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Compressibility Factor (Real Gas)
Corrects the ideal gas law for real-gas behavior; Z equals 1 for an ideal gas and deviates at high pressure or low temperature.
Interpretation
Compressibility factor: Z = PV/(nRT) accounts for deviation from ideal gas. Z=1 ideal; Z<1 attraction; Z>1 repulsion. Example: High pressure gives Z≠1.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| Z | Compressibility factor | |
| P | Absolute pressure | atm |
| V | Molar volume | L/mol |
| n | Moles of gas | mol |
| R | Universal gas constant | 0.08206 L.atm/mol.K |
| T | Absolute temperature | K |
What it means
The compressibility factor Z is a correction factor that accounts for the non‑ideal behaviour of real gases. It is defined as Z = PV/(nRT), where P is pressure, V is volume, n is moles, R is the gas constant, and T is temperature. For an ideal gas, Z = 1. For real gases, Z can be less than 1 (indicating intermolecular attraction reduces volume) or greater than 1 (repulsion forces dominate). Z is a function of temperature and pressure, and is often correlated using the principle of corresponding states (reduced temperature and pressure) or via equations of state like van der Waals, Peng‑Robinson, or Soave‑Redlich‑Kwong. The compressibility factor is essential for accurate calculations of gas properties in pipelines, compressors, and chemical reactors. It is also used in thermodynamic property estimation, such as enthalpy and entropy departures. Understanding Z is crucial for process design in the oil and gas, petrochemical, and power generation industries, where gases often deviate significantly from ideal behaviour.
Worked example
Compressibility Factor – Two Examples
Real‑World| Parameter | Value |
|---|---|
| P | 1 atm |
| V | 22.4 L/mol |
| T | 273 K |
| Parameter | Value |
|---|---|
| P | 50 atm |
| V | 0.4 L/mol |
| T | 300 K |
Common mistakes
- Pressure P: Absolute pressure, not gauge.
- Temperature T: In Kelvin.
- Volume V: In m³, molar volume in m³/mol.
- Ideal gas constant R: 8.314 J/(mol·K) – ensure units match.
- Z = 1 for ideal gas: Deviation increases at high pressure and/or low temperature; use an equation of state for accurate Z.
Applications
The compressibility factor, Z = PV/(nRT), corrects the ideal gas law for real gas behaviour. It is a function of temperature and pressure, with Z=1 for ideal gases, Z<1 indicating attractive forces dominate (usually at moderate pressures), and Z>1 indicating repulsive forces (at high pressures). Engineers use Z in calculations involving gases at high pressure, such as in natural gas pipeline design, compressors, and chemical reactors. It is essential for accurate volumetric flow rates, equipment sizing, and process design. Charts or equations of state (e.g., Peng‑Robinson) provide Z values. By using the compressibility factor, professionals can ensure safe and efficient design of gas handling and processing systems.
- Design of natural gas pipelines and storage facilities
- Sizing of compressors and gas expanders
- Process simulation of high‑pressure chemical reactors
- Calculation of gas densities and flow rates in custody transfer
- Safety analysis for gas pressurised systems and relief devices
Frequently Asked Questions
The compressibility factor (Z) is a correction factor to the ideal gas law for real gas behaviour: Z = PV / (nRT). For an ideal gas, Z = 1. For real gases, Z deviates from 1 due to intermolecular forces and finite molecular volume.
- Assuming Z = 1 at high pressures or low temperatures where non‑ideality is significant.
- Using the wrong equation of state to calculate Z (e.g., using the ideal gas law for Z).
- Ignoring the effect of mixture composition on Z – use mixing rules.
Z can be obtained from:
- Generalised compressibility charts (based on reduced pressure and temperature).
- Equations of state (e.g., van der Waals, Peng‑Robinson).
- Virial expansion: Z = 1 + B/V + C/V² + ... .
Reduced pressure P_r = P/P_c and reduced temperature T_r = T/T_c, where P_c and T_c are the critical properties. The compressibility factor is a function of P_r and T_r (using the principle of corresponding states).
At moderate pressures, attractive forces dominate, making Z < 1 (gas is more compressible than ideal). At very high pressures, repulsive forces dominate, making Z > 1.
Density = PM / (ZRT). For Z < 1, the density is higher than ideal gas prediction; for Z > 1, it is lower.
- Design of gas pipelines and compressors.
- Metering of natural gas (flow calculations).
- Chemical reactor design at high pressures.
- Predicting gas storage capacity.