A new closed-form solution for a radial two-layer drawdown equation for groundwater under constant-flux pumping in a finite-radius well

Yeh, Hund‐Der; Yang, Shaw Yang; Peng, Huan Yi

doi:10.1016/s0309-1708(03)00046-0

Cited by 65 publications

(70 citation statements)

References 19 publications

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“…Thus, a branch cut along the negative real axis of the contour should be chosen and thus a closed contour is produced. Such a procedure finally results in a complicated solution presented in Yeh et al (2003). On the other hand, the integration of the contour integral arisen from the Laplace domain solution in our model has a simple pole at the origin and finite number of poles at other locations.…”

Section: Introductionmentioning

confidence: 90%

“…In addition, they also gave a largetime solution based on the inverse relationship between the Laplace variable and time variable. Yeh et al (2003) presented an analytical drawdown solution for the pumping test in an infinite confined aquifer by taking into account the effects of the well storage and the finite-thickness skin. They mentioned that the effect of skin zone is negligible in short and large periods of pumping time.…”

Section: Introductionmentioning

confidence: 99%

“…The existing drawdown solutions for radial two-zone confined aquifers of infinite extent under constant-flux pumping were all developed in Laplace domain except the one given by Yeh et al (2003) which was a time domain solution. Yeh et al's (2003) solution is in terms of an improper integral integrating from zero to infinity and its integrand comprises a singularity at the origin.…”

Section: Introductionmentioning

confidence: 99%

“…Yeh et al's (2003) solution is in terms of an improper integral integrating from zero to infinity and its integrand comprises a singularity at the origin. In addition, the integrand is an oscillatory function with many product terms of the Bessel functions of the first and second kinds of zero and first orders.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Transient drawdown solution for a constant pumping test in finite two-zone confined aquifers

Wang

Hund-Der

Tsai

2012

Hydrol. Earth Syst. Sci.

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Abstract. The drawdown solution has been widely used toanalyze 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 constantflux 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 Laplaceand time-domain variables is used to develop the large time solution which can reduce to the Thiem solution if there is no skin zone.

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Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Transient drawdown solution for a constant pumping test in finite two-zone confined aquifers

Wang

Hund-Der

Tsai

2012

Hydrol. Earth Syst. Sci.

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“…Bakker and Hemker (2002) [4] considered the vertical flow in the layer interfaces of the multi-aquifers. Yeh et al (2003) [40] developed two layered aquifer model with skin effects. Based on the first order perturbation technique, problem of steady groundwater flow toward a pumping well in multi-aquifer system with anisotropy of the horizontal conductivity was solved by Meesters et al (2004) [21].…”

mentioning

confidence: 99%

Multi-Aquifer Parameterization with well loss in Vertical Flows

Majumdar¹

2015

JWRHE

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Abstract-Usually aquifer parameters are estimated through pumping/recharge test. Precondition for using those parameters in the numerical model is to ensure the synonymy of the hydro-geological condition between the field setup and the conceptual model. In many cases, it is erroneous. While numerical modelling in multi-aquifer considered vertical flow in general, it was reflected in the pumping solutions only to the extent of treating a leakage through the aquitard. As such well characterisation in multi aquifers separated by an aquiclude is illusive in the literature. As a result of which, interconnected aquifers were considered as isolated ones in the pumping/recharge tests. Therefore, estimated parameters were for a single aquifer, not for an aquifer connected to multi aquifers. In the present paper, the solution for a multi-aquifer system comprising of two interconnected aquifers separated by an aquiclude is presented. Vertical flow in the well bore with well loss due to friction has been considered. It is concluded that multi-aquifer parameters computed using present solution technique are more scientific and economical.

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A Semianalytical Model for Pumping Tests in Finite Heterogeneous Confined Aquifers With Arbitrarily Shaped Boundary

Wang

Dai

Xue

2018

Water Resources Research

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This study presents a Laplace‐transform‐based boundary element method to model the groundwater flow in a heterogeneous confined finite aquifer with arbitrarily shaped boundaries. The boundary condition can be Dirichlet, Neumann or Robin‐type. The derived solution is analytical since it is obtained through the Green's function method within the domain. However, the numerical approximation is required on the boundaries, which essentially renders it a semi‐analytical solution. The proposed method can provide a general framework to derive solutions for zoned heterogeneous confined aquifers with arbitrarily shaped boundary. The requirement of the boundary element method presented here is that the Green function must exist for a specific PDE equation. In this study, the linear equations for the two‐zone and three‐zone confined aquifers with arbitrarily shaped boundary is established in Laplace space, and the solution can be obtained by using any linear solver. Stehfest inversion algorithm can be used to transform it back into time domain to obtain the transient solution. The presented solution is validated in the two‐zone cases by reducing the arbitrarily shaped boundaries to circular ones and comparing it with the solution in Lin et al. (2016, https://doi.org/10.1016/j.jhydrol.2016.07.028). The effect of boundary shape and well location on dimensionless drawdown in two‐zone aquifers is investigated. Finally the drawdown distribution in three‐zone aquifers with arbitrarily shaped boundary for constant‐rate tests (CRT) and flow rate distribution for constant‐head tests (CHT) are analyzed.

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A new closed-form solution for a radial two-layer drawdown equation for groundwater under constant-flux pumping in a finite-radius well

Cited by 65 publications

References 19 publications

Transient drawdown solution for a constant pumping test in finite two-zone confined aquifers

Transient drawdown solution for a constant pumping test in finite two-zone confined aquifers

Multi-Aquifer Parameterization with well loss in Vertical Flows

A Semianalytical Model for Pumping Tests in Finite Heterogeneous Confined Aquifers With Arbitrarily Shaped Boundary

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