Steady flow to a partially penetrating blind-wall well in a
confined aquifer
Saivash Behrooz-Koohenjani,
1
Nozar Samani
1
* and Mazda Kompani-Zare
2
1
Department of Earth Sciences, College of Sciences, Shiraz University, Shiraz 71454, Iran
2
Department of Desert Region Management, College of Agriculture, Shiraz University, Shiraz, Iran
Abstract:
Wells in aquifers of loose collapsible sediment are cased so that they have a blind wall and gain water only from the bottom. The
hydraulic gradient established at the bottom of these wells during pumping brings the aquifer materials in a quicksand state,
which may cause abrasion of pipes and pumps and even the destruction of well structure. To examine the quicksand occurrence,
an analytical solution for the steady flow to a blind-wall partially penetrating well in a confined aquifer is developed. The validity
of the proposed solution is evaluated numerically. The sensitivity of maximum vertical gradient along the well bottom in
response to aquifer and well parameters is examined. The solution is presented in the form of dimensionless-type curves and
equations that can be easily used to design the safe pumping rate and optimum well geometry to protect the well against sand
production. The solution incorporates the anisotropy of aquifer materials and can also be used to determine the hydraulic
conductivity of the aquifer. Copyright © 2012 John Wiley & Sons, Ltd.
KEY WORDS analytical solution; bottom flow; partially penetrating well; safe pumping rate; sand production
Received 17 January 2012; Accepted 20 April 2012
INTRODUCTION
During pumping from a well in an aquifer of fine-grained
materials, fine sediments move to the well and damage
the well installation and cause the well structure to
collapse. To avoid this, the well wall is constructed blind,
and the water enters into the well only from the well
bottom. Aquifer materials may still enter into the well
from the bottom if pumping exceeds some critical rates.
These blind-wall wells (BWWs) penetrate to the upper
part of the aquifer. These wells have a low yield and a
high pumping rate that may cause them to be dried up. If
the blind wall terminated at the impervious top of the
confined aquifer and the well gain water from a cavity just
below the top of the aquifer, as is common in India and
Middle East, it is called nonpenetrating/cavity well. The
enlargement of the cavity during pumping may lead the
impervious top layer to collapse (Sen, 1990; Taneja and
Khepar, 1996).
Some solutions consider the contribution of flow
through the bottom of wells. Kirkham (1959) considered
bottom flow in an analytical solution of flow to a partially
penetrating well in a confined aquifer. Gupta and Singh
(1988) simulated flow to the bottom of a large diameter
partially penetrating well in a hard rock region by a two-
layer finite difference model. Sen (1990) and Taneja and
Khepar (1996) discussed a brief history of solution for
flow to nonpenetrating/cavity wells. Barua and Tiwari
(1995) considered steady flow into the bottom of an auger
hole in a water-table aquifer. Barua and Hoffmann (2005,
2007) accounted flow across the bottom of an auger hole
in a confined aquifer. Singh (2007) incorporated bottom
flow in the development of a semi-analytical model for
transient drawdown in and around a partially penetrating
large diameter well. Barua and Bora (2010) considered
bottom flow in the derivation of an analytical solution for
the steady flow to a partially penetrating well with skin
zone in a confined aquifer. Kompani-Zare et al. (2009)
simulated the unsteady flow to a BWW in an isotropic
unconfined aquifer by MODFLOW 2000 (Harbaugh et
al., 2000). They developed a set of type curves to design
the pumping rate, pumping duration and well radius to
prevent quicksand and drying up in a BWW where the
wellbore is partially filled with aquifer materials due to
gradual and long-time unsafe pumping rates.
The presented analytical solution in this article is for
the steady flow to a BWW in a homogeneous and
anisotropic confined aquifer that does not seem to have
been described in the groundwater literature. The solution
is presented in forms of dimensionless-type curves and
equations, which can be easily used by the practitioners to
design the safe pumping rate and optimum well geometry
to protect the well against sand production and conse-
quent aforementioned problems. The solution can also be
used to determine the hydraulic conductivity of the
aquifer.
MATHEMATICAL FORMULATION
A BWW of radius r
w
(L) that partially penetrates to depth
z
w
(L) below the impermeable top of a homogenous and
*Correspondence to: Nozar Samani, Department of Earth Sciences, Shiraz
University, Shiraz, Iran. E-mail: samani@susc.ac.ir
HYDROLOGICAL PROCESSES
Hydrol. Process. (2012)
Published online in Wiley Online Library
(wileyonlinelibrary.com) DOI: 10.1002/hyp.9353
Copyright © 2012 John Wiley & Sons, Ltd.
Journal Code Article ID Dispatch: 09.05.12 CE:
H Y P 9 3 5 3 No. of Pages: 9 ME:
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