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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}

where

LaTeX Math Inline
bodyq

 total sandface flowrate 

LaTeX Math Inline
bodyp_{wf}

LaTeX Math Inline
bodyp_r

formation pressure

LaTeX Math Inline
body\sigma

LaTeX Math Inline
body\epsilon

a model parameter depending on Productivity Index definitions and boundary type (

LaTeX Math Inline
body\epsilon =\{ 0, \, 0.5, \, 0.75 \}
, see table below)

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Drain-area Productivity Index

LaTeX Math Inline
bodyJ_r = \frac{q}{p_r - p_{wf}}

Drain-boundary Productivity Index 

LaTeX Math Inline
bodyJ_e = \frac{q}{p_e - p_{wf}}

Steady State flow regime (SS)


LaTeX Math Block
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J_r  = \frac{2 \pi \sigma}{ \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}



LaTeX Math Block
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J_e  = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + 0.5 + S}

The relation between the total sandface flowrate 

LaTeX Math Inline
bodyq
, bottomhole pressure 
LaTeX Math Inline
bodyp_{wf}
 and field-average formation pressure 
LaTeX Math Inline
bodyp_r
 during the stabilized reservoir flow:

corresponding to linear IPR with constant productivity index :

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anchor3AIXS
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 + 

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S}

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where

LaTeX Math Inline
body\sigma

LaTeX Math Inline
body\epsilon = 0.5

for Steady State (SS) well flow regime

LaTeX Math Inline
body\epsilon = 0.75

for Pseudo Steady State (PSS) well flow regime




See also

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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Well Testing / Pressure Testing

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