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Unformatted text preview: departures from the idealized assumptions.
The previous tests of the correction for the effects of
partial penetration used the MNW2 Package to represent
singlenode wells because they can approximate the geometry
and boundary conditions for which analytical solutions are
available, thus allowing the accuracy of the numerical solution
to be evaluated. If one or more nodes of a true multinode
well only partially penetrate the model layers to which they
are connected, then the flow between the cell and the well at
that node would also be reduced relative to a comparable well
that fully penetrates all cells. In other words, the correction for
partial penetration effects should be applied to any node of a
vertical multinode well that penetrates less than the full thickness of a cell. However, no analytical solutions are known to
apply to this situation. Therefore, the length of the well screen
of the multinode well in the Reilly problem was adjusted so
that one node (the uppermost one) will penetrate less than
the full thickness of the cell to which it is connected and the
Figure 14. Schematic cross
section of an unconfined
aquifer simulated as a
single “convertible” model
layer showing the relation
of the position of a partially
penetrating well screen to the
water table as the water table
declines sequentially over time
from A to D. As the saturated
thickness (b) is reduced with
time, 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 (a = l/b)
are automatically updated. 18 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model Figure 15. Schematic cross
section of an unconfined
aquifer represented by three
model layers, showing the
relation of a well screened in
model layer 2 to the water table
as the water table declines
over time (sequentially from
A to C). The well screen fully
penetrates model layer 2
in A–C, but is only partially
penetrating in D. The red
horizontal dotted lines
represent the boundaries of the
model layers used to simulate
the aquifer, and Dz is the layer
thickness. results can be compared to the fully penetrating case. The
evaluation is therefore limited to examining the relative effects
on head and flow in the well and assuring that the results are
logical and consistent.
To provide the basis of this test, the elevation of the top
of the screen was lowered in increments from the elevation
of the top of model layer 2 to the elevation of the bottom of
model layer 2. This corresponded to reducing the total screen
length from 60 ft to 55 ft (a reduction in length by 8.3 percent). Overall, one would expect that reducing the total length
of the well screen would reduce the total flow through the
well. This also corresponds with changing the partial penetration fraction (α) for the uppermost node of the multinode well
from a value of α = 1.0 to α = 0.0 as the elevation of the top of
the screen is reduced.
The results show that the adjustments of the penetration
fraction in just one of the 12 nodes comprising the well have
a very small effect on the head (or water level) in the well
(fig. 16A) and that the change in head over the total range of adjustment is only 0.00018 ft (fig. 16B). That is, the head
in the well goes down slightly as the penetration fraction
decreases. The low sensitivity of head in the well to these
adjustments can be contrasted with the relatively high sensitivity of the total flow through the borehole to the same changes
(fig. 17). The total intraborehole flow decreases from about
9.79 ft3/d to about 8.28 ft3/d (15.4 percent) as the uppermost
node changes from 100 percent penetration to 0 percent penetration. This change is about twice the percentage reduction
in total length of the well screen.
The change in flow shown in figure 17 can be attributed
primarily to reduced inflow in node 1 (the uppermost node
of the 12 nodes constituting this multinode well) as the
length of the screen in node 1 is sequentially reduced from
the full thickness of the cell to zero (fig. 18). The results
show a large change in flow in the uppermost node, where
the penetration is adjusted; nodal changes are propagated
downward to other nodes with diminishing effects with
distance. Figure 16. Plot showing the effect of variations in the penetration fraction for the uppermost node of the multinode well in the
Reilly problem on the computed water level (head) in A, the well; and B, on the corresponding change in water level relative to fully
penetrating well. Model Features and Processes
Overall, all of the observed effects in the numerical
experiments of partial penetration of one node out of 12
appear to be logical and consistent with hydrologic principles.
These results indicate that the partial penetration correction, as
applied to individual nodes of a multinode well, is working
correctly.
Because the correction for effects of partial penetration,
as implemented in the MNW2 Package, is clearly an approx...
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 Winter '14

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