IPR

Inflow Performance Relationship

Inflow Performance Relationship Curve

Inflow Performance Relationship is a curve of producing rates plotted against well bottomhole pressures for oil, water and gas wells.

IPR curve shows productive capacity and well performance.

IPR curve is used in Well Nodal Analysis for production systems design, analysis and optimization.

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.
• Composite IPR curve for oil wells producing water.
• 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