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)SR2RMSESIMAE
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)SR2RMSESIMAE
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

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