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Unformatted text preview: uracy of the partial penetration correction in
MNW2 was tested for the range of conditions depicted in figures 8–10. The results (fig. 11) show excellent agreement after
early time (in these examples, after a dimensionless time of
103 has passed, which is equivalent to less than 2 seconds of
real time in this example problem). The disagreement at early
times reflects the reliance of computing the head in the well
partly on the basis of the steadystate Thiem (1906) equation,
as discussed previously. The resulting error is limited to such
a small initial transient time period that it should not have any
effect on the reliability of results for regional groundwater
simulations over typical time periods.
The analytical solutions for calculating drawdown in a
partially penetrating well assume that the aquifer constitutes
a single layer bounded above and below by confining layers.
In a threedimensional groundwater model, however, the
vertical dimension may be discretized at a scale finer than
the thickness of an aquifer. A range of vertical discretization
possibilities are illustrated in figure 12. A well that is open
to the middle third of an aquifer is depicted in figure 12A. If
this aquifer were numerically simulated using a single model
layer, then the thickness of the model layer (Δz) would be
the same as the aquifer thickness. The head computed for the
finitedifference cell containing this well would be consistent
with that for a fully penetrating well withdrawing water from 15 the full volume of the cell. If observations of water levels in
that well are to be compared to modelcalculated values, then
the head calculated for the well would have to be corrected
for partial penetration effects, as well as for other possible
wellloss terms.
In figure 12B the aquifer is subdivided into three equally
thick model layers. In this case, the partial penetration effects
are explicitly modeled in MODFLOW because the well
is open to the full thickness of model layer 2 and the finer
vertical discretization allows the vertical components of flow
above and below the well to be calculated directly; therefore,
it is not necessary to simulate an additional drawdown term
to account for the effects of partial penetration. One can
question whether three model layers offers sufficient vertical
discretization to accurately represent vertical components of
flow near the well, but this can always be tested by trying an
even finer vertical discretization, for example, as shown in
figure 12C, where the aquifer is subdivided into six model
layers, so the well could be simulated as an MNW open to
(and fully penetrating) the middle two model layers.
The vertical head gradients above and below the open
interval can be computed at two nodes in this case versus one
node for the case in figure 12B. In figure 12D, the well screen
(or open interval) is slightly longer than onethird of the thickness of the aquifer, and in a sixlayer model of the aquifer,
the well would fully penetrate model layers 3 and 4, but only
penetrate about onethird of model layer 2. If this well were
represented by a MNW, then the correction for partial penetration would only affect the celltowell conductance in model
layer 2, so the net effect on the head in the well would be
substantially less than for a case in which a singlenode well
has a penetration fraction of 0.33. Figure 11. Plot showing
comparisons of analytical
and numerical solutions for
dimensionless drawdown
for selected cases shown in
figures 8–10 for the Lohman
problem. The well screen
is located in the middle of
the aquifer, except for one
indicated case. Analytical
solutions were calculated
using the WTAQ Program
(Barlow and Moench, 1999).
Numerical solutions (showing
every fourth data point) were
calculated using MNW2 in
MODFLOW–2000 (Harbaugh
and others, 2000). 16 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model Figure 12. Schematic crosssectional diagram showing
alternate vertical discretization
possibilities for simulating a
confined aquifer containing a
partially penetrating well. In A,
the aquifer is represented by
a single model layer, and the
vertical discretization in the
model (Dz) equals the aquifer
thickness. In cases B–D, the
red horizontal dotted lines
represent the boundaries of the
model layers used to simulate
the aquifer, and Dz is less than
the aquifer thickness. The alternative discretizations represented in figure
12A–C were evaluated with MODFLOW for the Lohman
problem using a single model layer. Figure 11 shows the
results of applying MNW2 to the problem for the case of α =
0.33; the numerical MNW2 results were essentially identical
to the analytical solution at dimensionless times greater than
104. These results can then be compared with a simulation
representing the threelayer conceptualization, as shown in
figure 12B. In this case, the well fully penetrates layer 2 of the
model, though it still penetrates only onethird of the aquifer.
When the pumping is represented...
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