If the potential discharge is less than the user

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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 user-specified discharge (|Qpot| > |Qdes|), then the latter is used in solving the ground-water flow equation (that is, the well discharge is not constrained). If the potential discharge is less than the user-specified discharge (|Qpot| < |Qdes|), then the former is used in solving the ground-water flow equation (and the well discharge is thereby constrained). In this manner, the applicable boundary condition represented by the multi-node well transitions from a specified-flux type of boundary condition to a general-head 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 multi-node well falls to 0, however, then cross-flow between model layers (via intraborehole flow in the multi-node 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 Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model are higher than hWELL, thereby allowing a net inflow to the multi-node well, which will balance the net discharge from the well. However, if the computed heads at the aquifer nodes connected to the multi-node 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 single-node 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 single-node 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 multi-node 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 multi-node well are also shown in figure 25. During the eighth time step, the heads at several nodes (those closest to the three single-node 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 multi-node 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 multi-node 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 multi-node 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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