A specific IPR model:

(1)	$\begin{array}{l}\displaystyle \frac{q_O}{q_{O,\rm max}} = 1 - \sum_{k=1}^N a_k \, \left( \frac{p_{wf}}{p_r} \right)^k \quad , \quad \{ p_b > p_r > p_{wf} \}, \quad \sum_{k=1}^N a_k =1, \quad \{ 0< a_k< 1 \}_{k=1..N}\end{array}$

where

$\begin{array}{l}q = q_O\end{array}$	surface production rate of rate
$\begin{array}{l}q_{\rm max}\end{array}$	Absolute Open Flow (AOF) for oil
$\begin{array}{l}p_{wf}\end{array}$	bottom-hole pressure (BHP)
$\begin{array}{l}p_r\end{array}$	drainarea formation pressure
$\begin{array}{l}p_b\end{array}$	bubble-point pressure
$\begin{array}{l}\{ 0< a_k< 1 \}_{k=1..N}\end{array}$	model parameters

This is a generalisation of Vogel model and reduces to Vogel model for $\begin{array}{l}a_1 = 0.2, \ a_2 = 0.8, \ \{ a_k = 0 \, | \ \forall \, k> 2 \}\end{array}$ .

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Wiggins IPR @ model

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References