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 |
|---|
body |
|---|
| LaTeX Math Block |
|---|
| q_t = q_o |
|
Gas gWater wTotal t
In this case
...
the relation between the Sandface flowrates
| LaTeX Math Inline |
|---|
| body | --uriencoded--\%7B q_ |
|---|
|
...
...
...
...
and Surface Flowrates
...
...
...
is given ...
by Modified Black Oil fluid @model:
| LaTeX Math Block |
|---|
|
q_o = \frac{ B_o \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s} |
| LaTeX Math Block |
|---|
|
\rho_o = \frac{
\dot m_o}{q_o}= \frac{\rho_O + \rho_G \, R_s}{B_o} |
| LaTeX Math Block |
|---|
anchor | m\dot m_o = \rho_o \cdot (\rho_O + \rho_G \, R_s) \cdot \frac{q_o}{} =
\frac{(\rho_O+ rho_G \, R_s) \ }{1- R_v \, R_s}
\frac{ B_g \cdot ( q_G - R_s \, q_O) |
|
}{1- R_v \, R_s}| alignment | left |
|---|
\rho_g = \frac{\dot m_g}{rho_g | _g}= \frac{\rho_G + \rho_O \, R_v}{Bg}| LaTeX Math Block |
|---|
|
\dot m_g = \rho_g \cdot q_g = (\rho_G + \rho_O \, R_v) \cdot \frac{q_g }{B_g} =
\frac{ (\rho_G + \rho_O \, R_v) \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s} |
| LaTeX Math Block |
|---|
anchor | q__w = B \cdotq_W| LaTeX Math Block |
|---|
|
\rho_w =\frac{\dot m_w}{q_w} \frac{\rho_W}{_w}| LaTeX Math Block |
|---|
anchor | m| alignment | left |
|---|
\dotm_w = \rho_w cdot q_w = \rho_W \cdot \frac{q_w}{B_w} = \rho_W \cdot q_W| LaTeX Math Block |
|---|
|
q_t = q_o + q_g + q_w |
| LaTeX Math Block |
|---|
|
q_t = \frac{B_o - B_g \R_s}{1-R_v \, R_s} \cdot _O
+\frac{B_g - B_o \, Rv}{1-R_v \, R_s} \cdot q_G
+ B_w \cdot q_| LaTeX Math Block |
|---|
anchorqt3 | | alignment | left |
|---|
q_t = \frac{B_o - B_g \, R_s}{1-R_v \, R_s } \cdot \frac{\dot m_O }{\rho_O}
+\frac{B_g - B_o \, R_v}{1-R_v \, R_s } \cdot \frac{\dot m_G }{\rho_G}
+ B_w\cdot \frac{\dot m_W}{\rho_W}
|
| LaTeX Math Block |
|---|
|
\dot m = \dot m_o + \dot m_g + \dot m_w = \dot m_O + \dot m_G + \dot m_G |
| LaTeX Math Block |
|---|
|
\rho_t = \frac{\dot m}{q_t} = \frac{\dot m_O + \dot m_G + \dot m_G}{
\frac{B_o - B_g \, R_s}{1-R_v \, R_s } \cdot \frac{\dot m_O }{\rho_O}
+\frac{B_g - B_o \, R_v}{1-R_v \, R_s } \cdot \frac{\dot m_G }{\rho_G}
+ B_w\cdot \frac{\dot m_W}{\rho_W}
} |
| LaTeX Math Block |
|---|
|
s_o = \frac{q_o}{q_t} = \frac{ B_o \, (q_O - R_v \, q_G)}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W } |
| LaTeX Math Block |
|---|
|
s_g = \frac{q_g}{q_t} = \frac{ B_g \, (q_G - R_s \, q_O)}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W } |
| LaTeX Math Block |
|---|
|
s_w = \frac{q_w}{q_t} = \frac{ B_w \, (1- R_v \, R_s) \, q_W}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W } |
...
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 ]
