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Following the application procedures of TSM and AMM, the transmissivity and storativity values of each experiment were estimated selecting and , as shown in Figure 4. These analyses were also implemented by employing a number of pre-defined normalized drawdown values which were considered to reflect the different characters of the slug test such as early, intermediate, and late time behavior. Table 1 summarizes the error analysis for several η12 ratios utilized in this example. In Table 1, the error metrics for drawdown analysis are given as the mean value of 41 distinct experiments. According to Table 1, the performance of the proposed methods increases if the late time behavior was preferred, which is not explicitly understood from the classical curve match based methods. For instance, choosing η1 and η2 values as 0.250 and 0.166, which is assumed to reflect late time behavior of the slug test, in both methods yields better estimation results in comparison with those employing 0.800 and 0.533. In general, when η1/η2 increases, the errors between the actual and estimated parameters reduce for both of the proposed methods for every time level used in this example.
Table 1

Estimation performance and error analysis of TSM and AMM for several η1 and η2 values

Transmissivity analysis
Storativity analysis
Drawdown analysis
Methodη1η12R2RMSESIMEMin AEMax AEMAER2RMSESIME
TSM 0.8 1.5 0.9661 0.0049 0.2185 −2.01 × 10−5 3.75 × 10−6 8.16 × 10−4 1.39 × 10−4 0.9999 0.0047 0.0128 −1.79 × 10−4 
  0.9906 0.0027 0.1234 4.41 × 10−4 2.26 × 10−5 4.66 × 10−4 9.00 × 10−5 0.9999 0.0040 0.0108 −1.70 × 10−4 
  0.9940 0.0021 0.0926 1.23 × 10−4 2.67 × 10−5 3.31 × 10−4 6.56 × 10−5 0.9999 0.0037 0.0099 −1.83 × 10−4 
  0.9952 0.0019 0.0838 2.00 × 10−4 3.19 × 10−5 3.08 × 10−4 5.34 × 10−5 0.9999 0.0036 0.0097 −1.61 × 10−4 
 0.5 1.5 0.9820 0.0035 0.1592 1.84 × 10−4 1.21 × 10−5 6.44 × 10−4 1.05 × 10−4 0.9999 0.0041 0.0111 −1.91 × 10−4 
  0.9904 0.0026 0.1172 5.17 × 10−5 2.14 × 10−5 2.92 × 10−4 6.04 × 10−5 0.9999 0.0036 0.0100 −1.96 × 10−4 
  0.9946 0.0020 0.0898 2.54 × 10−4 3.75 × 10−5 2.25 × 10−4 4.92 × 10−5 0.9999 0.0035 0.0096 −1.54 × 10−4 
  0.9981 0.0012 0.0536 1.07 × 10−4 4.12 × 10−5 1.86 × 10−4 3.18 × 10−5 0.9999 0.0034 0.0092 −1.50 × 10−4 
