Difference between revisions of "3 Phase IPR"

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__TOC__
 
__TOC__
 
==Three-phase Inflow Performance Relationship==
 
==Three-phase Inflow Performance Relationship==
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[[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/>]]
  
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[[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.
  
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[[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.
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[[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==
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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/>
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===For P<sub>b</sub> < P<sub>wf</sub> < P<sub>r</sub>===
 
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For pressures between reservoir pressure and bubble point pressure:
 
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:<math> q_t =J (P_r - P_{wf})</math> <ref name=KermitBrown1984/>
 
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===For P<sub>wfG</sub> < P<sub>wf</sub> < P<sub>b</sub>===
 
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For pressures between the bubble point pressure and the flowing bottom-hole pressures:
 
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:<math> q_t =\frac{-C+\sqrt{C^2-4B^2D}}{2B^2}\ for B \ne 0</math><ref name=KermitBrown1984/>
 
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:<math> q_t =D/C\ for B = 0</math><ref name=KermitBrown1984/>
 
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where:
 
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:<math> A=\frac{P_{wf}+0.125F_oP_b-F_wP_r}{0.125F_oP_b}</math><ref name=KermitBrown1984/>
 
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:<math> B=\frac{F_w}{0.125F_oP_bJ}</math><ref name=KermitBrown1984/>
 
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:<math> C=2AB+\frac{80}{q_{o_{max}}-q_b}</math><ref name=KermitBrown1984/>
 
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:<math> D=A^2-80\frac{q_b}{q_{o_{max}}-q_b}-81</math><ref name=KermitBrown1984/>
 
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=== For 0 < P<sub>wf</sub> < P<sub>wfG</sub>===
 
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:<math> q_t =\frac{P_{wfG}+q_{o_{max}}tan(\beta)-P_{wf}}{tan(\beta)}</math><ref name=KermitBrown1984/>
 
  
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where:
 
  
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:<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:
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:<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/>
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:<math> CG = 0.001 q_{o_{max}}</math><ref name=KermitBrown1984/>
 
  
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===And===
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<math> q_{t_{sc}} </math> is calculated as usual using:
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:<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
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:<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==
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Following the example problem #21, page 33 <ref name=KermitBrown1984 />:
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Following the well #1 example given by Brown<ref name=KermitBrown1984 />on Figure 5.8, page 191:
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===Given:===
 
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:<math>P_r</math> = 2550 psi
 
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:<math>P_b</math> = 2100 psi
 
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Test data:
 
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:<math>P_{wf}</math> = 2300 psi
 
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:<math>q_t</math> = 500 b/d
 
  
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===Calculate:===
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''In progress ...''
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Determine the [[3 Phase IPR]] curves for F<sub>w</sub>=0, 0.25, 0.5, 0.75, and 1.
 
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===Solution:===
 
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The problem was run through [[:Category:PQplot | PQplot]] software for different values of watercut.
 
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Result [[3 Phase IPR]] curves are shown on Fig.1. Points indicate results obtained by Brown <ref name=KermitBrown1984 />.
 
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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  ==
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:<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
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:<math> F_o </math> = oil fraction, fraction
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:<math> GLR</math> = gas liquid ratio, scf / bbl
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:<math> F_w </math> = water fraction, fraction
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:<math> q </math> = flowing rate, stb/d
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:<math> J </math> = productivity index, stb/d/psia
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:<math> R</math> = solution gas ration, scf / stb
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:<math> P </math> = pressure, psia
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:<math> V </math> = total volume of produced fluid rate (inducing gas), bbl/d
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:<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===
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:b = at bubble point<BR/>
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:g = gas<BR/>
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:max = maximum<BR/>
 
 
:o = oil<BR/>
 
:o = oil<BR/>
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:r = reservoir<BR/>
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:sc = standard conditions<BR/>
 
:t = total<BR/>
 
:t = total<BR/>
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:wf = well flowing bottomhole pressure<BR/>
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:w = water<BR/>
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: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
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|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. ↑ Jump up to: 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
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