Browsing by Author "Yeh, H. -D."

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Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer
(2016-01-01)
Huang, C. -S.
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Chen, J. -J.
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Yeh, H. -D.
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環境工程研究所
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Institute of Environmental Engineering
This study develops a three-dimensional (3-D) mathematical model for describing transient hydraulic head distributions due to pumping at a radial collector well (RCW) in a rectangular confined or unconfined aquifer bounded by two parallel streams and no-flow boundaries. The streams with low-permeability streambeds fully penetrate the aquifer. The governing equation with a point-sink term is employed. A first-order free surface equation delineating the water table decline induced by the well is considered. Robin boundary conditions are adopted to describe fluxes across the streambeds. The head solution for the point sink is derived by applying the methods of finite integral transform and Laplace transform. The head solution for a RCW is obtained by integrating the point-sink solution along the laterals of the RCW and then dividing the integration result by the sum of lateral lengths. On the basis of Darcy's law and head distributions along the streams, the solution for the stream depletion rate (SDR) can also be developed. With the aid of the head and SDR solutions, the sensitivity analysis can then be performed to explore the response of the hydraulic head to the change in a specific parameter such as the horizontal and vertical hydraulic conductivities, streambed permeability, specific storage, specific yield, lateral length, and well depth. Spatial head distributions subject to the anisotropy of aquifer hydraulic conductivities are analyzed. A quantitative criterion is provided to identify whether groundwater flow at a specific region is 3-D or 2-D without the vertical component. In addition, another criterion is also given to allow for the neglect of vertical flow effect on SDR. Conventional 2-D flow models can be used to provide accurate head and SDR predictions if satisfying these two criteria.
Estimations of tidal characteristics and aquifer parameters via tide-induced head changes in coastal observation wells
(2011)
Chen, Y. -J.
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Chen, G. -Y.
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Yeh, H. -D.
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Jeng, D. -S.
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環境工程研究所
The groundwater fluctuations due to tidal variations at an observation well in a coastal aquifer can be used to determine the tidal characteristics and aquifer parameters without conducting an aquifer test. In this study, a method, comprised of Jeng et al.'s solution (2005) and simulated annealing (SA) algorithm, is developed to determine the coastal aquifer parameters (hydraulic diffusivity, beach slope, and aquifer thickness) as well as the tidal characteristics (bichromatic-tide amplitudes, bichromatic-tide wave frequencies, and tidal phase lag) from the analysis of the tide-induced well-water-level (WWL) data. The synthetic WWL data generated from Jeng et al.'s solution (2005) with assumed parameter values and field data obtained from Barrenjoey beach, Australia, are analyzed. The estimated parameter values obtained from analyzing synthetic WWL data by the present method show good agreements with the previously assumed parameter values. The parameter estimation procedure may however fail in the case of a large shallow water parameter which in fact violates the constraint on the use of Jeng et al.'s solution (2005). In the analysis of field WWL data, the results indicate that the aquifer parameters estimated from the present method with single or multiple well data are significantly different from those given in Nielsen (1990). Inspecting the observed WWL data and the WWL data predicted from Jeng et al.'s solution (2005) reveals that the present method may provide better estimations for the aquifer parameters than those given in Nielsen (1990).
Groundwater fluctuations in heterogeneous coastal leaky aquifer systems
(2010)
Chuang, M. -H.
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Huang, C. -S.
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Li, G. -H.
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Yeh, H. -D.
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環境工程研究所
In the past, the coastal leaky aquifer system, including two aquifers and an aquitard between them, was commonly assumed to be homogeneous and of infinite extent in the horizontal direction. The leaky aquifer system may however be heterogeneous and of finite extent due to variations in depositional and post depositional processes. In this paper, the leaky aquifer system is divided into several horizontal regions for the heterogeneous aquitard and underlying aquifer. A one-dimensional analytical model is developed for describing the head fluctuation in such a heterogeneous leaky aquifer system. The hydraulic head of the upper unconfined aquifer is assumed constant. It is found that both the length and location of the discontinuous aquitards presented in the coastal area have significant effects on the amplitude and phase shift of the head fluctuation in the lower aquifer. In addition, the influence of the formation heterogeneity on the spatial head distribution is also investigated.
Investigation of solute transport in nonstationary unsaturated flow fields
(2012)
Chang, C. -M.
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Yeh, H. -D.
