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| LaTeX Math Block |
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G(t) = \sum_{p=1}^{N^{\uparrow}} \left[ R_O \cdot q^{\uparrow}_{O, p} + R_G \cdot q^{\uparrow}_{G, p} \right]
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_L \cdot q^{\uparrow}_{L, p}
- \sum_{p=1}^{N^{\uparrow}} C_O \cdot q^{\uparrow}_{O, p}
- \sum_{p=1}^{N^{\uparrow}} C_G \cdot q^{\uparrow}_{G, p}
- \sum_{p=1}^{N^{\uparrow}} C_W \cdot q^{\uparrow}_{W, p}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_W \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_G \cdot q^{\downarrow}_{G, i} \rightarrow \rm max
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where
| volume/day | oil production rate for -th producer, |
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volume/day | | cash/volume | cost of oil treatment at surface, |
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cash/volume cash/volume| |
| volume/day | gas production rate for -th producer, |
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volume/day | | cash/volume | cost of gas treatment at surface |
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, cash/volumegas price, | cash/volume | gas price |
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| volume/day | water production rate for -th producer |
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, volume/day | | cash/volume | cost of water treatment at surface |
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, cash/volume | | cash/volume | number of producers |
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| volume/day | liquid production rate for -th producer |
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, volume/day | | cash/volume | cost of fluid lift, cash/volume | | 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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| volume/day | water injection rate for -th water injector |
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, volume/day | | cash/volume | cost of water injection |
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, cash/volume| , including purchase, treatment, transportation and pumping | | 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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| volume/day | gas injection rate for -th gas injector |
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, volume/day | | cash/volume | cost of gas injection |
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, cash/volume| , including purchase, treatment, transportation and pumping | | months | time |
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This can be rewritten in terms of sandface flowrates:
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