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p_{wf} = p_{wf}(q)

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Fig. 1

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One of the two key concepts of Well Flow Performance analysis along with Vertical Lift Performance (VLP).

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The  Productivity Index can be constant (showing a straight line on IPR like on  Fig. 12) or dependent on bottomhole pressure 

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bodyp_{wf}
  or equivalently on flowrate 
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bodyq
 (showing a curved line on IPR like on  Fig. 23) .

In general case of multiphase flow the PI 

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 features a complex dependance on bottom-hole pressure 
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bodyp_{wf}
 (or equivalently on flowrate 
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bodyq
) which can be etstablished based on numerical simulations of multiphase formation flow.

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

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bodyJ_s = \rm const
 and IPR plot is reperented by a straight line (Fig. 12)


Fig. 12. IPR plot for constant productivity (water and dead oil)

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For gas producers, the fluid compressibility is high and formation flow is essentially non-linear, inflicting the downward trend on the whole IPR plot (Fig. 23).


Fig. 23. IPR for dry gas producer or gas injector into a gas formation

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For saturated oil reservoir the free gas flow inflict the downward trend of IPR plot  similar to dry gas (Fig. 34).


Fig. 34. IPR for 2-phase oil+gas production below and above bubble point

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When bottom-hole pressure goes below bubble point 

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bodyp_{wf} < p_b
  the near-reservoir zone free gas slippage also inflicts the downward trend at the right side of IPR plot (Fig. 35).

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


Fig. 35. IPR for 2-phase oil+gas production below and above bubble point

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For saturated 3-phase water-oil-gas reservoir the IPR analysis is represented by oil and water components separately (see Fig. 46.1 and Fig. 46.2).


Fig. 46.1. Oil IPR for saturated 3-phase (water + oil + gas) formation flow

Fig. 46.2. Water IPR for saturated 3-phase (water + oil + gas) formation flow

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For undersaturated 3-phase water-oil-gas reservoir the IPR analysis is represented by oil and water components separately (see Fig. 47.1 and Fig. 47.2).


Fig. 47.1. Oil IPR for udersaturated 3-phase (water + oil + gas) formation flow

Fig. 47.2. Water IPR for undersaturated 3-phase (water + oil + gas) formation flow

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