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Table S1. Compositional analysis of the reservoir oil
Component Reservoir oil(mol%)
N2 0.272CO2 0.874C1 47.749C2 3.921C3 2.085i-C4 0.445n-C4 0.878i-C5 0.429n-C5 0.467C6 0.871C7 2.505C8 4.071C9 2.992C10+ 32.441MW C10+ 282 g/mol
Table S2. Economic parameters used in NPV optimization case studies
Parameter Value
Oil price [$ / Sm3] 377
Methane price [$ / Sm3] 0.1
Ethane price [$ / Sm3] 0.21
Propane price [$ / Sm3] 0.79
Butane price [$ / Sm3] 1.7
Gas recycling cost [$ / Sm3] 70% of gas price
Water price [$ / Sm3] 6
Water recycling cost [$ / Sm3] 38
Interest rate [-] 5%
Table S3. The reference case and best operational points found by four trials of GA (case study 1: NPV optimization over 9 variables)
Variable ReferenceCase
GA Trial 1
GA Trial 2 GA Trial 3
GA Trial 4
Qw (F-1H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-1H) [Sm3/day] 1000 1000 1000 1000 1000
Qw (F-3H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-3H) [Sm3/day] 1000 1000 1000 1000 1000
BHP (E-2AH) [bar] 150 155.8* 171* 158.8* 156*
BHP (E-3CH) [bar] 150 150 150 150 150
BHP (E-3H) [bar] 150 150 150 150 150
Cycle ratio [-] 0.65 0.9* 0.9* 0.9* 0.9*
Cycle time [month] 4 4 4 5* 4
NPV [$ million] 135.45 146.29 146.20 146.56 146.29
Table S4. The reference case and best operational points found by four trials of PSO (case study 1: NPV optimization over 9 variables)
Variable ReferenceCase
PSO Trial 1 PSO Trial 2
PSO Trial 3 PSO Trial 4
Qw (F-1H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-1H) [Sm3/day] 1000 1000 1000 1000 1000
Qw (F-3H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-3H) [Sm3/day] 1000 1000 1000 1000 1000
BHP (E-2AH) [bar] 150 158.8* 158.8* 158.8 * 158.8*
BHP (E-3CH) [bar] 150 150 150 150 150
BHP (E-3H) [bar] 150 150 150 150 150
Cycle ratio [-] 0.65 0.9* 0.9* 0.9* 0.9*
Cycle time [month] 4 5* 5* 5* 5*
NPV [$ million] 135.45 146.56 146.56 146.56 146.56
Table S5. The reference case and best operational points found by four trials of GA (case study 2: NPV optimization over 12 variables)
Variable ReferenceCase
GA Trial 1 GA Trial 2
GA Trial 3 GA Trial 4
Qw (F-1H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-1H) [Sm3/day] 380620 1000* 1000* 1000* 110768*
Qw (F-3H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-3H) [Sm3/day] 1000 1000 1000 1000 1000
BHP (E-2AH) [bar] 150 159.4* 158.9* 158.9* 152*
BHP (E-3CH) [bar] 150 150 150 150 150
BHP (E-3H) [bar] 201.3 150* 150* 150* 150*
Cycle ratio [-] 0.7 0.9* 0.9* 0.9* 0.9*
Cycle time [month] 2 2 2 2 2
Mole fraction of C2 [-] 0.05 0.2* 0.2* 0.2* 0.2*
Mole fraction of C3 [-] 0.1 0.1 0.1 0.1 0.1
Mole fraction of C4 [-] 0.05 0.05 0.05 0.05 0.05
NPV [$ million] 132.09 148.65 148.66 148.66 146.69
Table S6. The reference case and best operational points found by four trials of PSO (case study 2: NPV optimization over 12 variables)
Variable Reference Case
PSO Trial 1 PSO Trial 2 PSO Trial 3 PSO Trial 4
Qw (F-1H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-1H) [Sm3/day] 380620 1000* 1000* 1000* 1000*
Qw (F-3H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-3H) [Sm3/day] 1000 1000 1000 1000 1000
BHP (E-2AH) [bar] 150 158.8* 158.8* 158.8* 158.8*
BHP (E-3CH) [bar] 150 150 150 150 150
BHP (E-3H) [bar] 201.3 150* 150* 150* 150*
Cycle ratio [-] 0.7 0.9* 0.9* 0.9* 0.9*
Cycle time [month] 2 5* 5* 5* 5*
Mole fraction of C2 [-] 0.05 0.2* 0.2* 0.2* 0.2*
Mole fraction of C3 [-] 0.1 0.1 0.1 0.1 0.1
Mole fraction of C4 [-] 0.05 0.05 0.05 0.05 0.05
NPV [$ million] 132.09 148.76 148.76 148.76 148.76
Table S7. The reference case and best operational points found by four trials of GA (case study 3: NPV optimization over 13 variables)
Variable ReferenceCase
GA Trial 1 GA Trial 2
GA Trial 3 GA Trial 4
Qw (F-1H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-1H) [Sm3/day] 1000 1000 1000 1000 1000
