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The objective function  

LaTeX Math Block Reference
anchorOF
can be rewritten in terms of Surface flowrates 
LaTeX Math Inline
body\{ q^{\uparrow}_L, q^{\downarrow}_W, q^{\downarrow}_G \}
:



LaTeX Math Block
anchorOF_L
alignmentleft
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_{WS} \cdot q_{WS}(t)
- C_{GS} \cdot q_{GS}(t)




LaTeX Math Block
anchorKPBIE
alignmentleft
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) 




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

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