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環境工程研究所
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Institute of Environmental Engineering
Most theoretical work on analyzing plume spreading at the field scale in a partially saturated heterogeneous formation assumes weak stationarity of velocity field. While this assumption is not applicable to the case of a bounded flow domain, the nonstationarity in fluctuations of unsaturated velocity fields is induced through the presence of the boundary conditions in the flow domain. In this work, we attempt to quantify the large-time macrodispersion in nonstationary unsaturated velocity fields caused by the presence of a fixed head boundary condition. Application of the perturbation-based nonstationary spectral approach leads to an analytical expression for the macrodispersion describing the field-scale dispersive solute flux in terms of the statistical moments of two formation parameters: the Gardener's parameter (alpha) and the saturated hydraulic conductivity (K-s). The results predicted from the expression indicate that the enhanced unsaturated plume spreading can arise from a larger correlation scale of ln K-s or ln alpha fields. In addition, the alpha-parameter takes the role in reducing the field-scale plume spreading.
Scale dependency of fractional flow dimension in a fractured formation
(2011)
Chang, Y. -C.
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Yeh, H. -D.
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Liang, K. -F.
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Kuo, M. -C. T.
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環境工程研究所
The flow dimensions of fractured media were usually predefined before the determination of the hydraulic parameters from the analysis of field data in the past. However, it would be improper to make assumption about the flow geometry of fractured media before site characterization because the hydraulic structures and flow paths are complex in the fractured media. An appropriate way to investigate the hydrodynamic behavior of a fracture system is to determine the flow dimension and aquifer parameters simultaneously. The objective of this study is to analyze a set of field data obtained from four observation wells during an 11-day hydraulic test at Chingshui geothermal field (CGF) in Taiwan in determining the hydrogeologic properties of the fractured formation. Based on the generalized radial flow (GRF) model and the optimization scheme, simulated annealing, an approach is therefore developed for the data analyses. The GRF model allows the flow dimension to be integer or fractional. We found that the fractional flow dimension of CGF increases near linearly with the distance between the pumping well and observation well, i.e. the flow dimension of CGF exhibits scale-dependent phenomenon. This study provides insights into interpretation of fracture flow at CGF and gives a reference for characterizing the hydrogeologic properties of fractured media.
Spectral approach to seawater intrusion in heterogeneous coastal aquifers
(2010)
Chang, C. -M.
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Yeh, H. -D.
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環境工程研究所
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Institute of Environmental Engineering
This work presents a two-dimensional horizontal plane model of seawater intrusion into a heterogeneous coastal unconfined aquifer under the spatially random recharge condition from a stochastic point of view. The stochastic response of the coastal unconfined aquifer is attributed to uncertainties related to the heterogeneity of aquifer properties and spatial variability of the recharge. Based on the sharp-interface assumption, analytical expressions for the variances of the seawater-freshwater interface elevation and specific discharge in the longitudinal and transverse directions are developed using the perturbation approximation and spectral Fourier-Stieltjes nonstationary representations. We focus on the study of the impact of the heterogeneity of aquifer properties and recharge on these results.
Stochastic analysis of field-scale heat advection in heterogeneous aquifers
(2012)
Chang, C. -M.
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Yeh, H. -D.
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環境工程研究所
;
Institute of Environmental Engineering
Owing to the analogy between the solute and heat transport processes, it can be expected that the rate of growth of the spatial second moments of the heat flux in a heterogeneous aquifer over relatively large space scales is greater than that predicted by applying the classical heat transport model. The motivation of stochastic analysis of heat transport at the field scale is therefore to quantify the enhanced growth of the field-scale second moments caused by the spatially varying specific discharge field. Within the framework of stochastic theory, an effective advection-dispersion equation containing effective parameters (namely, the macrodispersion coefficients) is developed to model the mean temperature field. The rate of growth of the field-scale spatial second moments of the mean temperature field in the principal coordinate directions is described by the macrodispersion coefficient. The variance of the temperature field is also developed to characterize the reliability to be anticipated in applying the mean heat transport model. It is found that the heterogeneity of the medium and the correlation length of the log hydraulic conductivity are important in enhancing the field-scale heat advection, while the effective thermal conductivity plays the role in reducing the field-scale heat advection.
Stream depletion rate with horizontal or slanted wells in confined aquifers near a stream
(2010)
Tsou, P. -R.
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Feng, Z. -Y.
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Yeh, H. -D.
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Huang, C. -S.
