Difference between revisions of "3 Phase IPR"

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(3 Phase IPR calculation example)
(3 Phase IPR calculation example)
 
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__TOC__
 
__TOC__
 
==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 at various [[WCUT | watercuts]].
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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> <ref name=KermitBrown1984/>
 
  
===For P<sub>wfG</sub> < P<sub>wf</sub> < P<sub>b</sub>===
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The total volume of produced fluid rate (liquid plus gas) at any conditions of pressure and temperature:
For pressures between the bubble point pressure and the flowing bottom-hole pressures:
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:<math> V=q_{t_{sc}} \times VF</math> <ref name=KermitBrown1984/>
:<math> q_t =\frac{-C+\sqrt{C^2-4B^2D}}{2B^2}\ for B \ne 0</math><ref name=KermitBrown1984/>
 
:<math> q_t =D/C\ for B = 0</math><ref name=KermitBrown1984/>
 
  
where:
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<math> q_{t_{sc}} </math> is calculated as usual using:
 +
:*[[Vogel's IPR]] equation
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:*[[Composite IPR]] equation
  
:<math> A=\frac{P_{wf}+0.125F_oP_b-F_wP_r}{0.125F_oP_b}</math><ref name=KermitBrown1984/>
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==[[3 Phase IPR]] calculation example==
:<math> B=\frac{F_w}{0.125F_oP_bJ}</math><ref name=KermitBrown1984/>
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Following the well #1 example given by Brown<ref name=KermitBrown1984 />on Figure 5.8, page 191:
:<math> C=2AB+\frac{80}{q_{o_{max}}-q_b}</math><ref name=KermitBrown1984/>
 
:<math> D=A^2-80\frac{q_b}{q_{o_{max}}-q_b}-81</math><ref name=KermitBrown1984/>
 
 
 
=== For 0 < P<sub>wf</sub> < P<sub>wfG</sub>===
 
:<math> q_t =\frac{P_{wfG}+q_{o_{max}}tan(\beta)-P_{wf}}{tan(\beta)}</math><ref name=KermitBrown1984/>
 
 
 
where:
 
 
 
:<math> tan(\beta) = CD/CG </math><ref name=KermitBrown1984/>
 
:<math> CD = F_w\frac{0.001q_{o_{max}}}{J}+F_o0.125P_b \left ( -1+\sqrt{81-80 \frac{0.999q_{o_{max}}-q_b}{q_{o_{max}}-q_b}} \right)</math><ref name=KermitBrown1984/>
 
:<math> CG = 0.001 q_{o_{max}}</math><ref name=KermitBrown1984/>
 
 
 
===And===
 
:<math> P_{wfG}=F_w \left ( P_r - \frac{q_{o_{max}}}{J}\right )</math><ref name=KermitBrown1984/>
 
:<math> q_{o_{max}}=q_b+\frac{JP_b}{1.8}</math><ref name=KermitBrown1984/>
 
  
==[[3 Phase IPR]] calculation example==
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''In progress ...''
Following the example problem #21, page 33 <ref name=KermitBrown1984 />:
 
  
 
== Nomenclature  ==
 
== Nomenclature  ==
:<math> A, B, C, D, tan(\beta), CD, CG </math> = calculation variables
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:<math> B</math> = volume factor, bbl/stb oil; bbl/scf gas
:<math> F_o </math> = oil fraction, fraction
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:<math> GLR</math> = gas liquid ratio, scf / bbl
:<math> F_w </math> = water fraction, fraction
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:<math> q </math> = flowing rate, stb/d
:<math> J </math> = productivity index, stb/d/psia
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:<math> R</math> = solution gas ration, scf / stb
:<math> P </math> = pressure, psia
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:<math> V </math> = total volume of produced fluid rate (inducing gas), bbl/d
:<math> q </math> = flowing rate, stb/d
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:<math> VF </math> = volume factor, bbl/stb
 
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:<math> WCUT</math> = water cut, fraction
 
===Subscripts===
 
===Subscripts===
:b = at bubble point<BR/>
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:g = gas<BR/>
:max = maximum<BR/>
 
 
:o = oil<BR/>
 
:o = oil<BR/>
:r = reservoir<BR/>
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:sc = standard conditions<BR/>
 
:t = total<BR/>
 
:t = total<BR/>
:wf = well flowing bottomhole pressure<BR/>
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:w = water<BR/>
:wfG = well flowing bottomhole pressure at point G<BR/>
 
  
 
== References ==
 
== References ==
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:[[IPR]]<BR/>
 
:[[IPR]]<BR/>
 
:[[Vogel's IPR]]<BR/>
 
:[[Vogel's IPR]]<BR/>
 +
:[[Composite IPR]]<BR/>
 
:[[Darcy's law]]<BR/>
 
:[[Darcy's law]]<BR/>
  
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|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=Three-phase inflow performance relationship for oil wells producing water.
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|description=Three-phase inflow performance relationship for total volume of produced rate (including free gas).
 
}}
 
}}
  
 
[[Category:PQplot]]
 
[[Category:PQplot]]
 +
[[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