One of the Productivity Diagnostics methods based on correlation between pressure drawdown integral:
G (t) = \frac{1}{t} \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) d\tau |
and total sandface flowrate cumulatives
Q_t(t) = \frac{1}{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 |
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Productivity Diagnostics