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It is related to Total sandface flowrate 

LaTeX Math Inline
body q_t
as:

LaTeX Math Block
anchorqLqt
alignmentleft
q_L = q_O + q_W = \frac{q_t}{} B_w Y_w +[ (B_o - R_s B_g] + B_g (GOR-R_s)] (1-Y_w)


where

where

LaTeX Math Inline
bodyq_w, \, q_o, \, q_g

water, oil and gas sandface flowrates

LaTeX Math Inline
bodyq_W, \, q_O, \, q_G

water, crude oiland natural gas surface flowrates

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\displaystyle Y_w = \frac{q_W}{q_L}

Production Water Cut

LaTeX Math Inline
body\displaystyle GOR= \frac{q_G}{q_O}

Production Gas-Oil-Ratio



Expand
titleDerivation

Starting with definition of Total sandface flowrate 

LaTeX Math Block Reference
anchorqt_VO
pageTotal sandface flowrate
 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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