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For a single layer formation with low-compressibility fluid (like water) the PI does not depend on drwadown drawdown (or flowrate) 

LaTeX Math Inline
body J_s = \rm const

 and WFP – Well Flow Performance plot is reperented by a straight line (Fig. 1)

This is a typical WFP – Well Flow Performance plot for water supply wells, water injectors and oil producers above bubble point.

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body \epsilon = 0.5

 for steady-state SS flow and 

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body \epsilon = 0.75

 for pseudo-steady state PSS flow.

For gas wells, condensate producers, light-oil producers, and oil producers below bubble point 

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body P_{wf} < P_b

  the fluid compressibility is high , and formation flow in well vicinity becomes non-linear (deviating from Darcy) and free gas slippage effects inflict fot high flowrates, inflicting the downward trend on WFP – Well Flow Performance plot (Fig. 2).

It can be interpreted as deterioration of near-reservoir zone permeability with fluid velocity is growing.

In general case of saturated oil, the PI 

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body J_s

 features a complex dependance on bottom-hole pressure 

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body p_{wf}

( or flowrate 

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body q

) which can be etstablished based on numerical simulations of multiphase formation flow.

But when field-average formation pressure is above bubble-point 

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body p_R > p_b

 (which means that most parts of the drainage area are saturated oil) the PI can be farily approximated  by some analytical correlations.

For 2-phase oil-gas formation flow below bubble point 

LaTeX Math Inline
body P_{wf} < P_b

  the free gas slippage effects inflict the downward trend on WFP – Well Flow Performance plot (Fig. 3).

It can be interpreted as deterioration of near-reservoir zone permeability when the fluid velocity is high and modelled as rate-dependant skin-factor.

For 3-phase water-oil-gas flow the IPR analysis is perfomed on oil and watr components (see Fig. 4.1 and Fig. 4.2).

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 nopanel true

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