This study investigates the problem of promoting the probability for finding a groundwater contamination source in three-dimensional heterogeneous aquifers.
Different heterogeneous aquifers are considered when employing the computer model SATS-GWT to estimate source location. The random hydraulic conductivity fields, generated by the program sasim with known conductivity as conditioning data, are log-normally distributed with a given mean, standard deviation of lnK, and spatial correlation structure. Three scenarios are designed to study the effects of various numbers and patterns of sampling points on the probability of obtaining correct source location.
In the first scenario, as the standard deviation of the hydraulic conductivity increases, the results of source identification get poorer. The results of MCS show that the use of six sampling points can give up to 50 % chance to get the correct source location for σy = 0.5. However, as the σy is increased to 1.0, nine
sampling points is needed to get more chance of finding correct source location.
Moreover, when the σy is increased to 1.5, 12 sampling points is needed.
In the second scenario, LHS is applied as an alternative to the MCS along with a source identification model for estimating the source location in three-dimensional
heterogeneous aquifers. A total of 1000 heterogeneous aquifers which have the same conditioning data and statistical parameters as scenario 1 are generated by the program sasim again. Those conductivity fields are sampled by LHS method and used to identify the source location by the model SATS-GWT again. The result demonstrates that when the σy = 0.5, 1.0 and 1.5, the chance to obtain correct source
location are all similar to MCS result from the statistical viewpoint.
The third scenario is to compare the effect of the five sampling point patterns on source identification estimation. The result demonstrates that when σy = 0.5, the
sampling points are arranged in a hexagon pattern at the downgradient of the source will also have good chance to get correct source location.
In sum, this study investigates different degrees of aquifer heterogeneity and different sampling techniques on the probability of identifying a contaminant source.
It can be concluded that the probability of identifying a contaminant source location and the effect of the uncertainty in heterogeneous groundwater sites can be reduced as the sampling numbers are increased. In addition, we suggest the sampling points allocated in a hexagon pattern at the downgradient of the source can obtain better identification results if the sampling points with four concentration zones are not available.
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Table 1 The measured concentrations and hydraulic conductivities in monitoring wells for MCS method Standard deviation of the lnK, σy
0.5 1.0 1.5
C1 35.641 3.277E-01 75.932 3.508E-01 313.790 4.678E-01 D2 20.065 7.252E-01 21.504 8.428E-01 29.742 1.144E+00 E2 11.165 2.957E-01 5.520 4.143E-01 4.264 3.733E-01 H2 13.902 5.684E-01 13.277 6.594E-01 20.328 9.029E-01
I1 19.786 3.180E-01 20.803 3.297E-01 33.483 3.339E-01 J1 14.069 2.935E-01 10.570 3.303E-01 15.975 4.253E-01 K2 18.543 4.568E-01 10.634 5.402E-01 10.606 6.254E-01 M2 7.486 1.266E-01 3.287 1.186E-01 1.051 1.318E-01
N4 14.629 3.172E-01 15.456 3.621E-01 14.055 4.988E-01 O2 16.194 2.997E-01 11.079 3.291E-01 17.087 4.410E-01 P1 35.766 2.294E-01 71.307 2.299E-01 110.388 3.152E-01 Q3 14.168 2.548E-01 21.349 2.642E-01 20.491 3.015E-01
Table 2 Results of source identification for MCS method as σy = 0.5 (m/day) Sampling numbers
6 9 12 Source location Source location Source location
x y z
Identification probability
(%) x y z
Identification probability
(%) x y z
Identification probability
(%) 220 540 -9 50 220 540 -9 54 220 540 -9 56 220 540 -3 20 220 540 -3 10 220 540 -3 18 260 540 -9 22 260 540 -9 12 220 540 -15 4 260 540 -3 4 260 540 -3 22 260 540 -9 6 180 540 -9 4 180 540 -3 2 260 540 -3 12
180 540 -3 4
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years.
Table 3 Results of source identification for MCS method as σy = 1.0 (m/day) Sampling numbers
6 9 12 Source location Source location Source location
x y z
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years.
Table 4Results of source identification for MCS method as σy = 1.5 (m/day) Sampling numbers
6 9 12 Source location Source location Source location
x y z
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years.