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環境工程研究所
Pumping in a vertical well may produce a large drawdown cone near the well. In this paper, the solution is first developed for describing the groundwater flow associated with a point source in a confined aquifer near a stream. Based on the principle of superposition, analytical solutions for horizontal and slanted wells are then developed by integrating the point source solution along the well axis. The solutions can be simplified to quasi-steady solutions by neglecting the exponential terms to describe the late-time drawdown, which can provide useful information in designing horizontal well location and length. The direction of the well axis can be determined from the best SDR subject to the drawdown constraint. It is found that hydraulic conductivity in the direction perpendicular to the stream plays a crucial role in influencing the time required for reaching quasi-steady SDR. In addition, the effects of the well length as well as the distance between the well and stream on the SDR are also examined.
Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer
(2015-01-01)
Huang, C. -S.
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Yang, S. -Y.
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Yeh, H. -D.
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環境工程研究所
;
Institute of Environmental Engineering
An aquifer consisting of a skin zone and a formation zone is considered as a two-zone aquifer. Existing solutions for the problem of constant-flux pumping in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model describing steady-state radial and vertical flows in a two-zone aquifer. Hydraulic parameters in these two zones can be different but are assumed homogeneous in each zone. A partially penetrating well may be treated as the Neumann condition with a known flux along the screened part and zero flux along the unscreened part. The aquifer domain is finite with an outer circle boundary treated as the Dirichlet condition. The steady-state drawdown solution of the model is derived by the finite Fourier cosine transform. Then, an approximate transient solution is developed by replacing the radius of the aquifer domain in the steady-state solution with an analytical expression for a dimensionless time-dependent radius of influence. The approximate solution is capable of predicting good temporal drawdown distributions over the whole pumping period except at the early stage. A quantitative criterion for the validity of neglecting the vertical flow due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the constant-flux pumping have good accuracy if satisfying the criterion.
Tidal propagation in an oceanic island with sloping beaches
(2010)
Chang, Y. -C.
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Jeng, D-S
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Yeh, H. -D.
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環境工程研究所
;
Institute of Environmental Engineering
In this study, a new analytical solution for describing the tide-induced groundwater fluctuations in oceanic islands with finite length and different slopes of the beaches is developed. Unlike previous solutions, the present solution is not only applicable for a semi-infinite coastal aquifer, but also for an oceanic island with finite length and different sloping beaches. The solution can be used to investigate the effect of higher-order components and beach slopes on the water table fluctuations. The results demonstrate the effect of higher-order components increases with the shallow water parameter or amplitude parameter and the water table level increases as beach slopes decrease.
Transient drawdown solution for a constant pumping test in finite two-zone confined aquifers
(2012)
Wang, C. -T.
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Yeh, H. -D.
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Tsai, C. -S.
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環境工程研究所
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Institute of Environmental Engineering
The drawdown solution has been widely used to analyze pumping test data for the determination of aquifer parameters when coupled with an optimization scheme. The solution can also be used to predict the drawdown due to pumping and design the dewatering system. The drawdown solution for flow toward a finite-radius well with a skin zone in a confined aquifer of infinite extent in radial direction had been developed before. To our best knowledge, the drawdown solution in confined aquifers of finite extent with a skin zone so far has never before been presented in the groundwater literature. This article presents a mathematical model for describing the drawdown distribution due to a constant-flux pumping from a finite-radius well with a skin zone in confined aquifers of finite extent. The analytical solution of the model is developed by applying the methods of Laplace transforms, Bromwich contour integral, and residue theorem. This solution can be used to investigate the effects of finite boundary and conductivity ratio on the drawdown distribution. In addition, the inverse relationship between Laplace- and time-domain variables is used to develop the large time solution which can reduce to the Thiem solution if there is no skin zone.
Variability of flow discharge in lateral inflow-dominated stream channels
(2015-01-01)
Chang, C. -M.
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Yeh, H. -D.
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環境工程研究所
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Institute of Environmental Engineering
The influence of the temporal changes in lateral inflow rate on the discharge variability in stream channels is explored through the analysis of the diffusion wave equation (i.e. the linearized Saint-Venant equation). To account for variability and uncertainty, the lateral inflow rate is regarded as a temporal random function. On the basis of the spectral representation theory, analytical expressions for the covariance function and evolutionary power spectral density of the random discharge perturbation process are derived to quantify variability in stream flow discharge induced by the temporal changes in lateral inflow rate. The treatment of the discharge variance (square root of the variance) gives us a quantitative estimate of uncertainty in predictions from the deterministic model. It is found that the discharge variability of stream flow is very large in the downstream reach, indicating large uncertainty anticipated from the use of the deterministic model. A larger temporal correlation scale of inflow rate fluctuations, representing more temporal consistency of fluctuations in inflow rate around the mean, introduces a higher variability in stream flow discharge.