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Unformatted text preview: WTAQ Program (Barlow and Moench, 1999)
includes analytical solutions for drawdown at a pumped well
(or an observation well) for a variety of cases, including that
of a partially penetrating pumped well. The WTAQ Program
implements the Laplacetransform solution of Moench (1997)
for flow in a watertable aquifer, a modified solution of Dougherty and Babu (1984) for flow to a partially penetrating well
in a confined aquifer, and the Theis solution for flow to a fully
penetrating well in a confined aquifer. The Laplacetransform
solutions are numerically inverted to the time domain by means
of the Stehfest (1970) algorithm (Barlow and Moench, 1999).
The numerical solution for the first test was generated
using one model layer to represent the 100ft thick aquifer and
an initial time step of 2.41×107 days, which was increased by
a factor of 1.2 in each successive time step (requiring a total
of 100 time steps to simulate a representative 100day stress
period). Because the cell where the pumping well is located
has a grid spacing of 5 ft by 5 ft, the equivalent well radius
(computed using eq. 6 of Halford and Hanson, 2002, p. 9) is
ro = 0.99 ft. Thus, the analytical solution for the drawdown in
the pumping well is based on a specified well radius of 0.99 ft
to maximize comparability and eliminate the need to correct for
any difference between the well radius and the effective radius
of the cell (that is, LOSSTYPE = NONE). The MODFLOW
numerical results show excellent agreement with equivalent
analytical solutions (fig. 3) for the pumping well and for observation wells at various distances (r) from the pumping well.
These results indicate that the numerical model of the hypothetical confined aquifer system is adequate to evaluate methods
(described later in the report) to compute additional drawdown
caused by partial penetration and other sources of well loss. Long, Unpumped Observation Well (Reilly
Problem)
Reilly and others (1989) used numerical experiments in a
hypothetical groundwater system to demonstrate that appreciable wellbore flow can occur in observation wells screened
through multiple layers, even in homogeneous aquifers having
small vertical head differences (less than 0.01 ft between Model Features and Processes
the top and bottom of the screen). Konikow and Hornberger
(2006a,b) slightly modified this test problem to evaluate solute
transport through a multinode well. This same test problem
(herein called the “Reilly” test problem) is used in this study
to help evaluate the MNW2 Package.
As described by Konikow and Hornberger (2006b),
the hypothetical unconfined groundwater system represents
regional flow that is predominantly lateral but includes some
vertical components because of diffuse areal recharge [at a rate
of 4.566×103 feet per day (ft/d)] and a constanthead boundary
condition at the surface of the right side of the regional groundwater system that controls discharge (fig. 4). Noflow boundaries are on all other external boundaries. The system is substantially longer (10,000 ft) than it is thick (205 ft) or wide (200 ft);
the width was selected to eliminate any important effect of the
position of the lateral noflow boundary on the solution in the
area of the well. A nonpumping borehole with a 60ft screen is
located close to the noflow boundary on left side of the system
(252 ft from that boundary) (fig. 4). Other properties of the system and the model are listed in table 2. Reilly and others (1989)
simulated the regional system with a twodimensional crosssectional model, arguing that the width of the cross section was
irrelevant for their analysis, and applied a local (approximately
a 100ftby100ft area) threedimensional flow model in the
vicinity of the wellbore. Their local model was discretized
vertically into 5ft layers and used a variably spaced areal grid
with a minimum spacing of about 0.33 ft by 0.33 ft around the
borehole. They represented the borehole using a relatively high
vertical hydraulic conductivity, the value of which was based
on equivalence of Darcy’s law to the equation for laminar pipe
flow (Reilly and others, 1989, p. 272).
Konikow and Hornberger (2006a,b) simulated the regional
flow system with a threedimensional model with a domain 9 width sufficient to minimize any effects of that dimension on
the flow field close to the borehole; they represented the borehole using the MNW Package (Halford and Hanson, 2002).
Because a vertical plane of symmetry is present and passes
through the well, they only simulated onehalf of the domain
outlined by Reilly and others (1989). The grid has a variable
spacing (fig. 5). In the local area around the well, however, a
relatively fine and uniform areal cell spacing of 2.5 ft by 2.5 ft
was used. This finest part of the grid included 20 rows, 40 columns, and 41 layers of cells. Outside the uniformly spaced part
of the grid, the lateral grid spacing was increased geometrically
to a maximum spacing of 50.25 ft in the row (x) direction and
9.55 ft in the column (y) direction (fig. 5). The vertical discretization (Δz) was 5 ft everywhere in the model domain, and the
top layer was...
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This document was uploaded on 01/20/2014.
 Winter '14

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