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on if the head in the well subsequently rises sufficiently. In
this variation of the previous test, heads were simulated for
two oneyear (365day) transient stress periods. During the
first transient stress period, the three nearby wells were set at 31 discharge rates equal to 4,000 ft3/d each, and during the second transient stress period, these three wells were shut off so
that heads would recover. During both transient stress periods,
the desired discharge from the multinode well was set equal
to 7,800 ft3/d. Both transient stress periods were simulated
using 15 time steps and a timestep multiplier of 1.2. The
results (fig. 33) show that the simulated net discharge from the
multinode well was reduced relative to the desired discharge
during every time step, until it was reduced to zero during
the 12th time step when the head in the well dropped below
the value yielding a lift greater than the maximum lift for this
pump (in this case, a head in the well of 23.75 ft for a lift of
33.75 ft). During the first time step of the second transient
stress period, when the three additional nearby wells were
shut off, the heads recovered sufficiently quickly such that the
pump in the multinode well was reactivated. The computed
net discharge continued to increase as the water levels rose in
response to shutting off the three nearby wells.
These two tests indicate that the pumpcapacity relations work as expected. Additional tests indicated that, under
some circumstances, oscillatory behavior or nonconvergence
occurred, but these problems could be eliminated or minimized by adjusting numerical parameters or timestep size.
Again, the use of pumpcapacity relations is optional, and the
user can deactivate it during any one or all stress periods. Horizontal and Slanted Wells
Most of the methods and literature about computing
water levels in wells represented in numerical models assume
that the wells are vertical. Although this is usually the case,
the construction and use of horizontal wells is becoming
more common, and horizontal wells at depth require slanted
(directional) drilling at shallower depths. Halford and Hanson Figure 32. Plot showing
results of applying the pumpcapacity relations to the
modified Reilly problem in
which the desired discharge
equals 7,800 cubic feet per day
for a 300day transient stress
period. When the head in the
well equals or exceeds 3.65
feet, the lift is equivalent to that
for the maximum discharge of
the pump. 32 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model (2002, p. 9) state that for horizontal wells equation 15 “is not
a good estimator of celltowell conductance (CWC). Suitable
equations for estimating CWC of horizontal wells are not well
defined.” This is also true for slanted wells or slanted sections
of wells. Thus, Halford and Hanson (2002, p. 9) recommend
that the user “experiment with defining CWC external to
MODFLOW and directly specifying appropriate CWC values
in the MNW Package input.” This approach, though still valid,
may create additional work for the user without a clear and
objective path to completion. Therefore, MNW2 offers the
user an alternate approach for a nonvertical well, in which
the model will calculate the appropriate value of CWC on the
basis of userdefined well characteristics. These calculations
are performed automatically by MNW2 whenever a nonvertical section of open interval is detected for which LOSSTYPE
equals THIEM, SKIN, or GENERAL.
As background to our approach, several aspects of hydraulic properties used in a numerical model such as MODFLOW
are noted. First, certain hydraulic properties, such as hydraulic
conductivity and transmissivity, have effective values that are
directionally dependent. Mathematically, these parameters
can be characterized as tensors. In threedimensional space, a
tensor is characterized by three orthogonal principal values. In
MODFLOW, it is inherently assumed that the three principal
directions of the hydraulic conductivity tensor are aligned with
the three coordinate axes. The directional properties of a tensor
quantity can be represented by an ellipsoid in which the lengths
of the semiaxes are directly proportional to the square roots of
the principal values of the tensor. Thus, the effective value of the
parameter in any direction can be resolved in terms of the equation describing an ellipsoid. Voss and Provost (2002) provide a
detailed example of these relations for the dispersion tensor.
The celltowell conductance term (CWC) (L2/T) is analogous to the conductance of a streambed, which is proportional
to the length of the streambed within a finitedifference cell, as
defined in the Streamflow Routing Package (Prudic, 1989). Finitedifference discretization requires an assumption that
a borehole is linear between sequential nodes in a multinode
well. The length of a borehole within a finitedifference cell is
constrained by the dimensions of the cell, as determined by the
local grid spacing, which can be represented as Δx, Δy, and Δz
for the grid spacing in the row,...
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