# IPR

From wiki.pengtools.com

## Contents

## Inflow Performance Relationship

** Inflow Performance Relationship** is a curve of producing rates plotted against well bottomhole pressures for oil, water and gas wells^{[1]}.

**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:

- 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:

- 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

- = formation volume factor, bbl/stb
- = dimensionless productivity index, dimensionless
- = permeability times thickness, md*ft
- = average reservoir pressure, psia
- = average reservoir pseudopressure, psia
^{2}/cP - = well flowing pressure, psia
- = average well flowing pseudopressure, psia
^{2}/cP - = flowing rate, stb/d
- = gas rate, MMscfd
- = temperature, °R

### Greek symbols

- = viscosity, cp

## References

- ↑ Vogel, J. V. (1968). "Inflow Performance Relationships for Solution-Gas Drive Wells".
*Journal of Petroleum Technology*.**20**(SPE-1476-PA).