and effective aquifer porosity.
A Laplace transform solution for tracer tests in a radially convergent flow field with upstream dispersion
(1996-09-01)
Chen, JS
;
Liu, CW
;
Chen, CS
;
Yeh, HD
;
環境工程研究所
When tracers are introduced into an injection borehole, noticeable concentration gradients at the injection well may cause a backward spreading of the initial plume during radially convergent tracer tests. Based on this concept a non-rigorous mathematical model is developed to estimate the effect of backward spreading. The injection well with an instantaneous slug input is treated as a mathematical source and the initial plume at the injection well is allowed to move upstream. The model assumes that advection and longitudinal dispersion are the transport mechanisms in a radially converging how field. The Laplace transform solution for solute concentration in an infinite porous medium is obtained using the method of Green's function. Breakthrough curves are computed by numerically inverting the Laplace transform solution. As compared with the solution of Moench, it is concluded that the presence of backward movement of initial plume yields a decrease of peak concentration and spreading out of breakthrough curve tails. This effect is significant for small Peclet numbers and can be neglected for large Peclet numbers. A field tracer test is carried out to demonstrate the applicability of the model. The experimental data are fitted with the type curves of this study, and those of Moench's study, to determine dispersivity and aquifer porosity. The results show that dispersivity values estimated by matching the two type curves are different. Because it neglects backward dispersion, Moench's solution overestimates the dispersivity and effective aquifer porosity.
A new closed-form solution for a radial two-layer drawdown equation for groundwater under constant-flux pumping in a finite-radius well
(2003-07-01)
Yeh, HD
;
Yang, SY
;
Peng, HY
;
環境工程研究所
;
Institute of Environmental Engineering
A mathematical model is presented for describing the groundwater flow in a radial two-layer confined aquifer system with a constant-flux pumping well that has a wellbore skin and finite well radius. The Laplace-domain solution for the model is first derived by the Laplace transforms; and the time-domain solution in terms of the aquifer drawdown is then obtained form the Laplace inversion using the Bromwich integral method. When neglecting the well radius, our Laplace-domain solution is shown to reduce to a Laplace-domain solution given by Butler [J. Hydrol. 101 (1988) 15]. A unified numerical approach including a root search approach, the Gaussian quadrature, and the Shanks method is employed for evaluating this time-domain solution. The evaluated results of the solution agree well with those of the Laplace-domain solution estimated by the modified Crump algorithm. This new solution can be used either to predict the spatial and temporal drawdown distributions in both the skin and formation zones or to investigate the effects of the skin type, skin thickness and well radius on the drawdown distribution. (C) 2003 Elsevier Science Ltd. All rights reserved.
A simple approach using Bouwer and Rice's method for slug test data analysis
(2004-09-01)
Yang, SY
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
Slug test data obtained from tests performed in an unconfined aquifer are commonly analyzed by graphical or numerical approaches to determine the aquifer parameters. This paper derives three fourth-degree polynomials to represent the relationship between Bouwer and Rice's coefficients and the ratio of the screen length to the radius of the gravel envelope. A numerical approach using the nonlinear least squares and Newton's method is used to determine hydraulic conductivity from the best fit of the slug test data. The method of nonlinear least squares minimizes the sum of the squares of the differences between the predicted and observed water levels inside the well. With the polynomials, the hydraulic conductivity can be obtained by simply solving the nonlinear least squares equation by Newton's method. A computer code, SLUGBR, was developed from the derived polynomials using the proposed numerical approach. The results of analyzing two slug test datasets show that SLUGBR can determine hydraulic conductivity with very good accuracy.
Aquifer parameter identification using the extended Kalman filter
(2003-03-19)
Leng, CH
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
[1] An approach using the extended Kalman filter (EKF) and cubic spline is proposed to identify the aquifer parameters in both confined and unconfined aquifer systems. The cubic spline applied to the observation data can generate interpolated data with uniform time intervals and facilitates the implementation of EKF. The EKF combined with the Theis solution or Neuman's model, using the interpolated drawdown data produced by cubic spline, can optimally determine the parameters through the recursive process. The proposed approach can quickly identify the parameters, using only part of observed drawdown data, and the obtained parameters are shown to have good accuracy. Thus length of time of pumping tests may be shortened. Comparisons of results from nonlinear least squares combined with finite difference Newton's method (NLN) and EKF show that the EKF allows a wider range of initial guess values than NLN and have the accuracy of the results on the same order of magnitude as that of NLN. When determining the aquifer parameters, the identification process of specific yield reflects the effect of gravity drainage on the drawdown curve and conforms to the physical nature of an unconfined aquifer. Furthermore, this study shows that EKF can be successfully applied to analyze the drawdown data even with white noises or temporally correlated noises.
