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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

LaTeX Math Inline
bodyQ_t(t)

total sandface cumulative offtake/intake

LaTeX Math Inline
body--uriencoded--Q_t(t) = \int_0%5et q_t(\tau) d\tau


Image Modified

Fig. 1. q-weighted J-plot

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LaTeX Math Inline
bodyJ

constant productivity index


Due to integration procedure the q-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.

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The main difference between q-weighted J-plot and t-weighted J-average and Normalized Hall Plotplot is the averaging methodology.

The Normalized Hall Plott-weighted J-plot gives equal weight to all data points

LaTeX Math Inline
body--uriencoded--\displaystyle w(t) = \frac%7B1%7D%7Bt%7D
, while q-weighted J-plot gives more weight to higher flowrate data points, lower weight to lower flowrate data points and zero weight to no-flow data points (
LaTeX Math Inline
bodyq=0
): 
LaTeX Math Inline
body--uriencoded--\displaystyle w(t) = \frac%7Bq_t%7D%7BQ%7D
.

When flowrate is constant 

LaTeX Math Inline
bodyq=\rm const
 both methods are equivalent because
LaTeX Math Inline
body--uriencoded--\displaystyle w(t) = \frac%7Bq_t%7D%7BQ%7D =\frac%7B1%7D%7Bt%7D
.


The q-weighted J-plot provides the same accuracy of productivity index estimation as Hall Plot but additionally provides a useful insight into the ranges of historically averaged flowrates and drawdowns.


See Also

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

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