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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)
- \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)
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with restrictions:
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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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oil production rate for
-th producer |
q^{\uparrow}_{WS}(t) + \sum_{k=1}^{N^{\uparrow}_P} |
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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)
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where
| 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 | O,k}cash/volume | cost of produced oil treatment and transportation from -th wellhead to CMS | | cash/volume | oil selling price |
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| LaTeX Math Inline |
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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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| LaTeX Math Inline |
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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 | --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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| 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 |
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| cash/volume | cost of water supply |
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| LaTeX Math Inline |
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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 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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| 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 | | 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 cost of gas injection, including purchase, treatment, transportation and pumping into -th well |
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The objective function
| LaTeX Math Block Reference |
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can be rewritten in terms of Surface flowrates ...
counts
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number of gas injectors at
| \{ q^{\uparrow}_L, q^{\downarrow}_W, q^{\downarrow}_G \} |
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:| LaTeX Math Block |
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G_t = \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{OGW}(t) \cdot |
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{L, p}(t)
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,i} \cdot q^{\downarrow}_{W, |
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G_t = i}(t)
- \sum_{pj=1}^{N^{\uparrow}_P}{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j}(t)
- C^{\uparrow}_{OGW}(t) WS,k} \cdot q^{\uparrow}_{L, pWS}(t)
- \sum_{i=1}^{N^{\downarrow}_W} |
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C^{\uparrow}_{OGW}(t) = \left[ (R_O(t) - C^{\downarrowuparrow}_{WO,ip}) \cdot q^{\downarrow}_{W, i}+ (R_G(t)
- \sum_{j=1}^{N^{\downarrowC^{\uparrow}_{G,p}) C^{\downarrow}\cdot Y_{Gg,j}p}(t) \right] \cdot q^{\downarrow}(1- Y_{Gw, jp}(t))
- C^{\uparrow}_{WSL,kp} \cdot- q^C^{\uparrow}_{W,p} \cdot Y_{WSw,p}(t)
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with restrictions:
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| anchor | KPBIE9TFSW |
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| alignment | left |
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C^q^{\uparrow}_{OGWWS}(t) =+ \left[ (R_O(t) - C^sum_{k=1}^{N^{\uparrow}_{O,p}) + (R_G(t) - P} C^{\uparrow}_{GW,pk}) \cdot Yq^{\uparrow}_{gW,p k}(t) \right] = \cdot (1- Y_{w,p}(t))
- C^{\uparrow}_{L,p} - C^{\uparrowsum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,pj} \cdot Yq^{\downarrow}_{wW,p i}(t)
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where
| LaTeX Math Inline |
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| body | --uriencoded--Y_%7Bw,k%7D(t) = q_%7BW,k%7D / q_%7BL,k%7D |
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| body | --uriencoded--Y_%7Bg,k%7D(t) = q_%7BG,k%7D / q_%7BO,k%7D |
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G = \sum_{k=1}^{N^{\uparrow}_P} G^{\uparrow}_{t,k} \cdot q^{\uparrow}_{t, k}
- \sum_{i=1}^{N^{\downarrow}_W} G^{\downarrow}_{w,i} \cdot
q^{\downarrow}_{w, i}
- \sum_{j=1}^{N^{\downarrow}_G} G^{\downarrow}_{g,j} \cdot q^{\downarrow}_{g, j} - C^{\uparrow}_{WS,k} \cdot q^{\uparrow}_{WS}(t) \rightarrow \rm max |
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G^{\uparrow}_{t,k} = \frac{\left[ (R_O - C^{\uparrow}_{O,k}) + (R_G - C^{\uparrow}_{G,k}) \cdot Y_{g,k} \right] \cdot (1- Y_{w,k})
- C^{\uparrow}_{L,k} - C^{\uparrow}_{W,k} \cdot Y_{w,k} }
{B_{w,k} Y_{w,k} + \left[ (B_{o,k} - R_{s,k} B_{g,k}) + (B_{g,k} - R_{v,k} B_{o,k}) \, Y_{g,k} \right] \cdot (1-Y_{w,k})} |
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