The disagreement at early times reflects the reliance

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: uracy of the partial penetration correction in MNW2 was tested for the range of conditions depicted in figures 8–10. The results (fig. 11) show excellent agreement after early time (in these examples, after a dimensionless time of 103 has passed, which is equivalent to less than 2 seconds of real time in this example problem). The disagreement at early times reflects the reliance of computing the head in the well partly on the basis of the steady-state Thiem (1906) equation, as discussed previously. The resulting error is limited to such a small initial transient time period that it should not have any effect on the reliability of results for regional ground-water simulations over typical time periods. The analytical solutions for calculating drawdown in a partially penetrating well assume that the aquifer constitutes a single layer bounded above and below by confining layers. In a three-dimensional ground-water model, however, the vertical dimension may be discretized at a scale finer than the thickness of an aquifer. A range of vertical discretization possibilities are illustrated in figure 12. A well that is open to the middle third of an aquifer is depicted in figure 12A. If this aquifer were numerically simulated using a single model layer, then the thickness of the model layer (Δz) would be the same as the aquifer thickness. The head computed for the finite-difference cell containing this well would be consistent with that for a fully penetrating well withdrawing water from 15 the full volume of the cell. If observations of water levels in that well are to be compared to model-calculated values, then the head calculated for the well would have to be corrected for partial penetration effects, as well as for other possible well-loss terms. In figure 12B the aquifer is subdivided into three equally thick model layers. In this case, the partial penetration effects are explicitly modeled in MODFLOW because the well is open to the full thickness of model layer 2 and the finer vertical discretization allows the vertical components of flow above and below the well to be calculated directly; therefore, it is not necessary to simulate an additional drawdown term to account for the effects of partial penetration. One can question whether three model layers offers sufficient vertical discretization to accurately represent vertical components of flow near the well, but this can always be tested by trying an even finer vertical discretization, for example, as shown in figure 12C, where the aquifer is subdivided into six model layers, so the well could be simulated as an MNW open to (and fully penetrating) the middle two model layers. The vertical head gradients above and below the open interval can be computed at two nodes in this case versus one node for the case in figure 12B. In figure 12D, the well screen (or open interval) is slightly longer than one-third of the thickness of the aquifer, and in a six-layer model of the aquifer, the well would fully penetrate model layers 3 and 4, but only penetrate about one-third of model layer 2. If this well were represented by a MNW, then the correction for partial penetration would only affect the cell-to-well conductance in model layer 2, so the net effect on the head in the well would be substantially less than for a case in which a single-node well has a penetration fraction of 0.33. Figure 11. Plot showing comparisons of analytical and numerical solutions for dimensionless drawdown for selected cases shown in figures 8–10 for the Lohman problem. The well screen is located in the middle of the aquifer, except for one indicated case. Analytical solutions were calculated using the WTAQ Program (Barlow and Moench, 1999). Numerical solutions (showing every fourth data point) were calculated using MNW2 in MODFLOW–2000 (Harbaugh and others, 2000). 16 Revised Multi-Node Well (MNW2) Package for MODFLOW Ground-Water Flow Model Figure 12. Schematic crosssectional diagram showing alternate vertical discretization possibilities for simulating a confined aquifer containing a partially penetrating well. In A, the aquifer is represented by a single model layer, and the vertical discretization in the model (Dz) equals the aquifer thickness. In cases B–D, the red horizontal dotted lines represent the boundaries of the model layers used to simulate the aquifer, and Dz is less than the aquifer thickness. The alternative discretizations represented in figure 12A–C were evaluated with MODFLOW for the Lohman problem using a single model layer. Figure 11 shows the results of applying MNW2 to the problem for the case of α = 0.33; the numerical MNW2 results were essentially identical to the analytical solution at dimensionless times greater than 104. These results can then be compared with a simulation representing the three-layer conceptualization, as shown in figure 12B. In this case, the well fully penetrates layer 2 of the model, though it still penetrates only one-third of the aquifer. When the pumping is represented...
View Full Document

Ask a homework question - tutors are online