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SynonymCumulative Productivity PlotHall Plot


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 cumulative offtake/intake:

(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

p_{wf}

bottomhole pressure  as function of time \tau


Fig. 1. Hall Plot 


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


Due to integration procedure the Hall 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 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



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