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proxy model of Productivity Index for stabilised reservoir flow in homogeneous reservoir:.

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J  = \frac{q}{p_{\rm frm} - p_{wf}} = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon + S}

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bodyq

depending on application may mean a total sandface flowrate (

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bodyq_t
) or a product of surface flowrate and FVF (
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bodyq = q_{\rm srf} B
)

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bodyp_{wf}

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bodyp_{\rm frm}

depending on application may mean a drain-boundary formation pressure (

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bodyp_e
) or drain-area formation pressure (
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bodyp_r
)

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body\sigma

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bodyr_w

wellbore radius

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bodyr_e

distance to a drainarea boundary

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bodyS

total skin

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body\epsilon

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

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body\epsilon =\{ 0, \, 0.5, \, 0.75 \}
, 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.

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