Synonym: Cumulative Productivity Plot = Hall Plot
One of the Productivity Index diagnostics methods based on plotting pressure integral LaTeX Math Inline |
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body | --uriencoded--G(t) = \int_0%5et \left( p_%7Bwf%7Dthe Productivity Diagnostics methods based on correlation between cumulative pressure drawdown: LaTeX Math Block |
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G (t) = \int_0^t \left( p_{wf}(\tau) - p_e(\tau) \right) d\tau |
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and total sandface cumulative offtake/intake:
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where
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| \tau | LaTeX Math Inline |
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body | --uriencoded--p_%7Bwf%7D |
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| bottomhole pressure as function of time |
It shows unit slope on log-log plot for stabilized reservoir flow:
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G(t) = J^{-1} Q_t(t) |
where
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 In case pressure data is available for a fair interpolation it is recommended to plot sandface cumulatives rather than surface which provides better linearity with pressure integral for Steady-State 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
is usually calculated over interpolated values of formation pressure and bottomhole pressure : LaTeX Math Block |
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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
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / SS Productivity Diagnostics