Unformatted text preview: using the standard WEL
Package of MODFLOW, the simulated results show a noticeable error (fig. 13). This is primarily caused by a discretization
that is too coarse to allow vertical head gradients near the well
to be calculated accurately. Therefore, as the discretization
is made finer, and the number of layers increases, the results
improve. When the aquifer is further subdivided into six layers and
the well assigned to the middle two layers, there is still a small
error. However, when the aquifer is divided into 15 model layers
and the well is represented with onefifth of the total discharge
in each of the middle five layers, the average head in the well
computed numerically agrees almost exactly with both the analytical and MNW2 results after a dimensionless time of about
103. This also illustrates the efficiency advantage of the MNW2
Package relative to the standard WEL Package; to obtain a
match to the analytical solution with only a single model layer,
the MNW2 results required 178 seconds of computational time,
whereas the 15layer model with the WEL Package used 3,396
seconds of computational time to produce an equivalent match.
For a watertable (unconfined) aquifer or a model layer
that is allowed to convert from confined to unconfined, special
care is required because the saturated thickness may change
over time. An unconfined aquifer represented as a single
Figure 13. Plot showing
comparisons of analytical
and numerical solutions for
dimensionless drawdown
for the Lohman problem
with a partial penetration
fraction of 0.33 and the well
screen located in the middle
of the aquifer. Numerical
solutions (showing the first
15 data points and then
every fourth data point
afterwards) calculated using
the standard WEL Package in
MODFLOW–2000 (Harbaugh
and others, 2000). Model Features and Processes
model layer is illustrated in figure 14, in which the water table
declines with time, represented sequentially from A to D.
Because the position of the well screen is fixed, but the water
table position changes with time, the relative position of the
screen within the cell also changes with time. Therefore, the
MNW2 Package will check to see if the saturated thickness (b)
of a cell has changed, and if so, then the model will automatically update the values of the depths below the water table
to the top and bottom of the well screen (zpd and zpl, respectively), the saturated length of the well screen (l = zpl – zpd),
and the penetration fraction (α = l/b), as appropriate. If the
watertable elevation drops below the bottom of the screen
within a cell, as in figure 14D, then all flow between the cell
and that node of the multinode well is cut off (equivalent to
resetting the celltowell conductance for that node to zero).
Note that if the water table subsequently rises, then the screen
will be assumed to rewet and become active again, with its
length and partial penetration fraction updated on the basis of
the new water table elevation and the screen characteristics.
An unconfined aquifer is often discretized vertically into
multiple model layers to obtain improved resolution of the
results, as depicted in figure 15, which shows a case where
an unconfined aquifer is subdivided into three model layers.
In this example, the well screen fully penetrates model layer
2, both at the initial conditions (fig. 15A) and after a small
decline of the water table within model layer 1 (fig. 15B).
However, after the water table declines further so that it
becomes located in model layer 2 (fig. 15C), model layer 1 at
that location becomes inactive and both the saturated thickness
of the cell and the saturated length of the well screen in layer
2 are reduced accordingly. If, however, the well screen were
originally shorter and only partially penetrated model layer 2
(fig. 15D), then after the water table declined into model layer
2, the depths below the water table to the top and bottom of
the well screen (zpd and zpl, respectively), the saturated length 17 of the well screen (l = zpl  zpd), and the penetration fraction
(α = l/b) would have to be adjusted (and so they are automatically updated in MNW2 after each time step).
The overriding assumption made in implementing the
partial penetration correction in the MNW2 Package is that
it can be applied on a model layer basis rather than on an
aquifer basis. The likely disparity here is that the analytical
solution assumes that the aquifer is bounded above and below
by an impermeable confining layer, whereas in a complex
threedimensional model of a heterogeneous groundwater
system, hydraulic conductivity values can vary by any amount
between vertically adjacent cells. Furthermore, the analytical
solution assumes that the aquifer is laterally homogeneous.
Because in reality, hydraulic conductivity can vary by any
amount between vertically and horizontally adjacent cells, the
accuracy of the computed corrections for partial penetration
effects may be compromised to some degree by these...
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This document was uploaded on 01/20/2014.
 Winter '14

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