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Total produced or injected flowrate of all fluids of natural gas across the well-reservoir contact with the volumes measured at the sandface temperature and pressure conditions.

Usually abbreviated as 

LaTeX Math Inline
bodyq_t
 or
LaTeX Math Inline
bodyqB
.


For the volatile oil fluid model the total sandface flowrate is related to surface flowrates of fluid components asnatural gas as:

LaTeX Math Block
anchor1
alignmentleft
q_tg = B_wg \, ( q_W + \frac{B_o G - R_v B_g}{1 - R_v R_s} \, q_O + \frac{B_g - R_s B_o}{1 - R_v R_s} \, q_G)

where

LaTeX Math Inline
body\{ q_W, \, q_O, \, q_G \}

water, crude oil, and natural gas surface flowrates

LaTeX Math Inline
body\{ B_w, \, B_o, \, B_g \}

formation volume factors between separator and sandface pressure/temperature conditions

LaTeX Math Inline
body\{ R_s, \, R_v \}

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



It simplifies for the Black Oil model to:

LaTeX Math Block
anchorZ7UHJ
alignmentleft
q_t = B_w \, q_W + B_o \, q_O + (B_g - R_s B_o) \, q_G

and simplifies further down to production from undersaturated reservoir as:

LaTeX Math Block
anchor4OV4F
alignmentleft
q_t = B_w \, q_W + B_o \, q_O 

...

simplifies for gas reservoir with surface flow rate

LaTeX Math Inline
bodyq_G
 and gas formation volume factor 
LaTeX Math Inline
bodyB_g
:

LaTeX Math Block
anchorVKDEW
alignmentleft
q_tg = q_G \cdot B_g


See also

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Non-linear multi-phase diffusion derivation @model

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