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

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

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

The Productivity Index concept also applies to aquifer expansion:

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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 is usually accepted that a given formation 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.

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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

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

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