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G(t) = \sum_{pk=1}^{N^{\uparrow}_P} \left[ R_O \cdot q^{\uparrow}_{O, pk} + R_G \cdot q^{\uparrow}_{G, pk} \right]
- \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{L,pk} \cdot q^{\uparrow}_{L, pk}
- \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{O,pk} \cdot q^{\uparrow}_{O, pk}
- \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{G,pk} \cdot q^{\uparrow}_{G, pk}
- \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,pk} \cdot q^{\uparrow}_{W, pk}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_{G,j} \cdot q^{\downarrow}_{G, j} \rightarrow \rm max
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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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| 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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| 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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| volume/day | liquid production rate for -th producer | | cash/volume | to the from reservoir to the -th wellhead, cash/volume | | counts | number of water injectors at |
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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 into -th well | | counts | number of gas injectors at |
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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 into -th well | | months | time |
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Left part of equation
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can be rewritten in terms of
Sandface flowrates:
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G = \sum_{p=1}^{N^{\uparrow}_P} G^{\uparrow}_{t,pk} \cdot q^{\uparrow}_{t, pk}
- \sum_{i=1}^{N^{\downarrow}_W} G^{\downarrow}_w \cdot
q^{\downarrow}_{w, i}
- \sum_{j=1}^{N^{\downarrow}_G} G^{\downarrow}_g \cdot q^{\downarrow}_{g, j} \rightarrow \rm max |
...
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G^{\uparrow}_{t,pk} = \frac{\left[ (R_O - C^{\uparrow}_{O,pk}) + (R_G - C^{\uparrow}_{G,pk}) \cdot Y_{g,pk} \right] \cdot (1- Y_{w,pk})
- C^{\uparrow}_{L,pk} \cdot q^{\uparrow}_{L, pk} - C^{\uparrow}_{W,pk} \cdot Y_{w,pk} }
{B_w Y_{w,pk} + \left[ (B_{o,k} - R_{s,k} B_{g,k}) + (B_{g,k} - R_{v,k} B_{o,k}) \, Y_{g,pk} \right] \cdot (1-Y_{w,pk})} |
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G^{\downarrow}_w = B_w \cdot C^{\downarrow}_W |
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G^{\downarrow}_g = B_g \cdot C^{\downarrow}_G |
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