A value of flowrate normalised by pressure difference between formation pressure and bottom hole pressure:
| (1) | J = \frac{q}{|p_e - p_{wf}|} |
where
q | flowrate (could be sandface or surface , see below) |
p_e | formation pressure |
p_{wf} | bottom hole pressure at sandface |
It is one of the key metrics of well performance.
The definition of flowrate q and formation pressure p_e may vary depending on application (see Definition specifics on formation pressure and productivity index).
Overall concept is applicable to both producers and injectors but can be explicitly defined as:
| Productivity Index of producer | Injectivity Index of injector | ||||||
|
| ||||||
q^{\uparrow} | production rate | q^{\downarrow} | injection rate | ||||
So when somone say
The Productivity Index concept also applies to aquifer expansion:
| (4) | J^{\downarrow}(t) = \frac{q^{\downarrow}(t)}{p(t) - p_{AQ}(t)} |
where
q(t) | volumetric water inflow rate from aquifer into hydrocarbon reservoir at time moment t |
p(t) | formation pressure in hydrocarbon reservoir at time moment t |
p_{AQ}(t) | formation pressure in aquifer at time moment t |
In practice, the Productivity Index is usually not known at all times due to scarce measurements of formation pressure.
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
Petroleum Industry / Upstream / Production / Subsurface Production / Subsurface E&P Disciplines / Production Technology
[ Definition specifics on formation pressure and productivity index ]
[ Sandface Productivity Index ] [ Surface Productivity Index ] [ Specific Productivity Index ] [ Injectivity Index ] [ Drain-area Productivity Index (Jr) ]