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The relation between the bottom-hole pressure 

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bodyp_{wf}
 and surface flow rate 
LaTeX Math Inline
bodyq
  during the stabilised formation flow:

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q = J \, (p_r - p_{wf})

corresponding to linear IPR with constant productivity index :

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anchor3AIXS
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J = \frac{2 \pi \sigma}{ \ln \frac{r_e}{r_w} + \epsilon+ S}

where 

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body\sigma
 is transmissibility above bubble point 
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anchorPerrine2phase_alpha
pageLinear Perrine multi-phase diffusion (model)
, 
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body\epsilon = 0.5
 for steady-state SS flow and 
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body\epsilon = 0.75
 for pseudo-steady state PSS flow.