Browsing by Author "Yang, Shaw-Yang"

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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
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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 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 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 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
;
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.
An analytical solution for describing the transient temperature distribution in an aquifer thermal energy storage system
(2010-12-15)
Li, Kuang-Yi
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Yang, Shaw-Yang
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Yeh, Hund-Der
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環境工程研究所
;
Institute of Environmental Engineering
A mathematical model is developed for predicting the temperature distribution in an aquifer thermal energy storage (ATES) system, which consists of a confined aquifer bounded from above and below by the rocks of different geological properties. The main transfer processes of heat include the conduction and advection in the aquifer and the conduction in the rocks. The semi-analytical solution in dimensionless form for the model is developed by Laplace transforms and its corresponding time-domain solution is evaluated by the modified Crump method. Field geothermal property data are used to simulate the temperature distribution in an ATES system. The results show that the heat transfer in the aquifer is fast and has a vast effect on the vicinity of the wellbore. However, the aquifer temperature decreases with increasing radial and vertical distances. The temperature in the aquifer may be overestimated when ignoring the effect of thermal conductivity. The temperature distribution in an ATES system depends on the vertical thermal conduction in the rocks and the horizontal advection and thermal conduction in the aquifer. The present solution is useful in designing and simulating the heat injection facility in the ATES systems. Copyright (C) 2010 John Wiley & Sons, Ltd.
Analytical Solutions for Constant-Flux and Constant-Head Tests at a Finite-Diameter Well in a Wedge-Shaped Aquifer
(2009-04-01)
Chen, Yen-Ju
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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
Neglecting the effect of well radius may lead to a significant error in the predicted drawdown distribution near the pumping well area. New analytical solutions describing aquifer responses to a constant pumping or a constant head maintained at a finite-diameter well in a wedge-shaped aquifer are derived based on the image-well method and applicable to an arbitrarily located well in the system. The solutions are useful for quantifying groundwater exploitation from a wedge-shaped aquifer and for determining the hydrogeological parameters of a wedge-shaped aquifer in inverse problems.
Approximate discharge for constant head test with recharging boundary Discussion
(2007-11-01)
Yeh, Hund-Der
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Yang, Shaw-Yang
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Chen, Yen-Ju
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環境工程研究所
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Institute of Environmental Engineering
Approximate Solution for a Transient Hydraulic Head Distribution Induced by a Constant-Head Test at a Partially Penetrating Well in a Two-Zone Confined Aquifer
(2014-07-01)
Yang, Shaw-Yang
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Huang, Ching-Sheng
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Liu, Chih-Hsuan
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Yeh, Hund-Der
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交大名義發表
A mathematical model describing the transient hydraulic head distribution induced by constant-head pumping/injection at a partially penetrating well in a radial two-zone confined aquifer is a mixed-type boundary value problem. The analytical solution of the model is in terms of an improper integral with an integrand having a singularity at the origin. The solution should rely on numerical methods to evaluate the integral and handle the problems of convergence and singularity. This study aims at developing a new approximate solution describing the transient hydraulic head distribution for a constant-head test (CHT) at a partially penetrating well in the aquifer. This approximate solution is acquired based on a time-dependent diffusion layer approximation proposed in the field of electrochemistry. The diffusion layer can be analogous to the radius of influence in the area of well hydraulics. The approximate solution is in terms of modified Bessel functions for aquifers with a partially penetrating well and can reduce to a simpler form in terms of a natural logarithmic function for the case of well full penetration. The predicted hydraulic heads from the present approximate solution are compared with those estimated by the Laplace-domain solution of the model. The result shows that the predicted spatial head distributions are accurate in the formation zone and fairly good in the skin zone. In addition, the present solution gives an accurate temporal head distribution at a specific location when the radius of influence is far away from the observation wells. This newly developed approximate solution has advantages of easy computing and good accuracy from practical viewpoint, and thus is a handy tool to evaluate temporal and spatial hydraulic head distributions for the CHT. (C) 2014 American Society of Civil Engineers.
Comment on "Evaluation of the Hantush's M(alpha, beta) function using binomial coefficients" by B. A. Mamedov and A. S. Ekenoglu
(2007-12-07)
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
Groundwater flow to a pumping well in a sloping fault zone unconfined aquifer
(2014-05-01)
Huang, Ching-Sheng
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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
This study develops a mathematical model for simulating the hydraulic head distribution in response to pumping in a sloping fault zone aquifer under a water table boundary condition. A two-dimensional equation with a sink term representing the pumping is used for describing the head distribution in the aquifer. In addition, a first-order free surface equation is adopted to represent the change in water table at the outcrop. The analytical solution of the model, derived by the Laplace and finite Fourier cosine transforms, is expressed in terms of a double series. A finite difference solution within a deformable grid framework is developed to assess the solution obtained by specifying the free surface equation at the outcrop. Based on the analytical solution, we have found that the model\'s prediction tends to overestimate drawdown in a late pumping period. The temporal head distribution is independent of the aquifer slope if the water table change is small, and exhibits a double-humped shape due to the effect of the free surface. The temporal drawdown predicted from the analytical solution is further compared with those measured from a pumping test conducted in northern Portugal.
