Engineering task and calculation objective
The Gasmix module calculates the thermophysical properties of gas mixtures composed of the eight components nitrogen (N2), oxygen (O2), hydrogen (H2), carbon monoxide (CO), carbon dioxide (CO2), water vapor (H2O), sulfur dioxide (SO2) and sulfur trioxide (SO3). From the specified composition it determines, among other quantities, the molar mass, gas constant, density, compressibility factor, specific heat capacity, enthalpy, isentropic exponent, thermal conductivity, viscosity and Prandtl number of the mixture. The calculation is based on the well-established mixing and correlation methods from Poling, Prausnitz, O'Connell: "The Properties of Gases & Liquids" (McGraw-Hill, 5th edition).
Engineers who need to calculate gas mixture properties use them above all for heat exchanger design, compressor and fan calculations, pressure drop calculations and safety valve relieving capacities: without consistent values for density, cp, isentropic exponent and viscosity, none of these calculations is reliable. Typical applications include flue gases, synthesis gases, process off-gases from sulfuric acid production, and inerted atmospheres in plant engineering.
The module assumes that all components are entirely in the gas phase. Possible partial condensation of water, sulfuric acid or sulfurous acid below the dew point is not modeled and must be checked separately.
Standard and calculation basis: Poling Bruce E., Prausnitz John M., O'Connell John P. "The Properties of Gases & Liquids", McGraw Hill, 5. Auflage
Calculation workflow
- Specify the composition: The fractions of the components nitrogen, oxygen, hydrogen, carbon monoxide, carbon dioxide, water vapor, sulfur dioxide and sulfur trioxide are entered. The module checks the sum of the fractions — it must equal 100% for the mixture to be consistently defined.
- Molar mass and gas constant of the mixture: The mean molar mass of the gas mixture is formed from the mole fractions and the molar masses of the pure components; the specific gas constant of the mixture follows directly from it.
- Caloric properties: Specific heat capacity, enthalpy and isentropic exponent are mixed proportionally from the temperature-dependent pure-component values. The compressibility factor corrects for the deviation from ideal gas behavior at higher pressures.
- Determine transport properties: Viscosity and thermal conductivity of the mixture are calculated with mixing rules according to Poling/Prausnitz/O'Connell that account for the different molar masses of the components — a simple linear mixing rule would be significantly wrong here, especially with hydrogen fractions present.
- Derived characteristic quantities: From the basic properties follow the density, thermal diffusivity, thermal expansion coefficient and Prandtl number at the desired pressure and temperature state. The values can be transferred directly into heat transfer and pressure drop modules.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Gas mixture | _Stoffname | – |
| Temperature | ϑ1 ϑ2 | °C |
| Temperature | ϑ1 ϑ2 | °C |
| Pressure | p1 p2 | Pa |
| Pressure | p1 p2 | Pa |
| Density | ρ1 ρ2 | kg/m³ |
| Density | ρ1 ρ2 | kg/m³ |
| Specific heat capacity | cp1 cp2 | J/(kg·K) |
| Specific heat capacity | cp1 cp2 | J/(kg·K) |
| Dynamic viscosity | η1 η2 | mPa·s |
| Dynamic viscosity | η1 η2 | mPa·s |
| Kinematic viscosity | ν1 ν2 | m²/s |
| Kinematic viscosity | ν1 ν2 | m²/s |
| Thermal conductivity | λ1 λ2 | W/(m·K) |
| Thermal conductivity | λ1 λ2 | W/(m·K) |
| Prandtl number | Pr1 Pr2 | - |
| Prandtl number | Pr1 Pr2 | - |
| Specific enthalpy | h1 h2 | J/kg |
| Specific enthalpy | h1 h2 | J/kg |
| Nitrogen | N2 | mol-% |
| Hydrogen | H2 | mol-% |
| Nitrogen | N2 | Ma-% |
| Hydrogen | H2 | Ma-% |
| Carbon monoxide | CO | mol-% |
Worked example
For a dry, SO2-free flue gas with 76 vol% N2, 4 vol% O2, 12 vol% CO2 and 8 vol% H2O, determine the molar mass, specific gas constant and density at 250 °C and 1.013 bar (abs.) — a typical worked example of a gas mixture property calculation.
Given values
| Nitrogen N2 | 76 vol% |
| Oxygen O2 | 4 vol% |
| Carbon dioxide CO2 | 12 vol% |
| Water vapor H2O | 8 vol% |
| Temperature T | 250 °C = 523.15 K |
| Pressure p (abs.) | 1.013 bar |
Solution
Mean molar mass of the mixture
Assuming ideal gas behavior, volume fractions equal mole fractions yi. With the molar masses M(N2) = 28.013, M(O2) = 31.999, M(CO2) = 44.010 and M(H2O) = 18.015 kg/kmol:
M = Σ yi · Mi = 0.76 · 28.013 + 0.04 · 31.999 + 0.12 · 44.010 + 0.08 · 18.015
M = 29.29 kg/kmol
Specific gas constant
R = Ru / M = 8,314.46 / 29.29 J/(kg·K)
R = 283.8 J/(kg·K)
Density from the ideal gas equation
ρ = p / (R · T) = 101,300 / (283.8 · 523.15) kg/m³
ρ = 0.682 kg/m³
Result
| Molar mass M | 29.29 kg/kmol |
| Specific gas constant R | 283.8 J/(kg·K) |
| Density ρ (250 °C; 1.013 bar) | 0.682 kg/m³ |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why can't I simply average the viscosity of a gas mixture linearly from the pure-component values?
The viscosity of gas mixtures depends strongly on the molar mass ratios of the components. For mixtures containing light components such as hydrogen alongside heavy ones such as SO2 or CO2, a linear mole-fraction average produces substantial errors. That is why the methods of Poling/Prausnitz/O'Connell use interaction terms (e.g. after Wilke) that capture these effects correctly.
What happens if the mixture contains water vapor and the temperature drops below the dew point?
The module always calculates for a single gas phase. Partial condensation of water — or, particularly critical for SO3-containing gases, of sulfuric acid — is not taken into account. Below the water or acid dew point, the calculated properties are therefore no longer representative; the dew point must be checked separately, for instance for flue gas condensation or in exhaust gas heat exchangers.
What do I need the isentropic exponent of the mixture for?
The isentropic exponent κ enters into compression work, nozzle and safety valve calculations as well as the determination of critical pressure ratios. Since κ = cp/cv depends on temperature and composition, it should be calculated for the actual operating state rather than simply assumed as 1.4 (air) — gases rich in CO2 or SO2 have significantly lower values.
Is the calculation also valid at high pressures?
The compressibility factor Z corrects for moderate deviations from ideal gas behavior. Near the critical point of individual components or at very high pressures, however, generalized correlations reach their limits; there, component-specific equations of state or reference property data are preferable.