3 Phase IPR

Three-phase Inflow Performance Relationship

3 Phase IPR Curve

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 .

3 Phase IPR curve is determined geometrically from those equations considering the fractional flow of oil and water .

Math and Physics

Oil well IPR equation

• Darcy's law equation for the single-phase flow of incompressible liquid:

$q = \frac{kh}{141.2 B \mu}\ (\bar{P} - P_{wf}) J_D$

• 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:

$q_g=\frac{kh}{1422 \times 10^3\ T_R}\ (P_{\bar{P}} - P_{P_{wf}})\ J_D$

• C and n equation

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

See also

141.2 derivation

Darcy's law

JD

Production Potential