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

Lin, Ying‐Fan; Yeh, Hund‐Der

doi:10.1002/2017wr021115

Cited by 12 publications

(18 citation statements)

References 40 publications

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“…In short, a greater τ sD would result in a larger s D while a greater τ qD would yield a smaller one. These findings are similar to the work of Lin and Yeh (), but their article deals with the flow in leaky aquifers.…”

Section: Resultssupporting

confidence: 87%

“…This study proposes a new analytical model for describing the spatiotemporal drawdown distribution induced by a CRP test in an unconfined aquifer considering the lagging effect proposed by Lin and Yeh () on the water table decline. Two lag times (i.e., τ q and τ s ) are introduced to Darcy's law for developing a new linearized free surface equation describing the water table decline.…”

Section: Discussionmentioning

confidence: 99%

“…The drainage behavior is affected by different levels of the pore sizes in the unsaturated zone. Recently, Lin and Yeh () added two time lag parameters in Darcy's law to reflect the lagging effects on flow due to CRP tests in leaky aquifers. Their model is analogous to the dual‐phase‐lag model developed by Tzou () for heat conduction problems.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Unconfined Flow Induced by Constant Rate Pumping Based on the Lagging Theory

Lin

Huang

Yeh

2019

Water Resources Research

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This study proposes a new mathematical model for describing the drawdown distribution due to a constant rate pumping (CRP) in an unconfined aquifer considering the lagging theory. We introduce two lag times in Darcy's law and in turn in a free surface equation to reflect the effects of the capillary fringe and the capillary suction on the water table motion. The present free surface equation can reduce to those used in previous studies. The Laplace and Weber transform methods are used to derive the semianalytical solution to the model including the effect of wellbore storage. The algorithm of numerical Laplace inversion is applied to obtain the transient solution of the model. We find that the delay index, commonly used in the literature, is equivalent to the lag time associated with the effect of the capillary suction. The sensitivity analysis is performed to assess the drawdown behavior in response to the change in each aquifer parameter. The drawdown distributions predicted by the present solution agree fairly well to the field data taken from CRP tests at Cape Cod, Massachusetts; the Canadian Forces Base Borden, Ontario; and Saint Pardon de Conques, Gironde (France). The lag times determined by both CRP tests seem to decrease linearly with increasing distance on the logarithmic scale from the pumping well. The consideration of two lag times considerably improves the accuracy in estimated specific yields.

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Section: Resultssupporting

confidence: 87%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of Unconfined Flow Induced by Constant Rate Pumping Based on the Lagging Theory

Lin

Huang

Yeh

2019

Water Resources Research

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“…Sensitivity analysis evaluates hydraulic head variation in response to the change in each of K r , K z , S s , S y , ω, and ε. The normalized sensitivity coefficient can be defined as (Liou and Yeh, 1997) Solutions 4 and 5 a Solution 6 a,b…”

Section: Sensitivity Analysismentioning

confidence: 99%

A general analytical model for head response to oscillatory pumping in unconfined aquifers: effects of delayed gravity drainage and initial condition

Huang

Tsai

Yeh

et al. 2019

Hydrol. Earth Syst. Sci.

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Abstract. Oscillatory pumping tests (OPTs) provide an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters when OPT data are analyzed based on an associated analytical model coupled with an optimization approach. There are a large number of analytical models presented for the analysis of the OPT. The combined effects of delayed gravity drainage (DGD) and the initial condition regarding the hydraulic head are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by the OPT in an unconfined aquifer. The model contains a groundwater flow equation with the initial condition of a static water table, Neumann boundary condition specified at the rim of a partially screened well, and a free surface equation describing water table motion with the DGD effect. The solution is derived using the Laplace, finite-integral, and Weber transforms. Sensitivity analysis is carried out for exploring head response to the change in each hydraulic parameter. Results suggest that the DGD reduces to instantaneous gravity drainage in predicting transient head fluctuation when the dimensionless parameter a1=ϵSyb/Kz exceeds 500 with empirical constant ϵ, specific yield Sy, aquifer thickness b, and vertical hydraulic conductivity Kz. The water table can be regarded as a no-flow boundary when a1<10-2 and P<104 s, with P being the period of the oscillatory pumping rate. A pseudo-steady-state model without the initial condition causes a time-shift from the actual transient model in predicting simple harmonic motion of head fluctuation during a late pumping period. In addition, the present solution agrees well with head fluctuation data observed at the Savannah River site. Highlights. An analytical model of the hydraulic head due to oscillatory pumping in unconfined aquifers is presented. Head fluctuations affected by instantaneous and delayed gravity drainages are discussed. The effect of the initial condition on the phase of head fluctuation is analyzed. The present solution agrees well with head fluctuation data taken from field oscillatory pumping.

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Section: Sensitivity Analysismentioning

confidence: 99%

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Yeh¹

2018

Preprint

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

Cited by 12 publications

References 40 publications

Analysis of Unconfined Flow Induced by Constant Rate Pumping Based on the Lagging Theory

Analysis of Unconfined Flow Induced by Constant Rate Pumping Based on the Lagging Theory

A general analytical model for head response to oscillatory pumping in unconfined aquifers: effects of delayed gravity drainage and initial condition

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