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} = \frac{2 \pi \cdot \frac{k \, h}{\mu} }{ \ln \frac{r_e}{r_w} - \epsilon + S} |
where
depending on application may mean a total sandface flowrate ( | |
depending on application may mean a drain-boundary formation pressure ( | |
| wellbore radius | |
| distance to a drainarea boundary | |
| total skin | |
a model parameter depending on Productivity Index definition and boundary type ( |
In case of homogeneous reservoir with only one vertical well producing the Dupuit PI @model is the exact analytical solution of Reservoir Flow Model (RFM).
Table 1. Variations to Dupuit PI @model depending on the reservoir flow regime and the definition/application of Productivity Index.
Steady State flow regime (SS) |
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Pseudo-Steady State flow regime (PSS) |
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For the fractured vertical well the geometrical skin-factor is related to Fracture half-length
as:
S_G = -\ln \left(\frac{X_f}{2\, r_w} \right) |
J = \frac{q}{p_{\rm frm} - p_{wf}} = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} - \epsilon + S} = \frac{2 \pi M \cdot h}{ \ln \frac{r_e}{r_w} - \epsilon + S} = \frac{2 \pi k_{abs} \cdot h}{ \ln \frac{r_e}{r_w} - \epsilon + S} \cdot M_r = T \cdot M_r(s_w, s_g) |