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 15: / Line 15: @@
 :<math> V=q_{t_{sc}} \times VF</math> <ref name=KermitBrown1984/>
-:<math> q_{t_{sc}} </math> is calculated as usual using:
+<math> q_{t_{sc}} </math> is calculated as usual using:
-*[[Vogel's IPR]] equation
+:*[[Vogel's IPR]] equation
-*[[Composite IPR]] equation
+:*[[Composite IPR]] equation
 ==[[3 Phase IPR]] calculation example==
-[[File:3 Phase IPR calculation example.png|thumb|right|400px| Figure.1 [https://www.pengtools.com/pqPlot?paramsToken=73eca3000d5f28d661700c874ebcf1f1 3 Phase IPR calculation example]]]
 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:===
+''In progress ...''
-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.
-Result [[3 Phase IPR]] curves are shown on '''Fig.1'''. Points indicate results obtained by Brown <ref name=KermitBrown1984 />.
-The  [[:Category:PQplot|PQplot]] model from this example is available online by the following link: [https://www.pengtools.com/pqPlot?paramsToken=73eca3000d5f28d661700c874ebcf1f1 3 Phase IPR calculation example]
 == 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 ==

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