The tolerance hwtol in dataset 2g is specified as an

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Unformatted text preview: st part of the top curve on the right side of figure 31), a convergence check is also applied to the changing value of head in the well. Specifically, if the value of hWELL changes from one iteration to the next by less than a user-specified tolerance, hWELL will be assumed to have stabilized, and the value of net discharge associated with that latest value of hWELL will be locked in for the remainder of that time step. (The tolerance, HWtol in dataset 2g, is specified as an absolute value and is analogous to the closure criteria HCLOSE in the flow equation solver; the value of HWtol should typically be about 10 to 100 times the value of HCLOSE.) If the pumpcapacity curves indicate a relatively large change in net discharge from one iteration to the next, then the code will limit the change in discharge to a maximum of 25 percent during a single iteration. This constraint, however, precludes the net discharge from reaching the limit of 0.0 if the lift is increasing. Therefore, at the beginning of a new time step, the model also checks the lift to see if the net discharge should equal zero, in which case it is set equal to 0.0. If the net discharge at the start of a time step is zero and the updated lift indicates that it should be increased, then when discharge is first updated, the initial increase will be limited to 50 percent of the calculated value. In spite of these preprogrammed measures to facilitate convergence, numerical problems may still be evident. In such cases, the user may have to change numerical solution tolerances, reduce the time-step size by adjusting the number of time steps or decreasing the time-step multiplier, increase the allowable number of iterations, or adjust the pump-capacity relations. The model will assume that, for any total dynamic head equal to or less than the minimum-head end point (on the right side of figure 31), the discharge will equal the maximum operating discharge (defined by Qdes in dataset 4a for a particular well). For any total dynamic head equal to or greater than the maximum-head end point (input variable LIFTq0), the model will assume that the discharge equals zero. If at a later time or subsequent iteration the water level in the well rises sufficiently that the lift does not exceed the maximum total dynamic head, then pumping will resume. The discharge may be turned on again at the beginning of the next time step if the water level is within the operating range of the pump. To provide the user with flexibility, the option to apply the pump capacity curves can be turned on or off for any particular stress period in MODFLOW. Furthermore, in any given stress period in which the use of pump capacity curves are active, fractional adjustments to the calculated yield are allowed through the use of a multiplication factor. For example, this might be used to represent increased inefficiency of a pump over time due to wear and tear by setting the multiplier to 0.8 for a later stress period. Then all computed yields would be equal to 80 percent of that calculated from the original head-capacity curves. (These options are implemented by use of input variable CapMult in dataset 4a of the input dataset.) To test and illustrate the use of head-capacity curves, the Reilly problem was modified so that the long borehole had a Model Features and Processes pump with a characteristic performance curve that followed the upper curve in figures 30 and 31. The desired pumping rate was set at -7,800 ft3/d. This pumping rate is artificially high so that the drawdown will be large enough to illustrate clearly the effects of using pump-capacity curves to limit discharge. The option to constrain pumping on the basis of a limiting water level in the well was turned off (that is, Qlimit = 0 in the input data). The three adjacent pumping wells were also turned off. In the first test, a 300-day transient stress period followed the initial steady-state stress period. The 300 days were divided into 20 time steps using a time-step multiplier of 1.2. The reference elevation for calculating lift (Hlift) was set equal to 10.0 ft, LIFTq0 and LIFTqmax were set equal to 33.75 ft and 13.65 ft, respectively, and the pump-capacity curve was defined using the four intermediate points shown for the upper curve in figure 31. The results (fig. 32) show that the net discharge remained unchanged at the desired rate until the fourth time step. During the first three time steps, the calculated lift was sufficiently small that the maximum discharge of the pump was allowed. In the fourth time step, the head in the well fell below -3.65 ft (yielding a lift exceeding 13.65 ft, which is the specified value of LIFTqmax), and the discharge was reduced (see top curve in figure 31). From the fourth time step on, the net discharge from the well was reduced gradually as the head in the well declined (and the pumping lift increased) continually during the remainder of the stress period. By the end of the simulation, the discharge had been reduced by about 15 percent. A second test was evaluated to assure that the pumpcapacity curves can shut a pump off if the lift increases substantially, as well as allow the pump to...
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This document was uploaded on 01/20/2014.

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