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

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

H(q) = \frac{\sum_{k=0}^m a_k \, (q/q_\mathrm{max})^k}{\sum_{k=0}^m b_k \, (q/q_\mathrm{max})^k} = 
\frac{a_0 + a_1 \cdot (q/q_\mathrm{max}) + a_2 \cdot (q/q_\mathrm{max})^2 + ... + a_m \cdot (q/q_\mathrm{max})^m}
{b_0 + b_1 \cdot (q/q_\mathrm{max}) + b_2 \cdot (q/q_\mathrm{max})^2 + ... + b_m \cdot (q/q_\mathrm{max})^m}

 p_b > p_r > p_{wf}

where

	bottom-hole pressure (BHP)
	bubble-point pressure
	sandface flowrate
	Absolute Open Flow (AOF)
	pseudo-pressure function specific to fluid type
	pseudo-pressure curvature
	laminar flow coefficient
	turbulent flow coefficient

It needs well tests at least three different rates to assess but obviously more tests will make assessment more accurate.

See also

References