Difference between revisions of "Hall Plot"
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[[Hall Plot]] is the engineering technique to analyze performance of injection wells published in '''1963''' by Howard Hall <ref name=Hall1963/>. | [[Hall Plot]] is the engineering technique to analyze performance of injection wells published in '''1963''' by Howard Hall <ref name=Hall1963/>. | ||
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| + | [[Hall Plot]] is applied to determine the change in the [[Injectivity index]] of the wells. | ||
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| + | [[Hall Plot]] uses readily available [[Well]] flowing data: injection rate and wellhead pressures. | ||
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| + | The interpretation technique is fitting the data points with the straight lines to estimate injectivity change. | ||
[[File:Hall Plot.png|link=https://ep.pengtools.com/waterflooding/hall-plot]] | [[File:Hall Plot.png|link=https://ep.pengtools.com/waterflooding/hall-plot]] | ||
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==Math & Physics== | ==Math & Physics== | ||
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| + | From [[Darcy's law]] for an unfractured injection well located in the center of a circular drainage area, the injection rate in pseudo-steady state is: | ||
| + | :<math> {q_{inj}} = \frac{kh}{141.2 B \mu} \times J_D \times (P_{wf} - \bar{P}) </math> | ||
| + | Hall integrated both sides with respect to time <ref name=Buell1990/>: | ||
| + | :<math> \sum q_{inj} \Delta t = \frac{kh}{141.2 B \mu} \times J_D \times \sum (P_{wf} - \bar{P}) \Delta t </math> | ||
| + | The Cartesian graph of cumulative injection versus cumulative <math>(P_{wf} - \bar{P})</math> yields a straight line with slope: | ||
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| + | :<math> m = \frac{kh}{141.2 B \mu} \times J_D </math> | ||
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| + | and [[Injectivity index]] is: | ||
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| + | :<math> I = \frac{1}{m} </math> | ||
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| + | ===Hall Plot Application with Wellhead Pressure=== | ||
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| + | Since bottomhole and reservoir pressures are not readily available, the [[Hall Plot]] can be used with tubing head pressure. | ||
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| + | Given: | ||
| + | :<math> P_{wf} = P_{tub} + \Delta P_{friction} + \Delta P_{gravity} </math> | ||
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| + | Rearranging above: | ||
| + | :<math> \sum P_{tub} \Delta t = \frac{141.2 B \mu}{kh J_D} \times \sum q_{inj} \Delta t + \sum ( \bar{P} - \Delta P_{friction} - \Delta P_{gravity} ) \Delta t </math> | ||
== Nomenclature == | == Nomenclature == | ||
==See Also== | ==See Also== | ||
| + | [[Injectivity index]] | ||
[[Category:E&P Portal]] | [[Category:E&P Portal]] | ||
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|publisher=World Oil | |publisher=World Oil | ||
|date=1963 | |date=1963 | ||
| + | }}</ref> | ||
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| + | <ref name=Buell1990>{{cite journal | ||
| + | |last1=Buell|first1=R.S. | ||
| + | |last2=Kazemi|first2=H. | ||
| + | |last3=Poettmann|first3=F.H. | ||
| + | |title=Analyzing Injectivity of Polymer Solutions With the Hall Plot | ||
| + | |journal=SPE Reservoir Engineering | ||
| + | |volume=5 | ||
| + | |issue=1 | ||
| + | |pages= | ||
| + | |date=1990 | ||
| + | |doi=10.2118/16963-PA | ||
}}</ref> | }}</ref> | ||
</references> | </references> | ||
Latest revision as of 16:34, 27 August 2026
Contents
Brief
Hall Plot is the engineering technique to analyze performance of injection wells published in 1963 by Howard Hall [1].
Hall Plot is applied to determine the change in the Injectivity index of the wells.
Hall Plot uses readily available Well flowing data: injection rate and wellhead pressures.
The interpretation technique is fitting the data points with the straight lines to estimate injectivity change.
Math & Physics
From Darcy's law for an unfractured injection well located in the center of a circular drainage area, the injection rate in pseudo-steady state is:
Hall integrated both sides with respect to time [2]:
The Cartesian graph of cumulative injection versus cumulative 
yields a straight line with slope:
and Injectivity index is:
Hall Plot Application with Wellhead Pressure
Since bottomhole and reservoir pressures are not readily available, the Hall Plot can be used with tubing head pressure.
Given:
Rearranging above:
Nomenclature
See Also
- ↑ Hall, H.N. (1963). "How To Analyze Waterflood Injection Well Performance". World Oil.
- ↑ Buell, R.S.; Kazemi, H.; Poettmann, F.H. (1990). "Analyzing Injectivity of Polymer Solutions With the Hall Plot". SPE Reservoir Engineering. 5 (1). doi:10.2118/16963-PA.
