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LaTeX Math Block
anchorZUICY
alignmentleft
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)


LaTeX Math Block
anchorWaterBalance8ZMLG
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q^{\uparrow}_{WS}(t) = \sum_{ki=1}^{N^{\uparrowdownarrow}_PW} C^{\uparrowdownarrow}_{W,kj} \cdot q^{\uparrowdownarrow}_{W, ki}(t) - \sum_{ik=1}^{N^{\downarrowuparrow}_WP} C^{\downarrowuparrow}_{W,jk} \cdot q^{\downarrowuparrow}_{W, ik}(t)

where

LaTeX Math Inline
bodyN_y

yearsassessment period

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bodyt

daysday within a given year

LaTeX Math Inline
bodyr

discount rate

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body--uriencoded--q%5e%7B\uparrow%7D_%7BO, k%7D(t)

volume/day

oil production rate for 

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bodyk
-th producer

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bodyC^{\uparrow}_{O,k}

cash/volume

cost of produced oil treatment and transportation from 

LaTeX Math Inline
bodyk
-th wellhead to CMS

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bodyR_O(t)

cash/volumeoil selling price

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body--uriencoded--q%5e%7B\uparrow%7D_%7BG, k%7D(t)

volume/day

gas production rate for 

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bodyk
-th producer

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

cash/volume

cost of produced gas treatment and transportation from 

LaTeX Math Inline
bodyk
-th wellhead to CMS

LaTeX Math Inline
bodyR_G(t)

cash/volumegas selling price

LaTeX Math Inline
body--uriencoded--q%5e%7B\uparrow%7D_%7BW, k%7D(t)

volume/day

water production rate for 

LaTeX Math Inline
bodyk
-th producer

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

cash/volume

cost of produced water treatment and transportation from 

LaTeX Math Inline
bodyk
-th wellhead to CMS

LaTeX Math Inline
body--uriencoded--N%5e%7B\uparrow%7D_P(t)

counts

number of producers at 

LaTeX Math Inline
bodyt

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body--uriencoded--q%5e%7B\uparrow%7D_%7BL, k%7D(t)

volume/day

liquid production rate for 

LaTeX Math Inline
bodyk
-th producer

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bodyC^{\uparrow}_{L, k}

cash/volume

cost of fluid lift from reservoir to the 

LaTeX Math Inline
bodyk
-th wellhead, cash/volume




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body--uriencoded--q%5e%7B\uparrow%7D_%7BWS%7D(t)

volume/day

water supply rate

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body--uriencoded--C%5e%7B\uparrow%7D_%7BWS%7D

cash/volumecost of water supply


LaTeX Math Inline
body--uriencoded--q%5e%7B\downarrow%7D_%7BW, i%7D(t)

volume/day

water injection rate for 

LaTeX Math Inline
bodyi
-th water injector

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

cash/volume

cost of water injection, including treatment, transportation and pumping into 

LaTeX Math Inline
bodyi
-th well

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body--uriencoded--N%5e%7B\downarrow%7D_W(t)

counts

number of water injectors at 

LaTeX Math Inline
bodyt

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body--uriencoded--q%5e%7B\downarrow%7D_%7BG, i%7D(t)

volume/day

gas injection rate for 

LaTeX Math Inline
bodyi
-th gas injector

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

cash/volume

cost of gas injection, including purchase, treatment, transportation and pumping into 

LaTeX Math Inline
bodyi
-th well

LaTeX Math Inline
body--uriencoded--N%5e%7B\downarrow%7D_G(t)


counts


number of gas injectors at 

LaTeX Math Inline
bodyt

...

LaTeX Math Block
anchorR0OIY
alignmentleft
q^{\uparrow}_{WS}(t) = \sum_{ki=1}^{N^{\uparrowdownarrow}_PW} C^{\uparrowdownarrow}_{W,kj} \cdot q^{\uparrowdownarrow}_{W, ki}(t) - \sum_{ik=1}^{N^{\downarrowuparrow}_WP} C^{\downarrowuparrow}_{W,jk} \cdot q^{\downarrowuparrow}_{W, ik}(t)

with restrictions

LaTeX Math Block
anchor9FIZQ
alignmentleft
q^{\uparrow}_{WS}(t) >0 

where

LaTeX Math Inline
body--uriencoded--Y_%7Bw,k%7D(t) = q_%7BW,k%7D / q_%7BL,k%7D

Watercut in 

LaTeX Math Inline
bodyk
-th well

LaTeX Math Inline
body--uriencoded--Y_%7Bg,k%7D(t) = q_%7BG,k%7D / q_%7BO,k%7D

Gas-Oil Ratio in 

LaTeX Math Inline
bodyk
-th well

...