Wellbore flow is called stabilised if the delta pressure across wellbore is not changing over time.
Reservoir flow is called stabilised if the well productivity index is not changing over time.
It's important to remember the difference between constant rate formation flow and stabilised reservoir flow.
The stabilised formation flow may go through a gradually changing flow rate due to formation pressure change, while the productivity index stays constant.
On the other hand, the constant rate formation flow may not represent a stabilised formation flow as the bottom-hole pressure and productivity index maybe still in transition after the last rate change.
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 regime (SS) and pseudo-steady state regime (PSS).
The steady state regime (SS) regime is reached when the flow is stabilised with the full pressure support at the external boundary.
The pseudo-steady state (PSS) regime 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 and bottom-hole pressure in PSS they will be synchronously varying while in SS they will be staying constant.
The table below is summarizing the major differences between SS and PSS regimes.
| Steady state regime (SS) | Pseudo-steady state (PSS) | ||
|---|---|---|---|
| Boundary | Full pressure support | No pressure support | |
| Productivity index (PI) | J(t) = \frac{q}{\Delta p} | constant | constant |
| Flowrate | q(t) | constant | constant |
\Delta p(t) = p_e(t) - p_{wf}(t) | constant | constant | |
| Botomhole pressure (BHP) | p_{wf}(t) | constant | varying |
| Formation pressure | p_e(t) | constant | varying |
It's again important to avoid confusion between the termines stationary conditions (which mean that refered properties are not chaning in time) and stabilised flow conditions which may admit pressure and rate vraition.
In practice, the productivity index is usually not known at all times as there is no routine procedure to assess it.
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
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics