Browsing by Author "Lin, Ye-Chen"

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A general analytical model for pumping tests in radial finite two-zone confined aquifers with Robin-type outer boundary
(2016-09)
Lin, Ye-Chen
;
Yang, Shaw-Yang
;
Fen, Chiu-Shia
;
Yeh, Hund-Der
;
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 Lagging Model for Describing Drawdown Induced by a Constant-Rate Pumping in a Leaky Confined Aquifer
(2017-10-01)
Lin, Ye-Chen
;
Yeh, Hund-Der
;
環境工程研究所
;
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 simple analytical solution for organic contaminant diffusion through a geomembrane to unsaturated soil liner: Considering the sorption effect and Robin-type boundary
(2020-07-01)
Lin, Ye-Chen
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
Landfill leachate often contains soluble hazardous substances. Geomembrane (GM) liner is commonly used to protect the subsurface water. The leachate however may diffuse through the GM and enter the underlying natural soil liner. Analytical or numerical modeling for the leachate transport in the soils helps assess the associated risk to groundwater resources. The analytical model has the advantages of simplicity and easy to implement over the numerical model. Yet there is only an analytical model developed for describing the leachate migration through the GM to the unsaturated soil liner. Its solution however is difficult to evaluate. We herein develop a new analytical model to include the sorption effect and simplify the leachate transport through the GM as a Robin-type boundary condition in the model. The solution of the model is in a simple form and very easy to evaluate. The present solution is then compared with a finite-difference solution and the existing solution. The effect of the retardation factor on the leachate migration is investigated. A sensitivity analysis is also performed to assess the effects of model parameters on the leachate distribution. Finally, the present solution is adopted to estimate the transport parameters based on the data from bench-scale composite liner experiments. Landfill leachate often contains soluble hazardous substances. Geomembrane (GM) liner is commonly used to protect the subsurface water. The leachate however may diffuse through the GM and enter the underlying natural soil liner. Analytical or numerical modeling for the leachate transport in the soils helps assess the associated risk to groundwater resources. The analytical model has the advantages of simplicity and easy to implement over the numerical model. Yet there is only an analytical model developed for describing the leachate migration through the GM to the unsaturated soil liner. Its solution however is difficult to evaluate. We herein develop a new analytical model to include the sorption effect and simplify the leachate transport through the GM as a Robin-type boundary condition in the model. The solution of the model is in a simple form and very easy to evaluate. The present solution is then compared with a finite-difference solution and the existing solution. The effect of the retardation factor on the leachate migration is investigated. A sensitivity analysis is also performed to assess the effects of model parameters on the leachate distribution. Finally, the present solution is adopted to estimate the transport parameters based on the data from bench-scale composite liner experiments.
An analytical model for flow induced by a constant-head pumping in a leaky unconfined aquifer system with considering unsaturated flow
(2017-09-01)
Lin, Ye-Chen
;
Li, Ming-Hsu
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
A new mathematical model is developed to describe the flow in response to a constant-head pumping (or constant-head test, CHT) in a leaky unconfined aquifer system of infinite lateral extent with considering unsaturated flow. The model consists of an unsaturated zone on the top, an unconfined aquifer in the middle, and a second aquifer (aquitard) at the bottom. The unsaturated flow is described by Richard's equation, and the flows in unconfined aquifer and second layer are governed by the groundwater flow equation. The well partially penetrates the unconfined aquifer with a constant head in the well due to CHT. The governing equations of the model are linearized by the perturbation method and Gardner's exponential model is adopted to describe the soil retention curves. The solution of the model for drawdown distribution is obtained by applying the methods of Laplace transform and Weber transform. Then the solution for the wellbore flowrate is derived from the drawdown solution with Darcy's law. The issue of the equivalence of normalized drawdown predicted by the present solution for constant-head pumping and Tartakovsky and Neuman's (2007) solution for constant-rate pumping is discussed. On the basis of the wellbore flowrate solution, the results of the sensitivity analysis indicate that the wellbore flowrate is very sensitive to the changes in the radial hydraulic conductivity and the thickness of the saturated zone. Moreover, the results predicted from the present wellbore flowrate solution indicate that this new solution can reduce to Chang's et al. (2010a) solution for homogenous aquifers when the dimensionless unsaturated exponent approaches 100. The unsaturated zone can be considered as infinite extent in the vertical direction if the thickness ratio of the unsaturated zone to the unconfined aquifer is equal to or greater than one. As for the leakage effect, it can be ignored when the vertical hydraulic conductivity ratio (i.e., the vertical hydraulic conductivity of the lower layer over that of the unconfined aquifer) is smaller than 0.1. The present solution is compared with the numerical solution from FEMWATER for validation and the results indicate good match between these two solutions. Finally, the present solution is applied to a set of field drawdown data obtained from a CHT for the estimation of hydrogeologic parameters. (C) 2017 Elsevier Ltd. All rights reserved.
Analysis of Unconfined Flow Induced by Constant Rate Pumping Based on the Lagging Theory
(2019-05-01)
Lin, Ye-Chen
;
Huang, Ching-Sheng
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
This study proposes a new mathematical model for describing the drawdown distribution due to a constant rate pumping (CRP) in an unconfined aquifer considering the lagging theory. We introduce two lag times in Darcy's law and in turn in a free surface equation to reflect the effects of the capillary fringe and the capillary suction on the water table motion. The present free surface equation can reduce to those used in previous studies. The Laplace and Weber transform methods are used to derive the semianalytical solution to the model including the effect of wellbore storage. The algorithm of numerical Laplace inversion is applied to obtain the transient solution of the model. We find that the delay index, commonly used in the literature, is equivalent to the lag time associated with the effect of the capillary suction. The sensitivity analysis is performed to assess the drawdown behavior in response to the change in each aquifer parameter. The drawdown distributions predicted by the present solution agree fairly well to the field data taken from CRP tests at Cape Cod, Massachusetts; the Canadian Forces Base Borden, Ontario; and Saint Pardon de Conques, Gironde (France). The lag times determined by both CRP tests seem to decrease linearly with increasing distance on the logarithmic scale from the pumping well. The consideration of two lag times considerably improves the accuracy in estimated specific yields.
