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G(t) = \sum_{p=1}^{N^{\uparrow}_P} \left[ R_O \cdot q^{\uparrow}_{O, p} + R_G \cdot  q^{\uparrow}_{G, p} \right] 
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_L \cdot q^{\uparrow}_{L, p}
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_O \cdot q^{\uparrow}_{O, p} 
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_G \cdot q^{\uparrow}_{G, p} 
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_W \cdot q^{\uparrow}_{W, p}
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_W \cdot q^{\downarrow}_{W, i} 
- \sum_{j=1}^{N^{\downarrow}_G} C^{\downarrow}_G \cdot q^{\downarrow}_{G, i} \rightarrow \rm max

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bodyq^{\uparrow}_{O, p}

volume/day

oil production rate for 

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bodyp
-th producer, 

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bodyC^{\uparrow}_O

cash/volumecost of produced oil treatment and transportation from wellhead to CMS

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bodyR_O

cash/volumeoil selling price

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bodyq^{\uparrow}_{G, p}

volume/day

gas production rate for 

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bodyp
-th producer, 

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bodyC^{\uparrow}_G

cash/volumecost of produced gas treatment and transportation from wellhead to CMS

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bodyR_G

cash/volumegas selling price

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bodyq^{\uparrow}_{W, p}

volume/day

water production rate for 

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bodyp
-th producer

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bodyC^{\uparrow}_W

cash/volumecost of produced water treatment and transportation from wellhead to CMS

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bodyN^{\uparrow}_P

counts

number of producers at 

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bodyt

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bodyq^{\uparrow}_{L, p}

volume/day

liquid production rate for 

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bodyp
-th producer

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bodyC^{\uparrow}_L

cash/volumecost of fluid lift, cash/volume

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bodyN^{\downarrow}_W

counts

number of water injectors at 

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bodyt

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bodyq^{\downarrow}_{W, i}

volume/day

water injection rate for 

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bodyi
-th water injector

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bodyC^{\downarrow}_W

cash/volumecost of water injection, including purchase, treatment, transportation and pumping

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bodyN^{\downarrow}_G

counts

number of gas injectors at 

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bodyt

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bodyq^{\downarrow}_{G, i}

volume/day

gas injection rate for 

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bodyi
-th gas injector

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bodyC^{\downarrow}_G

cash/volumecost of gas injection, including purchase, treatment, transportation and pumping

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bodyt

monthstime

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G = \sum_{p=1}^{N_N^{\rm produparrow}_P}} G^{\uparrow}_{ut,p} \cdot q^{\uparrow}_{t, p}
- \sum_{i=1}^{N^{N\downarrow_{W, \rm inj}} G^{\downarrow}_w  \cdot q^{\downarrow}_{w, i}
- \sum_{j=1}^{NN^{\downarrow_{G, \rm inj}} G^{\downarrow}_g  \cdot q^{\downarrow}_{g, i} \rightarrow \rm max

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