Difference between revisions of "3 Phase IPR"

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(Three-phase Inflow Performance Relationship)
(Three-phase Inflow Performance Relationship)
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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]] is a curve on the basis of total barrels of produced fluid, including gas.
 
[[3 Phase IPR]] is a curve on the basis of total barrels of produced fluid, including gas.

Revision as of 06:53, 17 April 2019

Three-phase Inflow Performance Relationship

3 Phase IPR Curve [1]

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

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

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]:

Given:

P_r = 2550 psi
P_b = 2100 psi

Test data:

P_{wf} = 2300 psi
q_t = 500 b/d

Calculate:

Determine the 3 Phase IPR curves for Fw=0, 0.25, 0.5, 0.75, and 1.

Solution:

The problem was run through PQplot software for different values of watercut.

Result 3 Phase IPR curves are shown on Fig.1. Points indicate results obtained by Brown [1].

The PQplot model from this example is available online by the following link: 3 Phase IPR calculation example

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 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