Engineering guide
The H2N2 module calculates the physical properties of the gas mixture of 98 vol% hydrogen and 2 vol% nitrogen as a function of temperature and pressure. This mixture is widely used as a cooling and process gas – for example as a forming gas variant in heat treatment plants, as generator cooling gas, or in hydrogenation plants where nitrogen is carried along as an inert fraction.
The outputs are density, specific heat capacity, thermal conductivity, dynamic and kinematic viscosity, Prandtl number, thermal diffusivity and coefficient of thermal expansion – each for two freely selectable state points, so that the inlet and outlet states of a piece of equipment can be evaluated in parallel. In addition, the module delivers the mixture constants molar mass, specific gas constant and standard density, as well as the compressibility factor to assess the deviation from ideal gas behavior.
These properties are needed for every heat transfer and pressure drop calculation with this mixture: hydrogen has an exceptionally high thermal conductivity and specific heat capacity at very low density, so correlations using air properties would give grossly wrong results here.
Scope
- Properties of a hydrogen-nitrogen mixture
Typical workflow
Define the state points
For up to two state points, temperature and (absolute) pressure are specified – typically the inlet and outlet states of the equipment under consideration, or two operating cases.
Form the mixture constants
From the fixed composition 98 vol% H2 / 2 vol% N2 follow the molar mass, the specific gas constant and the standard density of the mixture; these values are independent of the state.
Evaluate the compressibility factor
For both state points, the compressibility factor Z is determined; it shows how far the mixture departs from ideal gas behavior at the given pressure and corrects the density calculation.
Calculate transport and caloric properties
Density, specific heat capacity, thermal conductivity and dynamic and kinematic viscosity are determined as functions of temperature and pressure; the mixture values follow from the pure-component data via mixing rules.
Output the derived parameters
From the basic quantities, the Prandtl number, thermal diffusivity and coefficient of thermal expansion are formed – the input quantities for Nusselt correlations in forced and natural convection.
Frequently asked questions
Why is it not sufficient to calculate with the properties of pure hydrogen?
Even 2 vol% nitrogen raises the mixture molar mass from 2.016 to about 2.54 g/mol because of the 14 times larger molar mass of N2 – the density therefore increases by about 26% compared with pure hydrogen. This acts directly on the Reynolds number, the pressure drop and the volumetric heat capacity. Thermal conductivity and viscosity, in contrast, change only slightly because they are dominated by the H2 molecules.
How ideal is the mixture's behavior – when must the compressibility factor be considered?
Hydrogen has a very low critical temperature (33 K); at ambient and process temperatures Z is close to 1 and even slightly above (Z > 1, the gas is "stiffer" than ideal). Up to about 50 bar, the error of the ideal gas calculation stays in the low percent range; for high-pressure applications (hydrogenation reactors, storage from several hundred bar upwards) the compressibility factor must be taken into account.
What makes hydrogen mixtures so effective as a cooling gas?
Hydrogen combines the highest thermal conductivity of all gases (about seven times that of air) with a very high specific heat capacity of about 14 kJ/(kg·K) and low density, i.e. low blower power. This is why turbogenerators are hydrogen-cooled; the small N2 fraction there originates from the purging and inerting operations.
Can the module also handle other H2/N2 ratios?
No, H2N2 is designed for the fixed composition of 98/2 vol%. For different mixing ratios (e.g. classic forming gas 95/5 or ammonia cracking gas 75/25), general mixture property modules that accept the composition as an input must be used.
Worked example
For the mixture 98 vol% H2 / 2 vol% N2, determine the molar mass, the specific gas constant, the standard density and the density at 50 °C and 10 bar (abs.). Ideal gas behavior is assumed (Z ≈ 1).
Given
| Composition | 98 vol% H2, 2 vol% N2 |
|---|---|
| Molar mass H2 | 2.016 g/mol |
| Molar mass N2 | 28.013 g/mol |
| Operating temperature T | 50 °C = 323.15 K |
| Operating pressure p (abs.) | 10 bar = 1,000,000 Pa |
Solution
Molar mass of the mixture
For ideal gases, volume fractions equal mole fractions:
M = 0.98 · 2.016 + 0.02 · 28.013 = 1.976 + 0.560 = 2.536 g/mol
Specific gas constant
Rs = Rm / M = 8,314.46 / 2.536 · 10−3 kg/mol = 3,279 J/(kg·K)
For comparison: air has 287 J/(kg·K) – the high gas constant reflects the low molar mass.
Standard density (0 °C, 1.01325 bar)
ρN = pN / (Rs · TN) = 101,325 / (3,279 · 273.15) = 0.113 kg/m³
Density at operating conditions
ρ = p / (Rs · T) = 1,000,000 / (3,279 · 323.15) = 0.944 kg/m³
Even at 10 bar, the mixture is still about 1.25 times lighter than air at atmospheric pressure and 20 °C (1.20 kg/m³).
Result
| Molar mass M | 2.536 g/mol |
|---|---|
| Specific gas constant Rs | 3,279 J/(kg·K) |
| Standard density | 0.113 kg/m³ |
| Density at 50 °C / 10 bar | 0.944 kg/m³ |
Technical content source: LV-Solved-Problems-Content 628d313247e7