Qw (F-3H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-3H) [Sm3/day] 1000 1000 1000 1000 1000
BHP (E-2AH) [bar] 150 150 150 150 150
BHP (E-3CH) [bar] 150 150 150 150 150
BHP (E-3H) [bar] 150 237* 237.5* 239.8* 240*
Cycle ratio [-] 0.55 0.9* 0.9* 0.9* 0.9*
Cycle time [month] 2 5* 7* 3* 3*
Total time [month] 60 60 60 60 60
Mole fraction of C2 [-] 0.2 0.2 0.2 0.2 0.2
Mole fraction of C3 [-] 0.02 0.1* 0.1* 0.1* 0.1*
Mole fraction of C4 [-] 0.05 0.05 0.05 0.05 0.05
NPV [$ million] 194.72 221.55 221.65 220.98 220.98
Table S8. The reference case and best operational points found by four trials of PSO (case study 3: NPV optimization over 13 variables)
Variable ReferenceCase
PSO Trial 1 PSO Trial 2 PSO Trial 3 PSO Trial 4
Qw (F-1H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-1H) [Sm3/day] 1000 1000 1000 1000 1000
Qw (F-3H) [Sm3/day] 2700 2700 2700 2700 2700
Qg (F-3H) [Sm3/day] 1000 1000 1000 1000 1000
BHP (E-2AH) [bar] 150 150 150 150 150
BHP (E-3CH) [bar] 150 150 150 150 150
BHP (E-3H) [bar] 150 226.2* 226.2* 226.2* 226.2*
Cycle ratio [-] 0.55 0.9* 0.9* 0.9* 0.9*
Cycle time [month] 2 8* 8* 8* 8*
Total time [month] 60 60 60 60 60
Mole fraction of C2 [-] 0.2 0.2 0.2 0.2 0.2
Mole fraction of C3 [-] 0.02 0.1* 0.1* 0.1* 0.1*
Mole fraction of C4 [-] 0.05 0.05 0.05 0.05 0.05
NPV [$ million] 194.72 222.29 222.29 222.29 222.29
Table S9. The reference case and best operational points found by three trials of GA (oil recovery optimization)
Variable ReferenceCase
GA Trial 1 GA Trial 2 GA Trial 3
Qw (F-1H) [Sm3/day] 500 2700* 2700* 2700*
Qg (F-1H) [Sm3/day] 106 106 106 106
Qw (F-3H) [Sm3/day] 500 2700* 2700 * 2700*
Qg (F-3H) [Sm3/day] 106 106 106 968781*
BHP (E-2AH) [bar] 150 150 150 167*
BHP (E-3CH) [bar] 150 150 150 158*
BHP (E-3H) [bar] 240 240 237.5* 238*
Cycle ratio [-] 0.1 0.1 0.1 0.1
Cycle time [month] 2 4 * 8* 3*
Mole fraction of C2 [-] 0.2 0.2 0.2 0.2
Mole fraction of C3 [-] 0.1 0.1 0.1 0.1
Mole fraction of C4 [-] 0.01 0.05* 0.05* 0.05*
IRF [-] 4.45% 5.08% 5.08% 5.04%
Table S10. The reference case and best operational points found by three trials of PSO (oil recovery optimization)
Variable Reference
Case
PSO Trial 1 PSO Trial 2 PSO Trial 3
Qw (F-1H) [Sm3/day] 500 2700* 2700* 2700*
Qg (F-1H) [Sm3/day] 106 106 106 106
Qw (F-3H) [Sm3/day] 500 2700* 2700* 2700*
Qg (F-3H) [Sm3/day] 106 106 106 106
BHP (E-2AH) [bar] 150 150 150 150
BHP (E-3CH) [bar] 150 150 150 150
BHP (E-3H) [bar] 240 209* 209* 209*
Cycle ratio [-] 0.1 0.15* 0.15* 0.15*
Cycle time [month] 2 12* 12* 12*
Mole fraction of C2 [-] 0.2 0.2 0.2 0.2
Mole fraction of C3 [-] 0.1 0.1 0.1 0.1
Mole fraction of C4 [-] 0.01 0.05* 0.05* 0.05*
IRF [-] 4.45% 5.17% 5.17% 5.17%
Example: The total volumes of produced oil, gas and water and the total volumes of injected gas and water for optimized-recovery WAG are shown in Table S11. The NPV using equation (1) with the prices assumed in Table S2 for the optimal recovery point is calculated as follows
Table S11: The total volumes of injected and produced fluids for optimized-recovery WAG
Year number Qoprod [Sm3] Qg
prod [Sm3] Qwprod [Sm3] Qg
inj [Sm3] Qwinj [Sm3]
1 2.508×105 3.0527×107 1.382×106 6.1403×108 2.8342×105
2 2.0173×105 2.6553×107 1.5014×106 6.1133×108 2.934×105
3 2.0274×105 2.6373×107 1.8358×106 6.1024×108 2.9636×105
4 2.4177×105 4.5593×107 1.7425×106 6.0838×108 3.0137×105
5 3.0665×105 7.6897×107 1.4928×106 6.124×108 2.9053×105
Fig. S1. The E-segment of the Norne field at the end of 2006
Fig. S2. NPV vs. iteration index per trial for GA and PSO (case study 1: NPV optimization over 9 variables)
Fig. S3. NPV vs. iteration index per trial for GA and PSO (case study 2: NPV optimization over 12 variables)
Fig. S4. NPV vs. iteration index per trial for GA and PSO (case study 3: NPV optimization over 13 variables)
Fig. S5. Effect of economic parameters on the NPV
Fig. S6. IRF vs. iteration index per trial for GA and PSO (oil recovery optimization)
