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LaTeX Math Block
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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,p} \cdot q^{\uparrow}_{L, p}
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_{O,p} \cdot q^{\uparrow}_{O, p} 
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_{G,p} \cdot q^{\uparrow}_{G, p} 
- \sum_{p=1}^{N^{\uparrow}} C^{\uparrow}_{W,p} \cdot q^{\uparrow}_{W, p}
- \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, ij} \rightarrow \rm max

where

LaTeX Math Inline
bodyq^{\uparrow}_{O, p}

volume/day

oil production rate for 

LaTeX Math Inline
bodyp
-th producer, 

LaTeX Math Inline
bodyC^{\uparrow}_{O,p}

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

LaTeX Math Inline
bodyR_O

cash/volumeoil selling price

LaTeX Math Inline
bodyq^{\uparrow}_{G, p}

volume/day

gas production rate for 

LaTeX Math Inline
bodyp
-th producer, 

LaTeX Math Inline
bodyC^{\uparrow}_{G,p}

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

LaTeX Math Inline
bodyR_G

cash/volumegas selling price

LaTeX Math Inline
bodyq^{\uparrow}_{W, p}

volume/day

water production rate for 

LaTeX Math Inline
bodyp
-th producer

LaTeX Math Inline
bodyC^{\uparrow}_{W,p}

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

LaTeX Math Inline
bodyN^{\uparrow}_P

counts

number of producers at 

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyq^{\uparrow}_{L, p}

volume/day

liquid production rate for 

LaTeX Math Inline
bodyp
-th producer

LaTeX Math Inline
bodyC^{\uparrow}_{L, p}

cash/volumecost of fluid lift to the wellhead, cash/volume

LaTeX Math Inline
bodyN^{\downarrow}_W

counts

number of water injectors at 

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyq^{\downarrow}_{W, i}

volume/day

water injection rate for 

LaTeX Math Inline
bodyi
-th water injector

LaTeX Math Inline
bodyC^{\downarrow}_{W,i}

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

LaTeX Math Inline
bodyN^{\downarrow}_G

counts

number of gas injectors at 

LaTeX Math Inline
bodyt

LaTeX Math Inline
bodyq^{\downarrow}_{G, i}

volume/day

gas injection rate for 

LaTeX Math Inline
bodyi
-th gas injector

LaTeX Math Inline
bodyC^{\downarrow}_{G,j}

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

LaTeX Math Inline
bodyt

monthstime

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LaTeX Math Block
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G = \sum_{p=1}^{N^{\uparrow}_P}} G^{\uparrow}_{utt,p} \cdot q^{\uparrow}_{t, p}
- \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, ij} \rightarrow \rm max

where

LaTeX Math Inline
body\displaystyle G^{\uparrow}_{t,p}

LaTeX Math Inline
body\displaystyle G^{\downarrow}_w = B_w \cdot C^{\downarrow}_W

LaTeX Math Inline
body\displaystyle G^{\downarrow}_g = B_g \cdot C^{\downarrow}_G

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