41a it is also possible that a well may have been

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Unformatted text preview: ts associated node of the finite-difference grid. For example, when drilling a well, it is not unusual that the driller will use a larger diameter drill bit and casing for the upper part of the hole and then reduce the bit size and borehole diameter at greater depths. Thus, depending on the relative elevations of the tops and bottoms of model layers, it is possible that the diameter (and radius) of the open interval of a well may change within the thickness interval represented by a particular model layer (fig. 41A). It is also possible that a well may have been constructed with multiple screens and that a well may have different skin properties for different intervals. If the lengths of the screens are short relative to the thickness of a model layer representing an aquifer, then it is possible that more than one screen of a long well may lie within a single model layer (fig. 41B). Well A (fig. 41) fully penetrates all three model layers into which the aquifer is discretized. However, in this example the larger diameter screen penetrates the upper 40 percent of model layer 2, and the smaller diameter screen penetrates the deeper 60 percent of this cell. In cases like this, the MNW2 Package will compute a cell-to-well conductance value for each section of screen (or open interval) that has unique properties and then compute a length-weighted average conductance value for that node as (37) where CWCn is the effective cell-to-well conductance for the node, CWCi is the calculated cell-to-well conductance for the ith section of screen, k is the number of sections of screen (open intervals) in the cell, and Li is the length of each section of screen. The average effective well radius would be calculated in the same manner. If the specifications of top and bottom elevations of well screens indicate that there are multiple well screens within a single model layer (fig. 41B), then the model will compute the cell-to-well conductance for each interval and then compute a length-weighted average conductance value for that node using equation 37. Conductances are normally computed under an assumption that the screen is open to the full thickness of the model layer in which it is located. In the case where the sum of the lengths of the multiple well screens within the cell is less than the thickness of the cell (such as Well B in figure 41), the effective conductance of the combined length of well screen must be adjusted for the reduced total length relative to the thickness of the cell, and the effects of partial penetration on heads should also be considered. That is, if the sum of the lengths of the well screens in Well B for example, is 40 ft and the thickness of the cell is 100 ft, then the cell-to-well conductance would only be 40 percent of that for a fully penetrating length of well screen. Therefore, in such cases, equation 37 above must be modified to account for the effect on cell-to-well conductance of having a shorter total length of screen than the thickness of the cell as (38) where bn is the thickness of the cell. In the case where cell-towell conductance values for each screen interval are explicitly specified by the user (under the option in dataset 2b of LOSSTYPE=SPECIFYcwc), it is assumed that the specified value of conductance is already appropriate for the actual Model Features and Processes 37 Figure 38. Schematic cross-sectional view (looking west) of part of a MODFLOW grid containing a multi-node well that changes direction and is connected in sequence from node “j,i,k” to node “j,i +1,k+2.” The casing is assumed to be closed off to both cells in model layer k +1 through which the well passes. Each node of the well consists of two segments. A borehole is always assumed to extend vertically from its first node to the top of the model grid. Figure 39. Schematic crosssectional view through a MODFLOW grid showing a mostly horizontal multi-node well open to columns 2 through 5 in layer 5 and column 1 in layer 4 and assumed to extend vertically from the first node to the top of the model to compute total borehole length. The well changes direction at nodes 1 and 2, and the two segments associated with these two nodes are of unequal lengths; Lw1 and Lw2 are labeled for node 2. Modified from Konikow and Hornberger (2006b.) Figure 40. Schematic cross section of an unconfined aquifer represented by three model layers, showing the relation of the open and closed intervals (Lw and Lc, respectively) to the position of the water table within unconfined model layer 1. A, at the initial time (t 0), the water table coincides with the top of the vertical well screen segment and Lw equals the sum of the lengths of the two segments; B, at a later time (t 1), the water table has declined and part of the well screen is dry, so Lc has increased and Lw has decreased compared to t0. 38 Revised Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model length of the screen, and no further adjustments are made for its length relative to the layer thickness. To compute the additional drawdown due to partial penetrati...
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