Heat extraction from aquifer geothermal systems
(2012-01-01)
Yeh, Hund-Der
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Yang, Shaw-Yang
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Li, Kuang-Yi
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環境工程研究所
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Institute of Environmental Engineering
This study aims to model temperature distributions in an aquifer thermal extraction (ATE) system that contains a single extraction well in a thin confined aquifer. The aquifer is bounded by hot dry rocks with different thermomechanical properties and thicknesses. Based on the heat convectionconduction equation, a mathematical model is developed to describe the spatial and temporal temperature distributions of the ATE systems. The mechanisms of heat transfer in the model involve horizontal convection and thermal conduction in the aquifer, and vertical thermal conduction in both rocks. A semi-analytical solution in dimensionless form is developed using the Laplace transform technique and its corresponding time-domain result is computed by the modified Crump method. In addition, the steady-state solution is obtained by applying the final value theorem. The simulation results from the semi-analytical solution indicate that the aquifer temperature distributions are affected by aquifer thickness, the thermomechanical properties of the aquifer and rocks, geothermal gradient, outer boundary temperatures of the rocks, extraction rate, and operating time. The present solution can be used as a preliminary tool for assessing heat extraction efficiency in ATE systems. Copyright (c) 2010 John Wiley & Sons, Ltd.
Modeling heat extraction from hot dry rock in a multi-well system
(2009-06-01)
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 is developed for describing the heat energy extracted from a hot dry rock in a multi-well system. The solutions for the water temperature, accounting for a geothermal gradient in a geothermal reservoir, are given in the Laplace domain and computed by numerical inversion, the modified Crump method. The results show that the heat extraction effectiveness is affected significantly by the well spacing, well radius, reservoir thickness, and pumped flow rate in a multi-well system. The water temperature decreases with increasing pumping rate and increases with the well spacing, well radius, and reservoir thickness. The geothermal gradient affects only the early time heat extraction effectiveness significantly and has direct impact on the water temperature all the time if the vertical thickness of geothermal reservoir is large. The present solution is useful for designing and simulating the heat extraction project of geothermal energy exploitation in a multi-well system. (C) 2008 Elsevier Ltd. All rights reserved.
Modeling transient heat transfer in nuclear waste repositories
(2009-09-30)
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
The heat of high-level nuclear waste maybe generated and released from a canister at final disposal sites. The waste heat may affect the engineering properties of waste canisters, buffers, and backfill material in the emplacement tunnel and the host rock. This study addresses the problem of the heat generated from the waste canister and analyzes the heat distribution between the buffer and the host rock, which is considered as a radial two-layer heat flux problem. A conceptual model is first constructed for the heat conduction in a nuclear waste repository and then mathematical equations are formulated for modeling heat flow distribution at repository sites. The Laplace transforms are employed to develop a solution for the temperature distributions in the buffer and the host rock in the Laplace domain, which is numerically inverted to the time-domain solution using the modified Crump method. The transient temperature distributions for both the single- and multi-borehole cases are simulated in the hypothetical geological repositories of nuclear waste. The results show that the temperature distributions in the thermal field are significantly affected by the decay heat of the waste canister, the thermal properties of the buffer and the host rock, the disposal spacing, and the thickness of the host rock at a nuclear waste repository. (C) 2009 Elsevier B.V. All rights reserved.
Modelling transient temperature distribution for injecting hot water through a well to an aquifer thermal energy storage system
(2010-10-01)
Yang, Shaw-Yang
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Yeh, Hund-Der
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Li, Kuang-Yi
;
環境工程研究所
;
Institute of Environmental Engineering
P>Heat storage systems are usually used to store waste heat and solar energy. In this study, a mathematical model is developed to predict both the steady-state and transient temperature distributions of an aquifer thermal energy storage (ATES) system after hot water is injected through a well into a confined aquifer. The ATES has a confined aquifer bounded by aquicludes with different thermomechanical properties and geothermal gradients along the depth. Consider that the heat is transferred by conduction and forced convection within the aquifer and by conduction within the aquicludes. The dimensionless semi-analytical solutions of temperature distributions of the ATES system are developed using Laplace and Fourier transforms and their corresponding time-domain results are evaluated numerically by the modified Crump method. The steady-state solution is obtained from the transient solution through the final-value theorem. The effect of the heat transfer coefficient on aquiclude temperature distribution is appreciable only near the outer boundaries of the aquicludes. The present solutions are useful for estimating the temperature distribution of heat injection and the aquifer thermal capacity of ATES systems.
