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
q | depending on application may mean a total sandface flowrate ( q_t) or a product of surface flowrate and FVF ( q = q_{\rm srf} B) |
p_{wf} | |
p_{\rm frm} | depending on application may mean a drain-boundary formation pressure ( p_e) or drain-area formation pressure ( p_r) |
\sigma | |
r_w | wellbore radius |
r_e | distance to a drainarea boundary |
S | total skin |
\epsilon | a model parameter depending on Productivity Index definition and boundary type ( \epsilon =\{ 0, \, 0.5, \, 0.75 \}, see table below) |
Drain-area Productivity Index, J_r = \frac{q}{p_r - p_{wf}} | Drain-boundary Productivity Index J_e = \frac{q}{p_e - p_{wf}} | |||||
---|---|---|---|---|---|---|
Steady State flow regime (SS) |
|
| ||||
Pseudo-steady State flow regime (PSS) |
|
|
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.