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q_t = B_w \, qq^{\uparrow}_W + (B_o - R_s \, B_g) \, qq^{\uparrow}_O + B_g \, qq^{\uparrow}_G
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or
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q_t = \Big[ B_w Y_W + \Big( \, (B_o - R_s B_g) + Y_G \cdot B_g \, \Big) \cdot (1-Y_W) \Big] \cdot qq^{\uparrow}_L |
It simplifies further down to production from undersaturated reservoir as:
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q_t = B_w \, qq^{\uparrow}_W + B_o \, qq^{\uparrow}_O = \Big[ B_w Y_W + B_o \cdot (1- Y_W) \Big] \cdot qq^{\uparrow}_L
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and even simpler for single-phase fluid (water, dead oil or dry gas) with surface flow rate
and
formation volume factor B as below:
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q_t = q B, \quad {\rm meaning:} \quad q_t = qq^{\uparrow}_W \cdot B_w \quad {\rm or} \quad q_t = qq^{\uparrow}_O \cdot B_o \quad {\rm or} \quad q_t = qq^{\uparrow}_G \cdot B_G
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See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate
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