Difference between revisions of "3 Phase IPR"

Revision as of 08:23, 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 P_b < P_wf < P_r

For pressures between reservoir pressure and bubble point pressure:

q_t =J (P_r - P_{wf})

For P_wfG < P_wf < P_b

For pressures between the bubble point pressure and the flowing bottom-hole pressures:

q_t =/frac{-C+\sqrt(1)}{1}

0 < P_wf < For P_wfG

IPR calculator software

PQplot nodal analysis software is used to calculate the IPR curves. PQplot is available online at www.pengtools.com.
Excel
other

Nomenclature

B

= formation volume factor, bbl/stb

J_D

= dimensionless productivity index, dimensionless

kh

= permeability times thickness, md*ft

\bar{P}

= average reservoir pressure, psia

P_{\bar{P}}

= average reservoir pseudopressure, psia²/cP

P_{wf}

= well flowing pressure, psia

P_{P_{wf}}

= average well flowing pseudopressure, psia²/cP

q

= flowing rate, stb/d

q_g

= gas rate, MMscfd

T

= temperature, °R

Greek symbols

\mu

= viscosity, cp

References

↑ ^1.0 ^1.1 ^1.2 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 10: / Line 10: @@
 ==Math and Physics==
+Total flow rate equations:
 ===For P<sub>b</sub> < P<sub>wf</sub> < P<sub>r</sub>===
-For pressures between reservoir pressure and bubble point pressure
+For pressures between reservoir pressure and bubble point pressure:
+:<math> q_t =J (P_r - P_{wf})</math>
 ===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
+For pressures between the bubble point pressure and the flowing bottom-hole pressures:
+:<math> q_t =/frac{-C+\sqrt(1)}{1}</math>
 ===0 < P<sub>wf</sub> < For P<sub>wfG</sub>===
-===Oil well IPR equation===
-*[[Darcy's law]] equation for the single-phase flow of incompressible liquid:
-:<math> q = \frac{kh}{141.2 B \mu}\ (\bar{P} - P_{wf}) J_D</math>
-*[[Vogel's IPR]] two-phase flow equation (oil + gas) and it's combination with single phase liquid
-*[[3 Phase IPR]] three-phase flow equation (oil + gas + water)
-===Gas well IPR equation ===
-*[[Darcy's law]] gas inflow equation:
-:<math>q_g=\frac{kh}{1422 \times 10^3\ T_R}\ (P_{\bar{P}} - P_{P_{wf}})\ J_D </math>
-*C and n equation
 ==IPR calculator software==

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Difference between revisions of "3 Phase IPR"

Revision as of 08:23, 11 April 2019

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Three-phase Inflow Performance Relationship