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| LaTeX Math Block |
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G(t) = \sum_{p=1}^{N_N^{\rm produparrow}} \left[ R_O \cdot q^{\uparrow}_{O, p} + R_G \cdot q^{\uparrow}_{G, p} \right]
- \sum_{p=1}^{N_N^{\rm produparrow}} CC^{\uparrow}_L \cdot q^{\uparrow}_{L, p}
- \sum_{p=1}^{N_N^{\rm produparrow}} C_O \cdot q^{\uparrow}_{O, p}
- \sum_{p=1}^{N_N^{\rm produparrow}} C_G \cdot q^{\uparrow}_{G, p}
- \sum_{p=1}^{N_N^{\rm produparrow}} C_W \cdot q^{\uparrow}_{W, p}
- \sum_{i=1}^{N_N^{W, \rm inj}} C_{W, \rm inj} \downarrow}_W} C^{\downarrow}_W \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N_N^{G, \rm inj}\downarrow}_G} C_{G, \rm inj} \cdot q^{\downarrow}_{G, i} \rightarrow \rm max
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| 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 | | number of producers |
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| liquid production rate for -th producer, volume/day | | cost of fluid lift, cash/volume | | number of water injectors |
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| LaTeX Math Inline |
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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 | | number of gas injectors |
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| LaTeX Math Inline |
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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 | | time |
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This can be rewritten in terms of sandface flowrates:
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