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Unformatted text preview: normal with equation 12. Subsequently, if hWELL drops below
the level of hlim, then the maximum potential discharge (Qpot)
is computed using the same equation but with hlim substituted
for hWELL. If the potential discharge exceeds the userspecified
discharge (Qpot > Qdes), then the latter is used in solving
the groundwater flow equation (that is, the well discharge
is not constrained). If the potential discharge is less than the
userspecified discharge (Qpot < Qdes), then the former is used in solving the groundwater flow equation (and the well
discharge is thereby constrained). In this manner, the applicable boundary condition represented by the multinode well
transitions from a specifiedflux type of boundary condition
to a generalhead type of boundary condition (with hlim as the
controlling head). If hn at all aquifer nodes linked to a multinode well fall below hlim, then there will be no net discharge
from the well. Note that zero discharge is a limit to prevent
the net well discharge from artificially reversing signs and
change from discharging to recharging conditions during a
given stress period. If the net discharge from a multinode well
falls to 0, however, then crossflow between model layers (via
intraborehole flow in the multinode well) will still be simulated. Recharge (injection) wells are limited in the same manner, but the signs are reversed, and hlim represents a maximum
water level.
These relations are best illustrated by an example—one
also based on the Reilly test problem. To illustrate the use and
effects of constraints on a discharging well, the Reilly problem, as modified for the seepage face example (see tables 2
and 3), was used with a specified limiting head (hlim = 7.5 ft)
and no minimum pumping rate specified (Qcut = 0, where
Qcut is defined in input dataset 2f or 4b). All other parameters, stress periods, and time steps are identical to those
described for the seepage face example. The results (fig. 24)
show that once the head in the well reached the limiting head
(in the fifth time step, at about 19 days), it was prevented from
declining any further, and the computed discharge decreased
as the heads in adjacent nodes continued to decline with time.
Note that the discharge remained constant at the specified rate
(10,000 ft3/day) prior to the time when the head in the well
reached the limiting head.
The stabilization of hWELL at the value of hlim is reasonable as long as the heads at linked nodes in the aquifer 24 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model are higher than hWELL, thereby allowing a net inflow to the
multinode well, which will balance the net discharge from
the well. However, if the computed heads at the aquifer nodes
connected to the multinode well decline below the value of
hlim, then the net discharge would be reduced to zero, and the
head in the well would decline to deeper levels than specified by hlim. This was tested and demonstrated by rerunning
the previous example, but with specified withdrawals in three
singlenode wells added at nearby nodes (in layers 2, 7, and
13 of row 28, column 43) at rates of 4,000 ft3/day each. (Note
that because the singlenode pumping wells are not located on
the plane of symmetry, their effects on drawdown in the aquifer would be equivalent to each one having a matching well on
the other side of the plane of symmetry.) The additional drawdown in the multinode well caused by interference from the
three additional pumping wells causes the head in the multinode well to decline faster than before (fig. 25). In this case,
the head in the well reached the limiting head in the second
time step (at about 4.6 days), and the net discharge decreased
to 9,190 ft3/day from the 10,000 ft3/day rate during the first
time step. However, because of the additional drawdown
relative to the previous case, the net discharge continued to
decrease to zero in the ninth time step. After the discharge
ceased, the computed water level in the well again began to
decline further—to depths below the specified value of hlim.
For comparison, the average of the heads in the 12 aquifer
nodes connected to the multinode well are also shown in
figure 25. During the eighth time step, the heads at several
nodes (those closest to the three singlenode pumping wells)
are below the value of hlim, causing outflow from the multinode well (recharge to the aquifer) in these nodes, although
there is sufficient inflow to the multinode well (discharge from the aquifer) at the remaining nodes so that the net discharge,
though greatly reduced by this time, is still nonzero at about
100 ft3/day. In the ninth step the average head has dropped to
about 8.9 ft and is below the value of hlim at every one of the
12 aquifer nodes connected to the multinode well. Therefore,
the net discharge is zero, and the water level in the well drops
below hlim as it equilibrates to the new lower aquifer heads. As
expected, while there is a net discharge from the multinode
well, the head in the well is noticeably lower than the average
head in the aquifer adjacent to the well, but when the net discharge is zero, hW...
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 Winter '14

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