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# Productivity Index (PI or J)

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

 (1)

where

 $//$ flowrate (could be  sandface or surface , see below) $//$ formation pressure $//$ bottom hole pressure at sandface

It is one of the key metrics of well performance.

The definition of flowrate $//$ and formation pressure $//$ may vary depending on application (see Definition specifics on formation pressure and productivity index).

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

Productivity Index of producerInjectivity Index of injector
 (2)
 (3)

$//$

production rate

$//$

injection rate

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

The Productivity Index concept also applies to aquifer expansion:

 (4)

where

 $//$ volumetric water inflow rate from aquifer into hydrocarbon reservoir at time moment $//$ $//$ formation pressure in hydrocarbon reservoir at time moment $//$ $//$ formation pressure in aquifer at time moment $//$

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.

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