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One of the most general form of IPR model below bubble-point pressure:

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anchor9C1T3
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\Psi^n(p_r) - \Psi^n(p_{wf}) = q\cdot \Big[  \frac{1}{q_{\rm AOF}} \cdot \Psi^n(p_r) +  \cdot \frac{(q-q_{\rm AOF}) (q + d)}{ b_0 + b_1 \cdot q  + b_2 \cdot q^2} \Big] \quad , \quad p_b > p_r > p_{wf} 

where

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bodyp_{wf}

bottom-hole pressure (BHP)

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bodyp_r

drainarea formation pressure

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bodyp_b

bubble-point pressure

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bodyn

pseudo-pressure curvature

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bodya

laminar flow coefficient

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bodyb

turbulent flow coefficient

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body\Psi(p)

pseudo-pressure function specific to fluid type


It needs well tests at least three different rates to assess  

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body--uriencoded--\%7B a \, , \, b, \, p_r \%7D
 but obviously more tests will make assessment more accurate.

See also


Inflow Performance Relation (IPR)

Richardson and Shaw IPR @ model ] [ Wiggins IPR @ model ]


References