Table 5 The measured concentrations and hydraulic conductivities in monitoring wells for LHS method Standard deviation of the lnK, σy
0.5 1.0 1.5
C1 35.641 3.879E-01 75.932 2.873E-01 313.790 3.280E-01 D2 20.065 6.320E-01 21.504 4.822E-01 29.742 5.248E-01 E2 11.165 3.081E-01 5.520 2.326E-01 4.264 2.258E-01 H2 13.902 5.180E-01 13.277 4.055E-01 20.328 4.131E-01
I1 19.786 3.002E-01 20.803 2.542E-01 33.483 2.630E-01 J1 14.069 2.843E-01 10.570 2.454E-01 15.975 2.450E-01 K2 18.543 4.009E-01 10.634 3.469E-01 10.606 3.338E-01 M2 7.486 1.130E-01 3.287 1.456E-01 1.051 3.865E-02
N4 14.629 3.300E-01 15.456 2.516E-01 14.055 2.606E-01 O2 16.194 2.896E-01 11.079 2.481E-01 17.087 2.321E-01 P1 35.766 2.214E-01 71.307 2.311E-01 110.388 1.526E-01 Q3 14.168 2.364E-01 21.349 1.878E-01 20.491 1.633E-01
Table 6 Results of source identification for LHS method as σy = 0.5 (m/day) Sampling numbers
6 9 12 Source location Source location Source location
x y z Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years.
Table 7 Results of source identification for LHS method as σy = 1.0 (m/day) Sampling numbers
6 9 12 Source location Source location Source location
x y z
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years.
Table 8 Results of source identification for LHS method as σy = 1.5 (m/day) Sampling numbers
6 9 12 Source location Source location Source location
x y z
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years.
Table 9 The measured concentrations and hydraulic conductivities in different (1) Along the downgradient of the source
D2 13.902 6.7880E-01
(2) Along a line perpendicular to the flow direction at the downgradient of the source
A2 14.168 5.0630E-02
(3) Triangle pattern at the downgradient of the source
D2 13.902 7.8980E-01
(4) Hexagon pattern at the downgradient of the source
D2 13.902 7.7110E-01
Table 10 Results of source identification versus sampling location patterns as σy = 0.5 (m/day) Sampling patterns
Along the downgradient of the source
Along a line perpendicular to the flow direction at the downgradient
of the source
Source location Source location Source location
x y z
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years.
Fig. 1. Flowchart of SATS-GWT. The OFVCALO represent the objective function value of local optimal solution at candidate location
Fig. 2. The procedure for identifying source location along with the MCS method
Fig. 3. The procedure for identifying source location along with the LHS method
C onstant head and
Fig. 4. The aquifer system with an area of 1000m by 1000m and the locations of real source S1, eight suspicious sources near S1, and sampling points A to Q
0 10 20 30 40 50
Number of Monte Carlo Runs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability
MCS Method
sampling points = 6 sampling points = 9 sampling points = 12
Fig. 5. The performance curves of the probability versus σ =0.5 (m/day)y
0 10 20 30 40 50
Number of Monte Carlo Runs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability
MCS Method
sampling points = 6 sampling points = 9 sampling points = 12
Fig. 6. The performance curves of the probability versus σ =1.0 (m/day) y
0 10 20 30 40 50
Number of Monte Carlo Runs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability
MCS Method
sampling points = 6 sampling points = 9 sampling points = 12
Fig. 7. The performance curves of the probability versus σ =1.5 (m/day) y
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
Standard deviation of lnk
0 0.2 0.4 0.6 0.8 1
Probability
assign standard deviation of lnk
0.5 1.0 1.5
Fig. 8. The cumulative frequency distribution of 1000 conductivity fields data of σy
= 0.5, 1.0, and 1.5 (m/day)
0 10 20 30 40 50
Number of Monte Carlo runs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability
LHS Method
sampling points = 6 sampling points = 9 sampling points = 12
Fig. 9. The performance curves of the probability versus σ =0.5 (m/day) y
0 10 20 30 40 50
Number of Monte Carlo runs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability
LHS Method
sampling points = 6 sampling points = 9 sampling points = 12
Fig. 10. The performance curves of the probability versus σ =1.0 (m/day) y
0 10 20 30 40 50
Number of Monte Carlo runs
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Probability
LHS Method
sampling points = 6 sampling points = 9 sampling points = 12
Fig. 11. The performance curves of the probability versus σ =1.5 (m/day) y
0 10 20 30 40 50
Number of Monte Carlo runs
0
Along the downgradient of the source
Along a line perpendicular to the flow direction at the downgradient of the source
Triangle pattern at the downgradient of the source Hexagon pattern at the downgradient of the source
Fig. 12. The performance curves of the probability versus sampling location patterns as σ =0.5 (m/day) y