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| J = \frac{q}{p_{\rm frm} - p_{wf}} = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} - \epsilon + S} = |
J \frac{2 \pi \cdot \frac{k \, |
(p_r - p_{wf}) |
with constant productivity index:
h}{\mu} }{ \ln \frac{r_e}{r_w} - \epsilon + S} |
where
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. |
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| anchor | 3AIXS |
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| J_r = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} - 0.75 + |
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| J_e = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} - 0.5 + S} |
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For the fractured vertical well the geometrical skin-factor
is related to Fracture half-length as:| LaTeX Math Block |
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| S_G = -\ln \left(\frac{X_f}{2\, r_w} \right) |
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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
\sigma = \Big \langle \frac{k} {\mu} \Big \rangle \, h = k \, h\, \Big[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \Big] | – water-based or water-oil-based transmissbility above bubble point | LaTeX Math Block Reference |
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| anchor | Perrine2phase_alpha |
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| page | Linear Perrine multi-phase diffusion (model) |
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, for steady-state SS flow and for pseudo-steady state PSS flow.
