reservoir · inflow performance
Productivity Index (PI)
J = q / (Pres − Pwf)
click formula to derive ↑
Inputs
STB/d
psi
psi
Description
Computes the productivity index — production rate per unit drawdown — the fundamental linear measure of well deliverability, and projects the maximum (absolute open flow) rate at zero flowing bottomhole pressure.
Variables
| Symbol | Unit | Description |
|---|---|---|
| J | m³/d/kPa | Productivity Index |
| qmax | STB/d | Max Rate (AOF) |
| q | STB/d | Stabilized production rate at the flowing bottomhole pressure Pwf. |
| Pres | psi | Average reservoir (static) pressure. |
| Pwf | psi | Flowing bottomhole pressure at the measured rate q. |
Assumptions
- Flow is single-phase and the reservoir is above the bubble point, so the IPR is linear (constant J) across the drawdown range of interest
- The rate q and pressures Pres, Pwf are all measured at stabilized (pseudo-steady-state), not transient, conditions
- No significant change in near-wellbore conditions (skin, perforation efficiency) between the measurement and the rate being projected
Limitations
- Below the bubble point, two-phase flow makes the IPR curve concave and a constant J overestimates rate at low Pwf — use the Vogel IPR calculator instead
- A single-point PI measurement does not reveal whether low deliverability is due to poor reservoir quality (k·h) or wellbore damage (skin) — a buildup/drawdown test with skin analysis is needed to distinguish them
- AOF (q_max) is a theoretical extrapolation to Pwf=0 and is rarely an operationally achievable or recommended rate
Use Cases
- → Well deliverability benchmarking: Compare PI across wells in the same reservoir to rank deliverability and identify candidates for stimulation.
- → Artificial lift design input: Use PI and AOF to evaluate whether a proposed artificial lift system can achieve the desired production rate at the available drawdown.
- → Nodal analysis baseline: Provide the reservoir inflow (IPR) side of a nodal analysis, paired with tubing performance (outflow) curves to find the well's operating point.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring horizontal wells with multi-stage fracturing commonly show J equivalent to 0.05-0.5 STB/d/psi pre-stimulation matrix values dramatically improved by the fracture network.
Gulf of Mexico
High-quality unconsolidated Miocene sandstone completions can show J > 5-10 STB/d/psi, reflecting excellent reservoir quality and large wellbore/perforation flow area.
North Sea
Brent Group horizontal wells frequently report J of 1-5 STB/d/psi after acid stimulation of the near-wellbore region.
Global
Always pair a low measured J with a skin factor analysis before concluding the reservoir itself is poor — wellbore damage is a common and treatable cause of low apparent PI.
References
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