Radial Flow and the Productivity Index
Steady radial Darcy flow into a wellbore gives the productivity index, the barrels per day a well delivers for each psi of drawdown.
The equation
J = k h / (141.2 μ B (ln(re/rw) – 0.75))
- k is permeability in millidarcies, h is net pay in feet
- μ is viscosity in centipoise, B the formation volume factor
- re and rw are drainage and wellbore radii
Worked example
With 100 millidarcies, 50 feet of pay, 1 centipoise oil, B of 1.2, and ln(re/rw) of 6.9, J is about 4.8 barrels per day per psi. Draw the well down 500 psi and it makes roughly 2,400 barrels per day.
When to use it
The kh product is the prize of every well test. Skin damage subtracts directly from the log term, which is why a few points of skin can quietly halve a wells rate.
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.