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A specific IPR model:

Excerpt
LaTeX Math Block
anchorQF556
alignmentleft
\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

LaTeX Math Inline
bodyq_O

surface production rate of rate

LaTeX Math Inline
bodyq_{O, \rm max}

Absolute Open Flow (AOF) for oil

LaTeX Math Inline
bodyp_{wf}

bottom-hole pressure (BHP)

LaTeX Math Inline
bodyp_r

drainarea formation pressure

LaTeX Math Inline
bodyp_b

bubble-point pressure

LaTeX Math Inline
bodya

model parameter 

LaTeX Math Inline
body\{ 0<a<1 \}


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

LaTeX Math Inline
bodya = 0.2
.

See also

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

LaTeX Math Inline
body--uriencoded--\%7B a_1 = a, \, a_2 = 1-a, \, a_k = 0, \forall k> 2 \%7D


See also

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

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


References

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