Modelling transient temperature distribution for injecting hot water through a well to an aquifer thermal energy storage system
(2010-10-01)
Yang, Shaw-Yang
;
Yeh, Hund-Der
;
Li, Kuang-Yi
;
環境工程研究所
;
Institute of Environmental Engineering
P>Heat storage systems are usually used to store waste heat and solar energy. In this study, a mathematical model is developed to predict both the steady-state and transient temperature distributions of an aquifer thermal energy storage (ATES) system after hot water is injected through a well into a confined aquifer. The ATES has a confined aquifer bounded by aquicludes with different thermomechanical properties and geothermal gradients along the depth. Consider that the heat is transferred by conduction and forced convection within the aquifer and by conduction within the aquicludes. The dimensionless semi-analytical solutions of temperature distributions of the ATES system are developed using Laplace and Fourier transforms and their corresponding time-domain results are evaluated numerically by the modified Crump method. The steady-state solution is obtained from the transient solution through the final-value theorem. The effect of the heat transfer coefficient on aquiclude temperature distribution is appreciable only near the outer boundaries of the aquicludes. The present solutions are useful for estimating the temperature distribution of heat injection and the aquifer thermal capacity of ATES systems.
Radial groundwater flow to a finite diameter well in a leaky confined aquifer with a finite-thickness skin
(2009-11-15)
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 that describes the drawdown due to constant pumpage from a finite radius well in a two-zone leaky confined aquifer system is presented. The aquifer system is overlain by an aquitard and underlain by an impermeable formation. A skin zone of constant thickness exists around the wellbore. A general solution to a two-zone leaky confined aquifer system in Laplace domain is developed and inverted numerically to the time-domain solution using the modified Crump (1976) algorithm. The results show that the drawdown distribution is significantly influenced by the properties and thickness of the skin zone and aquitard. The sensitivity analyses of parameters of the aquifer and aquitard are performed to illustrate their effects on drawdowns in a two-zone leaky confined aquifer system. For the negative-skin case, the drawdown is very sensitive to the relative change in the formation transmissivity. For the positive-skin case, the drawdown is also sensitive to the relative changes in the skin thickness, and both the skin and formation transmissivities over the entire pumping period and the well radius and formation storage coefficient at early pumping time. Copyright (C) 2009 John Wiley & Sons, Ltd.
Semi-analytical solution for a slug test in partially penetrating wells including the effect of finite-thickness skin
(2008-08-30)
Yeh, Hund-Der
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Chen, Yen-Ju
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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
This paper presents a new semi-analytical solution for a slug test in a well partially penetrating a confined aquifer, accounting for the skin effect. This solution is developed based on the solution for a constant-flux pumping test and a formula given by Peres and co-workers in 1989. The Solution agrees with that of Cooper and co-workers and the KGS model when the well is fully penetrating. The present Solution can be applied to simulate the temporal and spatial head distributions in both the skin and formation zones. It can also be used to demonstrate the influences of skin type or skin thickness on the well water level and to estimate the hydraulic parameters of the skin and formation zones using a least-squares approach. The results of this study indicate that the determination of hydraulic conductivity using a conventional slug-test data analysis that neglects the presence of a skin zone will give an incorrect result if the aquifer has a skin zone. Copyright (C) 2008 John Wiley &, Sons. Ltd.
Semi-analytical solution of groundwater flow in a leaky aquifer system subject to bending effect
(2013-04-12)
Yu, Chia-Chi
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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
The bending of aquitard like a plate due to aquifer pumping and compression is often encountered in many practical problems of subsurface flow. This reaction will have large influence on the release of the volume of water from the aquifer, which is essential for the planning and management of groundwater resources in aquifers. However, the groundwater flow induced by pumping in a leaky aquifer system is often assumed that the total stress of aquifer maintains constant all the time and the mechanical behavior of the aquitard formation is negligible. Therefore, this paper devotes to the investigation of the effect of aquitard bending on the drawdown distribution in a leaky aquifer system, which is obviously of interest in groundwater hydrology. Based on the work of Wang et al. (2004) this study develops a mathematical model for investigating the impacts of aquitard bending and leakage rate on the drawdown of the confined aquifer due to a constant-rate pumping in the leaky aquifer system. This model contains three equations; two flow equations delineate the transient drawdown distributions in the aquitard and the confined aquifer, while the other describes the vertical displacement in response to the aquitard bending. For the case of no aquitard bending, this new solution can reduce to the Hantush Laplace-domain solution (Hantush, 1960). On the other hand, this solution without the leakage effect can reduce to the time domain solution of Wang et al. (2004). The results show that the aquifer drawdown is influenced by the bending effect at early time and by the leakage effect at late time. The results of sensitivity analysis indicate that the aquifer compaction is sensitive only at early time, causing less amount of water released from the pumped aquifer than that predicted by the traditional groundwater theory. The dimensionless drawdown is rather sensitive to aquitard's hydraulic conductivity at late time. Additionally, both the hydraulic conductivity and thickness of the aquifer are the most sensitive parameters in influencing the predicted dimensionless drawdown. (C) 2013 Elsevier B.V. All rights reserved.