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

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\Psi^n(p_b) - \Psi^n(p_{wf}) = (q - q_b) \left[  \frac{1}{(q_\mathrm{max}-q_b)} \cdot \Psi^n(p_b) +  \frac{(q-q_\mathrm{max})

...

H(q)\right]
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  H(q) = \frac{\sum_{k=1}^m a_k \, q^k}{\sum_{k=1}^{m+1} b_k \, q^k}

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 p_b > p_r > p_{wf} 

where
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bodyp_{wf}
bottom-hole pressure (BHP)
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bodyp_b
bubble-point pressure
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bodyq
sandface flowrate
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body--uriencoded--q_\mathrm%7Bmax%7D
Absolute Open Flow (AOF) 
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body\Psi(p)
pseudo-pressure function specific to fluid type
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bodyn
pseudo-pressure curvature
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bodya
laminar flow coefficient
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bodyb
turbulent flow coefficient
...