Difference between revisions of "3 Phase IPR"

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==[[3 Phase IPR]] calculation example==
 
==[[3 Phase IPR]] calculation example==
*[[: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].
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Following the example problem #21, page 33 <ref name=KermitBrown1984 />:
*Excel
 
*other
 
  
 
== Nomenclature  ==
 
== Nomenclature  ==

Revision as of 09:12, 11 April 2019

Three-phase Inflow Performance Relationship

3 Phase IPR Curve [1]

3 Phase IPR calculates IPR curve for oil wells producing water at various watercuts.

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 [1].

3 Phase IPR curve is determined geometrically from those equations considering the fractional flow of oil and water [1].

Math and Physics

Total flow rate equations:

For Pb < Pwf < Pr

For pressures between reservoir pressure and bubble point pressure:

 q_t =J (P_r - P_{wf}) [1]

For PwfG < Pwf < Pb

For pressures between the bubble point pressure and the flowing bottom-hole pressures:

 q_t =\frac{-C+\sqrt{C^2-4B^2D}}{2B^2}\ for B \ne 0[1]
 q_t =D/C\ for B = 0[1]

where:

 A=\frac{P_{wf}+0.125F_oP_b-F_wP_r}{0.125F_oP_b}[1]
 B=\frac{F_w}{0.125F_oP_bJ}[1]
 C=2AB+\frac{80}{q_{o_{max}}-q_b}[1]
 D=A^2-80\frac{q_b}{q_{o_{max}}-q_b}-81[1]

For 0 < Pwf < PwfG

 q_t =\frac{P_{wfG}+q_{o_{max}}tan(\beta)-P_{wf}}{tan(\beta)}[1]

where:

 tan(\beta) = CD/CG [1]
 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)[1]
 CG = 0.001 q_{o_{max}}[1]

And

 P_{wfG}=F_w \left ( P_r - \frac{q_{o_{max}}}{J}\right )[1]
 q_{o_{max}}=q_b+\frac{JP_b}{1.8}[1]

3 Phase IPR calculation example

Following the example problem #21, page 33 [1]:

Nomenclature

 A, B, C, D, tan(\beta), CD, CG = calculation variables
 F_o = oil fraction, fraction
 F_w = water fraction, fraction
 J = productivity index, stb/d/psia
 P = pressure, psia
 q = flowing rate, stb/d

Subscripts

b = at bubble point
max = maximum
o = oil
r = reservoir
t = total
wf = well flowing bottomhole pressure
wfG = well flowing bottomhole pressure at point G

References

  1. 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 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
Darcy's law