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One of the  Productivity Index diagnostics methods based on plotting pressure integral 

LaTeX Math Inline
bodyPt--uriencoded--G(t) = \int_0^t 0%5et \left( p_{wf}%7Bwf%7D(\tau) - p_e(\tau) \right) d\tau
 vs cumulatives 
LaTeX Math Inline
body--uriencoded--Q_t(t) = \int_0^t 0%5et q_t(\tau) d\tau

where

LaTeX Math Inline
body\tau

production/injection time

LaTeX Math Inline
bodyq_t

total sandface flowrate as function of time 

LaTeX Math Inline
body\tau

LaTeX Math Inline
bodyp_e

drain-area formation pressure as function of time 

LaTeX Math Inline
body\tau
LaTeX Math Inline
body\tau

LaTeX Math Inline
body--uriencoded--p_%7Bwf%7D

bottomhole pressure  as function of time 

LaTeX Math Inline
body\tau


It shows unit slope for stabilized reservoir flow:

LaTeX Math Block
anchorpwf
alignmentleft
PtG(t) = J^{-1} Q_t(t)

where

LaTeX Math Inline
bodyJ

constant productivity index

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