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Unformatted text preview: pumped well under fully penetrating conditions, Δhp
is the additional drawdown in the well due to the effects of
partial penetration, α is the fraction of partial penetration (ratio
of open interval to thickness), rw is the radius of the well, and
b is the saturated thickness of the aquifer.
However, estimating Δhf is problematic for use in a
simple numerical approximation. Prickett (1967) states that
a good approximation for the drawdown due to laminar flow
under fully penetrating conditions can be made using the
Thiem (1906) equation for steadystate flow in an areally
extensive, homogeneous, isotropic aquifer, which can be
expressed as
, (21) where re is the radial distance to a point where drawdown is
negligible.
Prickett (1967) indicates that a value of re = 2,000 ft
would be adequate for most regional simulation models of
confined aquifers. Walton (1962, p. 8) assumes that the partial
penetration correction can be based on values of re = 10,000 ft
for a confined aquifer and re = 1,000 ft for an unconfined aquifer. The approach of assuming a universal value of re and not
adjusting it for variations in aquifer dimensions or properties,
however, is overly simplistic and arbitrary. A difficulty arises
from the assumptions about the aquifer that are consistent with
the applicability of the Thiem (1906) equation. Kruseman and
De Ridder (1970, p. 51) note that a true steady state (where
drawdown is zero) is impossible in a nonleaky confined aquifer, so that an exact value for re is indeterminate. Nevertheless,
the method of Prickett (1967) was implemented and evaluated
for a range of assumptions about the value of re in a series of
numerical experiments. The results indicated that it worked
acceptably well in some tested cases, but yielded unacceptably erroneous values in too many other cases that included
plausible combinations of parameter values and boundary
conditions.
To yield greater accuracy in estimating the drawdown due
to partial penetration effects for a broader range of conditions, an analytical solution within the MNW2 Package was implemented to calculate the additional drawdown in a well that
does not fully penetrate the saturated thickness of an aquifer.
Following Moench (1993), the solution for drawdown (Δh)
in a well pumping from a nonleaky confined aquifer can be
expressed as the sum of two components
(22)
where ΔhT represents the drawdown computed with the Theis
(1935) solution for flow to a well in a nonleaky confined aquifer. The WTAQ source code for the confined aquifer solutions
(for both fully and partially penetrating conditions) has been
extracted and incorporated as a subroutine internally within
the MNW2 Package to calculate Δhp; this coding implementation is invisible to the user of MODFLOW and MNW2.
Note that figures 8 and 9 indicate that, if the partial penetration fraction (α) is large, say greater than 0.90, then there is
only a very small partial penetration effect on drawdown, and
if α ≥ 0.99, then the effect is negligible. Therefore, to avoid
potential numerical problems when α ≥ 0.99, it is automatically assumed that the well is effectively fully penetrating
whenever α ≥ 0.99 for a node in a multinode well and that
computation of drawdown due to partial penetration is not
necessary under these conditions.
When the partial penetration fraction is very low, the
drawdown correction may be very large (fig. 9) and very sensitive to small changes in the penetration fraction. Under these
conditions, it is possible that the analytically based WTAQ
solution for partial penetration effects will fail to converge. If
that happens for a node of a multinode well with a relatively
low partial penetration fraction (α < 0.20), then the celltowell conductance will be set equal to zero, shutting off flow
between the aquifer and that node of the well, and an appropriate informational message will be written to the output file;
if it fails to converge for a relatively large partial penetration
fraction (α ≥ 0.20), then no partial penetration correction will
be made (equivalent to assuming α = 1.0), and an appropriate
informational message will be written to the output file.
It is assumed that the same relations used to estimate
partial penetration effects in an aquifer are applicable to a well
that is only open to a fraction of the saturated thickness of a
model layer (or cell). The general wellloss equation introduced
in equation 2 can be expanded to account for additional drawdown due to partial penetration effects in a vertical well as
, (23) where Δhp is the additional drawdown in the well due to partial penetration.
Following the development of Halford and Hanson
(2002, p. 8), the flow between the cell and the well can be
expressed in terms of the head difference (equation 23) and a
celltowell conductance, CWC (L2/T), as
(24) Model Features and Processes
Assuming that the additional drawdown due to partial
penetration is additive with the other head loss terms, substituting the right side of equation 23 into equation 24, and
solving for CWC results in
(25)
The acc...
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This document was uploaded on 01/20/2014.
 Winter '14

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