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Geothermal Energy

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Table 4 A summary of the thirty-nine ANNs (proposed by Pérez-Zárate et al., 2019) for determining reservoir temperatures

From: GaS_GeoT: A computer program for an effective use of newly improved gas geothermometers in predicting reliable geothermal reservoir temperatures

ANN Input variables ANN architecture Statistical evaluation metrics
Original learning processa Full datab After applicability conditionsc
1 2 3 4 5 n data (r) training (r) validation (r) testing RMSE MAE MAPE RMSE MAE MAPE RMSE MAE MAPE
WG_SubDB1: q1=527
 1 ln(CO2)      [1-32-1] 527 0.69 0.58 0.62 34.83 27.08 10.29 34.83 27.08 10.29 34.83 27.08 10.29
 2 ln(H2S)      [1-3-1] 527 0.67 0.59 0.67 35.45 27.58 10.46 35.45 27.58 10.46 35.45 27.58 10.46
 3 ln(CO2/H2)      [1-13-1] 527 0.68 0.64 0.55 35.47 27.85 10.31 35.47 27.85 10.31 35.47 27.85 10.31
 4 ln(H2S/H2)      [1-26-1] 527 0.48 0.35 0.36 42.06 32.65 12.27 42.06 32.65 12.27 42.06 32.65 12.27
 5 ln(CH4/CO2) ln(H2S/H2)     [2-28-1] 527 0.69 0.57 0.31 38.21 27.94 10.44 38.21 27.94 10.44 36.68 27.36 10.25
 6 H2S/CO2 CH4/CO2 H2/CO2    [3-12-1] 527 0.80 0.74 0.74 29.26 20.98 7.99 29.26 20.98 7.99 29.12 20.88 7.94
 7 ln(H2S/CO2) ln(CH4/CO2) ln(H2/CO2)    [3-18-1] 527 0.85 0.80 0.64 26.84 18.39 6.87 26.84 18.39 6.87 26.46 18.17 6.78
 8 ln(CO2/H2S) ln(CH4/H2S) ln(H2/H2S)    [3-9-1] 527 0.83 0.80 0.61 28.22 19.45 7.31 28.22 19.45 7.31 28.22 19.45 7.31
 9 ln(CO2/CH4) ln(H2S/CH4) ln(H2/CH4)    [3-15-1] 527 0.85 0.82 0.63 26.45 18.94 7.14 26.45 18.94 7.14 26.43 18.91 7.12
 10 ln(CO2/H2) ln(H2S/H2) ln(CH4/H2)    [3-9-1] 527 0.83 0.79 0.70 27.24 19.36 7.27 27.24 19.36 7.27 27.24 19.36 7.27
 11 ilr1 ilr2 ilr3    [3-9-1] 527 0.83 0.82 0.59 27.94 19.93 7.40 27.94 19.93 7.40 27.92 19.89 7.38
 12 ln(CO2) ln(H2S) ln(CH4) ln(H2)   [4-13-1] 527 0.86 0.78 0.75 25.77 17.60 6.66 25.76 17.60 6.66 25.74 17.57 6.64
 13 ln(H2S/CO2) ln(CH4/CO2) ln(H2/CO2) ln(H2S) ln(H2S/H2) [5-9-1] 527 0.85 0.79 0.72 26.50 18.32 6.92 26.50 18.32 6.92 26.50 18.32 6.92
WG_SubDB2: q2=498
 14 ln(CO2)      [1-33-1] 498 0.71 0.66 0.71 33.68 26.39 10.10 40.13 30.11 11.37 34.40 26.82 10.19
 15 ln(H2S)      [1-34-1] 498 0.72 0.63 0.63 33.85 25.61 9.68 35.03 26.64 9.96 35.01 26.52 9.94
 16 ln(CO2/H2)      [1-16-1] 498 0.64 0.63 0.73 36.06 28.76 10.69 37.05 29.63 10.93 36.68 29.17 10.75
 17 ln(H2S/H2)      [1-25-1] 498 0.48 0.46 0.38 41.94 32.99 12.41 42.30 33.26 12.43 42.38 33.33 12.48
 18 ln(CH4/CO2) ln(H2S/H2)     [2-34-1] 498 0.61 0.56 0.54 38.29 28.22 10.62 39.54 29.38 10.96 38.62 28.46 10.64
 19 H2S/CO2 CH4/CO2 H2/CO2    [3-27-1] 498 0.82 0.80 0.80 27.74 19.94 7.64 146.81 41.14 14.80 28.59 20.39 7.74
 20 ln(H2S/CO2) ln(CH4/CO2) ln(H2/CO2)    [3-18-1] 498 0.83 0.79 0.83 26.85 19.00 7.27 29.22 20.66 7.78 27.46 19.30 7.29
