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The above workflow is very simplistic and assumes single-layer formation with no cross-flow complications.

In practise, the WFP analysis – Well Flow Performance analysis is often very tentative and production technologists spend some time experimenting with well regimes on well-by-well basis. 

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In general case of multiphase flow the PI 

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

Some analytical correlations can be used to approximate the numerical solutions For undersaturated reservoir the numerically-simulated WFP – Well Flow Performances have been approximated by analytical models and some of them are brought below. 

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But obviously more tests will make assessment more accruate.

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Undersaturated Oil IPR

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For Saturated Oil undersaturated oil reservoir with bottom-hole pressure below bubble point 

LaTeX Math Inline
bodyP_{wf} < P_b
  the near-reservoir zone free gas slippage also inflicts the downward trend at the right side of WFP – Well Flow Performance plot (Fig. 3).

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