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For volatile oil fluid model the oil surface flowrate 

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body--uriencoded--q_OO%5e%7B\uparrow%7D
 is related to oil sandface flowrate 
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bodyq_o
 and gas sandface flowrate
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bodyq_g
 as (see derivation):

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q_OO^{\uparrow} =(1-R_v \, R_s)^{-1} \left( \frac{q_o}{B_o} +\frac{R_v \, q_g}{B_g} \right) 

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q_OO^{\uparrow} = (1-Y_W) \cdot q_L


The oil surface flowrate 

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bodyq_O
 r relates to Total sandface flowrate 
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bodyq_t
 as:

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q_OO^{\uparrow} = \frac{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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q_O = \frac{q_o}{B_o} =(1-Y_W) \cdot q_L = \frac{1-Y_W}{B_w Y_W + \left[ (B_o - R_s B_g) + B_g \, Y_G \right] \cdot (1-Y_W)}  \cdot q_t

See Also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate

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