approximate analysis of three-dimensional groundwater flow toward a radial collector well in a finite-extent unconfined aquifer
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ID: 233236
2016
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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.
| Reference Key |
huang2016hydrologyapproximate
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|---|---|
| Authors | ;C.-S. Huang;J.-J. Chen;H.-D. Yeh |
| Journal | materials research bulletin |
| Year | 2016 |
| DOI |
10.5194/hess-20-55-2016
|
| URL | |
| Keywords |
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