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G = \sum_t G_t \rightarrow \rm max
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G_t = (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)
- \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} \rightarrow \rm max(t)
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where
q^{\uparrow}_{O, k}| --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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q^{\uparrow}_{G, k}| --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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q^{\uparrow}_{W, k}| --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 | | counts | |
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q^{\uparrow}_{L, k}| --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 | | counts | number of water injectors at |
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| --uriencoded--q%5e%7B\downarrow%7D_%7BW, i%7D(t) |
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q^{\downarrow}_{W, i} | volume/day | water injection rate for -th water injector | | cash/volume | cost of water injection, including purchase, treatment, transportation and pumping into -th well | | counts | number of gas injectors at |
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q^{\downarrow}_{G, i}| --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 | | months | time |
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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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:
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G(_t) = \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{OGW}(t) \cdot q^{\uparrow}_{L, p}(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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C^{\uparrow}_{OGW}(t) = \left[ (R_O(t) - C^{\uparrow}_{O,p}) + (R_G(t) - C^{\uparrow}_{G,p}) \cdot Y_{g,p}(t) \right] \cdot (1- Y_{w,p}}(t))
- C^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot Y_{w,p}(t)
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where
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| body | --uriencoded--Y_{w,k} %7Bw,k%7D(t) = q_{W%7BW,k} k%7D / q_{L%7BL,k}k%7D |
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| body | --uriencoded--Y_{g,k} %7Bg,k%7D(t) = q_{G%7BG,k} k%7D / q_{O%7BO,k}k%7D |
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...
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| anchor | RateLimit |
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| alignment | left |
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| q^{\uparrow}_{LMIN, p} \leq q^{\uparrow}_{L, p}(t) \leq q^{\uparrow}_{LMAX, p} |
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| anchor | RateLimit |
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| alignment | left |
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| q^{\downarrow}_{WMIN, i} \leq q^{\downarrow}_{W, i}(t) \leq q^{\downarrow}_{WMAX, i} |
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| anchor | RateLimit |
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| alignment | left |
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| q^{\downarrow}_{GMIN, j} \leq q^{\downarrow}_{G, j}(t) \leq q^{\downarrow}_{GMAX, j} |
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...
