Difference between revisions of "3 Phase IPR"

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:

Vogel's IPR equation
Composite IPR equation

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

↑ ^1.0 ^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.

@@ Line 1: / Line 1: @@
 __TOC__
 ==Three-phase Inflow Performance Relationship==
-[[File:3 Phase IPR Curve.png|thumb|right|300px|3 Phase IPR Curve <ref name=KermitBrown1984/>]]
+[[File:3 Phase IPR Curve.png|thumb|right|400px|3 Phase IPR Curve <ref name=KermitBrown1984/>]]
-[[3 Phase IPR]] calculates [[IPR]] curve for oil wells producing water at various [[WCUT | watercuts]].
+[[3 Phase IPR]] is an [[IPR]] curve calculated on the basis of total barrels of produced fluid, including gas.
-[[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/>.
+[[3 Phase IPR]] curve is used in [[:Category:PumpDesign|Pump Design]] software for pump sizing.
-[[3 Phase IPR]] curve is determined geometrically from those equations considering the fractional flow of oil and water  <ref name=KermitBrown1984/>.
 ==Math and Physics==
-Total flow rate equations:
+The volume of 1 stb of liquid plus associated gas at any pressure and temperature is given by<ref name=KermitBrown1984/>:
+:<math> VF=WCUT\ B_w + (1-WCUT)\ B_o + (GLR\ - (1-WCUT)R_s - WCUT\ R_{sw})B_g</math> <ref name=KermitBrown1984/>
-===For P<sub>b</sub> < P<sub>wf</sub> < P<sub>r</sub>===
-For pressures between reservoir pressure and bubble point pressure:
-:<math> q_t =J (P_r - P_{wf})</math> <ref name=KermitBrown1984/>
-===For P<sub>wfG</sub> < P<sub>wf</sub> < P<sub>b</sub>===
-For pressures between the bubble point pressure and the flowing bottom-hole pressures:
-:<math> q_t =\frac{-C+\sqrt{C^2-4B^2D}}{2B^2}\ for B \ne 0</math><ref name=KermitBrown1984/>
-:<math> q_t =D/C\ for B = 0</math><ref name=KermitBrown1984/>
-where:
-:<math> A=\frac{P_{wf}+0.125F_oP_b-F_wP_r}{0.125F_oP_b}</math><ref name=KermitBrown1984/>
-:<math> B=\frac{F_w}{0.125F_oP_bJ}</math><ref name=KermitBrown1984/>
-:<math> C=2AB+\frac{80}{q_{o_{max}}-q_b}</math><ref name=KermitBrown1984/>
-:<math> D=A^2-80\frac{q_b}{q_{o_{max}}-q_b}-81</math><ref name=KermitBrown1984/>
-=== For 0 < P<sub>wf</sub> < P<sub>wfG</sub>===
-:<math> q_t =\frac{P_{wfG}+q_{o_{max}}tan(\beta)-P_{wf}}{tan(\beta)}</math><ref name=KermitBrown1984/>
-where:
-:<math> tan(\beta) = CD/CG </math><ref name=KermitBrown1984/>
+The total volume of produced fluid rate (liquid plus gas) at any conditions of pressure and temperature:
-:<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/>
+:<math> V=q_{t_{sc}} \times VF</math> <ref name=KermitBrown1984/>
-:<math> CG = 0.001 q_{o_{max}}</math><ref name=KermitBrown1984/>
-===And===
+<math> q_{t_{sc}} </math> is calculated as usual using:
-:<math> P_{wfG}=F_w \left ( P_r - \frac{q_{o_{max}}}{J}\right )</math><ref name=KermitBrown1984/>
+:*[[Vogel's IPR]] equation
-:<math> q_{o_{max}}=q_b+\frac{JP_b}{1.8}</math><ref name=KermitBrown1984/>
+:*[[Composite IPR]] equation
 ==[[3 Phase IPR]] calculation example==
-Following the example problem #21, page 33 <ref name=KermitBrown1984 />:
+Following the well #1 example given by Brown<ref name=KermitBrown1984 />on Figure 5.8, page 191:
-===Given:===
-:<math>P_r</math> = 2550 psi
-:<math>P_b</math> = 2100 psi
-Test data:
-:<math>P_{wf}</math> = 2300 psi
-:<math>q_t</math> = 500 b/d
-===Calculate:===
-Determine the [[3 Phase IPR]] curves for F<sub>w</sub>=0, 0.25, 0.5, 0.75, and 1.
-===Solution:===
-The problem was run through [[:Category:PQplot | PQplot]] software for different values of watercut.
+''In progress ...''
-The result [[3 Phase IPR]] curves are shown on Fig.1. Points show results obtained by Brown .
 == Nomenclature  ==
-:<math> A, B, C, D, tan(\beta), CD, CG </math> = calculation variables
+:<math> B</math> = volume factor, bbl/stb oil; bbl/scf gas
-:<math> F_o </math> = oil fraction, fraction
+:<math> GLR</math> = gas liquid ratio, scf / bbl
-:<math> F_w </math> = water fraction, fraction
+:<math> q </math> = flowing rate, stb/d
-:<math> J </math> = productivity index, stb/d/psia
+:<math> R</math> = solution gas ration, scf / stb
-:<math> P </math> = pressure, psia
+:<math> V </math> = total volume of produced fluid rate (inducing gas), bbl/d
-:<math> q </math> = flowing rate, stb/d
+:<math> VF </math> = volume factor, bbl/stb
+:<math> WCUT</math> = water cut, fraction
 ===Subscripts===
-:b = at bubble point<BR/>
+:g = gas<BR/>
-:max = maximum<BR/>
 :o = oil<BR/>
-:r = reservoir<BR/>
+:sc = standard conditions<BR/>
 :t = total<BR/>
-:wf = well flowing bottomhole pressure<BR/>
+:w = water<BR/>
-:wfG = well flowing bottomhole pressure at point G<BR/>
 == References ==
@@ Line 89: / Line 54: @@
 :[[IPR]]<BR/>
 :[[Vogel's IPR]]<BR/>
+:[[Composite IPR]]<BR/>
 :[[Darcy's law]]<BR/>
@@ Line 95: / Line 61: @@
 |titlemode= replace
 |keywords=Inflow Performance Relationship, nodal analysis, IPR curve, IPR calculator
-|description=Three-phase inflow performance relationship for oil wells producing water.
+|description=Three-phase inflow performance relationship for total volume of produced rate (including free gas).
 }}
 [[Category:PQplot]]
+[[Category:PumpDesing]]

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