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

where

LaTeX Math Inline
bodyY_{w,k} = q_{W,k} / q_{L,k}

Watercut in 

LaTeX Math Inline
bodyk
-th well

LaTeX Math Inline
bodyY_{g,k} = q_{G,k} / q_{O,k}

Gas-Oil Ratio in 

LaTeX Math Inline
bodyk
-th well

Usually, each well has a fixed range of its rate variations: 

LaTeX Math Block
anchorRateLimit
alignmentleft
q^{\uparrow}_{LMIN, p} \leq q^{\uparrow}_{L, p} \leq  q^{\uparrow}_{LMAX, p}, \
q^{\downarrow}_{WMIN, i} \leq q^{\downarrow}_{W, i} \leq  q^{\downarrow}_{WMAX, i}, \ 
q^{\downarrow}_{GMIN, j} \leq q^{\downarrow}_{G, j} \leq q^{\downarrow}_{GMAX, j}

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