For this particular example, identifying aquifer parameters via classical curve matching, it is difficult to obtain a good visual match since the value is small. Table 2 summarizes the estimation performance of the proposed methods for both test scenarios. For instance, TSM predicted T and S values as 43.90 × 10−4 m2/min and 1.2642 × 10−7, respectively, for test Scenario 1 and those obtained by AMM were 44.09 × 10−4 m2/min and 1.1999 × 10−7, respectively. When T and S are uncorrelated as simulated in Scenario 1, the S estimates of proposed methods yield the geometric mean value of the fractures as tabulated in Table 2.
Table 2
Results and error analysis for fracture model
| Aquifer parameters | Drawdown comparison | |||||
|---|---|---|---|---|---|---|
| T (m2/min) | S | R2 | RMSE | SI | MAE | |
| Scenario 1 | ||||||
| Proposed TSM (η1 = 0.5, η2 = 0.25) | 4.39 × 10−3 | 1.26 × 10−7 | 1.0000 | 0.0002 | 0.0002 | 0.0001 |
| Proposed AMM (η1 = 0.5, η2 = 0.25) | 4.41 × 10−3 | 1.20 × 10−7 | 1.0000 | 0.0001 | 0.0002 | 0.0001 |
| Cooper et al. (1967), curve match | 1.90 × 10−3 | 1.00 × 10−3 | 0.9991 | 0.0156 | 0.0214 | 0.0115 |
| Singh (2007) | 4.70 × 10−3 | 1.00 × 10−7 | 0.9998 | 0.0066 | 0.0091 | 0.0037 |
| Scenario 2 | ||||||
| Proposed TSM (η1 = 0.5, η2 = 0.25) | 4.45 × 10−3 | 3.08 × 10−9 | 1.0000 | 0.0001 | 0.0002 | 0.0001 |
| Proposed AMM (η1 = 0.5, η2 = 0.25) | 4.46 × 10−3 | 2.92 × 10−9 | 1.0000 | 0.0002 | 0.0002 | 0.0001 |
| Cooper et al. (1967), curve match | 2.00 × 10−3 | 1.00 × 10−4 | 0.9995 | 0.0137 | 0.0183 | 0.0083 |
| Singh (2007) | 4.00 × 10−3 | 1.00 × 10−8 | 0.9999 | 0.0060 | 0.0081 | 0.0033 |
| Aquifer parameters | Drawdown comparison | |||||
|---|---|---|---|---|---|---|
| T (m2/min) | S | R2 | RMSE | SI | MAE | |
| Scenario 1 | ||||||
| Proposed TSM (η1 = 0.5, η2 = 0.25) | 4.39 × 10−3 | 1.26 × 10−7 | 1.0000 | 0.0002 | 0.0002 | 0.0001 |
| Proposed AMM (η1 = 0.5, η2 = 0.25) | 4.41 × 10−3 | 1.20 × 10−7 | 1.0000 | 0.0001 | 0.0002 | 0.0001 |
| Cooper et al. (1967), curve match | 1.90 × 10−3 | 1.00 × 10−3 | 0.9991 | 0.0156 | 0.0214 | 0.0115 |
| Singh (2007) | 4.70 × 10−3 | 1.00 × 10−7 | 0.9998 | 0.0066 | 0.0091 | 0.0037 |
| Scenario 2 | ||||||
| Proposed TSM (η1 = 0.5, η2 = 0.25) | 4.45 × 10−3 | 3.08 × 10−9 | 1.0000 | 0.0001 | 0.0002 | 0.0001 |
| Proposed AMM (η1 = 0.5, η2 = 0.25) | 4.46 × 10−3 | 2.92 × 10−9 | 1.0000 | 0.0002 | 0.0002 | 0.0001 |
| Cooper et al. (1967), curve match | 2.00 × 10−3 | 1.00 × 10−4 | 0.9995 | 0.0137 | 0.0183 | 0.0083 |
| Singh (2007) | 4.00 × 10−3 | 1.00 × 10−8 | 0.9999 | 0.0060 | 0.0081 | 0.0033 |