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

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

The PI concept 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 form.

It 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.

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. 

See Also

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

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