A general analytical model for pumping tests in radial finite two-zone confined aquifers with Robin-type outer boundary

Lin, Ying‐Fan; Yang, Shaw Yang; Fen, Chiu‐Shia; Yeh, Hund‐Der

doi:10.1016/j.jhydrol.2016.07.028

Cited by 32 publications

(24 citation statements)

References 35 publications

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“…Four different ρ R values from 20 to infinity are selected to the conduct the comparison. As shown in Figure a, the dimensionless drawdown curves obtained by our solutions agree very well with these in Lin et al (), which validates the accuracy of the present solutions. Figure b shows dimensionless wellbore drawdown versus dimensionless time under the constant flow rate pumping in a finite confined aquifers with the Robin‐type outer boundary (e.g., the deposits of the oceanic island seashore is fine) for α 1 =0.05.…”

Section: Resultssupporting

confidence: 90%

“…Figure b shows dimensionless wellbore drawdown versus dimensionless time under the constant flow rate pumping in a finite confined aquifers with the Robin‐type outer boundary (e.g., the deposits of the oceanic island seashore is fine) for α 1 =0.05. With our method presented in this paper, the drawdown solutions are consistent with these of Lin et al () under various values of ρ R from 20 to infinity when the transmissivity ratio T 2 /T 1 is 10, which also evidences the accuracy of the present solutions. As will be discussed later, our solutions allow one to consider more complex cases where the arbitrarily shaped boundary, the non‐centric well location, and multiple zones are necessary to characterize the heterogeneous confined aquifers.…”

Section: Resultssupporting

confidence: 88%

“…Figure shows the validation results of our solution by comparing our solutions with Lin (). Figure a shows dimensionless wellbore drawdown versus dimensionless time under the condition of the constant flow rate pumping in a finite confined aquifers with no‐flow outer boundary (e.g., the closed reservoir).…”

Section: Resultsmentioning

confidence: 99%

“…However, in the case of permeable boundary with a weak recharge, the boundary needs to be described with third type of boundary, named Robin boundary condition. The outer condition at

{normalΓ}_{N_{α}}

could be specified as Robin type (Duffy, 1988; Lin et al, )

σ_{1} s_{N_{α}}^{}^{} + σ_{2} \frac{\partial s_{N_{α}}^{}^{}}{\partial n} = σ_{3} a t {normalΓ}_{^{N_{α}}}

where, σ 1 , σ 2 , σ 3 are coefficients. Robin boundary condition is a linear combination of Dirichlet and Neumann conditions.…”

Section: Methodsmentioning

confidence: 99%

“…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 (2016Lin et al ( , https://doi.org/10.1016Lin et al ( /j.jhydrol.2016. The effect of boundary shape and well location on dimensionless drawdown in two-zone aquifers is investigated.…”

mentioning

confidence: 99%

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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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Section: Resultssupporting

confidence: 90%

Section: Resultssupporting

confidence: 88%

Section: Resultsmentioning

confidence: 99%

“…However, in the case of permeable boundary with a weak recharge, the boundary needs to be described with third type of boundary, named Robin boundary condition. The outer condition at

{normalΓ}_{N_{α}}

could be specified as Robin type (Duffy, 1988; Lin et al, )

σ_{1} s_{N_{α}}^{}^{} + σ_{2} \frac{\partial s_{N_{α}}^{}^{}}{\partial n} = σ_{3} a t {normalΓ}_{^{N_{α}}}

where, σ 1 , σ 2 , σ 3 are coefficients. Robin boundary condition is a linear combination of Dirichlet and Neumann conditions.…”

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

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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A Lagging Model for Describing Drawdown Induced by a Constant‐Rate Pumping in a Leaky Confined Aquifer

Lin

Yeh

2017

Water Resources Research

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This study proposes a generalized Darcy's law with considering phase lags in both the water flux and drawdown gradient to develop a lagging flow model for describing drawdown induced by constant‐rate pumping (CRP) in a leaky confined aquifer. The present model has a mathematical formulation similar to the dual‐porosity model. The Laplace‐domain solution of the model with the effect of wellbore storage is derived by the Laplace transform method. The time‐domain solution for the case of neglecting the wellbore storage and well radius is developed by the use of Laplace transform and Weber transform. The results of sensitivity analysis based on the solution indicate that the drawdown is very sensitive to the change in each of the transmissivity and storativity. Also, a study for the lagging effect on the drawdown indicates that its influence is significant associated with the lag times. The present solution is also employed to analyze a data set taken from a CRP test conducted in a fractured aquifer in South Dakota, USA. The results show the prediction of this new solution with considering the phase lags has very good fit to the field data, especially at early pumping time. In addition, the phase lags seem to have a scale effect as indicated in the results. In other words, the lagging behavior is positively correlated with the observed distance in the Madison aquifer.

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Non‐Darcian flow toward an injection well fully penetrating a leaky confined aquifer with clogging‐induced permeability reduction

et al. 2022

Num Anal Meth Geomechanics

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Managed aquifer recharge (MAR) using aquifer injection wells is generally developed with the validity of Darcy's law and assumption of a constant hydraulic conductivity, hence ignoring the non-Darcian nature of groundwater flow and the spatiotemporal permeability reduction owing to well and aquifer clogging. In this study, an Izbash's law-based analytical model is proposed for constant-rate recharge (CRR) and constant-head recharge (CHR) with special consideration of well and aquifer clogging using a time-dependent hydraulic conductivity (K) function. By means of linearization approximations, variable substitutions and Hankel and Weber transforms, approximate analytical solutions for the model are derived. The early-time and late-time solutions and the steady-state solutions are also derived using the developed approximate solutions. A comparison with numerical solutions indicates that the approximate solutions are highly accurate except during the short period of initial recharge stage. Then, a semi-log graphic approach based on the developed solutions is tendered for estimating parameters associated with the clogging effect and non-Darcian aquifer property. The proposed model offers a straightforward way for the quantitative assessment of the non-Darcian flow dynamics in confined aquifers experiencing clogging and can be adopted for the estimation and prediction of clogging-related permeability reduction in MAR using aquifer injection wells.

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A general analytical model for pumping tests in radial finite two-zone confined aquifers with Robin-type outer boundary

Cited by 32 publications

References 35 publications

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

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

A Lagging Model for Describing Drawdown Induced by a Constant‐Rate Pumping in a Leaky Confined Aquifer

Non‐Darcian flow toward an injection well fully penetrating a leaky confined aquifer with clogging‐induced permeability reduction

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