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.
+[[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==
+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/>
-==Math and Physics==
-Total flow rate equations:
-===For P<sub>b</sub> < P<sub>wf</sub> < P<sub>r</sub>===
+The total volume of produced fluid rate (liquid plus gas) at any conditions of pressure and temperature:
-For pressures between reservoir pressure and bubble point pressure:
+:<math> V=q_{t_{sc}} \times VF</math> <ref name=KermitBrown1984/>
-:<math> q_t =J (P_r - P_{wf})</math>
-===For P<sub>wfG</sub> < P<sub>wf</sub> < P<sub>b</sub>===
+<math> q_{t_{sc}} </math> is calculated as usual using:
-For pressures between the bubble point pressure and the flowing bottom-hole pressures:
+:*[[Vogel's IPR]] equation
-:<math> q_t =/frac{-C+\sqrt{C^2-4B^2D}}{2B^2}</math>
+:*[[Composite IPR]] equation
-===0 < P<sub>wf</sub> < For P<sub>wfG</sub>===
+==[[3 Phase IPR]] calculation example==
+Following the well #1 example given by Brown<ref name=KermitBrown1984 />on Figure 5.8, page 191:
-==IPR calculator software==
+''In progress ...''
-*[[:Category:PQplot | PQplot]] nodal analysis software is used to calculate the [[IPR]] curves. [[:Category:PQplot | PQplot]]  is available online at [https://www.pengtools.com www.pengtools.com].
-*Excel
-*other
 == Nomenclature  ==
-:<math> B </math> = formation volume factor, bbl/stb
+:<math> B</math> = volume factor, bbl/stb oil; bbl/scf gas
-:<math> J_D </math> = dimensionless productivity index, dimensionless
+:<math> GLR</math> = gas liquid ratio, scf / bbl
-:<math> kh</math> = permeability times thickness, md*ft
+:<math> q </math> = flowing rate, stb/d
-:<math> \bar{P} </math> = average reservoir pressure, psia
+:<math> R</math> = solution gas ration, scf / stb
-:<math> P_{\bar{P}} </math> = average reservoir pseudopressure, psia<sup>2</sup>/cP
+:<math> V </math> = total volume of produced fluid rate (inducing gas), bbl/d
-:<math> P_{wf} </math> = well flowing pressure, psia
+:<math> VF </math> = volume factor, bbl/stb
-:<math> P_{P_{wf}} </math> = average well flowing pseudopressure, psia<sup>2</sup>/cP
+:<math> WCUT</math> = water cut, fraction
-:<math> q </math> = flowing rate, stb/d
+===Subscripts===
-:<math> q_g </math> = gas rate, MMscfd
+:g = gas<BR/>
-:<math> T </math> = temperature, °R
+:o = oil<BR/>
+:sc = standard conditions<BR/>
-===Greek symbols===
+:t = total<BR/>
+:w = water<BR/>
-:<math> \mu </math> = viscosity, cp
-=== References ===
+== References ==
 <references>
 <ref name= KermitBrown1984 >{{cite book
@@ Line 56: / Line 52: @@
 ==See also==
-:[[141.2 derivation]]<BR/>
+:[[IPR]]<BR/>
+:[[Vogel's IPR]]<BR/>
+:[[Composite IPR]]<BR/>
 :[[Darcy's law]]<BR/>
-:[[JD]]<BR/>
-:[[Production Potential]]
 {{#seo:
-|title=Inflow Performance Relationship
+|title=3 Phase IPR curve
 |titlemode= replace
 |keywords=Inflow Performance Relationship, nodal analysis, IPR curve, IPR calculator
-|description=IPR curve formula for well performance.
+|description=Three-phase inflow performance relationship for total volume of produced rate (including free gas).
 }}
 [[Category:PQplot]]
-[[Category:pengtools]]
+[[Category:PumpDesing]]

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