One of the Productivity Diagnostics methods based on correlation between cumulative pressure drawdown:
| (1) | G (t) = \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) d\tau |
and total sandface flowrate cumulatives
| (2) | Q_t(t) = \int_0^t q_t(\tau) d\tau |
where
\tau | production/injection time |
q_t | total sandface flowrate as function of time \tau |
p_e | drain-area formation pressure as function of time \tau \tau |
p_{wf} | bottomhole pressure as function of time \tau |
It shows unit slope on log-log plot for stabilized reservoir flow:
| (3) | G(t) = J^{-1} Q_t(t) |
where
J | 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 G(t) 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