 0.25 1.5 0.9708 0.0046 0.2070 5.88 × 10−4 1.92 × 10−5 7.50 × 10−4 1.48 × 10−4 0.9999 0.0044 0.0124 −1.55 × 10−4 
  0.9903 0.0026 0.1169 −8.79 × 10−5 2.92 × 10−5 3.39 × 10−4 4.31 × 10−5 0.9999 0.0036 0.0099 −1.62 × 10−4 
  0.9968 0.0015 0.0690 −9.78 × 10−5 3.49 × 10−5 1.88 × 10−4 3.15 × 10−5 0.9999 0.0035 0.0095 −1.39 × 10−4 
  0.9988 0.0010 0.0450 2.04 × 10−4 5.09 × 10−5 1.74 × 10−4 2.21 × 10−5 0.9999 0.0035 0.0094 −1.42 × 10−4 
AMM 0.8 1.5 0.9658 0.0049 0.2193 2.74 × 10−5 3.72 × 10−6 8.33 × 10−4 1.41 × 10−4 0.9999 0.0047 0.0129 −1.76 × 10−4 
  0.9906 0.0028 0.1238 4.53 × 10−4 2.16 × 10−5 4.84 × 10−4 9.07 × 10−5 0.9999 0.0040 0.0108 −1.69 × 10−4 
  0.9939 0.0021 0.0939 1.39 × 10−4 2.61 × 10−5 3.33 × 10−4 6.66 × 10−5 0.9999 0.0037 0.0100 −1.83 × 10−4 
  0.9950 0.0019 0.0856 2.11 × 10−4 3.10 × 10−5 3.09 × 10−4 5.47 × 10−5 0.9999 0.0036 0.0097 −1.62 × 10−4 
 0.5 1.5 0.9820 0.0035 0.1594 1.50 × 10−4 1.18 × 10−5 6.36 × 10−4 1.05 × 10−4 0.9999 0.0041 0.0111 −1.91 × 10−4 
  0.9902 0.0026 0.1183 2.48 × 10−5 2.12 × 10−5 2.88 × 10−4 6.03 × 10−5 0.9999 0.0036 0.0100 −1.97 × 10−4 
  0.9950 0.0019 0.0862 2.07 × 10−4 3.79 × 10−5 2.19 × 10−4 4.71 × 10−5 0.9999 0.0035 0.0096 −1.52 × 10−4 
  0.9982 0.0012 0.0520 7.49 × 10−5 4.09 × 10−5 1.82 × 10−4 3.10 × 10−5 0.9999 0.0034 0.0092 −1.50 × 10−4 
 0.25 1.5 0.9722 0.0045 0.2012 5.17 × 10−4 1.86 × 10−5 6.95 × 10−4 1.42 × 10−4 0.9999 0.0044 0.0123 −1.54 × 10−4 
  0.9904 0.0026 0.1166 −1.11 × 10−4 2.87 × 10−5 3.38 × 10−4 4.27 × 10−5 0.9999 0.0036 0.0099 −1.62 × 10−4 
  0.9970 0.0015 0.0671 −1.02 × 10−4 3.53 × 10−5 1.84 × 10−4 3.06 × 10−5 0.9999 0.0035 0.0095 −1.39 × 10−4 
  0.9988 0.0010 0.0440 1.73 × 10−4 5.04 × 10−5 1.72 × 10−4 2.15 × 10−5 0.9999 0.0035 0.0094 −1.42 × 10−4 
Transmissivity analysis
Storativity analysis
Drawdown analysis
Methodη1η12R2RMSESIMEMin AEMax AEMAER2RMSESIME
TSM 0.8 1.5 0.9661 0.0049 0.2185 −2.01 × 10−5 3.75 × 10−6 8.16 × 10−4 1.39 × 10−4 0.9999 0.0047 0.0128 −1.79 × 10−4 
  0.9906 0.0027 0.1234 4.41 × 10−4 2.26 × 10−5 4.66 × 10−4 9.00 × 10−5 0.9999 0.0040 0.0108 −1.70 × 10−4 
  0.9940 0.0021 0.0926 1.23 × 10−4 2.67 × 10−5 3.31 × 10−4 6.56 × 10−5 0.9999 0.0037 0.0099 −1.83 × 10−4 
  0.9952 0.0019 0.0838 2.00 × 10−4 3.19 × 10−5 3.08 × 10−4 5.34 × 10−5 0.9999 0.0036 0.0097 −1.61 × 10−4 
 0.5 1.5 0.9820 0.0035 0.1592 1.84 × 10−4 1.21 × 10−5 6.44 × 10−4 1.05 × 10−4 0.9999 0.0041 0.0111 −1.91 × 10−4 
