Engineering task and calculation objective
This module calculates the thermophysical properties of carbon dioxide (CO2) as a function of temperature and pressure according to the property data sheets of the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019). Available properties include density, specific heat capacity, enthalpy, entropy, enthalpy of vaporization, thermal conductivity, dynamic viscosity, Prandtl number, thermal diffusivity, coefficient of thermal expansion, speed of sound, and surface tension, as well as the characteristic data of the critical point and the triple point.
Engineers who need to calculate CO2 properties encounter them in almost every heat transfer task: when designing heat exchangers and evaporators in CO2 refrigeration systems (R744), in transcritical processes, in CO2 capture and compression (CCS), in flue gas calculations, or as a component in gas mixtures. The correlations cover the single-phase region from −55 °C to 900 °C at pressures from 1 bar to 2000 bar; for the boiling two-phase region, the range from −56 °C to 30 °C along the vapor pressure curve applies.
This allows the gas and liquid phases as well as the supercritical state to be described consistently – an essential prerequisite for reliable heat transfer and pressure drop calculations with carbon dioxide.
Standard and calculation basis: VDI Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the state: The calculation options specify whether a single-phase state (input of temperature and pressure) or the boiling state (input of the boiling temperature or the saturation pressure along the vapor pressure curve) is to be calculated.
- Check the range of validity: The module checks the inputs against the validity limits of the VDI correlations: single-phase −55 °C to 900 °C and 1 bar to 2000 bar, boiling −56 °C to 30 °C. States outside these limits are not extrapolated.
- Determine the phase region: Using the vapor pressure curve, the critical point (approx. 31 °C, 73.8 bar), and the triple point (approx. −56.6 °C, 5.18 bar), the module determines whether the state is liquid, gaseous, boiling, or supercritical – this decides which correlations have to be applied.
- Evaluate the properties: For the identified state, the caloric quantities (enthalpy, entropy, heat capacity, enthalpy of vaporization at saturation), the transport properties (viscosity, thermal conductivity, thermal diffusivity, Prandtl number), as well as density, coefficient of expansion, speed of sound, and – where applicable – surface tension are calculated.
- Use the results downstream: The properties feed directly into subsequent calculations, such as heat transfer correlations (Nusselt relations), pressure drop calculations, or energy balances of refrigeration and process plants.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature | ϑ1 ϑ2 | °C |
| Temperature | ϑ1 ϑ2 | °C |
| Pressure | p1 p2 | Pa |
| Pressure | p1 p2 | Pa |
| Density | ρ ρ | kg/m³ |
| Density | ρ ρ | kg/m³ |
| Specific heat capacity | cp cp | J/(kg·K) |
| Specific heat capacity | cp cp | J/(kg·K) |
| Thermal conductivity | λ λ | W/(m·K) |
| Thermal conductivity | λ λ | W/(m·K) |
| Surface tension | σ σ | mN/m |
| Surface tension | σ σ | mN/m |
| Dynamic viscosity | η η | mPa·s |
| Dynamic viscosity | η η | mPa·s |
| Kinematic viscosity | ν ν | m²/s |
| Kinematic viscosity | ν ν | m²/s |
| Specific enthalpy | h h | J/kg |
| Specific enthalpy | h h | J/kg |
| Prandtl number | Pr Pr | - |
| Prandtl number | Pr Pr | - |
| Density | ρ ρ | kg/m³ |
| Density | ρ ρ | kg/m³ |
| Specific heat capacity | cp cp | J/(kg·K) |
| Specific heat capacity | cp cp | J/(kg·K) |
Calculation options
Calculation options
boiling · single phase
Frequently asked questions
Why is the region near the critical point particularly critical?
At the critical point (approx. 31 °C, 73.8 bar), density, heat capacity, and the transport properties change extremely rapidly; the isobaric heat capacity tends toward infinity there. In transcritical CO2 processes – for example in R744 refrigeration systems with a gas cooler – calculations must therefore use fine temperature and pressure resolution, because averaged properties near the pseudo-critical region cause considerable errors in heat transfer and balance calculations.
Why does the boiling region end at 30 °C?
Above the critical temperature of about 31 °C, there is no longer a phase boundary between liquid and vapor – CO2 is then supercritical and can no longer boil. The vapor pressure curve extends from the triple point at about −56.6 °C to the critical point; the module's calculation range (−56 °C to 30 °C) covers this region with a small safety margin to the critical point.
Can the module also calculate solid CO2 (dry ice) or sublimation?
No. Below the triple point pressure of about 5.18 bar, liquid CO2 does not enter the boiling state; instead, solid CO2 passes directly into the gas phase (sublimation). The solid state and the sublimation line lie outside the range of validity; when expanding CO2 to atmospheric pressure, the possible formation of dry ice must be assessed separately.
Are the values comparable with reference equations of state such as Span/Wagner?
The property data sheets of the VDI Heat Atlas are based on high-quality reference equations and are sufficiently accurate for engineering design work. For custody-transfer or certification purposes with the highest accuracy requirements, a comparison with the reference equation of state by Span and Wagner may be advisable; for caloric quantities, the different reference points of enthalpy and entropy must also be observed.