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Unformatted text preview: n results in substantial
computational savings for many cases. Furthermore, for a
broad range of realistic parameter values, tD = 104 is equivalent to an actual elapsed time of just a few minutes, which is
rarely of concern in a groundwater model analysis.
Another relation that can be seen in figure 8 is the
sensitivity of Δhp to the fraction of the aquifer penetrated
by the well. If a well is open to more than 90 percent of the
aquifer thickness, then the additional drawdown due to partial
penetration effects is very small. As the partial penetration
fraction decreases, the effect increases at an increasing rate (fig. 9). Figure 9 also illustrates the effect of the position of the
open interval on the drawdown caused by partial penetration
effects. All else being the same, the well with an open interval
adjacent to a bounding impermeable confining layer (such
as Well B in fig. 7) will have greater drawdown than a well
with an open interval that is vertically centered (such as Well
C in fig. 7), although the difference is negligible for penetration fractions greater than 0.5. For penetration fractions less
than 0.05, the error caused by assuming that the position of
the open interval is centered vertically when in fact it is at the
edge of the aquifer may exceed 50 percent.
The effect of the relative vertical position of a fixed length
of well screen within the aquifer is also illustrated in figure
10 for the case of a well screen that penetrates 33 percent of
the saturated thickness of a confined aquifer. At extremely
early times, there is only a negligible effect, followed by a
relatively short transition period when the curves diverge. At
late times, the curves are parallel and the differences among
them remain constant over time. The maximum drawdown due
to partial penetration occurs when the well screen is adjacent
to the aquifer boundary, and the difference from the case of a
vertically centered well screen is almost 10 percent. Because
the effect of well screen position can substantially affect the
additional drawdown, especially when the penetration fraction
is small, the MNW2 Package is coded to automatically account
for this effect (using either the top and bottom elevations of the
well screens as specified by the user or the model assumed well
screen positions, as described above). Figure 8. Semilog plots of
dimensionless drawdown
in a vertical pumping well
with an open interval
centered vertically in a
nonleaky, homogeneous,
isotropic, confined aquifer
(the Lohman problem),
showing the sensitivity of
the analytical solution to the
partial penetration fraction
(a). Drawdown for a fully
penetrating well (a = 1.0),
representing the Theis solution,
shown for comparison.
Drawdowns are calculated
using the WTAQ Program
(Barlow and Moench, 1999). Model Features and Processes 13 Figure 9. Plots showing
the relation of dimensionless
drawdown to penetration
fraction (a) for a vertical
pumping well in a nonleaky,
homogeneous, isotropic,
confined aquifer, for wells
located vertically in the middle
of the aquifer and at the edge
of the aquifer (adjacent to a
noflow boundary formed by
the overlying or underlying
impermeable confining layer).
Drawdowns calculated using
the WTAQ Program (Barlow
and Moench, 1999). If the aquifer has vertical anisotropy (that is, Kh > Kz),
then the effects of partial penetration on drawdown in the well
would be greater than for an isotropic aquifer. Jacob (1963,
p. 274) notes that for a partially penetrating well in an anisotropic aquifer, flow “becomes radial at a distance from the well
equal to twice the aquifer thickness multiplied by the square
root of the ratio of the horizontal to the vertical permeability”
(that is,
). The algorithm incorporated in the new
MNW2 Package accounts for the effect of vertical anisotropy on drawdown in a partially penetrating well. If the cell properties include horizontal anisotropy (that is, Kx ≠ Ky), then
Kh is determined internally by MNW2 from
(19)
Prickett (1967) corrected for partial penetration effects
in electric analog models by adding another resistor in series
to a well node to represent additional head loss due to partial
penetration—meaning that it is additive to the other wellloss contributions. Prickett’s correction is based on Kozeny’s Figure 10. Drawdown due to
partial penetration effects in
a vertical pumping well that
is open to 33 percent of the
saturated thickness of the
aquifer, showing sensitivity
to the vertical position of the
well screen within the aquifer.
Elevation of the model layer
ranges from 0.0 to 100.0 feet.
Drawdowns calculated using
the WTAQ Program (Barlow
and Moench, 1999). 14 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model (1933) empirical expression. Jacob (1963, p. 272) states that
Kozeny’s empirical expression “is a sufficient approximation
for many purposes.” However, Driscoll (1986) offers some
words of caution about the use of Kozeny’s equation, noting
that the equation may not be valid for certain conditions, such
as when aquifer thickness is small or the well radius is large.
Prickett (1967) calculates a partial penetration constant,
D, which represents the normalized drawdown resulting from
partial penetration effects as
, (20) in which Δhf is the drawdown due to laminar flow of water
through an areally extensive, homogeneous, isotropic aquifer
to the...
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