A proxy model of Productivity Index for stabilised reservoir flow.
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 () | |
depending on application may mean a drain-boundary formation pressure () or drain-area formation pressure () | |
wellbore radius | |
distance to a drainarea boundary | |
total skin | |
a model parameter depending on Productivity Index definition and boundary type (, see Table 1 below) |
The Dupuit PI @model is actually exact for homogeneous reservoir.
Table 1. Variations to Dupuit PI @model depending on the reservoir flow regime and the definition/application of Productivity Index.
Drain-boundary Productivity Index | ||||
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Steady State flow regime (SS) |
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Pseudo-Steady State flow regime (PSS) |
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing
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.