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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


The alternative way to define the 

LaTeX Math Inline
bodyp_{wf}
 vs
LaTeX Math Inline
bodyq
 correlation is to present
LaTeX Math Inline
bodyq
 as a function of  
LaTeX Math Inline
bodyp_{wf}
:

LaTeX Math Block
anchorIPRq
alignmentleft
q = q(p_{wf})



Note
titleImportant Note

Despite of terminological similarity there is a big difference in the way 

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WFP  and Well Testing deal with formation pressure and flowrates which results in a big difference in productivity index definition and corresponding analysis.

This difference is summarized in the table below:


WFPWell Testing
Formation pressure

LaTeX Math Inline
bodyp_R
– field-average pressure within the drainage area
LaTeX Math Inline
bodyA_e


LaTeX Math Inline
bodyp_e
– pressure value at boudary of the drainage area
LaTeX Math Inline
bodyA_e


Flow rate

LaTeX Math Inline
bodyq_{\rm liq}=q_o+q_w
– surface liquid rate

LaTeX Math Inline
bodyq_t = B_w \, q_W + \frac{B_o - R_s B_g}{1 - R_v R_s} \, q_O + \frac{B_g - R_v B_o}{1 - R_v R_s} \, q_G
– total flowrate at sandface












For single-layer formation with low-compressibility fluid the PI does not depend on flowrate 

LaTeX Math Inline
bodyJ_s = \rm const
 and WFP – Well Flow Performance plot is reperented by a straight line (Fig. 1)

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