Well d has three separate screens which improves well

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Unformatted text preview: n lengths, but because the screen in Well B is adjacent to a no-flow 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 cross-sectional 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 multi-node 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 Multi-Node Well (MNW2) Package for MODFLOW Ground-Water 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 early-time 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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