The relation between surface flow rate , bottom-hole pressure  and field-average formation pressure  during the stabilised reservoir flow:

q = J \, (p_r - p_{wf})

corresponding to linear IPR with constant productivity index :

J = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S}

where

transmissibility above bubble point

for Steady State (SS) well flow regime

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.