Difference between revisions of "3 Phase IPR"

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==Three-phase Inflow Performance Relationship==
 
==Three-phase Inflow Performance Relationship==
[[File:3 Phase IPR Curve.png|thumb|right|300px|3 Phase IPR Curve <ref name=KermitBrown1984/>]]
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[[File:3 Phase IPR Curve.png|thumb|right|400px|3 Phase IPR Curve <ref name=KermitBrown1984/>]]
  
[[3 Phase IPR]] calculates IPR curve for oil wells producing water.
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[[3 Phase IPR]] is an [[IPR]] curve calculated on the basis of total barrels of produced fluid, including gas.
  
[[3 Phase IPR]] equation was derived by Petrobras based on combination of [[Vogel's IPR]] equation for oil flow and constant productivity for water flow <ref name=KermitBrown1984/>.
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[[3 Phase IPR]] curve is used in [[:Category:PumpDesign|Pump Design]] software for pump sizing.
 
 
[[3 Phase IPR]] curve is determined geometrically from those equations considering the fractional flow of oil and water  <ref name=KermitBrown1984/>.
 
  
 
==Math and Physics==
 
==Math and Physics==
Total flow rate equations:
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The volume of 1 stb of liquid plus associated gas at any pressure and temperature is given by<ref name=KermitBrown1984/>:
 
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:<math> VF=WCUT\ B_w + (1-WCUT)\ B_o + (GLR\ - (1-WCUT)R_s - WCUT\ R_{sw})B_g</math> <ref name=KermitBrown1984/>
===For P<sub>b</sub> < P<sub>wf</sub> < P<sub>r</sub>===
 
For pressures between reservoir pressure and bubble point pressure:
 
:<math> q_t =J (P_r - P_{wf})</math>  
 
  
===For P<sub>wfG</sub> < P<sub>wf</sub> < P<sub>b</sub>===
 
For pressures between the bubble point pressure and the flowing bottom-hole pressures:
 
:<math> q_t =\frac{-C+\sqrt{C^2-4B^2D}}{2B^2}\ for B \ne 0</math>
 
:<math> q_t =D/C\ for B\ = 0</math>
 
  
where:
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The total volume of produced fluid rate (liquid plus gas) at any conditions of pressure and temperature:
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:<math> V=q_{t_{sc}} \times VF</math> <ref name=KermitBrown1984/>
  
:<math> A=\frac{P_{wf}+0.125F_oP_b-F_wP_r}{0.125F_oP_b}</math>
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<math> q_{t_{sc}} </math> is calculated as usual using:
:<math> B=\frac{F_w}{0.125F_oP_bJ}</math>
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:*[[Vogel's IPR]] equation
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:*[[Composite IPR]] equation
  
===0 < P<sub>wf</sub> < For P<sub>wfG</sub>===
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==[[3 Phase IPR]] calculation example==
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Following the well #1 example given by Brown<ref name=KermitBrown1984 />on Figure 5.8, page 191:
  
==IPR calculator software==
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''In progress ...''
*[[:Category:PQplot | PQplot]] nodal analysis software is used to calculate the [[IPR]] curves. [[:Category:PQplot | PQplot]]  is available online at [https://www.pengtools.com www.pengtools.com].
 
*Excel
 
*other
 
  
 
== Nomenclature  ==
 
== Nomenclature  ==
:<math> B </math> = formation volume factor, bbl/stb
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:<math> B</math> = volume factor, bbl/stb oil; bbl/scf gas
:<math> J_D </math> = dimensionless productivity index, dimensionless
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:<math> GLR</math> = gas liquid ratio, scf / bbl
:<math> kh</math> = permeability times thickness, md*ft
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:<math> q </math> = flowing rate, stb/d
:<math> \bar{P} </math> = average reservoir pressure, psia
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:<math> R</math> = solution gas ration, scf / stb
:<math> P_{\bar{P}} </math> = average reservoir pseudopressure, psia<sup>2</sup>/cP
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:<math> V </math> = total volume of produced fluid rate (inducing gas), bbl/d
:<math> P_{wf} </math> = well flowing pressure, psia
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:<math> VF </math> = volume factor, bbl/stb
:<math> P_{P_{wf}} </math> = average well flowing pseudopressure, psia<sup>2</sup>/cP
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:<math> WCUT</math> = water cut, fraction
:<math> q </math> = flowing rate, stb/d
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===Subscripts===
:<math> q_g </math> = gas rate, MMscfd
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:g = gas<BR/>
:<math> T </math> = temperature, °R
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:o = oil<BR/>
 
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:sc = standard conditions<BR/>
===Greek symbols===
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:t = total<BR/>
 
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:w = water<BR/>
:<math> \mu </math> = viscosity, cp
 
  
=== References ===
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== References ==
 
<references>
 
<references>
 
<ref name= KermitBrown1984 >{{cite book
 
<ref name= KermitBrown1984 >{{cite book
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==See also==
 
==See also==
:[[141.2 derivation]]<BR/>
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:[[IPR]]<BR/>
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:[[Vogel's IPR]]<BR/>
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:[[Composite IPR]]<BR/>
 
:[[Darcy's law]]<BR/>
 
:[[Darcy's law]]<BR/>
:[[JD]]<BR/>
 
:[[Production Potential]]
 
  
 
{{#seo:
 
{{#seo:
|title=Inflow Performance Relationship
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|title=3 Phase IPR curve
 
|titlemode= replace
 
|titlemode= replace
 
|keywords=Inflow Performance Relationship, nodal analysis, IPR curve, IPR calculator
 
|keywords=Inflow Performance Relationship, nodal analysis, IPR curve, IPR calculator
|description=IPR curve formula for well performance.
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|description=Three-phase inflow performance relationship for total volume of produced rate (including free gas).
 
}}
 
}}
  
 
[[Category:PQplot]]
 
[[Category:PQplot]]
[[Category:pengtools]]
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[[Category:PumpDesing]]

Latest revision as of 07:51, 17 April 2019

Three-phase Inflow Performance Relationship

3 Phase IPR Curve [1]

3 Phase IPR is an IPR curve calculated on the basis of total barrels of produced fluid, including gas.

3 Phase IPR curve is used in Pump Design software for pump sizing.

Math and Physics

The volume of 1 stb of liquid plus associated gas at any pressure and temperature is given by[1]:

 VF=WCUT\ B_w + (1-WCUT)\ B_o + (GLR\ - (1-WCUT)R_s - WCUT\ R_{sw})B_g [1]


The total volume of produced fluid rate (liquid plus gas) at any conditions of pressure and temperature:

 V=q_{t_{sc}} \times VF [1]

 q_{t_{sc}} is calculated as usual using:

3 Phase IPR calculation example

Following the well #1 example given by Brown[1]on Figure 5.8, page 191:

In progress ...

Nomenclature

 B = volume factor, bbl/stb oil; bbl/scf gas
 GLR = gas liquid ratio, scf / bbl
 q = flowing rate, stb/d
 R = solution gas ration, scf / stb
 V = total volume of produced fluid rate (inducing gas), bbl/d
 VF = volume factor, bbl/stb
 WCUT = water cut, fraction

Subscripts

g = gas
o = oil
sc = standard conditions
t = total
w = water

References

  1. 1.0 1.1 1.2 1.3 1.4 Brown, Kermit (1984). The Technology of Artificial Lift Methods. Volume 4. Production Optimization of Oil and Gas Wells by Nodal System Analysis. Tulsa, Oklahoma: PennWellBookss. 

See also

IPR
Vogel's IPR
Composite IPR
Darcy's law