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Volumetric flowrate of the fluid phase across all fluids across the well-reservoir contact.


In most popular practical case of a 
3-phase fluid model this will be:

Oil

LaTeX Math Inline
bodyq_o

Gas sandface flowrate

LaTeX Math Block
anchorq_t
alignmentleft
q_t = q_o + q_g + q_w

LaTeX Math Inline
bodyq_

g

o

Water

Gas sandface flowrate

LaTeX Math Inline
bodyq_

w

g

Total

Water sandface flowrate

LaTeX Math Inline
bodyq_

t

w


In this case

...

the relation between the Sandface flowrates

LaTeX Math Inline
body--uriencoded--\%7B q_

...

o, \, q_

...

g, \, q_

...

w \%7D

...

 and Surface Flowrates 

LaTeX Math Inline
body--uriencoded--\%7B

...

q_O, \,

...

q_G, \,

...

q_W \%7D
 is given

...

by Modified Black Oil fluid @model

LaTeX Math Block
anchorq_o
alignmentleft
q_o =
\frac{
 B_o \cdot (
q_O - R_v \, q_G)
}{1- R_v \, R_s} LaTeX Math Block
anchorrho_o
alignmentleft
\rho_o = \frac{ \dot m_o}{q_o}= \frac{\rho_O + \rho_G \, R_s}{B_o}
LaTeX Math Block
anchor
m_oalignment
left\dot m_o = \rho_o \cdot
q
_o = (\rho
_
O + \rho_G \, R_s) \cdot \frac{ q_o}{B_o} LaTeX Math Blockanchorq_
g
alignmentleft
q_g = 
\frac{
B_g \cdot ( q_G - R_s \, q_O)
}{1- R_v \, R_s}
LaTeX Math Block
anchor
rho_galignmentleft\rho_g = \frac{\dot m_g}{q_g}= \frac{\rho_G + \rho_O \, R_v}{B_g}
LaTeX Math Block
anchorq_w
alignmentleft
q_w = B_w \cdot q_W
LaTeX Math Block
anchorrho_w
alignmentleft
\rho_w =\frac{\dot m_w}{
LaTeX Math Block
anchorm_g
alignmentleft
\dot m_g = \rho_g \cdot q_g = (\rho_G + \rho_O \, R_v) \cdot \frac{q_g }{B_g}
q
_w}= \frac{\rho_W}{B
_w
} LaTeX Math Blockanchor
m_w
alignmentleft
\dot m_w = \rho_w \cdot
q_w =
\rho_W
 
\cdot \frac{q_w}{
B
_w} LaTeX Math Block
anchorqt
alignmentleft
q
_
t = q_o + q_g + q_
w
LaTeX Math Block
anchorqt2
alignmentleft
q_t = \frac{B_o - B_g \, R_v}{1-R_v \, R_s} \cdot q_O +\frac{B_g -
 
B_o
\,
R_v}{1-R_v \, R_s} \cdot
 q_
G + B_w \cdot q_
W
LaTeX Math Blockanchorqt3alignment
left
q_t = \frac{B_o - B_g \, R_v}{(1-R_v \, R_s) \rho_O} \cdot \dot m_O 

+\frac{B_g - B_o \, R_v}{(1-R_v \, R_s) \, \rho_G} \cdot \dot m_G 

+ \frac{B_w}{\rho_W} \cdot \dot m_W
LaTeX Math Block
anchorqt2
alignmentleft
\rho_t = (\dot m_O + \dot m_G + \dot m_G)/q_t

...

titleDerivation


Panel
borderColorwheat
bgColormintcream
borderWidth7

Derivation of the volatile oil sandface/surface flowrates relation

See Also

...

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

...

Surface flowrates ] [ Oil surface flowrate ] [ Gas surface flowrate ] [ Water surface flowrate ] [ Total sandface flowrate ]

Volatile Oil Fluid @model ]