Finite Layer Method for Flow in Layered Radial Two‐Zone Aquifer Systems

Wang, Xudong; Xu, Jin; Cai, Zhiyong

doi:10.1111/j.1745-6584.2011.00849.x

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…Chen (1984) derived an analytical solution for drawdown in a circular aquifer with the Dirichlet boundary condition of zero drawdown and provided a quantitative criterion describing the beginning time of the boundary effect on the drawdown. Yang et al (2006) developed an analytical solution describing aquifer drawdown due to a partially penetrating well with a finite radius. The effect of partial penetration on temporal drawdown distributions was discussed.…”

Section: Introductionmentioning

confidence: 99%

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

Huang¹,

Yang²,

Yeh³

2015

Preprint

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Abstract. 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 (CFP) in a two-zone confined aquifer involve laborious calculation. This study develops a new approximate solution for the problem based on a mathematical model including two steady-state flow equations with different hydraulic parameters for the skin and formation zones. 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 boundary 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 component due to a partially penetrating well is also provided. Conventional models considering radial flow without the vertical component for the CFP have good accuracy if satisfying the criterion.

show abstract

Section: Introductionmentioning

confidence: 99%

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

Huang¹,

Yang²,

Yeh³

2015

Preprint

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Finite Layer Formulations for Land Subsidence due to Groundwater Withdrawal

Zhou

Wang

2017

Int. J. Geomech.

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Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

Huang

Yang

Yeh

2015

Hydrol. Earth Syst. Sci.

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Abstract. 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.

show abstract

Finite Layer Method for Flow in Layered Radial Two‐Zone Aquifer Systems

Cited by 3 publications

References 16 publications

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

Finite Layer Formulations for Land Subsidence due to Groundwater Withdrawal

Technical Note: Approximate solution of transient drawdown for constant-flux pumping at a partially penetrating well in a radial two-zone confined aquifer

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