26 to demonstrate the ability of the mnw2 package to

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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 single-node 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 multi-node 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 multi-node well. Average of heads in 12 aquifer nodes ( ) linked to the multi-node 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 multi-node 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 150-day stress period during which the three nearby single-node wells are shut off, thereby leading to water-level 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, one-half 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 150-day 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 single-node 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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