Engineering task and calculation objective
This module calculates the condensation of multicomponent mixtures according to Section J2 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019), the standard German reference work for heat transfer. Unlike a pure fluid, a mixture does not condense at a fixed temperature but along a condensation curve between the dew point and the bubble point; the lighter-boiling components and any inert gases present accumulate in front of the phase interface and build up a mass transfer resistance that limits the heat transfer in addition to the condensate film.
This calculation is needed for the design of condensers in distillation and rectification plants, for vapor condensers with inert gas fractions, and generally wherever vapor mixtures are condensed. The module determines the phase equilibrium via Antoine vapor pressure equations and activity coefficients, works through the condensation curve step by step, and delivers for each step the resulting overall heat transfer coefficient, taking the coolant into account.
Because equilibrium, mass transfer, and heat transfer influence one another, the method works iteratively; the number of iterations and calculation steps is adjustable in the module.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the mixture and its equilibrium: For each component, the Antoine constants of the vapor pressure curve are stored; real liquid phases are described via activity coefficients. From these follow the dew point and bubble point of the mixture at the operating pressure.
- Establish the condensation curve: The condensation line is traversed step by step between dew point and bubble point: for each temperature step, the condensing quantity, the compositions of vapor and condensate, and the heat to be removed (condensation plus gas-cooling share) are balanced.
- Capture the vapor-phase mass transfer resistance: The accumulation of less condensable components and of inert gas at the phase interface is accounted for via diffusive mass transport in the gas boundary layer — it lowers the effective interface temperature and thus the heat flow.
- Calculate the overall heat transfer for each step: Condensate film, gas boundary layer, wall, fouling, and the coolant-side heat transfer (with coolant inlet and outlet temperatures) are combined into the resulting overall heat transfer coefficient of the respective section.
- Iterate and integrate the area: Since interface temperature, condensed quantity, and overall heat transfer depend on one another, each step is iterated to consistency (number of iterations adjustable); summation over all steps yields the required condenser area.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Activity coefficient | γ | – |
| Activity coefficient | γ | – |
| Masse(1) | Mi | g/mol |
| Masse(2) | Mi | g/mol |
| Diffusionsvolumen(1) | vi | – |
| Diffusionsvolumen(2) | vi | – |
| Gas(1) | ηG,i | mPa·s |
| Gas(2) | ηG,i | mPa·s |
| Gas(1) | λG,i | W/(m·K) |
| Gas(2) | λG,i | W/(m·K) |
| Gas(1) | cpG,i | J/(kg·K) |
| Gas(2) | cpG,i | J/(kg·K) |
| Film(1) | cpF,i | J/(kg·K) |
| Film(2) | cpF,i | J/(kg·K) |
| dHv(1) | ϑ0,i | °C |
| dHv(2) | ϑ0,i | °C |
| Verdampungsenthalpie(1) | Δhv,i | J/kg |
| Verdampungsenthalpie(2) | Δhv,i | J/kg |
| Temperature of the cooling medium | ϑK | °C |
| Mean driving temperature difference | Δϑm | K (diff) |
| Heat transfer coefficient cooling medium | αK | W/(m²·K) |
| Heat transfer coefficient wall | αW | W/(m²·K) |
| Heat transfer coeff. condensate film | αF | W/(m²·K) |
| Resulting overall heat transfer coefficient | k' [21a] | W/(m²·K) |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature of the condensate film | ϑF [31] | °C |
| Molar fraction of the inert gas in film | My2,F | % |
| Molar fraction of liquid-inert in film | Mx2,F | % |
| Heat flux | q [24] | W/m² |
| Condensing mass flux | m [23] | kg/(m²·s) |
Calculation options
Bauform
Local heat and mass transfer during film condensation with an inert gas · Global heat and mass transfer during film condensation with inert gas · Local heat and mass transfer for film condensation of binary mixture · Antoine constants
Frequently asked questions
Why can't I simply size a mixture condenser with a mean temperature difference?
Because the condensation temperature drops along the apparatus from the dew point to the bubble point, and the heat release can be distributed very unevenly along the way — at the dew point the heavy boiler condenses preferentially, and at the end a residual gas rich in light boilers or inert gas remains. An LMTD calculation with a constant condensation temperature overestimates the driving difference and underestimates the area; that is why the condensation curve is worked through step by step.
How much do inert gases degrade the heat transfer?
Drastically: even a few volume percent of non-condensable gases accumulate at the phase interface, the condensing vapor has to diffuse through this gas layer, and the effective saturation temperature at the interface drops. Reductions of the heat transfer by 50% and more are common. The design should therefore provide deliberate gas routing and venting of the inerts at the cold end of the condenser.
What are the Antoine constants and activity coefficients needed for?
The Antoine equation gives the saturation vapor pressure of each pure component as a function of temperature; together with the activity coefficients, which describe the non-ideal behavior of the liquid phase, this yields the vapor-liquid equilibrium of the mixture. Faulty Antoine parameters (wrong validity range, wrong units, or wrong logarithm base) are among the most frequent causes of implausible dew and bubble points.
What distinguishes integral from differential condensation?
In integral condensation, condensate and vapor remain in contact and in equilibrium (typical for tube bundles with entrained condensate); in differential condensation, the condensate is continuously withdrawn, so the remaining vapor becomes more enriched in light boilers and must be cooled further. Real operation usually lies in between; the assumption noticeably influences the condensation curve and the required area.