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G_t = \sum_{k=1}^{N^{\uparrow}_P} \left[ R_O(t) \cdot q^{\uparrow}_{O, k}(t) + R_G(t) \cdot q^{\uparrow}_{G, k}(t) \right]
- \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{L,k} \cdot q^{\uparrow}_{L, k}(t)
- \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{O,k} \cdot q^{\uparrow}_{O, k} (t)
- \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{G,k} \cdot q^{\uparrow}_{G, k} (t)
- \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,k} \cdot q^{\uparrow}_{W, k}(t)
- C^{\uparrow}_{WS,k} \cdot q^{\uparrow}_{WS}(t)
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}(t)
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}(t)
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| years | assessment period | | days | day within a given year | | – | discount rate |
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body | --uriencoded--q%5e%7B\uparrow%7D_%7BO, k%7D(t) |
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| volume/day | oil production rate for -th producer | | cash/volume | cost of produced oil treatment and transportation from -th wellhead to CMS | | cash/volume | oil selling price |
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body | --uriencoded--q%5e%7B\uparrow%7D_%7BG, k%7D(t) |
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| volume/day | gas production rate for -th producer | | cash/volume | cost of produced gas treatment and transportation from -th wellhead to CMS | | cash/volume | gas selling price |
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body | --uriencoded--q%5e%7B\uparrow%7D_%7BW, k%7D(t) |
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| volume/day | water production rate for -th producer | | cash/volume | cost of produced water treatment and transportation from -th wellhead to CMS | LaTeX Math Inline |
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body | N^{\uparrow}_P--uriencoded--N%5e%7B\uparrow%7D_P(t) |
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| counts | |
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body | --uriencoded--q%5e%7B\uparrow%7D_%7BL, k%7D(t) |
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| volume/day | liquid production rate for -th producer | | cash/volume | cost of fluid lift from reservoir to the -th wellhead, cash/volume | |
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| N^{\downarrow}_W | --uriencoded--q%5e%7B\uparrow%7D_%7BWS%7D(t) |
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| volume/day | | counts | number of water injectors at | LaTeX Math Inline |
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body | --uriencoded--C%5e%7B\uparrow%7D_%7BWS%7D |
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| cash/volume | cost of water supplyt |
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body | --uriencoded--q%5e%7B\downarrow%7D_%7BW, i%7D(t) |
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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 into -th well | LaTeX Math Inline |
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body | N^{\downarrow}_G--uriencoded--N%5e%7B\downarrow%7D_W(t) |
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| counts | number of gas water injectors at |
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body | --uriencoded--q%5e%7B\downarrow%7D_%7BG, i%7D(t) |
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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 into -th well | LaTeX Math Inline |
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body | --uriencoded--N%5e%7B\downarrow%7D_G(t) |
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| counts
| number of gas injectors at |
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The objective function
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can be rewritten in terms of
Surface flowrates LaTeX Math Inline |
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body | \{ q^{\uparrow}_L, q^{\downarrow}_W, q^{\downarrow}_G \} |
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