Comment on "Application of BEM with extended Kalman filter to parameter identification of an elastic plate under dynamic loading" by M. Tanaka, T. Matsumoto and H. Yamamura [Engineering Analysis with Boundary Elements 28 (2004) 213-219]
(2005-01-01)
Yeh, HD
;
Huang, YC
;
環境工程研究所
;
Institute of Environmental Engineering
Conditional expectation for evaluation of risk groundwater flow and solute transport: one-dimensional analysis
(1997-12-10)
Liou, TS
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
A one-dimensional groundwater transport equation with two uncertain parameters, groundwater velocity and longitudinal dispersivity, is investigated in this paper. The analytical uncertainty of the predicted contaminant concentration is derived by the first-order mean-centered uncertainty analysis. The risk of the contaminant transport is defined as the probability that the concentration exceeds a maximum acceptable upper limit. Five probability density functions including the normal, lognormal, gamma, Gumbel, and Weibull distributions are chosen as the models for predicting the concentration distribution. The risk for each distribution is derived analytically based on the conditional probability. The mean risk and confidence interval are then computed by Monte Carlo simulation where the groundwater velocity and longitudinal dispersivity are assumed to be lognormally and normally distributed, respectively. Results from the conditional expectation of an assumed damage function show that the unconditional expectation generally underestimates the damage for low risk events. It is found from the sensitivity analysis that the mean longitudinal dispersivity is the most sensitive parameter and the variance of longitudinal dispersivity is the least sensitive one among those distribution models except the gamma and Weibull distributions. (C) 1997 Elsevier Science B.V.
Finite element modelling for land displacements due to pumping
(1996-02-01)
Yeh, HD
;
Lu, RH
;
Yeh, GT
;
土木工程學系
;
環境工程研究所
Equations of equilibrium (force balance) and flow in multidimensions were coupled in this paper to describe land displacements due to pressure decline in aquifers. A Galerkin finite element model based on these equations was developed. The saturated/unsaturated behaviour and the isotropic/anisotropic properties of permeability and elasticity were considered when the model was formulated. This model was verified by comparing its simulation results with those of known analytical solutions for simplified cases. The simulation of displacements due to pressure decline in unsaturated media was also performed. Those results demonstrated that the choice of boundary ranges for an aquifer with infinite domain may significantly affect the estimated horizontal and vertical displacements. To obtain a good estimation of land displacements, the boundary ranges should be carefully chosen. The displacements occurring in unconfined aquifers are caused by the drop of the water table and the change in body force in the dewatering zone. Simulation results also indicated that the change in body force should be considered once an unconfined aquifer has been pumped. Otherwise, the horizontal and vertical displacements in unconfined aquifers would be overestimated and underestimated, respectively. The behaviour of land displacements due to pumping was shown to be affected by changes in the total stresses in aquifers.
Improved numerical evaluation of the radial groundwater flow equation
(2002-06-01)
Peng, HY
;
Yeh, HD
;
Yang, SY
;
環境工程研究所
;
Institute of Environmental Engineering
The closed-form solution for the hydraulic head, derived for the radial groundwater flow equation subject to the constant-head boundary condition at the wellbore, is in an integral form that covers an integration range from zero to infinity. The integral is difficult to evaluate due to the integrand not only consisting of the product and the square of the Bessel functions but also having a singularity at the origin. A unified numerical method is proposed to evaluate the solution with accuracy to five decimal places and for very wide ranges of dimensionless distances and times. This approach includes a singularity removal scheme, Newton's method, the Gaussian quadrature, and Shanks' method. It gives the dimensionless heads in tabular forms with better accuracy while comparing to those given by other approaches. A formula describing the flow rate across the wellbore, derived by the authors based on Darcy's law, is proved to equal those presented by Jaeger [Proc Royal Soc Edinburgh 61 (1942) 223] and Jacob and Lohman [Am Geo Union 33 (4) (1952) 559]. The same singularity removal scheme and the Gaussian quadrature are also employed to evaluate the wellbore flow rate. Computed values of dimensionless flow rate versus dimensionless time expressed in tabular forms are also correct to five decimal places. Both the tabular results of dimensionless hydraulic head and dimensionless flow rate may be useful in engineering applications. (C) 2002 Elsevier Science Ltd. All rights reserved.
