One of the Productivity Index diagnostics methods based on plotting pressure integral $\begin{array}{l}P(t) = \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) d\tau\end{array}$ vs cumulatives $\begin{array}{l}Q(t) = \int_0^t q_t(\tau) d\tau\end{array}$

It shows unit slope for stabilized reservoir flow:

(1)	$\begin{array}{l}\displaystyle P(t) = J^{-1} Q(t)\end{array}$

where

$\begin{array}{l}J\end{array}$

constant productivity index

In case pressure data is available for a fair interpolation it is recommended to plot subsurface cumulatives rather than surface which provides better linearity with pressure integral for Steady-State flow.

Although it is equally applicable to producers and injectors, due to lack of BHP and formation pressure data availability for producers in most practical cases in the past the Hall plot analysis was mostly applied for water injectors.

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