Engineering task and calculation objective
The HX module calculates the state variables of humid gases according to the Mollier h-x diagram. A state is defined by temperature, pressure and humidity; from these the module determines the absolute humidity (moisture content x), the specific enthalpy, dew point, saturation and partial pressures, densities and further property data. Besides air, other carrier gases such as nitrogen, biogas, natural gas or CO2-containing mixtures can be treated as humid gas.
Two calculation modes are available: the change of state of a humid gas stream – heating, cooling with and without condensate formation, humidification and dehumidification – with output of the enthalpy difference, temperature difference, humidity difference, condensate mass flow and heat flow rate, and the mixing of two humid gas streams with the resulting mixture state.
The calculation of humid air is needed in drying technology, for cooling towers and air-cooled condensers, in air conditioning and process air engineering, and in exhaust gas and vapor condensation: in all these cases, the moisture content decides how much heat is transferred sensibly and how much latently, and at which temperature condensate begins to form. A worked example is given below.
Calculation workflow
- Define the state: Temperature, total pressure and relative humidity (or an equivalent humidity quantity) of the humid gas are specified; for carrier gases other than air, additionally the gas composition with molar mass and gas constant.
- Determine saturation and partial pressure: At the state point, the saturation pressure of the water vapor is evaluated; from the relative humidity and the total pressure follow the water vapor partial pressure, the absolute humidity x and the dew point.
- Calculate enthalpy and densities: The specific enthalpy of the humid gas – referred to 1 kg of dry gas – is formed from the sensible contribution of the carrier gas, the enthalpy of vaporization and the superheating of the vapor fraction; in addition, the density and further property data are output.
- Calculate a change of state or a mixing process: For a change of state, the enthalpy difference, temperature difference and humidity difference between the initial and final states are balanced; if the final state drops below the dew point, the module reports the mass flow of the condensate formed. For the mixing of two streams, the mixture point follows from the mass and enthalpy balance.
- Report the heat flow rate: With the mass flow of the dry gas, the enthalpy difference yields the heat flow rate to be supplied to or removed from the process – the interface to the design of heaters, coolers and condensers.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Molar mass | MG | kg/kmol |
| Molar mass | MV | kg/kmol |
| Heat of evaporation at ϑ0 | Δhv | J/kg |
| Specific gas constant | RG | J/(kg·K) |
| Specific gas constant | RV | J/(kg·K) |
| Temperature | ϑ1 ϑ2 | °C |
| Temperature | ϑ1 ϑ2 | °C |
| Total pressure | pg1 pg2 | Pa |
| Total pressure | pg1 pg2 | Pa |
| Relative humidity | φ1 φ2 | % |
| Relative humidity | φ1 φ2 | % |
| Inert gas | cpG cpG | J/(kg·K) |
| Inert gas | cpG cpG | J/(kg·K) |
| Vapor | cpV cpV | J/(kg·K) |
| Vapor | cpV cpV | J/(kg·K) |
| Liquid | cpL cpL | J/(kg·K) |
| Liquid | cpL cpL | J/(kg·K) |
| Saturation pressure | ps1 ps2 | Pa |
| Saturation pressure | ps1 ps2 | Pa |
| Partial pressure | pi1 pi2 | Pa |
| Partial pressure | pi1 pi2 | Pa |
| Humidity level | x1 x2 | kg/kg |
| Humidity level | x1 x2 | kg/kg |
| Humidity level (saturation) | xs1 xs2 | kg/kg |
Worked example
For humid air at 30 °C, 1.01325 bar total pressure and 50% relative humidity, determine the moisture content x, the specific enthalpy h1+x and the dew point.
Given values
| Temperature t | 30 °C |
| Total pressure p | 1,013.25 hPa |
| Relative humidity φ | 50 % |
Solution
Saturation and partial pressure of the water vapor
Saturation pressure from the Magnus formula:
ps = 6.112 · exp[17.62 · t / (243.12 + t)] = 6.112 · exp(528.6/273.12) = 42.34 hPa
Partial pressure: pD = φ · ps = 0.5 · 42.34 = 21.17 hPa
Moisture content
x = 0.622 · pD / (p − pD) = 0.622 · 21.17 / (1,013.25 − 21.17) = 0.0133 kg/kg (13.3 g of water per kg of dry air)
The factor 0.622 is the molar mass ratio of water to air (18.015/28.963).
Specific enthalpy
h1+x = 1.006 · t + x · (2,501 + 1.86 · t)
= 1.006 · 30 + 0.01327 · (2,501 + 1.86 · 30)
= 30.2 + 33.9 = 64.1 kJ/kg dry air
A good half of the enthalpy is stored as latent heat in the vapor fraction.
Dew point
The dew point is the temperature at which ps(td) = pD = 21.17 hPa. Solving the Magnus formula gives:
td = 243.12 · ln(pD/6.112) / [17.62 − ln(pD/6.112)] = 18.4 °C
Cooling surfaces below 18.4 °C will collect condensate at this air state.
Result
| Water vapor partial pressure | 21.17 hPa |
| Moisture content x | 13.3 g/kg |
| Specific enthalpy h1+x | 64.1 kJ/kg dry air |
| Dew point | 18.4 °C |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why is the enthalpy referred to 1 kg of dry gas and not to the humid mixture?
During changes of state, the dry gas fraction is conserved, while water is added or removed through condensation or humidification. With the reference to 1 kg of dry gas, the balance quantities h and x remain additive along the process – this is exactly why changes of state and mixing processes can be represented in the h-x diagram as simple straight lines and lever rules.
What happens on cooling below the dew point?
The water vapor partial pressure reaches the saturation pressure, and excess vapor condenses out. The gas then follows the saturation line: the moisture content x decreases, and the removed heat consists of a sensible contribution plus the enthalpy of condensation. The module reports the condensate mass flow separately – important for condensate drainage and material selection (corrosion by acidic condensate with exhaust gases).
What influence does the total pressure have on the humidity quantities?
The saturation pressure depends only on temperature, but the moisture content x depends on the ratio of partial pressure to (total pressure minus partial pressure). At higher total pressure, the gas takes up less water at the same temperature – this is why condensate forms in compressed air systems downstream of the compressor even though the intake air was unsaturated. Calculations with the 1 bar h-x diagram are valid only at atmospheric pressure.
Can mixing two unsaturated streams produce fog?
Yes. The mixing line between two state points in the h-x diagram can run below the saturation line even though both source streams are unsaturated – then fog or condensate forms at the mixture point. This is typical when warm, humid exhaust gas mixes with cold outside air (visible plumes at the stack).