Laplace-domain solutions for radial two-zone flow equations under the conditions of constant-head and partially penetrating well
(2005-03-01)
Yang, SY
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
A mathematical model is presented for a constant-head test performed in a partially penetrating well with a finite-thickness skin. The model uses a no-flow boundary condition for the casing and a constant-head boundary condition for the screen to represent the partially penetrating well. The Laplace-domain solutions for the dimensionless flow rate at the wellbore and the hydraulic heads in the skin and formation zones are derived using the Laplace and finite Fourier cosine transforms. The solutions of hydraulic heads have been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the pressure head and flow rate at the interface of the skin zone and undisturbed formation. In addition, an efficient algorithm for evaluating those solutions is also presented. The dimensionless flow rates obtained from new solutions have been shown to be better than those of Novakowski's solutions, especially when the penetration ratio is large.
New analytical solutions for groundwater flow in wedge-shaped aquifers with various topographic boundary conditions
(2006-03-01)
Yeh, HD
;
Chang, YC
;
環境工程研究所
;
Institute of Environmental Engineering
The hydraulic head distribution in a wedge-shaped aquifer depends on the wedge angle and the topographic and hydrogeological boundary conditions. In addition, an equation in terms of the radial distance with trigonometric functions along the boundary may be suitable to describe the water level configuration for a valley flank with a gentle sloping and rolling topography. This paper develops a general mathematical model including the governing equation and a variety of boundary conditions for the groundwater flow within a wedge-shaped aquifer. Based on the model, a new closed-form solution for transient flow in the wedge-shaped aquifer is derived via the finite sine transform and Hankel transform. In addition, a numerical approach, including the roots search scheme, the Gaussian quadrature, and Shanks' method, is proposed for efficiently evaluating the infinite series and the infinite integral presented in the solution. This solution may be used to describe the head distribution for wedges that image theory is inapplicable, and to explore the effects of the recharge from various topographic boundaries on the groundwater flow system within a wedge-shaped aquifer. (c) 2005 Elsevier Ltd. All rights reserved.
On the equivalence between magnetic-field-induced phase transitions in the integer quantum Hall effect
(2003-04-01)
Huang, CF
;
Chang, YH
;
Cheng, HH
;
Yang, ZP
;
Wang, SY
Magnetic-field-induced phase transitions in the two-dimensional electron system in a AlGaAs/InGaAs/GaAs heterostructure are studied. Two kinds of magnetic-field-induced phase transitions, plateau-plateau (P-P) and insulator-quantum Hall conductor (I-QH) transitions, are observed in the integer quantum Hall effect regime at high magnetic fields. In the P-P transition, both the semicircle law and the universality of critical conductivities are broken and we do not observe the universal scaling. However, the P-P transition can still be mapped to the I-QH transition by the Landau-level addition transformation, and as the temperature decreases the critical points of these two transitions appear at the same temperature. Our observations indicate that the equivalence between P-P and I-QH transitions can be found by the suitable analysis even when some expected universal properties are invalid. (C) 2003 Elsevier Science Ltd. All rights reserved.
Parameter estimation for leaky aquifers using the extended Kalman filter, and considering model and data measurement uncertainties
(2005-02-01)
Yeh, HD
;
Huang, YC
;
環境工程研究所
;
Institute of Environmental Engineering
A method using the extended Kalman filter (EKF) is proposed to identify the hydraulic parameters in leaky aquifer systems both with and without considering the aquitard storage. In the case without considering the aquitard storage, Hantush and Jacob's model combined with EKF can optimally determine the parameters for the leaky aquifer when analyzing the drawdown data. Coupled with Neuman and Witherspoon's model, the EKF is also employed to estimate the four parameters of aquifers. The observed drawdown data may be either interpolated using the Lagrangian polynomial or recursively used while implementing the EKF. The proposed method can identify the parameters, using part of the interpolated drawdown data or recursively used data, and obtains results with good accuracy. In the field-pumping test, a long pumping time may not be necessary if the proposed method is implemented on a computer, which is connected to pressure transducers and a data logger. In the process of parameter estimation, the leakage coefficient changes marginally for the first few observations. This phenomenon reflects the fact that there is a time lag between the start of pumping and the leakage effect on the drawdown. The analyses of the data uncertainty demonstrate that the EKF approach is applicable for drawdown data even when it contains white noise or temporal correlated noise. Finally, the choice between Hantush and Jacob's model and Neuman and Witherspoon's model depends on the hydrogeological condition of the aquifer system indicated in the analyses of the model uncertainty. Hantush and Jacob's model is shown to be a good choice for representing the leaky aquifer system if, the aquitard storage is comparatively small. (C) 2004 Elsevier B.V. All rights reserved.
