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Finite difference approximation in a non-isothermal and non-adiabatic fixed bed adsorption model: an application to n-hexane

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In this work, we solved the differential equations of mass and energy balance describing the n-hexane adsorption and desorption process in 5A zeolite under non-isothermal and non-adiabatic conditions. The solution provided a theoretical model that may be used to determine the significance of the mass and thermal transfer effects applied to transient adsorption. We validated numerical results with experimental data from the literature, finding the n-hexane adsorption to be exothermic. Because the diffusion in the system is fast, the breakthrough curves showed the typical form of thermal limitation. We found desorption depends on the desorbent fluid and feed rate. We evaluated the stability of the numerical method using the eigenvalues of the matrix system. Hence, the computational code developed may be used to simulate real operating conditions for the adsorption/desorption process of gases with porous adsorbents once the process parameters are known.

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a p :

Specific area of the pellet, ap = 3/Rp (m2 m−3)

a c :

Specific area of the column, ac = 2/Rc (m2 m−3)

C f :

Concentration at time zero (feed) (kg m−1)

C pg :

Heat capacity of gas (kg m2 s−2 mol−1 K−1)

C ps :

Heat capacity of solid (m2 s−2 K−1)

D :

Source term added the Dirichlet boundary conditions (K)

D L :

Axial dispersion (m2 s−1)

F :

Total molar flux (mol m−2 s−1)

h p :

Film heat-transfer coefficient (kg s−3 K−1)

h w :

Wall heat-transfer coefficient at the wall (kg s−3 K−1)

J :

Total flow rate (kg s−1)

K L :

Effective axial bed thermal conductivity (kg m s−3 K−1)

K ads :

Adsorption equilibrium constant (atm−1)

k 0 :

Parameter of the isotherm of Nitta et al. (1984) (atm−1)

K gl :

Global mass-transfer coefficient (m s−1)

θ a :

Parameter of the isotherm of Nitta et al. (1984) (dimensionless)


Column length (m)

N :

Parameter of the isotherm of Nitta et al. (1984) (dimensionless)

P 0 :

System pressure (atm)

Q a :

Concentration of the chemical species “a” adsorbed in the solid phase (kg kg−1)

\(\overline{{q_{a} }}\) :

Average adsorbent phase concentration (kg kg−1)

\({q}_{max}\) :

Maximum concentration absorbable (kg kg−1)

R :

Ideal gas constant (kcal mol−1 K−1)

R c :

Radius of the column (m)

R p :

Radius of the pellet (m)

S :

Source term (K)

T :

Temperature in the gas phase (K)

T s :

Temperature in the solid phase (K)

T w :

Wall temperature (K)

t :

Time (s)

u f :

Feed velocity (m s−1)

u :

Apparent velocity (m s−1)

W :

Discrete sink term (kg m−1)

y a :

Mole fraction of sorbate in gas phase (mol mol−1)

\(\bar{y}_{a}\) :

Average mole fraction of sorbate in gas phase (mol mol−1)

y af :

Mole fraction of sorbate in gas phase at feed conditions (mol mol−1)


Distance variable in the longitudinal direction of the column (m)

ɛ b :

Bed porosity (dimensionless)

ΔHads :

Isosteric heat of adsorption (kcal mol−1)

ρ a :

Apparent density (kg m−3)

Δt :

Time interval of integration (s)

Δz :

Length of an elementary volume (m)


Time discretization


Axial coordinate in bed (m)


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The authors thank the Federal University of Fronteira Sul—UFFS, campus Erechim, and the Fundação Universidade do Estado de Santa Catarina—UDESC Oeste—SC, for the infrastructure yielded for the development of the research.

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Correspondence to Luiz A. Richit.

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Richit, L.A., Wolf, T.C., Ribeiro, M.C. et al. Finite difference approximation in a non-isothermal and non-adiabatic fixed bed adsorption model: an application to n-hexane. Braz. J. Chem. Eng. (2020). https://doi.org/10.1007/s43153-020-00015-z

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  • Adsorption
  • Desorption
  • n-Hexane
  • Non-isothermal
  • Non-adiabatic