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

J  = \frac{q}{p_{\rm frm} - p_{wf}} = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon + S}

where

	depending on application may mean a total sandface flowrate () or a product of surface flowrate and FVF ()
	bottomhole pressure
	depending on application may mean a drain-boundary formation pressure () or drain-area formation pressure ()
	formation transmissibility
	wellbore radius
	distance to a drainarea boundary
	total skin
	a model parameter depending on Productivity Index definition and boundary type (, see table below)

Drain-area Productivity Index,

Drain-boundary Productivity Index

Steady State flow regime (SS)

J_r  = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + 0.5 + S}

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

Pseudo-steady State flow regime (PSS)

J_r  = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + 0.75 + S}

J_e  = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + 0.5 + S}

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.

See also

Reference