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Unformatted text preview: assumed to be unconfined (convertible).
The well was assumed to have a 60ft screen that was
open to layers 2 through 13 (that is, connected to 12 vertically
aligned nodes of the grid) in the bounding row of cells. Reilly
and others (1989) reported that their well was represented by
Table 2. Selected physical parameters used in MODFLOW
simulation of groundwater flow in a threedimensional, steadystate flow system containing a multinode well.
[Abbreviations used: feet, ft; feet per day, ft/d] Parameter
Horizontal hydraulic conductivity
Vertical hydraulic conductivity
Well radius
Well skin hydraulic conductivity
Well skin radius
Recharge rate Value
250 ft/d
50 ft/d
0.133 ft
125 ft/d
1.795 ft
0.004566 ft/d Figure 3. Semilog plot
showing comparisons
between drawdowns
computed numerically using
MODFLOW and drawdowns
computed using the Theis
(1935) analytical solution for
selected distances (r) from a
well pumping at a rate of 96,000
cubic feet per day. Every fifth
data point shown for numerical
solutions. 10 Revised MultiNode Well (MNW2) Package for MODFLOW GroundWater Flow Model Figure 4. Conceptual
diagram showing geometry
and boundaries for threedimensional test problem with
a nonpumping multinode well
(modified from Konikow and
Hornberger, 2006a). a cell having areal dimensions of 0.333 ft by 0.333 ft, which
yields a crosssectional area of 0.111 square feet (ft2). Because
the well lies on the plane of symmetry in the grid, a well
radius is assigned in the model that yields an equivalent crosssectional area to onehalf of the crosssectional area of the
well in the simulation of Reilly and others (0.0555 ft2). For a
well with a circular casing, this equivalent crosssectional area
would require a well radius of 0.133 ft. It is also assumed that
there would be a linear wellloss coefficient consistent with a
lower permeability well skin. The values of the skin properties
were adjusted during model calibration to achieve a vertical
profile of flows between the aquifer and the well that closely
matched that of Reilly and others (1989) (fig. 2).
Heads were calculated using the Preconditioned Conjugate Gradient (PCG2) solver in MODFLOW–2000, and
the flow model iteratively converged to a steadystate head
distribution with a 0.00 percent discrepancy. Konikow and
Hornberger (2006a,b) obtained almost exactly the same heads
and flows as did Reilly and others (1989). The calculated
head in the well was 4.9322 ft. The head distribution in the
aquifer near the nonpumping multinode well indicated that
water should flow from the aquifer into the upper part of the
borehole and discharge back into the aquifer through the lower
part of the well (fig. 6), which is consistent with the results of
Reilly and others (1989). Inflow to the well is greatest near the top of the well screen, and outflow is greatest near the bottom
of the well screen. The calculated total flow into the borehole was 9.79 ft3/d, which compares closely with 9.63 ft3/d
reported by Reilly and others (1989). Partial Penetration
If a well only partially penetrates an aquifer or is only
open to a fraction of the full thickness of the aquifer, then it
is widely recognized that consequent vertical flow components will cause an additional drawdown in the well beyond
that computed on the basis of assuming horizontal flow (for
example, see Walton, 1962; Driscoll, 1986; Kruseman and
de Ridder, 1990). Thus, if the three wells shown in figure 7
are all pumping at the same rate, then the drawdown in well
A, which is fully penetrating, would be less than expected in
wells B, C, or D, which are only partially penetrating. Driscoll
(1986, p. 249) notes that: “For a given yield, … the drawdown
in a pumping well is greater if the aquifer thickness is only
partially screened. For a given drawdown, the yield from a
well partially penetrating the aquifer is less than the yield from
one completely penetrating the aquifer.” Similarly, if a well
represented in the model is open to a vertical interval less than
the thickness of the model cell, then the drawdown in the well Figure 5. Map view of
MODFLOW finitedifference
grid showing location of
fine grid area and of the
nonpumping multinode well
in the Reilly test problem
(modified from Konikow and
Hornberger, 2006a). Model Features and Processes 11 Figure 6. Calculated
head distribution in vertical
section near well on plane
of symmetry. For clarity, only
upgradient 5 percent of domain
is shown (flow model domain
extends to 10,000 feet in
xdirection). From Konikow and
Hornberger, 2006a. should be greater than that computed by the model for the
associated cell and for a well that fully penetrates the cell.
Driscoll (1986) also demonstrates that the position and
(or) distribution of well screens within an aquifer can influence
the effects of partial penetration. Referring to figure 7, Wells B,
C, and D are all open to 33 percent of the saturated thickness
of the aquifer (α = 0.33, where α is the fraction of the aquifer
thickness to which the well is open—the partial penetration
fraction). Wells B and C both have identical scree...
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