 21 ln(CO2/H2S) ln(CH4/H2S) ln(H2/H2S)    [3-6-1] 498 0.80 0.75 0.75 29.13 21.26 8.11 30.64 22.25 8.41 29.90 21.72 8.21
 22 ln(CO2/CH4) ln(H2S/CH4) ln(H2/CH4)    [3-34-1] 498 0.88 0.80 0.79 24.91 16.60 6.33 48.58 22.76 8.38 23.76 16.33 6.12
 23 ln(CO2/H2) ln(H2S/H2) ln(CH4/H2)    [3-15-1] 498 0.85 0.77 0.77 26.01 18.19 6.84 31.94 20.69 7.68 26.54 18.47 6.87
 24 ilr1 ilr2 ilr3    [3-14-1] 498 0.85 0.76 0.77 26.44 18.45 7.00 35.17 21.90 8.12 27.16 18.89 7.10
 25 ln(CO2) ln(H2S) ln(CH4) ln(H2)   [4-10-1] 498 0.86 0.80 0.79 24.93 17.20 6.47 59.96 22.64 8.55 25.80 17.66 6.58
 26 ln(H2S/CO2) ln(CH4/CO2) ln(H2/CO2) ln(H2S) ln(H2S/H2) [5-5-1] 498 0.81 0.78 0.82 27.86 20.55 7.81 323.58 69.74 24.67 28.34 20.86 7.87
WG_SubDB3: q3=97
 27 ln(CO2)      [1-10-1] 97 0.77 0.73 0.83 23.95 17.37 6.31 126.01 71.75 25.33 44.39 36.45 12.60
 28 ln(H2S)      [1-14-1] 97 0.81 0.83 0.82 21.62 15.60 5.81 57.35 39.24 14.34 41.09 32.97 12.02
 29 ln(CO2/H2)      [1-4-1] 97 0.56 0.59 0.51 30.51 22.72 8.25 49.59 41.80 14.66 50.63 42.93 14.62
 30 ln(H2S/H2)      [1-8-1] 97 0.71 0.71 0.68 25.98 19.71 7.01 52.31 40.83 15.11 49.80 38.88 14.12
 31 ln(CH4/CO2) ln(H2S/H2)     [2-9-1] 97 0.86 0.82 0.73 20.05 13.47 4.80 107.09 61.29 22.34 52.88 38.80 13.19
 32 H2S/CO2 CH4/CO2 H2/CO2    [3-8-1] 97 0.90 0.87 0.86 16.88 10.63 3.86 172.56 67.79 24.89 36.21 26.83 9.45
 33 ln(H2S/CO2) ln(CH4/CO2) ln(H2/CO2)    [3-8-1] 97 0.95 0.92 0.91 12.56 8.64 3.08 93.54 57.17 20.69 44.15 31.54 11.23
 34 ln(CO2/H2S) ln(CH4/H2S) ln(H2/H2S)    [3-8-1] 97 0.92 0.90 0.90 14.83 10.94 3.88 63.15 42.59 16.23 40.54 29.64 10.57
 35 ln(CO2/CH4) ln(H2S/CH4) ln(H2/CH4)    [3-11-1] 97 0.94 0.92 0.86 14.18 9.64 3.50 124.97 65.67 23.30 50.39 37.10 12.78
 36 ln(CO2/H2) ln(H2S/H2) ln(CH4/H2)    [3-7-1] 97 0.92 0.91 0.79 15.87 11.45 4.14 88.95 53.02 19.17 45.02 33.73 11.70
 37 ilr1 ilr2 ilr3    [3-9-1] 97 0.92 0.93 0.82 16.08 10.74 3.78 63.24 40.40 15.03 35.66 25.94 9.08
 38 ln(CO2) ln(H2S) ln(CH4) ln(H2)   [4-8-1] 97 0.94 0.92 0.92 14.56 10.33 3.68 102.77 64.26 22.86 43.31 32.94 11.29
 39 ln(H2S/CO2) ln(CH4/CO2) ln(H2/CO2) ln(H2S) ln(H2S/H2) [5-6-1] 97 0.92 0.90 0.88 15.37 10.75 3.84 66.45 44.07 15.72 39.57 29.27 10.21
  1. aThe global learning process was reported in Pérez-Zárate et al. (2019): n data (number of samples used in each sub-database); (r) training, validation and testing (the correlation coefficient calculated between the bottom-hole temperatures (measured) and the temperature estimates (predicted) by ANNs; RMSE, MAE and MAPE (residuals calculated between the bottom-hole temperatures and temperature estimates by ANNs)
  2. bFull data: RMSE, MAE and MAPE (residuals calculated using the largest representative sub-database: q1 = 527)
  3. cAfter applicability conditions: RMSE, MAE and MAPE (residuals calculated using the samples that fulfil the applicability conditions of the ANN architectures (reported in Table 8)
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