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LaTeX Math Block
anchorqL
alignmentleft
q_L = \frac{q_t}{B_w Y_wW + \left[ (B_o - R_s B_g) + (B_g - R_v B_o) \, Y_gG \right] \cdot (1-Y_wW)}

where

LaTeX Math Inline
bodyq_t

Total sandface flowrate

LaTeX Math Inline
bodyB_w, \, B_o, \, B_g

formation volume factors between separator and sandface pressure/temperature conditions

LaTeX Math Inline
bodyR_s, \, R_v

Solution GOR and Vaporized oil ratio at sandface pressure/temperature conditions

LaTeX Math Inline
body--uriencoded--\displaystyle Y_w W = \frac{q_W}{q_L}frac%7Bq_W%7D%7Bq_L%7D

Production Water Cut

LaTeX Math Inline
body--uriencoded--\displaystyle Y_gG= \frac{q_G}{q_O}frac%7Bq_G%7D%7Bq_O%7D

Production Gas-Oil-Ratio



Expand
titleDerivation

Starting with definition of Total sandface flowrate 

LaTeX Math Block Reference
anchorqt_VO
pageTotal sandface flowrate (= qt)
 and substituting the expression of Oil surface flowrate, Gas surface flowrate, Water surface flowrate through Liquid production rate one arrives to 
LaTeX Math Block Reference
anchorqL
.

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