The relation between surface flow rate $\begin{array}{l}q\end{array}$ , bottom-hole pressure $\begin{array}{l}p_{wf}\end{array}$ and field-average formation pressure $\begin{array}{l}p_r\end{array}$ during the stabilised reservoir flow:

$\begin{array}{l}\displaystyle q = J \, (p_r - p_{wf})\end{array}$

corresponding to linear IPR with constant productivity index :

(1)	$\begin{array}{l}\displaystyle J = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S}\end{array}$

where

$\begin{array}{l}\sigma\end{array}$	transmissibility above bubble point Error rendering macro 'mathblock-ref' : Math Block with anchor=Perrine2phase_alpha could not be found on page with id=16155929.
$\begin{array}{l}\epsilon = 0.5\end{array}$	for Steady State (SS) well flow regime
$\begin{array}{l}\epsilon = 0.75\end{array}$	for Pseudo Steady State (PSS) well flow regime

Reference

Dupuit, J., Etudes theoriques et pratiques sur le mouvement des eaux dans les canaux decouverts et a travers les terrains permeables, 2eme edition; Dunot, Paris, 1863.

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Dupuit equation @model

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