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# Productivity index (J)

The productivity index is a measure of the well potential or ability to produce and is a commonly measured well property^{1}. The symbol J is commonly used to express the productivity index; as well as, being the preferred symbol by the Society of Petroleum Engineers.

## Understanding well property

The productivity index is the ratio of the total liquid surface flowrate to the pressure drawdown at the midpoint of the producing interval. The units typically are in field units, STB/D/psi as shown below:

Productivity Index = J = Q/(Pe-Pwf)

- J = Productivity Index, STB/day/psi
- Q = Surface flowrate at standard conditions, STB/D
- Pe = External boundary radius pressure, psi
- Pwf = Well sand-face mid-perf pressure, psi

**Example 1:**

A well is producing 1000 STB/D of liquid with a pressure drop of 500 psi would have a J=2 STB/D/psi.

A subsurface pressure gauge is used to determine the static pressure Pe after a sufficient shut-in period and also the flowing bottom-hole pressure, Pw, after the well has flowed at a stabilized rate for a sufficient period of time. The difference (Pe - Pw) is called the pressure drawdown.

**Example 2:**

- Q = 500 STB/D
- Pe= 3000 psi
- Pwf = 250 psi

J = 500 STB/D / ( 3000 psi – 250 psi) = 0.18 STB/D/psi

The productivity index can also be expanded to a semi-steady state Darcy law type formulation where:

J = .0078 k h/ (u B ( ln (re/rw) – 0.5 – S))

Where

- k = permeability, md
- h = net thickness, ft
- u = fluid viscosity, cp
- B = formation volume factor, rb/STB
- re = external boundary radius, ft
- rw = wellbore radius, ft
- S = Skin

This approach is less common, as the production and pressure data are more readily available, and in most cases can be more accurately measured.

This same concept can be applied to injection wells to calculate an injectivity index (II), using the same equations.

## References

1. Craft, B. C., and Murray F. Hawkins. 1959. Applied petroleum reservoir engineering. WorldCat

## Noteworthy papers in OnePetro

Alarifi, S., AlNuaim, S., & Abdulraheem, A. 2015. Productivity Index Prediction for Oil Horizontal Wells Using different Artificial Intelligence Techniques. Society of Petroleum Engineers. http://dx.doi.org/10.2118/172729-MS

Al Gahtani, A. M. 2011. A New Productivity Index Formula for ESP-Lifted Wells. Society of Petroleum Engineers. http://dx.doi.org/10.2118/141984-MS

## External links

Schlumberger Oilfield glossary