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This is a typical IPR plot for water supply wells, water injectors and dead oil producers.

The For the oil/water production the PI can be estimated using the Darcy equation Dupuit PI @model:

LaTeX Math Block
anchor3AIXS
alignmentleft
J_s = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S}

where 

LaTeX Math Inline
body\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 transmissibility above bubble point 
LaTeX Math Block Reference
anchorPerrine2phase_alpha
pageLinear Perrine multi-phase diffusion @model
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