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 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 variation.
See Also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics