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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}} CC^{\uparrow}_O \cdot q^{\uparrow}_{O, p}
- \sum_{p=1}^{N^{\uparrow}} CC^{\uparrow}_G \cdot q^{\uparrow}_{G, p}
- \sum_{p=1}^{N^{\uparrow}} CC^{\uparrow}_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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C at surface, , |
| volume/day | gas production rate for -th producer, | |
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C gas treatment at surface price| selling price |
| volume/day | water production rate for -th producer | |
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C water treatment at surface| produced water treatment and transportation from wellhead to CMS | |
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cash/volumecash/volume| counts | number of water injectors at |
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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 | | cash/volume | cost of water injection, including purchase, treatment, transportation and pumping | |
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cash/volume| counts | number of gas injectors at |
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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 | | cash/volume | cost of gas injection, 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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