In this thesis, a new approach combines SA and TS to incorporate a three-dimensional groundwater flow and solute transport model, MODFLOW-GWT, for solving the source identification problem. In the proposed approach, TS is employed to generate the candidate source locations and SA is employed to generate the release concentration and release period at the candidate source location. The MODFLOW-GWT is employed to simulate the three-dimensional plume concentrations at the monitoring wells. The effects of the values of initial guess and measurement error on the results when employing the proposed approach to perform source information estimation are studied. The proposed approach is also employed to investigate the requirements for the optimal number of sampling points and the conditions for effectively estimating source information. In addition, a guideline to optimally allocate the sampling points in the estimation of source information for an aquifer with steady-state groundwater flow is suggested. Six conclusions can be drawn in this study.
First, the approach we developed is capable for solving the three-dimensional groundwater source information estimation problem in both homogeneous and heterogeneous aquifer and the estimated results obtained from this study are similar
and accurate. Second, the identification results of the source location, release concentration, and release period are independent on the initial guess, indicating that an inexperienced investigator could use this approach to estimate source information.
Third, the effect of large upper bound values on the accuracy of source information estimation is insignificant. In contrast, small upper bound value may give wrong results if the real source is located outside the upper bound. Fourth, the proposed approach is applicable even the measured concentrations contain measurement error level up to 10%. Fifth, it is found that at least five sampling points with four concentration zones are needed to ensure good source information estimation if the both the source and sampling points are located at the same depths. However, six sampling points with four concentration zones is required when the sampling points are installed at various depths. Finally, we suggest installing the sampling points at different depth to obtain the reliable identification results if the real source depth is unknown.
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Table. 1 The sampling points and the measured concentrations for the homogeneous aquifer when the real source is located at the depth of -9 m.
Sampling point Measured concentration (ppm)
A2 0.4877
A3 0.4029
B1 0.2260
B2 0.2194
B3 0.1993
B4 0.1828
C2 0.3880
D1 0.2279
D2 0.2206
E2 0.0815
F1 0.2903
F2 0.2592
F4 0.2442
G2 0.0564
H2 0.1342
I1 0.1388
I2 0.1337
J2 0.1528
J3 0.1396
Table 2 The results of 7 cases designed in the first scenario for studying the effect of initial guesses on source information estimation
Initial guess value Result
Case Guess source
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years, and the sampling points contain A2, B2, C2, F2, I2, J2.
Table 3 The results of 6 cases designed in the second scenario for the examination of the solution domain
Upper bound value Results
Case Release
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years, and the sampling points contain A2, B2, C2, F2, I2, J2.
Table 4 The results of 3 cases designed in the third scenario for the effect of measurement error on source information estimation Identified result
Case Error level
(%) Source location (m)
Release concentration
(ppm)
Release period
(year)
Optimal objective function value
(×10-5)
1 1 (220,540, -9) 99.54 3.01 0.36
2 5 (220,540, -9) 104.08 3.03 4.70
3 10 (220,540, -9) 97.72 3.07 38.64
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, real release period is 3 years, and the sampling points contain A2, B2, C2, F2, I2, J2.
Table 5 The results for 5 cases designed in the fourth scenario for the examination of the number of sampling points Identified result
Case
Number of sampling
points
Sampling points Source location (m)
Release concentration
(ppm)
Release period
(year)
Optimal objective function value
(×10-5)
1 3 A2, F2, J2 (220,540, -9) 81.86 3.45 3.41
2 4 A2, B2, F2, J2 (220,540, -9) 98.59 2.97 0.98
3 5 A2, B2, F2, I2, J2 (220,540, -9) 103.50 3.02 0.94
4 6 A2, B2, F2, H2, I2, J2 (220,540, -9) 102.32 3.04 1.31
5 7 A2, B2, F2, G2, H2, I2, J2 (220,540, -9) 99.89 3.00 0.01
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, and real release period is 3 years.
Table 6 The results of 11 cases designed in the fifth scenario to find the guideline for effectively source information estimation Result
Case Sampling points Concentrati
on zones Source location (m)
Note that the real source is located at (220m, 540m, -9m), real release concentration is 100 ppm, and real release period is 3 years.
Table 7 The results of 16 cases designed in the sixth scenario to verify the guideline for effectively source information estimation Identified result
Case Sampling points Concentration
zones Source location
Table 8 The measured concentrations used in seventh scenario when real source is located at -3 m, -9m, -15 m, or -21 m Measured concentration
(ppm) Real source
location
(m) A2 B1 B2 C2 F2 F4 I1 I2 J2 J3
(220, 540, -3) 0.4577 0.2377 0.2181 0.3894 0.2788 0.2144 0.1435 0.1355 0.1490 0.1328 (220, 540, -9) 0.4877 0.2260 0.2194 0.3880 0.2592 0.2442 0.1388 0.1337 0.1528 0.1396 (220, 540, -15) 0.4035 0.1892 0.1990 0.3498 0.2565 0.2854 0.1252 0.1262 0.1374 0.1512 (220, 540, -21) 0.3425 0.1643 0.1821 0.3101 0.2425 0.2968 0.1153 0.1206 0.1295 0.1474
Table 9 The results of 8 cases designed in the seventh scenario for the examination of source depths Note that the real release concentration is 100 ppm and real release period is 3 years.
Table 10 The sampling points and the measured concentrations for a heterogeneous aquifer when the real source is located at the depth of -9 m.
Measured concentration (ppm)
Sampling point
Unconditional simulation
Conditional simulation
A2 0.4876 0.5005
B1 0.2039 0.2295
B2 0.1967 0.2217
C2 0.3363 0.3816
F2 0.2422 0.2899
F4 0.2202 0.2470
I1 0.1401 0.1407
I2 0.1368 0.1443
J2 0.1466 0.1507
J3 0.1358 0.1400
Table 11 The results of 4 cases designed in the eighth scenario for the examination of heterogeneous aquifer Identified result
Case Conditional
simulation Sampling points Source location (m)
Release concentration
(ppm)
Release period
(year)
Optimal objective function value
(×10-5)
1 Yes A2, B2, C2, F2, I2, J2 (220,540, -9) 99.78 3.01 4.22
2 Yes A2, B1, C2, F4, I1, J3 (220,540, -9) 100.43 3.00 0.49
3 No A2, B2, C2, F2, I2, J2 (220,540, -9) 102.47 3.02 9.92
4 No A2, B1, C2, F4, I1, J3 (220,540, -9) 98.75 3.01 3.67
Figure 1 Flowchart of tabu search. CUS represents the current solution, CAS
represents the adjacent candidate solution, GOOV represent the global objective
value and BOV represent the objective value of best adjacent candidate solution.
Figure 2 Flowchart of SATS-GWT. The OFVGO represents the objective function value of global optimal solution, OFVCULO represents the objective function value of the optimal solution at current location, OFVCALO represents the objective function value of the optimal solution at candidate location, and CAL represents the candidate location.
Figure 3 Flowchart of TS process in SATS-GWT. The OFV
GOrepresents the
objective function value of global optimal solution, OFV
CULOrepresents the
objective function value of the optimal solution at current location, OFV
CALOrepresents the objective function value of the optimal solution at candidate location,
CAL represents the candidate location, and CUL represents the current location.
A
Figure 4 The aquifer system with an area of 1000m by 1000m (not to scale) and the locations of real source S1, eight suspicious source near S1, and well A to well J.