Analytical Model for Heat Transfer Accounting for Both Conduction and Dispersion in Aquifers With a Robin-Type Boundary Condition at the Injection Well
(2019-08-01)
Lin, Ye-Chen
;
Hu, Ting-Fang
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
In the past, the analytical model developed for a radially divergent heat flow in an aquifer thermal energy storage (ATES) system considers only the process of either thermal conduction or thermal dispersion. In addition, the existing models commonly regarded the inner boundary at the injection well as the constant-temperature condition, which does not meet the continuity condition of heat flux at the wellbore. We herein propose an analytical model for a realistic representation of heat flow in an ATES system by considering the effects of both thermal conduction and thermal dispersion in the heat transfer equation and a Robin-type boundary condition at the injection well. The model consists of three heat flow equations depicting the temperature distributions in the confined aquifer and its underlying and overlying rocks. The Laplace transform method is applied to solve the proposed model. The solutions for the cases of dispersion- and conduction-dominant flow fields are also developed and discussed. Comparisons between the present solutions with five existing solutions developed for similar heated water injection problems are made. A global sensitivity method is also performed to analyze the thermal response to the change in each of the aquifer parameters. Finally, our solution is validated through the comparison with the finite difference solution and observed data from an ATES experiment site in Mobile, Alabama.
New analytical model for constant-head pumping: Considering rate-dependent factor at well screen
(2020-02-01)
Lin, Ye-Chen
;
Yeh, Hund-Der
;
環境工程研究所
;
Institute of Environmental Engineering
Non-Darcy flow due to pumping may occur at the well screen and yields some head loss. Unlike the wellbore skin yielding a constant head loss at the well, the studies in petroleum engineering indicate that the head loss due to the non-Darcy flow is proportional to the pumping rate. The head loss due to non-Darcy flow is quantified by a rate-dependent factor at the well screen. To our knowledge, such a head loss is never considered in the area of groundwater hydraulics. In light of this, this study develops a groundwater flow model for the constant-head pumping with a head loss expressed in terms of a rate-dependent factor at a fully penetrating well in a confined aquifer. A skin factor representing the head loss due to the presence of wellbore skin is also incorporated into the model. The consideration of the rate-dependent factor, however, would make the model nonlinear. The model has a steady-state flow equation with a time-dependent finite outer boundary to approximate the transient groundwater flow in the aquifer system. The solutions to the model for the drawdown and wellbore flowrate are developed and compared with the finite difference solutions. With the help of the present solutions, the sensitivity analyses of the aquifer drawdown and wellbore flowrate are made. The effects of the wellbore skin and non-Darcy flow on the drawdown are also investigated. The wellbore flowrate solution is then applied to estimate the aquifer parameters based on the field data from a constant-head injection test in a confined aquifer. The prediction of the present solution gives the best fit to the field measured data as compared with three existing solutions, indicating that the consideration of the rate-dependent factor improves the aquifer parameter estimation. The results of the parameter estimation also reflect the quality of the well installation.
New Analytical Models for Flow Induced by Pumping in a Stream-Aquifer System: A New Robin Boundary Condition Reflecting Joint Effect of Streambed Width and Storage
(2020-04-01)
Huang, Ching-Sheng
;
Wang, Zicheng
;
Lin, Ye-Chen
;
Yeh, Hund-Der
;
Yang, Tao
A Robin type boundary condition (BC), commonly adopted at stream-aquifer interface, excludes a term associated with streambed accounting for the effects of streambed storage and width. This study presents two new analytical models for describing confined flow induced by pumping in a stream-aquifer system. One model considers a single-zone aquifer and treats the streambed as a lagging Robin BC with a time lag parameter related to the effects. The other considers a two-zone aquifer consisting of aquifer and streambed zones. A Dirichlet BC for stream water level is specified at the edge of the streambed. The time-domain solutions of both models are developed to describe spatiotemporal drawdown and temporal stream filtration/depletion rate (SDR). The finite element solutions (FESs) of both models are also built. Results suggest the lag time equals the half of the squared streambed width divided by the streambed hydraulic diffusivity. The effects of streambed width and storage on SDR should be considered when their lumped parameter exceeds 0.1. Neglecting their effects causes 25% difference in SDR when the lumped parameter equals 10. Based on the FESs, the use of the lagging Robin BC takes nearly a tenth of computing time of obtaining accurate steady-state SDR for the simulation of the two-zone aquifer. In addition, the present solutions agree to a field SDR experiment conducted by Hunt et al. (2001, ). To conclude, this study presents two new models for describing groundwater flow in a stream-aquifer system and explores the joint effect of streambed width and storage on SDR. Key Points Two new analytical solutions are developed to estimate aquifer drawdown and stream depletion rate in a pumped stream-aquifer system One treats streambed as a Robin type boundary based on the lagging theory while the other considers streambed as a finite-width zone The lag time in the Robin boundary equals the half of squared streambed width divided by the streambed hydraulic diffusivity