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Vogel Inflow Performance Relationship Formula

qo=qmax[10.2(PwfPr)0.8(PwfPr)2]q_o = q_{max}\left[1 - 0.2\left(\frac{P_{wf}}{P_r}\right) - 0.8\left(\frac{P_{wf}}{P_r}\right)^2\right]

The Vogel IPR estimates oil well inflow rate under two-phase flow conditions using flowing bottomhole pressure and average reservoir pressure.

Calculate

How engineers use this formula

Use it for solution-gas-drive oil wells where the inflow curve is nonlinear below bubblepoint pressure.

Assumptions

  • The well behavior matches the empirical Vogel oil IPR relationship.
  • Reservoir pressure and bottomhole flowing pressure are representative.
  • The equation is applied within its intended oil-well inflow context.

Limitations

  • Not a gas deliverability equation.
  • Not a substitute for a calibrated nodal-analysis model when detailed system behavior is needed.

Common mistakes

  • Applying Vogel directly to dry-gas wells.
  • Using wellhead pressure instead of bottomhole flowing pressure.
  • Forgetting that pressure ratio terms should be dimensionless.

Default example

Using the default inputs, q_o equals 700 STB/day.

q_maxSTB/day

1000

P_wfpsi

1500

P_rpsi

3000

Inputs

q_max

STB/day

Maximum Oil Rate at Zero Flowing Bottom-Hole Pressure

P_wf

psi

Bottom-Hole Flowing Pressure

P_r

psi

Average Reservoir Pressure

Outputs

q_o

STB/day

Oil Flow Rate

q_max

STB/day

Maximum Oil Rate at Zero Flowing Bottom-Hole Pressure

x

dimensionless

Vogel Pressure Ratio

P_wf

psi

Bottom-Hole Flowing Pressure

P_r

psi

Average Reservoir Pressure

Source and review

reviewed

Vogel, J.V. 1968. Inflow Performance Relationships for Solution-Gas Drive Wells.

Source

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