When the aquifer is further subdivided into six

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Unformatted text preview: using the standard WEL Package of MODFLOW, the simulated results show a noticeable error (fig. 13). This is primarily caused by a discretization that is too coarse to allow vertical head gradients near the well to be calculated accurately. Therefore, as the discretization is made finer, and the number of layers increases, the results improve. When the aquifer is further subdivided into six layers and the well assigned to the middle two layers, there is still a small error. However, when the aquifer is divided into 15 model layers and the well is represented with one-fifth of the total discharge in each of the middle five layers, the average head in the well computed numerically agrees almost exactly with both the analytical and MNW2 results after a dimensionless time of about 103. This also illustrates the efficiency advantage of the MNW2 Package relative to the standard WEL Package; to obtain a match to the analytical solution with only a single model layer, the MNW2 results required 178 seconds of computational time, whereas the 15-layer model with the WEL Package used 3,396 seconds of computational time to produce an equivalent match. For a water-table (unconfined) aquifer or a model layer that is allowed to convert from confined to unconfined, special care is required because the saturated thickness may change over time. An unconfined aquifer represented as a single Figure 13. Plot showing comparisons of analytical and numerical solutions for dimensionless drawdown for the Lohman problem with a partial penetration fraction of 0.33 and the well screen located in the middle of the aquifer. Numerical solutions (showing the first 15 data points and then every fourth data point afterwards) calculated using the standard WEL Package in MODFLOW–2000 (Harbaugh and others, 2000). Model Features and Processes model layer is illustrated in figure 14, in which the water table declines with time, represented sequentially from A to D. Because the position of the well screen is fixed, but the water table position changes with time, the relative position of the screen within the cell also changes with time. Therefore, the MNW2 Package will check to see if the saturated thickness (b) of a cell has changed, and if so, then the model will automatically update the values of the depths below the water table to the top and bottom of the well screen (zpd and zpl, respectively), the saturated length of the well screen (l = zpl – zpd), and the penetration fraction (α = l/b), as appropriate. If the water-table elevation drops below the bottom of the screen within a cell, as in figure 14D, then all flow between the cell and that node of the multi-node well is cut off (equivalent to resetting the cell-to-well conductance for that node to zero). Note that if the water table subsequently rises, then the screen will be assumed to rewet and become active again, with its length and partial penetration fraction updated on the basis of the new water table elevation and the screen characteristics. An unconfined aquifer is often discretized vertically into multiple model layers to obtain improved resolution of the results, as depicted in figure 15, which shows a case where an unconfined aquifer is subdivided into three model layers. In this example, the well screen fully penetrates model layer 2, both at the initial conditions (fig. 15A) and after a small decline of the water table within model layer 1 (fig. 15B). However, after the water table declines further so that it becomes located in model layer 2 (fig. 15C), model layer 1 at that location becomes inactive and both the saturated thickness of the cell and the saturated length of the well screen in layer 2 are reduced accordingly. If, however, the well screen were originally shorter and only partially penetrated model layer 2 (fig. 15D), then after the water table declined into model layer 2, the depths below the water table to the top and bottom of the well screen (zpd and zpl, respectively), the saturated length 17 of the well screen (l = zpl - zpd), and the penetration fraction (α = l/b) would have to be adjusted (and so they are automatically updated in MNW2 after each time step). The overriding assumption made in implementing the partial penetration correction in the MNW2 Package is that it can be applied on a model layer basis rather than on an aquifer basis. The likely disparity here is that the analytical solution assumes that the aquifer is bounded above and below by an impermeable confining layer, whereas in a complex three-dimensional model of a heterogeneous ground-water system, hydraulic conductivity values can vary by any amount between vertically adjacent cells. Furthermore, the analytical solution assumes that the aquifer is laterally homogeneous. Because in reality, hydraulic conductivity can vary by any amount between vertically and horizontally adjacent cells, the accuracy of the computed corrections for partial penetration effects may be compromised to some degree by these...
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