Volumetric flowrate of the fluid phase across the all fluids across the well-reservoir contact.
In most popular practical case of a 3-phase fluid model this will be:
Oil | Gas sandface flowrate |
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LaTeX Math Block |
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| q_t = q_o + q_g + q_w |
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gWater wTotal t
In this case
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the relation between the Sandface flowrates
LaTeX Math Inline |
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body | --uriencoded--\%7B q_ |
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and Surface Flowrates
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is given ...
by Modified Black Oil fluid @model:
\frac{ }{1- R_v \, R_s} LaTeX Math Block |
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\rho_o = \frac{
\dot m_o}{q_o}= \frac{\rho_O + \rho_G \, R_s}{B_o}m_o | alignment | left\dot m_o = \rho_o \cdot q_o = (\rho_O + \rho_G \, R_s) \cdot \frac{ q_o}{B_o} =
\frac{(\rho_O + \rho_G \, R_s) \cdot ( O - R_v \, q_G) }{1- R_v \, R_s}
LaTeX Math Block |
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anchor | q_\frac{ B_g \cdot ( q_G - R_s \, q_O) |
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}{1- R_v \, R_s} LaTeX Math Block |
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\rho_g = \frac{\dot m_g}{q_g}= \frac{\rho_G + \rho_O \, R_v}{B_g}m_g | alignment | left |
\dot m_g = \rho_g \cdot q_g = (\rho_G + \rho_O \, R_v) \cdot \frac{_g }{Bg} =
\frac{ (\rho_G + \rho_O \, R_v) \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s} LaTeX Math Block |
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anchor | q_cdot q_W LaTeX Math Block |
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\rho_w =\frac{\dot m_w}{q_w}= \frac{\rho_W}{B_w} |
LaTeX Math Block |
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\dot m_w = \rho_w \cdot q_w = \rho_W \cdot \frac{q_w}{B_w} = \rho_W \cdot q_W |
LaTeX Math Block |
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q_t = q_o + q_g + q_w |
LaTeX Math Block |
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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 |
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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}
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LaTeX Math Block |
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\dot m = \dot m_o + \dot m_g + \dot m_w = \dot m_O + \dot m_G + \dot m_G LaTeX Math Block |
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\rho_t = \frac{\dot m}{_t} = \frac{\dot mO + \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_}
} ...
See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing (WT) / Flowrate Testing / Flowrate
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[ Surface flowrates ] [ Oil surface flowrate ] [ Gas surface flowrate ] [ Water surface flowrate ] [ Total sandface flowrate ]
[ Volatile Oil Fluid @model ]