Well Inflow and the Productivity Index

How Hard a Well Pulls

A well produces by drawing its flowing pressure below the reservoir pressure. The productivity index is the rate per unit of that drawdown, $J = \dfrac{q}{P_r - P_{wf}}$.

Radial Inflow and Skin

For radial Darcy flow into a well the index is $J = \dfrac{k,h}{141.2,\mu,B,[\ln(r_e/r_w) + s]}$: it rises with permeability k and net pay h, falls with viscosity, and is throttled by the skin s, near-well damage that adds resistance exactly where the pressure gradient is steepest. A stimulated well has negative skin and a steeper inflow line.

The Inflow Performance Relationship

Plotting flowing pressure against rate gives the inflow performance relationship: a straight line from the reservoir pressure at zero rate down to the absolute open flow at zero flowing pressure, with slope equal to the productivity index. It is how a well's deliverability is read and how a stimulation job is justified.