Difference between revisions of "3 Phase IPR"

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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>===
 
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><ref name=KermitBrown1984/>
 
:<math> q_t =D/C\ for B = 0</math><ref name=KermitBrown1984/>
 
 
 
where:
 
 
 
:<math> A=\frac{P_{wf}+0.125F_oP_b-F_wP_r}{0.125F_oP_b}</math><ref name=KermitBrown1984/>
 
:<math> B=\frac{F_w}{0.125F_oP_bJ}</math><ref name=KermitBrown1984/>
 
:<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/>
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The total volume of produced fluid rate (liquid plus gas) at any conditions of pressure and temperature:
:<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/>
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:<math> V=q_{t_{sc}} \times VF</math> <ref name=KermitBrown1984/>
:<math> CG = 0.001 q_{o_{max}}</math><ref name=KermitBrown1984/>
 
  
===And===
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<math> q_{t_{sc}} </math> is calculated as usual using:
:<math> P_{wfG}=F_w \left ( P_r - \frac{q_{o_{max}}}{J}\right )</math><ref name=KermitBrown1984/>
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:*[[Vogel's IPR]] equation
:<math> q_{o_{max}}=q_b+\frac{JP_b}{1.8}</math><ref name=KermitBrown1984/>
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:*[[Composite IPR]] equation
  
 
==[[3 Phase IPR]] calculation example==
 
==[[3 Phase IPR]] calculation example==
[[File:3 Phase IPR calculation example.png|thumb|right|400px| Figure.1 [https://www.pengtools.com/pqPlot?paramsToken=73eca3000d5f28d661700c874ebcf1f1 3 PhaseIPR calculation example]]]
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Following the well #1 example given by Brown<ref name=KermitBrown1984 />on Figure 5.8, page 191:
Following the example problem #21, page 33 <ref name=KermitBrown1984 />:
 
===Given:===
 
:<math>P_r</math> = 2550 psi
 
:<math>P_b</math> = 2100 psi
 
Test data:
 
:<math>P_{wf}</math> = 2300 psi
 
:<math>q_t</math> = 500 b/d
 
  
===Calculate:===
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''In progress ...''
Determine the [[3 Phase IPR]] curves for F<sub>w</sub>=0, 0.25, 0.5, 0.75, and 1.
 
===Solution:===
 
 
 
The problem was run through [[:Category:PQplot | PQplot]] software for different values of watercut.
 
 
 
Result [[3 Phase IPR]] curves are shown on '''Fig.1'''. Points indicate results obtained by Brown <ref name=KermitBrown1984 />.
 
 
 
The  [[:Category:PQplot|PQplot]] model from this example is available online by the following link: [https://www.pengtools.com/pqPlot?paramsToken=73eca3000d5f28d661700c874ebcf1f1 3 Phase IPR calculation example]
 
  
 
== 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/>
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:[[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]]
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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