The general form of objective function for production targets optimisation is given by:
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G = \sum_{p=1}^{N_{\rm prod}} \left[ R_O \cdot q^{\uparrow}_{O, p} + R_G \cdot q^{\uparrow}_{G, p} \right]
- \sum_{p=1}^{N_{\rm prod}} C_L \cdot q^{\uparrow}_{L, p}
- \sum_{p=1}^{N_{\rm prod}} C_O \cdot q^{\uparrow}_{O, p}
- \sum_{p=1}^{N_{\rm prod}} C_G \cdot q^{\uparrow}_{G, p}
- \sum_{p=1}^{N_{\rm prod}} C_W \cdot q^{\uparrow}_{W, p}
- \sum_{i=1}^{N_{W, \rm inj}} C_{W, \rm inj} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_{G, \rm inj}} C_{G, \rm inj} \cdot q^{\downarrow}_{G, i} \rightarrow \rm max
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where
| oil production rate for -th producer, volume/day | | cost of oil treatment, cash/volume | | oil price, cash/volume |
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| gas production rate for -th producer, volume/day | | cost of gas treatment, cash/volume | | gas price, cash/volume |
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| water production rate for -th producer, volume/day | | cost of water treatment, cash/volume |
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| liquid production rate for -th producer, volume/day | | cost of fluid lift, cash/volume |
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| body | q^{\downarrow}_{W, i} |
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| water injection rate for -th water injector, volume/day | | cost of water injection, cash/volume |
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| body | q^{\downarrow}_{G, i} |
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| gas injection rate for -th gas injector, volume/day | | cost of gas injection, cash/volume |
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This can be rewritten in terms of sandface flowrates:
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G = \sum_{p=1}^{N_{\rm prod}} G^{\uparrow}_{ut,p} \cdot q^{\uparrow}_{t, p}
- \sum_{i=1}^{N_{W, \rm inj}} G^{\downarrow}_w \cdot q^{\downarrow}_{w, i}
- \sum_{j=1}^{N_{G, \rm inj}} G^{\downarrow}_g \cdot q^{\downarrow}_{g, i} \rightarrow \rm max
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where
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| body | \displaystyle G^{\uparrow}_{t,p} |
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| body | \displaystyle G^{\downarrow}_w = B_w \cdot C_{W, \rm inj} |
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| body | \displaystyle G^{\downarrow}_g = B_g \cdot C_{G, \rm inj} |
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| Expand |
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| G = \sum_{p=1}^{N_{\rm prod}} \left[ (R_O -C_O) \cdot q^{\uparrow}_{O, p} + (R_G-C_G) \cdot q^{\uparrow}_{G, p}
- C_L \cdot q^{\uparrow}_{L, p} - C_W \cdot q^{\uparrow}_{W, p} \right]
- \sum_{i=1}^{N_{W, \rm inj}} C_{W, \rm inj} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_{G, \rm inj}} C_{G, \rm inj} \cdot q^{\downarrow}_{G, i} \rightarrow \rm max
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| G = \sum_{p=1}^{N_{\rm prod}} \left[ \left[ (R_O -C_O) + (R_G-C_G) \cdot GOR \right] \cdot q^{\uparrow}_{O, p}
- (C_L + C_W \cdot Y_w) \cdot q^{\uparrow}_{L, p} \right]
- \sum_{i=1}^{N_{W, \rm inj}} C_{W, \rm inj} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_{G, \rm inj}} C_{G, \rm inj} \cdot q^{\downarrow}_{G, i} \rightarrow \rm max
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| G = \sum_{p=1}^{N_{\rm prod}} \left[ \left[ (R_O -C_O) + (R_G-C_G) \cdot GOR \right] \cdot (1-Y_w)
- (C_L + C_W \cdot Y_w) \right] \cdot q^{\uparrow}_{L, p}
- \sum_{i=1}^{N_{W, \rm inj}} C_{W, \rm inj} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_{G, \rm inj}} C_{G, \rm inj} \cdot q^{\downarrow}_{G, i} \rightarrow \rm max
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See Also
Petroleum Industry / Upstream / Production / Field Development Plan
Subsurface Production / Well & Reservoir Management / [ Production Targets ]
Subsurface E&P Disciplines / Production Technology
