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 userspecified 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 timestep
size by adjusting the number of time steps or decreasing the
timestep multiplier, increase the allowable number of iterations,
or adjust the pumpcapacity relations.
The model will assume that, for any total dynamic head
equal to or less than the minimumhead 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 maximumhead 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
headcapacity 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 headcapacity 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 pumpcapacity 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 300day transient stress period followed
the initial steadystate stress period. The 300 days were divided
into 20 time steps using a timestep 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 pumpcapacity 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.
 Winter '14

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