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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2018-482
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2018-482
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 01 Nov 2018

Research article | 01 Nov 2018

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This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

A General Analytical Model for Head Response to Oscillatory Pumping in Unconfined Aquifers: Consider the Effects of Delayed Gravity Drainage and Initial Condition

Ching-Sheng Huang1, Ya-Hsin Tsai2, Hund-Der Yeh2, and Tao Yang1 Ching-Sheng Huang et al.
  • 1State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Global Change and Water Cycle, Hohai University, Nanjing 210098, China
  • 2Institute of Environmental Engineering, National Chiao Tung University, Hsinchu 300, Taiwan

Abstract. Oscillatory pumping test (OPT) is an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters without net water extraction. There is a large number of analytical models presented for the analysis of OPT. The combined effects of delayed gravity drainage (DGD) and 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 OPT in an unconfined aquifer. The model contains a groundwater flow equation with the initial condition of static water table, Neumann boundary condition specified at the rim of a finite-radius well, and a free surface equation describing water table motion with the DGD effect. The solution of the model is derived by the Laplace transform, finite integral transform, and Weber transform. Sensitivity analysis is carried out for exploring head response to the change in each of hydraulic parameters. Results suggest the DGD reduces to instantaneous gravity drainage in predicting transient head fluctuation when 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. A pseudo-steady state model without initial condition causes a certain 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 to head fluctuation data observed at the Savannah River site.

Ching-Sheng Huang et al.
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This study develops a new model describing head fluctuation induced by oscillatory pumping test (OPT) in unconfined aquifer with the effects of delayed gravity drainage (DGD) and initial condition regarding the hydraulic head prior to OPT. The DGD reduces to instantaneous gravity drainage when a dimensionless parameter exceeds 500. A pseudo-steady state model excluding initial condition causes a time shift from the actual transient model in predicting simple harmonic motion of head fluctuation.
This study develops a new model describing head fluctuation induced by oscillatory pumping test...
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