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
\sigma | |
\epsilon | a model parameter depending on Productivity Index definitions 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}} | |||||
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| Steady State flow regime (SS) |
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| Pseudo-steady State flow regime (PSS) |
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The relation between the total sandface flowrate q, bottomhole pressure p_{wf} and field-average formation pressure p_r during the stabilized reservoir flow:
corresponding to linear IPR with constant productivity index :
| (1) | J_r = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S} |
where
\sigma | |
\epsilon = 0.5 | for Steady State (SS) well flow regime |
\epsilon = 0.75 | 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.