A boundary dominated Reservoir flow around the well with well productivity index is not changing over time:

There should be no confusion between stabilised reservoir flow and constant-rate production.

Constant-rate production may not represent stabilised reservoir flow as productivity index maybe still in transition after the last rate change.

On the other hand, a stabilised reservoir flow may go through a gradually changing flow rate due to formation pressure change with productivity index staying constant.

The WFP methods are not applicable if the well flow is not stabilised even if the flow rate is maintained constant. 

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

• Steady State flow regime (SS) 

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.

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.

The formation pressure  $//<![CDATA[ \begin{array}{l}p_e(t)\end{array} //]]>$ and bottom-hole pressure  $//<![CDATA[ \begin{array}{l}p_{wf}(t)\end{array} //]]>$ in PSS they will be synchronously varying while in SS they will be staying constant.

The table below is summarising the major differences between SS and PSS regimes.

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

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