Vogel Equation for Inflow Performance

Below the bubble point, free gas strangles oil inflow, and the Vogel curve replaces the straight line productivity relationship.

The equation

• pwf is flowing bottomhole pressure, pr the reservoir pressure
• qmax is the absolute open flow at zero bottomhole pressure
• The curve bends because gas saturation grows as pressure falls

Worked example

Flowing at half the reservoir pressure gives q/qmax = 1 – 0.1 – 0.2 = 0.70. The straight line PI would have promised only 0.50 at that drawdown, and the difference feeds directly into artificial lift design.

When to use it

For solution gas drive wells below bubble point. Above it, stay with the linear PI, and composite forms exist for wells that straddle the two regimes.

Related Calculators and Reference

• Mud Weight and Pressure Gradient Calculator: convert between ppg, SG, and psi per foot.
• Probabilistic STOIIP Calculator: volumes with uncertainty ranges.
• PetroWiki by SPE: the industry reference for petroleum engineering.