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providing that  

LaTeX Math Inline
bodyq
 has a specific meaning and sign as per the table below:

LaTeX Math Inline
body-

for for producer

LaTeX Math Inline
body+

for for injector

LaTeX Math Inline
bodyq=q_o

for oil oil producer

LaTeX Math Inline
bodyq=q_g

for gas gas producer or or injector

LaTeX Math Inline
bodyq=q_w

for water water injector or water water producer or water production from oil oil producer


See more on the variations of PI definition between Dynamic Modelling,  Well Flow Performance and Well Testing. 

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The  Productivity Index can be constant (showing a straight line on IPR like on  Fig. 1) or dependent on bottom-hole pressure on bottomhole pressure 

LaTeX Math Inline
bodyp_{wf}
  or equivalently on flowrate 
LaTeX Math Inline
bodyq
 (showing a curved line on IPR like on  Fig. 2) .

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