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Modelling of non-isothermal adsorption of gases in nanoporous adsorbent based on Langmuir equilibrium

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Abstract

The non-isothermal adsorption/desorption of gas in a cylindrical column filled with adsorbent particles has been considered theoretically. The model is based on Langmuir theory for equilibrium adsorption. Using the Heaviside operational method the analytical solutions for kinetics of changes of concentration of adsorbate in the inter- and intra-particle spaces were obtained. The numerical calculations of gas adsorption at different temperature of the gas flow (Ta = 273–373 K) followed by desorption by the flow of inert gas through the column at Td = 673 K were done. The results revealed the rather complex interrelations between spatial–temporal dependencies in distribution of concentrations of adsorbed gas inside adsorption column and temperatures of inlet gas.

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Abbreviations

a :

Concentration of adsorbate in the intra-particle space (nanopores) (ppmv)

a m :

Maximum value of a (ppmv)

c :

Concentration of adsorbate in the inter-particle space (ppmv)

c m :

Maximum value of c (ppmv)

D :

Effective diffusion coefficient in the interparticle space (m2/c)

l :

Length of adsorption column (m)

h g :

Heat capacity of gas; kJ /(kg·K)

h t :

Effective heat capacity of gas and adsorbent kJ /(kg·K);

ΔH :

Activation energy of adsorption/desorption (kJ/mol)

Q ads :

Heat of adsorption in nanopores (kJ/kg)

R :

Universal gas constant (= 8.314 4621(75) J/(K mol));

r :

Radius of adsorption column (m)

T :

Temperature (K)

T a :

Temperature of the inlet gas flow for adsorption, Ta = 273–373 K (K)

T d :

Temperature of the inlet inert gas flow for desorption, Td = 623 K, (K)

T e :

Equilibrium temperature (K)

t :

Time (s)

u :

Linear velocity of the gas flow (m/c)

z :

Distance along the column starting from the inlet (m)

α h :

Coefficient of heat transfer from the gas-phase to the wall (W/(m2K))

β :

total mass transfer coefficient (C−1)

Λ :

Coefficient of thermal diffusion of fluid (kJ /(m2·K·s))

ρ :

Bulk density –of particle packing in the adsorbent (kg/m3)

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Acknowledgements

The research results mentioned in this work were partly supported by Grant SSHN Campus France, 2021, funding from the Ministry of Education and Science of Ukraine, Project # DI 247-22, 0122U001859, and Projects KPKVK # 6541230, # 23BF05101.

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Authors and Affiliations

  1. Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine

    M. Petryk & I. Boyko

  2. Faculty of Science and Engineering, Sorbonne University, ESPCI, Paris, France

    J. Fraissard

  3. Laboratory of Physical Chemistry of Disperse Minerals, F D Ovcharenko Institute of Biocolloidal Chemistry, National Academy of Sciences, Kyiv, Ukraine

    N. Lebovka

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  1. M. Petryk
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Petryk, M., Boyko, I., Fraissard, J. et al. Modelling of non-isothermal adsorption of gases in nanoporous adsorbent based on Langmuir equilibrium. Adsorption 29, 141–150 (2023). https://doi.org/10.1007/s10450-023-00389-9

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  • DOI: https://doi.org/10.1007/s10450-023-00389-9

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