A value of flowrate normalised by pressure difference between formation pressure and bottom hole pressure:

J = \frac{q}{\delta P}|p_e - p_{wf}|}

where

It is one of the key metrics of well performance.

The definition of flowrate 

Overall concept is applicable to both producers and injectors but can be explicitly defined as:

J^{\uparrow} = \frac{q^{\uparrow}}{p_e - p_{wf}}

J^{\downarrow} = \frac{q^{\downarrow}}{p_{wf} - p_e}

So when someone mention Productivity Index of injector it's normally meant Injectivity Index.

The Productivity Index concept also applies to aquifer expansion:

J^{\downarrow}(t) = \frac{q^{\downarrow}(t)}{p(t) - p_{AQ}(t)}

where

In practice, the Productivity Index is usually not known at all times due to scarce measurements of formation pressure and bottom hole pressure.

It started changing with advent of Permanent Downhole Gauges (PDG). 

When assessing formation pressure it is often accepted that reservoir takes the same time to stabilise the flow after any change in well flow conditions and the stabilisation time is assessed based on the well tests analysis.

Although, this is not strictly true and the flow stabilisation time depends on well-formation contact and reservoir property variation around a given well.

This is also compromised in multi-layer formations with cross-layer communication. 

The best practise in this case is to perform proper Pressure Transient Analysis (PTA) or use deconvolution.

See Also

...

Petroleum Industry / Upstream / Production / Subsurface Production / Subsurface E&P Disciplines / Production Technology 

[  in between Dynamic Modelling, Well Flow Performance and Well TestsDefinition specifics on formation pressure and productivity index in between Dynamic Modelling, Well Flow Performance and Well Tests ] 

[ Sandface Productivity Index ] [ Surface Productivity Index ] [ Specific Productivity Index ] [ Injectivity Index ] [ Drain-area Productivity Index (J_r) ]

[ Productivity Index @model ] [ Dupuit PI @model ]nopaneltrue