One of the Productivity Diagnostics methods based on correlation between time-weighted average pressure drawdown 

\overline {\delta p} (t) = \frac{1}{t} \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) d\tau

and time-weighted average total sandface flowrate :

\bar 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 


Fig. 1. t-weighted J-plot


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

\overline {\delta p}(t) = J^{-1} \bar q_t(t)

where

constant productivity index


Due to integration procedure the t-weighted J-plot has a better tolerance to uncertainties in formation pressure and bottomhole pressure comparing to Unweighted J-plot and usually results in more accurate estimation of productivity index.


It is highly recommended to plot sandface flowrates rather than surface flowrates to achieve better linearity in correlation 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 normalized Hall plot analysis was mostly applied for water injectors.


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

\overline {\delta p} (t) = \frac{1}{t} \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) d\tau = \frac{1}{t}  \sum_k \left( p_{wf}(\tau_k) - p_e(\tau_k) \right) \delta \tau_k 


The main difference  Normalized Hall Plot and traditional Hall Plot is that Normalized Hall Plot is using conventional properties along the axis: average pressure drawdown :  and  total sandface flowrate cumulatives :.


See Also


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