Volumetric flowrate of the fluid phase across the well-reservoir contact
In most popular practical case of a 3-phase fluid model this will be:
In case of Volatile Oil Reservoir the relation to surface flowrates
| LaTeX Math Inline |
|---|
| body | --uriencoded--\%7B q_O, \, q_G, \, q_W \%7D |
|---|
|
and
mass flowrates | LaTeX Math Inline |
|---|
| body | --uriencoded--\%7B \dot m_O, \, \dot m_G, \, \dot m_W \%7D |
|---|
|
is given by following equations:
| 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 |
|---|
| \dot m_o = \rho_o \cdot q_o = (\rho_O + \rho_G \, R_s) \cdot \frac{ q_o}{B_o} = \frac{B_o - B_g \, R_s}{1-R_v \, R_s} \cdot q_O |
|
| LaTeX Math Block |
|---|
| q_g = \frac{ B_g \cdot ( q_G - R_s \, q_O)}{1- R_v \, R_s} |
|
| LaTeX Math Block |
|---|
| \rho_g = \frac{\dot m_g}{q_g}= \frac{\rho_G + \rho_O \, R_v}{B_g} |
|
| LaTeX Math Block |
|---|
| \dot m_g = \rho_g \cdot q_g = (\rho_G + \rho_O \, R_v) \cdot \frac{q_g }{B_g} = \frac{B_g - B_o \, R_v}{1-R_v \, R_s} \cdot q_G |
|
| LaTeX Math Block |
|---|
| q_w = B_w \cdot q_W |
|
| LaTeX Math Block |
|---|
| \rho_w =\frac{\dot m_w}{q_w}= \frac{\rho_W}{B_w} |
|
| LaTeX Math Block |
|---|
| \dot m_w = \rho_w \cdot q_w = \rho_W \cdot \frac{q_w}{B_w} = B_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 q_O
+\frac{B_g - B_o \, R_v}{1-R_v \, R_s} \cdot q_G
+ B_w \cdot q_W |
|
| LaTeX Math Block |
|---|
| 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}
} |
|
See Also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate
[ Well & Reservoir Surveillance ]
[ Sandface flowrates ] [ Oil sandface flowrate ] [ Gas sandface flowrate ] [ Water sandface flowrate ]
[ Surface flowrates ] [ Oil surface flowrate ] [ Gas surface flowrate ] [ Water surface flowrate ] [ Total sandface flowrate ]
