One of the Productivity Index diagnostics methods based on plotting pressure integral vs cumulatives

where

	production/injection time
	total sandface flowrate as function of time
	drain-area formation pressure as function of time
	bottomhole pressure as function of time

It shows unit slope on log-log plot for stabilized reservoir flow:

G(t) = J^{-1} Q_t(t)

where

constant productivity index

In case pressure data is available for a fair interpolation it is recommended to plot sandface 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.

The pressure integral is usually calculated over interpolated values of formation pressure and bottomhole pressure :

G(t) = \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) d\tau = \sum_k \left( p_{wf}(\tau_k) - p_e(\tau_k) \right) \delta \tau_k

See Also