A proxy model of Productivity Index for stabilised flow in homogeneous reservoir:


Drain-area Productivity Index Drain-boundary Productivity Index


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



q = J_e \, (p_e - p_{wf})




The relation between the total sandface flowrate , bottomhole pressure  and field-average formation pressure  during the stabilized reservoir flow:

corresponding to linear IPR with constant productivity index :

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

where

transmissibility

for Steady State (SS) well flow regime

for Pseudo Steady State (PSS) well flow regime


See also

Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing

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.