Analytical solutions for periodic well recharge in rectangular aquifers with third-kind boundary conditions

Latinopoulos, P.

doi:10.1016/0022-1694(85)90213-6

Cited by 21 publications

(17 citation statements)

References 8 publications

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“…(9). The Shanks method developed by Shanks [114] is a nonlinear sequence-to-sequence transformation.…”

Section: Crump Methodsmentioning

confidence: 99%

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Recent advances in modeling of well hydraulics

Yeh¹,

Chang²

2013

Advances in Water Resources

121

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“…(9). The Shanks method developed by Shanks [114] is a nonlinear sequence-to-sequence transformation.…”

Section: Crump Methodsmentioning

confidence: 99%

“…Several studies provided analytical solutions for groundwater flow problems in aquifers whose plan views are rectangular [7][8][9], wedge-shaped [10][11][12][13][14][15] and triangular [16], and in aquifers whose cross sectional views are step-like [17,18].…”

Section: Aquifer Of Finite or Infinite Extent In Horizontal Directionmentioning

confidence: 99%

Recent advances in modeling of well hydraulics

Yeh¹,

Chang²

2013

Advances in Water Resources

121

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“….∞, α m = m π/w x , K y 0 is defined in Eq. (A2) with y = y 0 , and β n represents eigenvalues equaling the roots of the following equation as (Latinopoulos, 1985) tan…”

Section: Head Solution For Point Sinkmentioning

confidence: 99%

“…The formula for the inverse finite integral transform can be written as (Latinopoulos, 1985, Eq. 14)…”

mentioning

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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Groundwater flow to a pumping well in a sloping fault zone unconfined aquifer

2014

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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 twodimensional 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.

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Analytical solutions for periodic well recharge in rectangular aquifers with third-kind boundary conditions

Cited by 21 publications

References 8 publications

Recent advances in modeling of well hydraulics

Recent advances in modeling of well hydraulics

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

Groundwater flow to a pumping well in a sloping fault zone unconfined aquifer

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