Difference between revisions of "Hall Plot"

From wiki.pengtools.com
Jump to: navigation, search
(→‎Math & Physics)
 
(36 intermediate revisions by the same user not shown)
Line 3: Line 3:
 
[[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/>.
  
−
<br clear="all" />
+
[[Hall Plot]] is applied to determine the change in the [[Injectivity index]] of the wells.
  
−
[[File:Hall Plot.png|center|600px|Hall Plot in the [[:Category:E&P Portal|E&P Portal]]]]
+
[[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.
 +
 
 +
[[File:Hall Plot.png|link=https://ep.pengtools.com/waterflooding/hall-plot]]
 +
 
 +
<center>[[Hall Plot]] in the [https://ep.pengtools.com/waterflooding/hall-plot E&P Portal]</center>
  
 
==Math & Physics==
 
==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:
 +
:<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 <math>(P_{wf} - \bar{P})</math> versus cumulative injection yields a straight line with slope:
 +
 +
:<math> m = \frac{141.2 B \mu}{khJ_D} </math>
 +
 +
and [[Injectivity index]] is:
 +
 +
:<math> I = \frac{1}{m} </math>
 +
 +
===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:
 +
:<math> P_{wf} = P_{tub} + \Delta P_{friction} + \Delta P_{gravity} </math>
 +
 +
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]]
  
 
{{#seo:
 
{{#seo:
−
|title=Injectivity Index
+
|title=Hall Plot
 
|titlemode= replace
 
|titlemode= replace
−
|keywords=well injectivity index, injection well performance, water injectivity, gas injectivity
+
|keywords=Hall plot, injection well analysis, waterflood performance, injectivity analysis, formation damage detection
−
|description=Injectivity index for water or gas injection wells, defining injection rate per unit pressure increase.
+
|description=Hall Plot method for analyzing waterflood injection well performance, detecting formation damage, and evaluating stimulation effectiveness.
 
}}
 
}}
 
<references>
 
<references>
Line 28: Line 57:
 
  |publisher=World Oil  
 
  |publisher=World Oil  
 
  |date=1963
 
  |date=1963
 +
}}</ref>
 +
 +
<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 17:36, 27 August 2026

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.

Hall Plot.png

Hall Plot in the E&P Portal

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:

{q_{inj}} = \frac{kh}{141.2 B \mu} \times J_D \times (P_{wf} - \bar{P})

Hall integrated both sides with respect to time [2]:

\sum q_{inj} \Delta t = \frac{kh}{141.2 B \mu} \times J_D \times \sum (P_{wf} - \bar{P}) \Delta t

The Cartesian graph of cumulative (P_{wf} - \bar{P}) versus cumulative injection yields a straight line with slope:

m = \frac{141.2 B \mu}{khJ_D}

and Injectivity index is:

I = \frac{1}{m}

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:

P_{wf} = P_{tub} + \Delta P_{friction} + \Delta P_{gravity}

Rearranging above:

\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

Nomenclature

See Also

Injectivity index

  1. ↑ Hall, H.N. (1963). "How To Analyze Waterflood Injection Well Performance". World Oil. 
  2. ↑ 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. 
Retrieved from "https://wiki.pengtools.com/index.php?title=Hall_Plot&oldid=8021"