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The gas surface flowrate 

LaTeX Math Inline
body--uriencoded--q_G%5e%7B\uparrow%7DG
 relates to Total sandface flowrate 
LaTeX Math Inline
bodyq_t
 as:

LaTeX Math Block
anchorqL
alignmentleft
q_G^G = \frac{ Y_G \cdot  (1-Y_W)}{B_w Y_W + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \, Y_G \right] \cdot (1-Y_W)}  \cdot q_t

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