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LaTeX Math Inline
body-

for producer

LaTeX Math Inline
body+

for injector

LaTeX Math Inline
bodyq=q_{\rm liq}=q_o+q_w

for oil producer

LaTeX Math Inline
bodyq=q_g

for gas producer or injector

LaTeX Math Inline
bodyq=q_w

for water injector or water-supply producer



Note

Excerpt Include
Definition specifics on formation pressure and productivity index in between Dynamic Modelling, Well Flow Performance and Well Tests
Definition specifics on formation pressure and productivity index in between Dynamic Modelling, Well Flow Performance and Well Tests
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The  Productivity Index can be constant or dependent on bottom-hole pressure 

LaTeX Math Inline
bodyp_{wf}
  or equivalently on flowrate 
LaTeX Math Inline
bodyq
.

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Fig. 4.1. Oil WFP – Well Flow Performance for 3-phase (water + oil + gas) formation flow

Fig. 4.2. Water WFP – Well Flow Performance for 3-phase (water + oil + gas) formation flow



The analytical correlation for 3-phase oil flow is given by Wiggins model:

LaTeX Math Block
anchor51ACM
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\frac{q_o}{q_{o, \, max}} = 1 - 0.52 \, \frac{p_{wf}}{p_R} - 0.48 \Bigg(\frac{p_{wf}}{p_R} \Bigg)^2  
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LaTeX Math Block
anchor8CM49
alignmentleft
\frac{q_w}{q_{w, \, max}} = 1 - 0.72 \, \frac{p_{wf}}{p_R} - 0.28 \Bigg(\frac{p_{wf}}{p_R} \Bigg)^2 
Note
Excerpt Include
Definition specifics on formation pressure and productivity index in between Dynamic Modelling, Well Flow Performance and Well TestsDefinition specifics on formation pressure and productivity index in between Dynamic Modelling, Well Flow Performance and Well Testsnopanel





Anchor
VLP
VLP

OPR – Outflow Performance Relation

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