CHAPTER 4 RESULTS AND DISCUSSION
4.2 Sensitivity Analysis of Aquifer Parameters
The synthetic time-drawdown data for a leaky aquifer listed in Table 8 are generated from Hantush and Jacob’s model [1955]. The Q is 3000 m3/day, r is 30 m, T is 1000 m2/day, S is 10-4, and L is 0.03. The observed pumping period ranges from 0.017 to 1000 minutes.
The time-drawdown data and the normalized sensitivities are plotted in Figure 7. This figure indicates that the distribution curve of each normalized sensitivity of the aquifer parameters
reflects the temporal change of the drawdown in response to the relative change of each parameter. In other words, the non-zero periods in the normalized sensitivity curves imply that the aquifer parameters have influences on the drawdown at that time. In addition, this figure also indicates that all aquifer parameters have their own influence period to the drawdown. The influence period of parameter S increases from the start of pumping and decreases after 3 minutes. The drawdown is very sensitive to T except at the early period of the pumping and the normalized sensitivity is continuously increased through the end of the pumping. The parameter of leakage coefficient L appears to have influence on the drawdown from 1.5 minutes through the end of pumping. Such a phenomenon can be related to the physical behavior of the leaky aquifer. The normalized sensitivity of L keeps zero before 1.5 minutes, and it may ascribe to the fact that there is a time lag between the start of pumping and the response of the drawdown to the leakage effect. In contrast, the normalized sensitivities indicate that the parameters T and S have influence on the drawdown right at the beginning of pumping. In addition, the influence of S is larger than that of T at early pumping period. This result to some extend reflects the physical behavior of parameters T and S during the pumping.
The time-drawdown data set 1 of an unconfined aquifer, generated by Neuman’s model [1974], for pumping starting from 1 to 176360 seconds (49 hours) in an unconfined aquifer are listed in Table 9. The b is 10 m, Q is 3000 m3/day, and r is 10 m. The parameters Kr,
Kz, S, and Sy are set to 1×10-3 m/sec, 1×10-4 m/sec, 1×10-4, and 1×10-1, respectively. The time-drawdown data and related normalized sensitivities are plotted in Figure 8. Similar to Figure 7, the distribution curve of each normalized sensitivity reflects the temporal change of the drawdown in response to the relative change of each parameter, and all aquifer parameters affect the drawdown at different periods. The normalized sensitivity of parameter S starts from 1 to 10 seconds, Kz ranges from 1 to 1000 seconds, and Sy appears from 80 seconds to the end of pumping. The drawdown is most sensitive to the parameter Kr except at the early period of the pumping and the influence of Kr on the drawdown increases at the beginning and through the end of the pumping. The normalized sensitivity of S starts with highest value and drops quickly after the beginning of pumping. The normalized sensitivity of Kz
reaches its highest value in a range between 10 and 1000 seconds, implying that the slow decline of the water table is attributed to the contribution of the Kz at the moderate pumping time. The drawdown stops increasing when the normalized sensitivity of Kz approaches its maximum. The temporal distribution of Kr’s normalized sensitivity, displaying three segments during the pumping period, is similar to the drawdown curve. The second segment appears at 10 seconds and vanishes at 1000 seconds (16.67 min). Figure 8 shows that the drawdown increases in the third segment along with the decrease of Kz’s normalized sensitivity, clearly indicating rapid decrease of vertical drainage. The sensitivity curve demonstrates that the aquifer parameter Sy does not have any contribution in response to the
pumping at the beginning of the test and starts to react at about 80 seconds (1.33 min).
The time-drawdown data set 2 listed in Table 10 is generated by Moench’s model [1997].
The pumping starts from 0.6 to 600000 seconds (1000 minutes). The b is 10 m, Q is 1000 m3/day, and the r is 10 m. The parameters Kr, Kz, S, Sy, and rw, are set to 1×10-3 m/sec, 1×10-4 m/sec, 1×10-4, 1×10-1, and 1 m respectively. The time-drawdown data and related normalized sensitivities are plotted in Figure 9. The upper part of Figure 9 is the same plot but the normalized sensitivity of Kr is removed because the magnitude of Kr’s normalized sensitivity is relatively large at the end of pumping, and removing it is much helpful to recognize the small change of other parameter’s normalized sensitivities at the early period of pumping. The normalized sensitivity of rw ranges from 2 to 2000 seconds, S starts from 0.6 to 1000 seconds, Kz ranges from 100 to 10000 seconds, and Sy appears from 100 seconds to the end of pumping. The drawdown is most sensitive to the parameter Kr after pumping for 300 seconds and the influence of Kr on the drawdown increases at the beginning and through the end of the pumping.
The normalized sensitivity of rw starts at the beginning of the pumping, reflecting the physical phenomenon that the effect of well bore storage contributes to the drawdown immediately after pumping. The normalized sensitivity of S is relatively small compared with those of other parameters. The normalized sensitivity of Kz reaches its highest value in a range between 600 and 2000 seconds. Similar to Figure 8, the drawdown slowly
increasing when the normalized sensitivity of Kz approaches its maximum, indicating that the slow decline of the water table is attributed to the contribution of the Kz at the moderate pumping time. Figure 9 also shows that the effect of well bore storage is larger than that of Kr at early pumping period. This phenomenon indicates that the water is removed from the well first after pumping and the groundwater flow into the well since the head difference between the well and the aquifer. Certainly, the parameter Sy still does not have any contribution in response to the pumping at the beginning of the test and starts to react at about 100 seconds (1.67 min). Figures 8 and 9 indicate that the normalized sensitivities of parameters Kr, Kz, S, and Sy have similar temporal distributions but different magnitudes. In Moench’s model, the effect of S is relatively small, the influence periods of S and Kz are longer than that of Neuman’s model, and the effect of rw is smaller than that of Kr at the beginning of pumping.