Difference between revisions of "3 Phase IPR"

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(IPR calculator software)
(Nomenclature)
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== Nomenclature  ==
 
== Nomenclature  ==
:<math> B </math> = formation volume factor, bbl/stb
+
 
 
:<math> J </math> = productivity index, stb/d/psia
 
:<math> J </math> = productivity index, stb/d/psia
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
 
:<math> J_D </math> = dimensionless productivity index, dimensionless
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:<math> q </math> = flowing rate, stb/d
 
:<math> q </math> = flowing rate, stb/d
 
:<math> S </math> = skin factor, dimensionless
 
:<math> S </math> = skin factor, dimensionless
 
===Greek symbols===
 
 
:<math> \mu </math> = viscosity, cp
 
  
 
===Subscripts===
 
===Subscripts===

Revision as of 08:50, 11 April 2019

Three-phase Inflow Performance Relationship

3 Phase IPR Curve [1]

3 Phase IPR calculates IPR curve for oil wells producing water.

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

Nomenclature

 J = productivity index, stb/d/psia
 J_D = dimensionless productivity index, dimensionless
 kh = permeability times thickness, md*ft
 P = pressure, psia
 \bar{P} = average reservoir pressure, psia
 q = flowing rate, stb/d
 S = skin factor, dimensionless

Subscripts

b = at bubble point pressure
max = maximum
o = oil
test = well test
wf = well flowing bottomhole pressure

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

141.2 derivation
Darcy's law
JD
Production Potential