However the reduction in pumpage arising from

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: fered as an option, and the user need not implement it if it is not appropriate to the simulation. The capability is activated by setting input variable PUMPCAP > 0 in the MNW2 input file. The pump capacity option has a similarity to the option for imposing a constraint on pumpage based on a limiting water level in a well in that both can lead to the well discharge being set to zero in response to water-level declines. However, the reduction in pumpage arising from constraints will be relatively abrupt with no change in discharge over a 29 Figure 30. Hypothetical but representative performance (headcapacity) curves for three models (and sizes) of vertical turbine pump, with the top curve representing the largest and most powerful pump. relatively large range in water levels. Conversely, the reduction in pumpage arising from the pump capacity option will lead to a much more gradual adjustment of the pumping rate over a large range in water levels. Because the constraint based on a limiting water level in the well is linked to the intake location in the borehole, whereas the pump capacity relations are based on the elevation of the outflow (discharge) location, it is possible that a user may want to impose both types of conditions for a single well. In this case, both conditions are evaluated separately, and whichever condition is more constraining (that is, leads to a lesser pumping rate) will take precedence. The pump capacity condition is only allowed for a withdrawal well and is not available for an injection well or a nonpumping well. If this option is activated, then the user must specify a reference elevation corresponding to the elevation of the discharge point (input variable Hlift). The model will then automatically compute the lift (or total dynamic head) based on the difference between the reference elevation and the most recent calculated water level in the well. If the user wants to account for head loss due to friction and turbulence in the pipes, the reference elevation can be increased proportionately. During successive iterations in solving the flow equation, the MNW2 routines alternate between specifying the MNW2 boundary condition as a fixed head in the well and as a fixed flux. If the pump capacity option is activated, at the beginning of each iteration cycle the MNW2 routines will update the net discharge from the well on the basis of the most recent value of the water level in the well. The user must input data to approximate the head-capacity curve for the pump. The end points of the applicable curve, representing values of total dynamic head corresponding with both zero discharge and the maximum design discharge, must be specified by use of input variables LIFTq0 and LIFTqmax, 30 Revised Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model respectively. In addition, a minimum of one additional intermediate point on the curve must be specified. The model will apply linear interpolation to estimate the yield (discharge rate) for any value of total dynamic head between defined points. As seen in figure 31, the more intermediate points that are used, the more accurately the model can follow the curve and estimate the reduction in discharge. For the representative curves shown, even the use of only one intermediate point leads to an error of a few percentage points at most and is probably adequate for many problems. The use of three or four intermediate points leads to a very accurate approximation over the entire range of head. If the pump-capacity option is active, then after the first iteration in a given time step is completed, the model will determine the lift (total dynamic head) based on the value of the head in the well calculated during the previous iteration. The lift is next used to estimate the net discharge for the next iteration. Because the pump-capacity curves may be nonlinear and, where gently sloping, small changes in lift may induce large changes in discharge, the overall numerical solution may become unstable, fail to converge, or oscillate. To minimize such numerical problems, several steps are taken in the code. First, to help the numerical solution stabilize, at the beginning of a time step, the updated net discharge will not be applied during the first two iteration cycles. Subsequently, if the estimated discharge changes by less than 1.0 percent from the previous value, then it will be assumed that the net discharge has stabilized, and no further changes related to pump-capacity curves will be allowed during that time step. Because this may Figure 31. Hypothetical performance (head-capacity) curves for three models (and sizes) of vertical turbine pumps, showing points defined for approximation using linear interpolation for two of the performance curves. The user must always define end points and an optional number of intermediate points (one intermediate point used for the bottom curve and four intermediate points used for the top curve in this example). not occur if the range of head changes during a time step are on a part of the curve where yield is relatively insensitive to changes in head (for example, the steepe...
View Full Document

This document was uploaded on 01/20/2014.

Ask a homework question - tutors are online