The relation between the bottom-hole pressure  and surface flow rate   during the stabilised formation 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  is transmissibility above bubble point ,  for steady-state SS flow and  for pseudo-steady state PSS flow.