One of the Productivity Diagnostics methods based on correlation between cumulative pressure drawdown:

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

and total sandface flowrate cumulatives

Q_t(t) = \int_0^t q_t(\tau) d\tau

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 for stabilized reservoir 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 drawdown 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


Petroleum Industry / Upstream /  Production / Subsurface Production / Field Study & Modelling / Production Analysis / Productivity Diagnostics