Parameter identification of an unconfined aquifer using extended Kalman filter
(2002)
Yeh, HD
;
Leng, CH
;
環境工程研究所
;
Institute of Environmental Engineering
A method using extended Kalman filter (EKF) and cubic spline is proposed to identify the aquifer parameters of an unconfined aquifer system. Neuman's model combined with EKF, using the interpolated drawdown data produced by cubic spline, can optimally determine the parameters for unconfined aquifers through the recursive filtering process. The proposed method can quickly identify the parameters, using only part of observed drawdown data, and achieves good accuracy. Thus, the lengthy pumping test may be shortened. In addition, the comparisons of results among using conventional graphical methods, nonlinear least-squares combined with finite-difference Newton's method (NLN), and EKF are presented. The EKF is shown to allow a wider range of initial guess values, though the results are slightly less accurate than those by NLN, but much more accurate than those by graphical methods. Finally, the identification process of specific yield reflects the effect of gravity drainage on the drawdown curve and conforms to the physical nature of an unconfined aquifer, when determining the aquifer parameters.
Radionuclide transport in a multiple and parallel fractured system
(2003-09-01)
Liu, CT
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
This paper is to study the effects of fracture width on the transport of a radionuclide in a multiple and parallel fractured rock formation. The equation describing the transport of the radionuclide released from the geological repository includes the following mechanisms: advection, dispersion, radioactive decay, and adsorption on the fracture surfaces. The concentration at the inlet of each fracture is assumed constant. An analytical solution was derived based on such a mathematical model by the Laplace transform technique. The solution indicates that identical concentration distributions can be observed in each fracture of the equal-width parallel fractured system. In an unequal-width fractured system, the penetration distances along wide fractures are generally larger than that in a single uniform fractured system. The radionuclide concentration in the wide fracture quickly reaches source concentration in the near-field environment, confirming that the fracture width plays an important role in radionuclide transport through a system of multiple and parallel fractured media.
Reply to comment by A.F. Moench on "Aquifer parameter identification using the extended Kalman filter''
(2004-04-28)
Leng, CH
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
Solution for flow rates across the wellbore in a two-zone confined aquifer
(2002-02-01)
Yang, SY
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
A closed-form solution for transient flow rates across the wellbore in a confined aquifer is derived from a two-zone radial ground-water flow equation subject to the boundary condition of keeping a constant head at the well radius. An aquifer may be considered as a two-zone system if the formation properties near the wellbore are significantly changed due to the well construction and/or well development. An efficient numerical approach is used to evaluate this newly derived solution. Values of the transient flow rate are provided in a tabular form and compared with those obtained by numerical inversion for the Laplace-domain solution. The results show that the two solutions are in good agreement. This newly derived solution can be used not only for predicting the transient flow rate across the wellbore but also for identifying the effects of a skin with a finite thickness on the estimation of transient flow rates in a ground-water system with two different formation properties.
Some exact solutions of convection-diffusion and diffusion equations - Comment
(1996-02-01)
Wang, CT
;
Yeh, HD
;
交大名義發表
;
環境工程研究所
;
National Chiao Tung University
Trihalomethane species forecast using optimization methods: Genetic algorithms and simulated annealing
(2005-07-01)
Lin, YC
;
Yeh, HD
;
環境工程研究所
;
Institute of Environmental Engineering
Chlorination is an effective method for disinfection of drinking water. Yet chlorine is a strong oxidizing agent and easily reacts with both organic and inorganic materials. Trihalomethanes (THMs), formed as a by-product of chlorination, are carcinogenic to humans. Models can be derived from linear and nonlinear multiregression analyses to predict the THM species concentration of empirical reaction kinetic equations. The main objective of this study is to predict the concentrations of THM species by minimizing the nonlinear function, representing the errors between the measured and calculated THM concentrations, using the genetic algorithm (GA) and simulated annealing (SA). Additionally, two modifications of SA are employed. The solutions obtained from GA and SA are compared with the measured values and those obtained from a generalized reduced gradient method (GRG2). The results indicate that the proposed heuristic methods are capable of optimizing the nonlinear problem. The predicted concentrations may provide useful information for controlling the chlorination dosage necessary to assure the safety of water drinking.