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AG_y = \sum_t G_t
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| anchor | ZUICYGt |
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| alignment | left |
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G_t = G_t^{+} - G_t^{-}
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| anchor | GtPlus |
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| alignment | left |
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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]
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| anchor | GtMinus |
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| alignment | left |
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G_t^{-} =
\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)
- +\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)
-+ C^{\uparrow}_{WS,k} \cdot q^{\uparrow}_{WS}(t)
+ C^{\uparrow}_{GS} \cdot q^{\uparrow}_{GS}(t)
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q^{\uparrow}_{WS}(t) = \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}(t) - \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,k} \cdot q^{\uparrow}_{W, k}(t)
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where
| years | assessment period | | days | day within a given year | | – | discount rate |
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| LaTeX Math Inline |
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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 | |
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C^{\uparrow}_{O,k}| --uriencoded--C%5e%7B\uparrow%7D_%7BO,k%7D(t) |
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| 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 | |
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C^{\uparrow}_{G,k}| --uriencoded--C%5e%7B\uparrow%7D_%7BG,k%7D(t) |
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| 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 | |
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C^{\uparrow}_{W,k}| --uriencoded--C%5e%7B\uparrow%7D_%7BW,k%7D(t) |
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| cash/volume | cost of produced water treatment and transportation from -th wellhead to CMS | | LaTeX Math Inline |
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| body | --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 | |
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C^{\uparrow}_{L, k}| --uriencoded--C%5e%7B\uparrow%7D_%7BL, k%7D(t) |
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| cash/volume | cost of fluid lift from reservoir to the -th wellhead, cash/volume | |
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| LaTeX Math Inline |
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| body | --uriencoded--q%5e%7B\uparrow%7D_%7BWS%7D(t) |
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| volume/day | | | LaTeX Math Inline |
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| body | --uriencoded--C%5e%7B\uparrow%7D_%7BWS%7D(t) |
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| cash/volume | cost of water supply |
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| body | --uriencoded--q%5e%7B\ |
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downarrow%7D%7BW, i%7Dwater injection for -th water injectori | | --uriencoded--C%5e%7B\uparrow%7D_%7BGS%7D(t) |
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| cash/volume | cost of gas supply |
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C^{\downarrow}_{W,i}| --uriencoded--q%5e%7B\downarrow%7D_%7BW, i%7D(t) |
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| volume/day | water injection rate for -th water injector | | LaTeX Math Inline |
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| body | --uriencoded--C%5e%7B\downarrow%7D_%7BW,i%7D(t) |
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| cash/volume | cost of water injection, including treatment, transportation and pumping into -th well | | LaTeX Math Inline |
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| body | --uriencoded--N%5e%7B\downarrow%7D_W(t) |
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| counts | number of water injectors at |
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| LaTeX Math Inline |
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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 | |
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C^{\downarrow}_{G,j}| --uriencoded--C%5e%7B\downarrow%7D_%7BG,j%7D(t) |
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| 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
| LaTeX Math Block Reference |
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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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