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Excerpt |
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A proxy model of Productivity Index for stabilised reservoir flow. LaTeX Math Block |
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| 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 |
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| distance to a drainarea boundary | | total skin | | a model parameter depending on Productivity Index definition and boundary type ( LaTeX Math Inline |
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body | \epsilon =\{ 0, \, 0.5, \, 0.75 \} |
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| , see Table 1 below) |
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. qJ, (p_r - p_{wf}) |
corresponding to linear IPR with constant productivity index :
ln \frac{r_e}{r_w} - 0.5 + S} |
| LaTeX Math Block |
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| J_e = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + S} |
| Pseudo-Steady State flow regime (PSS) | LaTeX Math Block |
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| J_r = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} - 0.75 + S} |
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LaTeX Math Block |
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anchor | 3AIXS |
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| J_e = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} - |
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+\epsilon |
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For the fractured vertical well the geometrical skin-factor
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| S_G = -\ln \left(\frac{X_f}{2\, r_w} \right) |
LaTeX Math Block |
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| 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) |
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See also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing
Reference
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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.
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