Reilly and others 1989 reported that their well was

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Unformatted text preview: assumed to be unconfined (convertible). The well was assumed to have a 60-ft 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 ground-water flow in a three-dimensional, steadystate flow system containing a multi-node 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 Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model Figure 4. Conceptual diagram showing geometry and boundaries for threedimensional test problem with a nonpumping multi-node well (modified from Konikow and Hornberger, 2006a). a cell having areal dimensions of 0.333 ft by 0.333 ft, which yields a cross-sectional 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 one-half of the cross-sectional area of the well in the simulation of Reilly and others (0.0555 ft2). For a well with a circular casing, this equivalent cross-sectional area would require a well radius of 0.133 ft. It is also assumed that there would be a linear well-loss 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 steady-state 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 multi-node 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 finite-difference grid showing location of fine grid area and of the nonpumping multi-node 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 x-direction). 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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This document was uploaded on 01/20/2014.

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