modelAdsorptionEnthalpy
Information
This model calculates the adsorption enthalpy of water vapour for an microporous absorbent. It is based on the Dubinin-Astakhov equation for sorption. All equations are taken from [1].
The actual water uptake w of the absorbent is calculated as follows.
w = w0 exp[-F(-T ln(φ))n]
Here F and n are material specific adsorption characteristic constants. The temperature T and the relative humidty φ are inputs of the model. The maximum water uptake w0 is calculated as following:
w0 = ρ(T) v0
The specific micropore volume of the adsobent v0 has to be set as an parameter. The density of water is calculated by the following term.
ρ(T) = 1 ⁄ (A T + B⁄T)
A and B are constants with A = 1.8105⋅10-6 m3 kg-1 K-1 and B = 138.08⋅10-3 m3 kg-1 K .
With the specific vaporization enthalpy of water Δhv and the gas constant of water vapour Rg the specific adsorption enthalpy can be calculated by the following equation.
Δhads = Δhv + Rg T[-1 ⁄F ln(w ⁄w0)]1 ⁄n [1 ⁄T + 1 ⁄(n w0 ln(w ⁄w0) (∂w0 ⁄∂T)]
Known Limitations
- Calculated adsorption enthalpy for high relative humidities is not reliable (increases up to very high values, as the ln-function aproximates zero).
- Not solvable for complete dry air as the ln(0) is not defined
References
[1]: Min,J.; Wang,L.: Coupled heat and mass transfer during moisture exchange across a mebrane. Journal of Membrane Science. 430 (2013). pp.150-157
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Real | F | material specific asdoprtion characteristic constant | |
| Real | n | material specific asdoprtion characteristic constant | |
| Modelica.Units.SI.SpecificVolume | v_0 | micropore volume per unit mass of absorbent |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| Modelica.Units.SI.MassFraction | w | actual water uptake of adsorbent in kg/kg | |
| Modelica.Units.SI.MassFraction | w_0 | maximum water uptake of adsorbent in kg/kg (material specific) | |
| Modelica.Units.SI.Density | rho | density of water vapour | |
| Real | dw0_dT | derivative of maximum water uptake by temperature | |
| Modelica.Units.SI.SpecificEnthalpy | dh_v | vaporization enthalpy of water | |
| Modelica.Units.SI.SpecificEnthalpy | q_st | adsorption enthalpy of water | |
| Modelica.Units.SI.Temperature | T | Temperature in K | |
| Real | phi | relative Humidity, range:0.01...0.99 | |
| Modelica.Blocks.Interfaces.RealOutput | dhAds | adsorption enthalpy in J/kgK |
Revisions
- November 23, 2018, by Martin Kremer:
Changed RealInputs to inputs to use the model inside other models - November 22, 2018, by Martin Kremer:
First Implementation