Another relation that can be seen in figure 8 is the

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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 ground-water 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 no-flow 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 Multi-Node Well (MNW2) Package for MODFLOW Ground-Water 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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This document was uploaded on 01/20/2014.

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