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LaTeX Math Block
anchorqt_VO
alignmentleft
q_t = q_w + q_o + q_g = B_w \, qq^{\uparrow}_W + (B_o - R_s \, B_g) \, qq^{\uparrow}_O + (B_g - R_v \, B_o) \, qq^{\uparrow}_G

where

LaTeX Math Inline
bodyq_w
, 
LaTeX Math Inline
bodyq_o
, 
LaTeX Math Inline
bodyq_g

water sandface flowrate, oil sandface flowrate, gas sandface flowrate

LaTeX Math Inline
bodyq--uriencoded--q%5e%7B\uparrow%7D_W
, 
LaTeX Math Inline
bodyq--uriencoded--q%5e%7B\uparrow%7D_O
, 
LaTeX Math Inline
bodyq--uriencoded--q%5e%7B\uparrow%7D_G

Water surface flowrate, Oil surface flowrate, Gas surface flowrate

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

formation volume factors between sandface pressure/temperature conditions and surface measurement unit (usually separator or processing plant)

LaTeX Math Inline
bodyR_s, \, R_v

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

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LaTeX Math Block
anchorqt
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q_t = \Big[ B_w Y_W + \Big( \, (B_o - R_s B_g) +  Y_G \cdot (B_g - R_v B_o) \,  \Big) \cdot (1-Y_W) \Big] \cdot qq^{\uparrow}_L

where

LaTeX Math Inline
body--uriencoded--\displaystyle Y_G W = \frac%7Bq_W%7D%7Bqfrac%7Bq%5e%7B\uparrow%7D_W%7D%7Bq%5e%7B\uparrow%7D_L%7D

Production Water Cut

LaTeX Math Inline
body--uriencoded--\displaystyle Y_G = \frac%7Bq_G%7D%7Bqfrac%7Bq%5e%7B\uparrow%7D_G%7D%7Bq%5e%7B\uparrow%7D_O%7D

Production Gas-Oil-Ratio = GOR

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