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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}

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LaTeX Math Block
anchorRateLimit
alignmentleft
q^{\downarrow}_{WMIN, i} \leq q^{\downarrow}_{W, i} \leq  q^{\downarrow}_{WMAX, i}

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LaTeX Math Block
anchorRateLimit
alignmentleft
q^{\downarrow}_{GMIN, j} \leq q^{\downarrow}_{G, j} \leq q^{\downarrow}_{GMAX, j}





The objective function  

LaTeX Math Block Reference
anchorOF_L
can be further rewritten in terms of Sandface flowrates 
LaTeX Math Inline
body\{ q^{\uparrow}_t, q^{\downarrow}_w, q^{\downarrow}_g \}
:

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