An analytical solution for a radial collector well near a stream with a low-permeability streambed

Huang, Ching‐Sheng; Tsou, Pei Rong; Yeh, Hund‐Der

doi:10.1016/j.jhydrol.2012.04.028

Cited by 19 publications

(15 citation statements)

References 17 publications

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“…Under these three conditions, the present head and SDR predictions are close to those in Huang et al (2011), the head solution of which agrees well with measured data from a field experiment executed by Mohamed and Rushton (2006). On the other hand, before the time when the boundary effect occurs at x = 0, x = w x , and y = w y , the present head and SDR solutions for a RCW give close predictions to those in Huang et al (2012), the head and SDR solutions of which agree well with observation data taken from two field experiments carried out by Schafer (2006) and Jasperse (2009) …”

Section: Unconfined Aquifer Of Semi-infinite Extentsupporting

confidence: 82%

“…Huang et al (2011) developed an analytical SDR solution for a horizontal well in unconfined aquifers near a stream regarded as a constant-head boundary. Huang et al (2012) provided an analytical solution for SDR induced by a RCW in unconfined aquifers adjacent to a stream with a low-permeability streambed under the Robin condition. The influence of the configuration of the laterals on temporal SDR and spatial drawdown distributions was analyzed.…”

Section: C-s Huang Et Al: Approximate Analysis Of Three-dimensionamentioning

confidence: 99%

“…At present, existing analytical solutions associated with flow toward a RCW in unconfined aquifers have involved laborious calculation (Huang et al, 2012) and predicted approximate results (Hantush and Papadopoulos, 1962). The Huang et al (2012) solution involves numerical integration of a triple integral in predicting the hydraulic head and a quintuple integral in predicting SDR.…”

Section: C-s Huang Et Al: Approximate Analysis Of Three-dimensionamentioning

confidence: 99%

“…The Huang et al (2012) solution involves numerical integration of a triple integral in predicting the hydraulic head and a quintuple integral in predicting SDR. The integrand is expressed in terms of an infinite series expanded by roots of nonlinear equations.…”

Section: C-s Huang Et Al: Approximate Analysis Of Three-dimensionamentioning

confidence: 99%

“…In addition, RCWs can extract water from an aquifer underlying obstacles such as buildings, but vertical wells cannot. Recently, Huang et al (2012) reviewed semi-analytical and analytical solutions associated with RCWs. Since then, Yeh and Chang (2013) provided a valuable overview of articles associated with RCWs.…”

Section: Introductionmentioning

confidence: 99%

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Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

Huang

Chen

Yeh

2016

Hydrol. Earth Syst. Sci.

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Abstract. 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.

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Section: Unconfined Aquifer Of Semi-infinite Extentsupporting

confidence: 82%

Section: C-s Huang Et Al: Approximate Analysis Of Three-dimensionamentioning

confidence: 99%

Section: C-s Huang Et Al: Approximate Analysis Of Three-dimensionamentioning

confidence: 99%

Section: C-s Huang Et Al: Approximate Analysis Of Three-dimensionamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

Huang

Chen

Yeh

2016

Hydrol. Earth Syst. Sci.

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Base flow recession from unsaturated‐saturated porous media considering lateral unsaturated discharge and aquifer compressibility

Liang

Zhang

et al. 2017

Water Resources Research

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Unsaturated flow is an important process in base flow recessions and its effect is rarely investigated. A mathematical model for a coupled unsaturated‐saturated flow in a horizontally unconfined aquifer with time‐dependent infiltrations is presented. The effects of the lateral discharge of the unsaturated zone and aquifer compressibility are specifically taken into consideration. Semianalytical solutions for hydraulic heads and discharges are derived using Laplace transform and Cosine transform. The solutions are compared with solutions of the linearized Boussinesq equation (LB solution) and the linearized Laplace equation (LL solution), respectively. A larger dimensionless constitutive exponent κD (a smaller retention capacity) of the unsaturated zone leads to a smaller discharge during the infiltration period and a larger discharge after the infiltration. The lateral discharge of the unsaturated zone is significant when κD≤1, and becomes negligible when κD≥100. The compressibility of the aquifer has a nonnegligible impact on the discharge at early times. For late times, the power index b of the recession curve −dQ/dt∼ aQb, is 1 and independent of κD, where Q is the base flow and a is a constant lumped aquifer parameter. For early times, b is approximately equal to 3 but it approaches infinity when t→0. The present solution is applied to synthetic and field cases. The present solution matched the synthetic data better than both the LL and LB solutions, with a minimum relative error of 16% for estimate of hydraulic conductivity. The present solution was applied to the observed streamflow discharge in Iowa, and the estimated values of the aquifer parameters were reasonable.

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Spatiotemporal Responses of Groundwater Flow and Aquifer‐River Exchanges to Flood Events

Liang

Zhan

Schilling

2018

Water Resources Research

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Rapidly rising river stages induced by flood events lead to considerable river water infiltration into aquifers and carry surface‐borne solutes into hyporheic zones which are widely recognized as an important place for the biogeochemical activity. Existing studies for surface‐groundwater exchanges induced by flood events usually limit to a river‐aquifer cross section that is perpendicular to river channels, and neglect groundwater flow in parallel with river channels. In this study, surface‐groundwater exchanges to a flood event are investigated with specific considerations of unconfined flow in direction that is in parallel with river channels. The groundwater flow is described by a two‐dimensional Boussinesq equation and the flood event is described by a diffusive‐type flood wave. Analytical solutions are derived and tested using the numerical solution. The results indicate that river water infiltrates into aquifers quickly during flood events, and mostly returns to the river within a short period of time after the flood event. However, the rest river water will stay in aquifers for a long period of time. The residual river water not only flows back to rivers but also flows to downstream aquifers. The one‐dimensional model of neglecting flow in the direction parallel with river channels will overestimate heads and discharge in upstream aquifers. The return flow induced by the flood event has a power law form with time and has a significant impact on the base flow recession at early times. The solution can match the observed hydraulic heads in riparian zone wells of Iowa during flood events.

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An analytical solution for a radial collector well near a stream with a low-permeability streambed

Cited by 19 publications

References 17 publications

Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

Approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer

Base flow recession from unsaturated‐saturated porous media considering lateral unsaturated discharge and aquifer compressibility

Spatiotemporal Responses of Groundwater Flow and Aquifer‐River Exchanges to Flood Events

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