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Unformatted text preview: ELL is almost exactly equal to the average of
the adjacent nodal heads. Note that even with this net discharge
of zero, there exists a complex intraborehole flow pattern in
which water flows out of the well in layers containing one of
the three discharging singlenode wells and water flows into
the well in other layers—though inflows from the aquifer will
exactly balance outflows to the aquifer (fig. 26).
To demonstrate the ability of the MNW2 Package to shut
off a pumping well when the constraints cause the discharge
rate to fall below a specified minimum rate, the same problem
was resimulated with the minimum pumping rate (Qfrcmn)
set to 20 percent of the specified desired rate (that is, Qfrcmn
= 0.20, which is equivalent to Qfrcmn = 2,000 ft3/day). The
results (fig. 27) can be compared with those shown in figure
25 for the case without a minimum rate imposed. During the
seventh time step, the net discharge would have been calculated to equal about 1,460 ft3/day, which is less than the
minimum pumping rate. Because the calculated net discharge
fell below the value of Qfrcmn during the iterations to solve
the flow equation during the seventh time step, the pump was
shut off and the net discharge was set to equal zero during
this time step. Thus, because Qnet is reduced to 0.0 during the Figure 24. Plot showing
relation between computed net
discharge (Qnet) from a multinode well and computed head
in the well (hWELL) for case
in which well is subject to a
constraint in which the limiting
head (hlim) is set at 7.5 feet.
Arrows indicate proper axis
labels for each variable plotted. Model Features and Processes 25 Figure 25. Plot showing
relation between computed
net discharge (Qnet) from a
multinode well and computed
head in the well (hWELL) for
case in which well is subject
to a constraint in which the
limiting head (hlim) is set at
7.5 feet and additional nearby
pumping wells cause additional
drawdown in the multinode
well. Average of heads in 12
aquifer nodes ( ) linked to the
multinode well are shown for
comparison. seventh time step, the water level in the well and the heads in
the aquifer all show a small recovery relative to the situation
when pumping continues through the seventh time step. Once
the net discharge equals zero, the head in the well becomes
almost equal to the average of the heads in the 12 aquifer
nodes connected to this multinode well, and calculations of
intraborehole flow continue.
Once the pumpage is shut off by constraints during a time
step, the pump is not allowed to turn back on during the same
time step in order to facilitate stability and convergence of the
numerical solution. Also note that the constraints are implemented slightly differently in MNW2 than in MNW1, in which
the well would have been shut off for the next time step rather
than the present time step in which the constraining condition
for the minimum pumping rate is met. One consequence of the
lag implemented in MNW1 is that the net discharge computed
for the last time step before the pump is shut off can actually be
less than the allowable minimum, if one is specified.
To demonstrate the capability to restart a pumping well
when water levels rise again after earlier declines that cause
the well to shut off, the previous problem was again modified—this time by adding another 150day stress period
during which the three nearby singlenode wells are shut off,
thereby leading to waterlevel recovery in the aquifer. The
minimum allowable pumping rate to shut off the well was
arbitrarily set at 10 percent of the desired rate (equivalent to Qfrcmn = 1,000 ft3/day, onehalf the rate specified for
the case illustrated in figure 27), and the minimum rate
that must be exceeded to reactivate the well was arbitrarily set at 15 percent of the desired rate (equivalent to
Qfrcmx = 1,500 ft3/day).
The effect of specifying a lower value of Qfrcmn can be
seen during the first 150day stress period (fig. 28), in that now
the net discharge (Qnet) does not go to zero until the eighth time
step (at about 48 days), whereas previously Qnet went to zero in
the seventh time step (at about 35 days). During the recovery
stress period, the water levels rise in response to shutting off
the three nearby singlenode pumping wells. In the seventh
time step of the second stress period (at about 185 days), the
water level in the well and heads in the aquifer have risen sufficiently such that the computed potential net discharge exceeds
the value of Qfrcmx. Consequently, the pump is turned back on
during the seventh time step of the second stress period, and
the computed net discharge at that time is about 1,922 ft3/day.
The restarted discharge from the well causes the water level
in the well to drop back down to the value of hlim and the rate
of recovery of heads in the aquifer adjacent to the well to slow
down. As with shutting off a pump, a small difference between
MNW2 and MNW1 in restarting a pump is that in MNW2
the pump is restarted during the same time step in which th...
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 Winter '14

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