reservoir · inflow performance
Inflow Performance Relationship (IPR) — Vogel's Equation
q/qmax = 1 − 0.2(Pwf/Pres) − 0.8(Pwf/Pres)²
click formula to derive ↑
Inputs
STB/d
psi
psi
Description
Computes inflow rate from Vogel's empirical IPR equation, developed for saturated (two-phase, below-bubble-point) solution-gas-drive oil reservoirs. Unlike the constant-PI linear IPR, Vogel's curve is concave, reflecting reduced relative permeability to oil as free gas saturation increases near the wellbore.
Variables
| Symbol | Unit | Description |
|---|---|---|
| q | STB/d | Inflow Rate |
| q/qmax | fraction | Inflow Ratio (q/qmax) |
| qmax | STB/d | Absolute open flow potential — the rate at Pwf=0, from a multi-point well test or extrapolation. |
| Pres | psi | Average reservoir (static) pressure, at or below the bubble point for Vogel's equation to apply. |
| Pwf | psi | Flowing bottomhole pressure at which to evaluate the inflow rate. |
Assumptions
- The reservoir is at or below the bubble point with solution-gas drive as the dominant mechanism (two-phase flow near the wellbore)
- qmax (AOF) is representative of current reservoir conditions — it declines over time as reservoir pressure depletes and must be periodically re-tested
- The Vogel curve shape, originally fit to a range of simulated reservoirs, is assumed transferable to the specific well being analyzed
Limitations
- Not valid above the bubble point — use the linear (constant-J) productivity index model for undersaturated reservoirs
- A single qmax value becomes outdated as reservoir pressure depletes; periodic well testing is needed to update the IPR over time
- Does not account for non-Darcy (turbulent) pressure losses near high-rate gas wells or multilateral/complex completion geometries
Use Cases
- → Solution-gas-drive well IPR: Predict producible rate at a target Pwf for oil wells producing below the bubble point, where the linear PI model would overstate rate.
- → Artificial lift sizing: Generate the reservoir-side IPR curve needed to pair with pump or gas-lift performance curves in a nodal analysis design.
- → AOF estimation from limited test data: Back-calculate qmax from a single stabilized (q, Pwf) test point using the Vogel relationship, avoiding the need for a full multi-rate test.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Spraberry wells producing below the bubble point in mature areas commonly use Vogel IPR for artificial lift and nodal analysis design once natural flow has declined.
Eagle Ford
Volatile-oil intervals below the bubble point often deviate somewhat from the standard Vogel curve due to higher gas-oil ratios — a modified Vogel or Fetkovich exponent fit is sometimes preferred.
Gulf of Mexico
Many GOM oil wells remain above the bubble point for most of their producing life, making the simpler linear PI model more broadly applicable than Vogel; switch to Vogel only once pressure has depleted below Pb.
Global
Always confirm reservoir pressure has dropped below the bubble point before applying Vogel — using it above Pb misrepresents the true (linear) IPR shape.
References
Primary source
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.