Composite IPR

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Composite Inflow Performance Relationship

Composite IPR Curve [1]

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

Composite IPR equation was derived by Petrobras based on combination of Vogel's IPR equation for oil flow and constant productivity for water flow [1].

Composite 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]

Composite 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 Composite 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 Composite 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: Composite 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 1.16 1.17 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
3 Phase IPR
Darcy's law