S CENARIO 1: E FFECT OF THE L EVEL OF A QUIFER H ETEROGENEITY

The level of heterogeneity of the hydraulic conductivity is an important factor which influences the contaminant transport and results of contaminant identification.

Standard deviation of the hydraulic conductivity is one of the key parameters that quantify the degree of heterogeneity. In order to detect contamination distribution and estimate the source location in heterogeneous aquifer, the number of sampling points is crucial. However, what is an appropriate number of monitoring wells to find the source location in a heterogeneous aquifer needs to be explored. In this scenario, three cases are designed to study the effect of variation in heterogeneous hydraulic conductivity aquifer and the number of sampling points on the probability of obtaining correct source identification.

Chang and Yeh (2005) proposed a guideline indicating that the use of six sampling points with four concentration zones can give good results when employing the SATS-GWT in source information estimation. It means that the six sampling points should be installed such that the sampled concentrations at those sampling points can be divided into four zones with a dimensionless concentration difference of 0.001. The measured concentrations at these sampling points are simulated by

MODFLOW-GWT with the assumed release concentration at known source. Thus, six sampling points H2, J1, M2, N4, P1, and Q3 are taken to identify the source information in the first case study. The hydraulic conductivities and measured concentrations at these sampling points are listed in Table 1. The name of the sampling points given in Table 1 consists of the well name and layer number. Based on the information of the six sampling points, a hypothetical site is generated by the program sasim with y = 2.7 m/day, σ_y = 0.5 m/day. For identifying the contaminant source, the MCS and the computer code sasim are employed to produce new 50 realizations of random conditional conductivity field with the same known conductivity data and statistical parameters as the previous one to analyze the source information.

Table 2 shows the estimated results of case 1. The performance curves are shown in Fig. 5 in which the horizontal and vertical axes present the MCS runs and the probability of obtaining correct solution, respectively. In Table 2, the results indicate that in identifying the source location from 36 candidate sources, the use of six sampling points gives a 50 % chance to obtain the correct result. It implies that among those 50 MCS runs, a total of 25 runs obtain the correct source location (220 m, 540 m, -9 m). Such a result is very promising if compared with the chance of 2.8

% that is to randomly select one out of 36 candidate sources from a heterogeneous

aquifer formation. Besides, base the guideline of well design, when three sampling points C1, D2, and E2 are added to identify the source location, the average identification probability of the real source increases to 54 %. Moreover, when the sampling points I1, K2, and O2 are added to identify the source location, the chance can be increased to 56 % and more likely to estimate the source location. Thus, if the aquifer is heterogeneous with σ_y = 0.5, the use of SATS-GWT with 6, 9, and 12

sampling points can determine the real source location when employing with the MCS.

The second case assumes that the mean of hydraulic conductivities at the sampling points are also 2.7 m/day, but field conductivity σ_y = 1.0. Table 3 shows

the estimated results when the sampling numbers are 6, 9 and 12, and the performance curves is demonstrated in Fig. 6. The sampling points used to identify the suspicious source location are the same as case 1. When the sampling numbers are six, Table 3 shows that the estimated average probability of correct source location is 18 %, but 40

% chance in getting the wrong location (260m, 540m, -9m). It implies that six sampling points are not enough to obtain the correct result in this case.

As sampling numbers increase to nine, the chance of getting the correct source location increases to 32 %. In contrast, the highest average probability of getting the wrong location (220m, 540m, -15m) is only 20 %. It implies that the use of nine

sampling points can improve the poor estimation of using only six sampling points.

Moreover, when sampling numbers increase to 12, the chance of getting the correct source location is increased to 40 %. Contrarily, the highest average probability of obtaining the wrong location (260m, 540m, -9m) is 22 %. The chance of getting the correct source location is higher than those of other suspicious locations. Thus, if the aquifer is heterogeneous with σ_y = 1.0, the use of 9 or 12 sampling points can

both give good source location estimation from statistical viewpoint.

The third case considers σ_y = 1.5; the aquifer has more variety in hydraulic

conductivity. Fig. 7 shows that the chance of obtaining the correct source location is 16 % for six sampling points after 50 MCS runs, and the chance is 22 % after 50 MCS runs for nine sampling points. However, the highest chance of getting the wrong location (260m, 540m, -9m) is 48 % for six sampling points, and the highest chance of getting the wrong location (260m, 540m, -9m) is 30 % for nine sampling points.

Thus, the estimated results of using six and nine sampling points are both poor as indicated in Table 4. When sampling numbers increase to 12, the chance of getting the correct source location is increased to 32 %. The highest average probability of finding the wrong location (260m, 540m, -9m) decreases to 28 %. Obviously, the increase of sampling points improves the estimated result. It also implies that the contaminant source in a highly heterogeneous aquifer is difficult to identify and more

sampling points can have higher chance to get the correct source location estimation.

In sum, the performance of source identification becomes poorer as the standard deviation of the field hydraulic conductivity increases. However, the influence of the degree of uncertainty in hydraulic conductivity on the estimated result can be improved by increasing the number of sampling points as demonstrated in the analysis of cases 2 and 3.