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There are two special reservoir flow regimes which are both stabilised and maintain constant flow rate:  

• Steady State flow regime (SS)

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and 

• Pseudo-Steady State flow regime (PSS).

The Steady State flow regime (SS) is reached when the flow is stabilised with the full pressure support at the external boundary.

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The Pseudo-steady State flow regime (PSS) is reached when the flow is stabilised with no pressure support at the external boundary.

In both above cases, the drawdown and flow rate will stay constant upon productivity stabilisation.

As for formation The formation pressure 

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It's again important to avoid confusion between the term:

• Stationary ( or Steady State) reservoir flow, which means that all dynamic properties are not changing in time,

and 

• Stabilised reservoir flow which may happen during pressure variation.

See Also

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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics