(1)	$\begin{array}{l}\displaystyle J = \frac{q}{\|p_e - p_{wf}\|}\end{array}$

where

$\begin{array}{l}q\end{array}$	flowrate (the specification of which may differ, see below)
$\begin{array}{l}p_e\end{array}$	formation pressure
$\begin{array}{l}p_{wf}\end{array}$	bottom hole pressure at sandface

The definition of flowrate $\begin{array}{l}q\end{array}$ and formation pressure $\begin{array}{l}p_e\end{array}$ may vary depending on application.

Overall concept is applicable to both producers and injectors but can be split into specific definitions:

(2)	$\begin{array}{l}\displaystyle J^{\uparrow} = \frac{q^{\uparrow}}{p_e - p_{wf}}\end{array}$

(3)	$\begin{array}{l}\displaystyle J^{\downarrow} = \frac{q^{\downarrow}}{p_{wf} - p_e}\end{array}$

$\begin{array}{l}q^{\uparrow}\end{array}$

$\begin{array}{l}q^{\downarrow}\end{array}$

The PI concept also applies to aquifer expansion:

(4)	$\begin{array}{l}\displaystyle J^{\downarrow} = \frac{q^{\downarrow}}{p(t) - p_{AQ}(t)}\end{array}$

where

$\begin{array}{l}q\end{array}$	volumetric water inflow rate from aquifer into hydrocarbon reservoir
$\begin{array}{l}p(t)\end{array}$	formation pressure in hydrocarbon reservoir
$\begin{array}{l}p_{AQ}(t)\end{array}$	formation pressure in aquifer

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