  0.9904 0.0026 0.1172 5.17 × 10−5 2.14 × 10−5 2.92 × 10−4 6.04 × 10−5 0.9999 0.0036 0.0100 −1.96 × 10−4 
  0.9946 0.0020 0.0898 2.54 × 10−4 3.75 × 10−5 2.25 × 10−4 4.92 × 10−5 0.9999 0.0035 0.0096 −1.54 × 10−4 
  0.9981 0.0012 0.0536 1.07 × 10−4 4.12 × 10−5 1.86 × 10−4 3.18 × 10−5 0.9999 0.0034 0.0092 −1.50 × 10−4 
 0.25 1.5 0.9708 0.0046 0.2070 5.88 × 10−4 1.92 × 10−5 7.50 × 10−4 1.48 × 10−4 0.9999 0.0044 0.0124 −1.55 × 10−4 
  0.9903 0.0026 0.1169 −8.79 × 10−5 2.92 × 10−5 3.39 × 10−4 4.31 × 10−5 0.9999 0.0036 0.0099 −1.62 × 10−4 
  0.9968 0.0015 0.0690 −9.78 × 10−5 3.49 × 10−5 1.88 × 10−4 3.15 × 10−5 0.9999 0.0035 0.0095 −1.39 × 10−4 
  0.9988 0.0010 0.0450 2.04 × 10−4 5.09 × 10−5 1.74 × 10−4 2.21 × 10−5 0.9999 0.0035 0.0094 −1.42 × 10−4 
AMM 0.8 1.5 0.9658 0.0049 0.2193 2.74 × 10−5 3.72 × 10−6 8.33 × 10−4 1.41 × 10−4 0.9999 0.0047 0.0129 −1.76 × 10−4 
  0.9906 0.0028 0.1238 4.53 × 10−4 2.16 × 10−5 4.84 × 10−4 9.07 × 10−5 0.9999 0.0040 0.0108 −1.69 × 10−4 
  0.9939 0.0021 0.0939 1.39 × 10−4 2.61 × 10−5 3.33 × 10−4 6.66 × 10−5 0.9999 0.0037 0.0100 −1.83 × 10−4 
  0.9950 0.0019 0.0856 2.11 × 10−4 3.10 × 10−5 3.09 × 10−4 5.47 × 10−5 0.9999 0.0036 0.0097 −1.62 × 10−4 
 0.5 1.5 0.9820 0.0035 0.1594 1.50 × 10−4 1.18 × 10−5 6.36 × 10−4 1.05 × 10−4 0.9999 0.0041 0.0111 −1.91 × 10−4 
  0.9902 0.0026 0.1183 2.48 × 10−5 2.12 × 10−5 2.88 × 10−4 6.03 × 10−5 0.9999 0.0036 0.0100 −1.97 × 10−4 
  0.9950 0.0019 0.0862 2.07 × 10−4 3.79 × 10−5 2.19 × 10−4 4.71 × 10−5 0.9999 0.0035 0.0096 −1.52 × 10−4 
  0.9982 0.0012 0.0520 7.49 × 10−5 4.09 × 10−5 1.82 × 10−4 3.10 × 10−5 0.9999 0.0034 0.0092 −1.50 × 10−4 
 0.25 1.5 0.9722 0.0045 0.2012 5.17 × 10−4 1.86 × 10−5 6.95 × 10−4 1.42 × 10−4 0.9999 0.0044 0.0123 −1.54 × 10−4 
  0.9904 0.0026 0.1166 −1.11 × 10−4 2.87 × 10−5 3.38 × 10−4 4.27 × 10−5 0.9999 0.0036 0.0099 −1.62 × 10−4 
  0.9970 0.0015 0.0671 −1.02 × 10−4 3.53 × 10−5 1.84 × 10−4 3.06 × 10−5 0.9999 0.0035 0.0095 −1.39 × 10−4 
  0.9988 0.0010 0.0440 1.73 × 10−4 5.04 × 10−5 1.72 × 10−4 2.15 × 10−5 0.9999 0.0035 0.0094 −1.42 × 10−4 
Figure 4

The overall performance of: (a) T estimates by TSM, (b) S estimates by TSM, (c) T estimates by AMM, and (d) S estimates by AMM.

Figure 4

The overall performance of: (a) T estimates by TSM, (b) S estimates by TSM, (c) T estimates by AMM, and (d) S estimates by AMM.

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