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LaTeX Math Block

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q^{\uparrow}_{WS}(t) = \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdot q^{\downarrow}_{W, i}(t) - \sum_{k=1}^{N^{\uparrow}_P} C^q^{\uparrow}_{W, k}(t) \cdot > 0

LaTeX Math Block

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q^{\uparrow}_{W, kGS}(t)

where

 = \sum_{j=1}^{N^{\downarrow}_G}  q^{\downarrow}_{G, j}(t) - \sum_{k=1}^{N^{\uparrow}_P} q^{\uparrow}_{G, k}(t) >0

where

oil production rate for

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body	N_y

years

assessment period

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body	t

days

day within a given year

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body	r

–

discount rate

LaTeX Math Inline

body	N_y

years

assessment period

LaTeX Math Inline

body	t

days

day within a given year

LaTeX Math Inline

body	r

–

discount rate

LaTeX Math Inline

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

volume/day

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body	k

-th producer

LaTeX Math Inline

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

volume/day

oil production rate for

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body	k

-th producer

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

cash/volume

cost of produced oil treatment and transportation from

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body	k

-th wellhead to CMS

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body	R_O(t)

cash/volumeoil selling price

LaTeX Math Inline

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

volume/day

gas production rate for

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body	k

-th producer

LaTeX Math Inline

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

cash/volume

cost of produced gas treatment and transportation from

LaTeX Math Inline

body	k

-th wellhead to CMS

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body	R_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

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body	k

-th producer

LaTeX Math Inline

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

cash/volume

cost of produced water treatment and transportation from

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body	k

-th wellhead to CMS

LaTeX Math Inline

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

counts

number of producers at

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body	t

LaTeX Math Inline

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

volume/day

liquid production rate for

LaTeX Math Inline

body	k

-th producer

LaTeX Math Inline

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

cash/volume

cost of fluid lift from reservoir to the

LaTeX Math Inline

body	k

-th wellhead, cash/volume

LaTeX Math Inline

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

volume/day

water supply rate

LaTeX Math Inline

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

cash/volumecost of water supply

LaTeX Math Inline

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

volume/daygas supply rate

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body	--uriencoded--C%5e%7B\uparrow%7D_%7BGS%7D(t)

cash/volumecost of gas supply

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

volume/day

water injection rate for

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body	i

-th water injector

LaTeX Math Inline

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

cash/volume

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

LaTeX Math Inline

body	i

-th well

LaTeX Math Inline

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

counts

number of water injectors at

LaTeX Math Inline

body	t

LaTeX Math Inline

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

volume/day

gas injection rate for

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body	i

-th gas injector

LaTeX Math Inline

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

cash/volume

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

LaTeX Math Inline

body	i

-th well

LaTeX Math Inline

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

counts

number of gas injectors at

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body	t

The objective function

LaTeX Math Block Reference

anchor	OF

can be rewritten in terms of Surface flowrates

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body	\{ q^{\uparrow}_L, q^{\downarrow}_W, q^{\downarrow}_G \}

:

--uriencoded--C%5e%7B\downarrow%7D_%7BG,j%7D(t)

cash/volume

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

LaTeX Math Inline

body	i

-th well

LaTeX Math Inline

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

counts

number of gas injectors at

LaTeX Math Inline

body	t

The objective function

LaTeX Math Block Reference

anchor	OF

can be rewritten in terms of Surface flowrates

LaTeX Math Inline

body	\{ q^{\uparrow}_L, q^{\downarrow}_W, q^{\downarrow}_G \}

:

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anchor	OF_L
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G_t = \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{OGW}(t)  \cdot q^{\uparrow}_{L, p}(t)
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,i} \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)
-C^{\uparrow}_{GS} \cdot q^{\uparrow}_{GS}(t)

LaTeX Math Block

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C^{\uparrow}_{OGW}(t) = \left[  (R_O(t) -  C^{\uparrow}_{O,p}) + (R_G(t) - C^{\uparrow}_{G,p}) \cdot  Y_{g,p}(t) \right]  \cdot (1- Y_{w,p}(t)) 
- C^{\uparrow}_{L,p} - C^{\uparrow}_{W,p} \cdot Y_{w,p}(t)

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q^{\uparrow}_{WS}(t) =

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anchor	OF_L
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G_t = \sum_{p=1}^{N^{\uparrow}_P} C^{\uparrow}_{OGW}(t)  \cdot q^{\uparrow}_{L, p}(t)
- \sum_{i=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,ij} \cdot q^{\downarrow}_{W, i}(t) 
- \sum_{jk=1}^{N^{\downarrowuparrow}_GP} C^{\downarrowuparrow}_{GW,jk} \cdot q^{\downarrow}_{G, j}(t)
- C^{\uparrow}_{WSW,k} \cdot q^{\uparrow}_{WS k}(t)

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C^q^{\uparrow}_{OGWWS}(t) = \left[  (R_O(t) -  C^{\uparrow}_{O,p}) + (R_G(t) - C^{\uparrow}_{G,p}) \cdot  Y_{g,p}(t) \right]  \cdot (1- Y_{w,p}(t)) 
- C^{\uparrow}_{L,p} - C^sum_{i=1}^{N^{\downarrow}_W}  q^{\downarrow}_{W, i}(t) - \sum_{k=1}^{N^{\uparrow}_P} q^{\uparrow}_{W,p} \cdot Y_{w,p k}(t) 
&gt; 0

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q^{\uparrow}_{WSGS}(t) = \sum_{ij=1}^{N^{\downarrow}_W} C^{\downarrow}_{W,j} \cdotG}  q^{\downarrow}_{WG, ij}(t) - \sum_{k=1}^{N^{\uparrow}_P} C^{\uparrow}_{W,k} \cdot q^{\uparrow}_{WG, k}(t)

with restrictions

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q^{\uparrow}_{WS}(t) >0  &gt;0

where

LaTeX Math Inline

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

Watercut in

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body	k

-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

body	k

-th well

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