Unformatted text preview: n lengths, but
because the screen in Well B is adjacent to a noflow boundary,
there can be no contribution from vertical flow above the screen
and it will experience greater drawdown for the same pumping
rate compared with Well C. Well D has three separate screens,
which improves well efficiency by spreading the intake across
a longer effective section of the aquifer, so it would experience
less drawdown than either Well B or Well C, even though the
total lengths of screen are identical in all three cases.
In developing numerical models, one often has to evaluate tradeoffs among accuracy, generality, and simplicity.
In developing the code for partial penetration effects in the
MNW2 Package, a single well screen (or open interval) can Figure 7. Schematic crosssectional diagram showing A, fully
penetrating, and B–D, partially penetrating wells in a nonleaky
confined aquifer. Well B is open to the uppermost third of the aquifer
thickness, Well C is screened in the middle third of the aquifer
thickness, and Well D has three separate screens with a cumulative
length of screen (open interval) the same as Wells B and C. occur at any position within a model layer if the user specifies the elevation of the top and bottom of the well screen (as
illustrated by Wells B and C in fig. 7). Alternatively, if a multinode well is defined by nodes and partial penetration fractions
(see appendix 1), then the model will assume that the center of
the well screen is located at the vertical center of the cell (that
is, the center of the screen would be assumed to be located
halfway between the top and bottom elevations of the cell).
The only exception is for a well node located in the uppermost
active layer for its row and column location. In this case, if the
layer is unconfined, then the bottom of the well screen will be
assumed to be aligned with the bottom elevation of the cell.
MNW2 will not compute drawdowns due to partial penetration for the case of multiple well screens within a single
model layer—that is, the situation represented by Well D in
figure 7. If the user specifies multiple well screens in a single
multinode well and their elevations indicate multiple screens
within a single cell of the grid, then the model will sum the
individual screen lengths to compute a total composite length
and a partial penetration fraction for that cumulative length. It
is further assumed that the individual sections of screen within
a cell are contiguous and that the equivalent composite well
screen is vertically located in the middle of the cell. As above,
an exception to this rule is made for a well node located in the
uppermost active layer of the grid. In this case, if the layer is
unconfined, then the bottom of the composite well screen is
assumed to be aligned with the bottom elevation of the lowermost section of well screen located within the cell. Furthermore, partial penetration corrections are only implemented for
vertical wells or vertical sections of wells, and are not enabled
for horizontal or slanted sections of wells. A well screen (or
open interval) is considered to be vertical if all nodes within
a contiguous open interval and the immediately adjacent well
nodes above and (or) below that interval are all located in the
same row and column location of the MODFLOW grid.
The nature of the partial penetration effect is illustrated
by the analytical solutions obtained using the WTAQ Program
(Barlow and Moench, 1999) for a range of penetration fractions in the Lohman test problem (fig. 8); system properties
are listed in table 1. The solutions are generalized by presenting them in terms of dimensionless time (tD) and dimensionless drawdown (ΔhD). Moench (1993) defines these terms as
tD = Tt / r2S and ΔhD = 4πTΔh / Q, where T is transmissivity
(L2/T), t is time (T), r is radial distance (L), and S is storage coefficient (dimensionless). One important inference can 12 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model be drawn from the results shown in figure 8—namely, that
the additional drawdown due to partial penetration (Δhp)
approaches a constant value after a relatively short time has
elapsed. For example, for α = 0.33, an additional dimensionless drawdown of about 10 units greater than the fully
penetrating case (α =1.0) is reached for dimensionless times
greater than about 104. That is, for all cases for tD greater than
about 104, the drawdown increases linearly with the log of
time (that is, the family of solutions represent straight parallel lines after the earlytime transient change has passed).
Therefore, for tD > 104, the additional drawdown due to partial
penetration effects is a constant value for a given set of conditions. Because most applications of MODFLOW are oriented
toward regional analyses over time scales of months to years
to decades, the early time transient changes are ignored and
the constant value of Δhp calculated for the given set of conditions are assumed to apply over all times during a given stress
period. This conceptual simplificatio...
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