If one or more nodes of a true multi node well only

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: departures from the idealized assumptions. The previous tests of the correction for the effects of partial penetration used the MNW2 Package to represent single-node wells because they can approximate the geometry and boundary conditions for which analytical solutions are available, thus allowing the accuracy of the numerical solution to be evaluated. If one or more nodes of a true multi-node well only partially penetrate the model layers to which they are connected, then the flow between the cell and the well at that node would also be reduced relative to a comparable well that fully penetrates all cells. In other words, the correction for partial penetration effects should be applied to any node of a vertical multi-node well that penetrates less than the full thickness of a cell. However, no analytical solutions are known to apply to this situation. Therefore, the length of the well screen of the multi-node well in the Reilly problem was adjusted so that one node (the uppermost one) will penetrate less than the full thickness of the cell to which it is connected and the Figure 14. Schematic cross section of an unconfined aquifer simulated as a single “convertible” model layer showing the relation of the position of a partially penetrating well screen to the water table as the water table declines sequentially over time from A to D. As the saturated thickness (b) is reduced with time, 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 (a = l/b) are automatically updated. 18 Revised Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model Figure 15. Schematic cross section of an unconfined aquifer represented by three model layers, showing the relation of a well screened in model layer 2 to the water table as the water table declines over time (sequentially from A to C). The well screen fully penetrates model layer 2 in A–C, but is only partially penetrating in D. The red horizontal dotted lines represent the boundaries of the model layers used to simulate the aquifer, and Dz is the layer thickness. results can be compared to the fully penetrating case. The evaluation is therefore limited to examining the relative effects on head and flow in the well and assuring that the results are logical and consistent. To provide the basis of this test, the elevation of the top of the screen was lowered in increments from the elevation of the top of model layer 2 to the elevation of the bottom of model layer 2. This corresponded to reducing the total screen length from 60 ft to 55 ft (a reduction in length by 8.3 percent). Overall, one would expect that reducing the total length of the well screen would reduce the total flow through the well. This also corresponds with changing the partial penetration fraction (α) for the uppermost node of the multi-node well from a value of α = 1.0 to α = 0.0 as the elevation of the top of the screen is reduced. The results show that the adjustments of the penetration fraction in just one of the 12 nodes comprising the well have a very small effect on the head (or water level) in the well (fig. 16A) and that the change in head over the total range of adjustment is only -0.00018 ft (fig. 16B). That is, the head in the well goes down slightly as the penetration fraction decreases. The low sensitivity of head in the well to these adjustments can be contrasted with the relatively high sensitivity of the total flow through the borehole to the same changes (fig. 17). The total intraborehole flow decreases from about 9.79 ft3/d to about 8.28 ft3/d (15.4 percent) as the uppermost node changes from 100 percent penetration to 0 percent penetration. This change is about twice the percentage reduction in total length of the well screen. The change in flow shown in figure 17 can be attributed primarily to reduced inflow in node 1 (the uppermost node of the 12 nodes constituting this multi-node well) as the length of the screen in node 1 is sequentially reduced from the full thickness of the cell to zero (fig. 18). The results show a large change in flow in the uppermost node, where the penetration is adjusted; nodal changes are propagated downward to other nodes with diminishing effects with distance. Figure 16. Plot showing the effect of variations in the penetration fraction for the uppermost node of the multi-node well in the Reilly problem on the computed water level (head) in A, the well; and B, on the corresponding change in water level relative to fully penetrating well. Model Features and Processes Overall, all of the observed effects in the numerical experiments of partial penetration of one node out of 12 appear to be logical and consistent with hydrologic principles. These results indicate that the partial penetration correction, as applied to individual nodes of a multi-node well, is working correctly. Because the correction for effects of partial penetration, as implemented in the MNW2 Package, is clearly an approx...
View Full Document

Ask a homework question - tutors are online