A specific IPR model:

\frac{q_O}{q_{O, \rm max}} = 1 - a \, \frac{p_{wf}}{p_r} - (1-a) \Bigg(\frac{p_{wf}}{p_r} \Bigg)^2  \quad , \quad p_b > p_r > p_{wf}, \quad \{ 0<a<1 \}

where

This is a generalisation of Vogel model and reduces to Vogel model for .

It also goes as a partial case of the Wiggins IPR @ model  with 

See also

Petroleum Industry / Upstream /  Production / Subsurface Production / Subsurface E&P Disciplines / Field Study & Modelling / Production Analysis / Productivity Diagnostics / Inflow Performance Relation (IPR)

[ Vogel IPR @model ] [ Richardson and Shaw IPR @ model ] [ Wiggins IPR @ model ][ LIT IPR @ model ][ PADE IPR @ model ]

References

• Richardson, J. M., & Shaw, A. H. (1982, March 1). Two-rate IPR Testinga Practical Production Tool. Petroleum Society of Canada. doi:10.2118/82-02-01
  
  
• Vogel, J. V. (1968, January 1). Inflow Performance Relationships for Solution-Gas Drive Wells. Society of Petroleum Engineers. doi:10.2118/1476-PA
  
  
• Archer, R. A., Del Castillo, Y., & Blasingame, T. A. (2003, January 1). New Perspectives on Vogel Type IPR Models for Gas Condensate and Solution-Gas Drive Systems. Society of Petroleum Engineers. doi:10.2118/80907-MS
  
  
• Seidle, J. P., & Erickson, D. J. (1993, January 1). Use of Vogel's Inflow Performance Relation for Coal Wells. Society of Petroleum Engineers. doi:10.2118/26201-MS