# Gas Compressibility Factor

Gas compressibility factor, abbreviated as Z, a dimensionless number, is a factor independent of the quantity of gas and determined by the character of the gas, the temperature, and pressure. It's used in thermodynamics and fluid dynamics to describe how much a real gas deviates from ideal behavior at a given set of conditions (pressure, temperature, and composition). It accounts for the non-ideal behavior of gases, taking into consideration intermolecular forces and molecular volume.

The ideal gas law, $PV=nRT$, describes the behavior of ideal gases under most conditions. However, real gases deviate from this ideal behavior, especially at high pressures and low temperatures. The gas compressibility factor is introduced to correct for these deviations. The gas compressibility factor is defined as the ratio of the actual volume of the gas to the volume predicted by the ideal gas law at the same conditions.

### Key points about gas compressibility factor

- $Z=1$ indicates ideal gas behavior. Deviations from 1 indicate non-ideal behavior.
- At low pressures and high temperatures, most gases behave closely to ideal gases, so $Z$ is close to 1.
- At high pressures or low temperatures, intermolecular forces and molecular volume become significant, causing $Z$ to deviate from 1.
- The compressibility factor is used in the general form of the real gas equation, which is more accurate for real gases under a wide range of conditions.
- Accurate predictions of gas behavior require knowledge of the compressibility factor, especially in applications such as gas transportation, reservoir engineering, and chemical process design.

Various equations of state, such as the Van der Waals equation and the Peng-Robinson equation, are used to model the behavior of real gases and calculate their compressibility factors under different conditions.

## Gas compressibility factor formula |
||

\( Z \;=\; p \; V \;/\; n \; R \; T \) ( \( p \;=\; Z \; n \; R \; T \;/\; V \) \( V \;=\; Z \; n \; R \; T \;/\; p \) \( n \;=\; p \; V \;/\; Z \; R \; T \) \( R \;=\; p \; V \;/\; Z \; n \; T \) \( T \;=\; p \; V \;/\; Z \; n \; R \) |
||

Symbol |
English |
Metric |

\( Z \) = Gas Compressibility factor | \( dimensionless \) | \( dimensionless \) |

\( p \) = Pressure | \(lbf\;/\;in^2\) | \(Pa\) |

\( V \) = Volume | \(in^3\) | \(mm^3\) |

\( n \) = Number of Moles | \( dimensionless \) | \( dimensionless \) |

\( R \) = Specific Gas Constant | \(lbf-ft\;/\;lbm-R\) | \(J\;/\;kg-K\) |

\( T \) = Temperature | \(F\) | \(K\) |