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Multiphysics modeling of electric-swing adsorption system with in-vessel condensation

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Abstract

Mathematical modeling of an Electric-Swing Adsorption (ESA) system (adsorption cycle with electrothermal desorption step, performed by direct heating of the adsorbent particles by passing electric current through them), with annular, radial-flow, cartridge-type fixed-bed and in-vessel condensation, is performed by using Comsol Multiphysics™ software. Three multiphysics models are built, in order to describe three stages of a compete ESA cycle: adsorption, electrothermal desorption before the start of condensation and electrothermal desorption with in-vessel condensation. In order to describe the complete ESA cycle the models for the three stages are integrated, by using a combination of Comsol Multiphysics™ and Matlab™. The models were successfully used for simulation of separate stages of the process and of the complete ESA cycles, as well as for investigation of the influences of the main operational parameters on the process performance.

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Abbreviations

a (m2/m3):

Specific surface area

b (K−1):

Temperature coefficient of the bed electrical resistivity

C (mol/mol):

Adsorbate concentration in the gas phase

C *(mol/mol):

Adsorbate concentration in the gas phase in equilibrium with the solid phase

C break (mol/mol):

Breakthrough concentration

C sat (mol/mol):

Saturation concentration

c pg (J/mol/K):

Specific heat capacity of the inert gas

c pl (J/mol/K):

Specific heat capacity of liquid adsorbate

c ps (J/g/K):

Heat capacity of the solid phase

c pv (J/mol/K):

Specific heat capacity of gaseous adsorbate

D m (mol/cm/s):

Mass transfer dispersion coefficient

D hg t (W/K/cm):

Heat diffusivity of the gas phase

D hs t (W/K/cm):

Heat diffusivity of the solid phase

E (J/mol):

Adsorption energy of the adsorbate (D-R equation)

g (cm/s2):

Gravitation constant

G (mol/s):

Flow rate of the inert gas

H (cm):

Bed axial dimension (Fig. 2)

h 1 (cm):

Adsorber dimension (Fig. 2)

h b (J/cm2/K):

Solid to gas heat transfer coefficient within the bed

h s1 (J/cm2/K):

Heat transfer coefficient from the solid phase to the gas phase in the central tube(s)

h s2 (J/cm2/K):

Heat transfer coefficient from the solid phase to the gas phase in the annular tube

h wg (J/cm2/K):

Gas to ambient heat transfer coefficient (heat losses)

J (A/cm2):

Current density

J cond (mol/cm2/s):

Condensation flux

k (cm2):

Asorbent bed permeability

k m (mol/cm2/s):

Mass transfer coefficient in the adsorbent bed

k m1 (mol/cm2/s):

Mass transfer coefficient between the adsorbent bed and the gas in the central tube

k m2 (mol/cm2/s):

Mass transfer coefficient between the adsorbent bed and the gas in the annular tube

\(\dot{L}_{\mathit{cond}}\ (\mbox{mol}/\mbox{s})\) :

Flow-rate of the condensed liquid

L cond (mol):

Total amount of the condensed liquid

p (Pa):

Gas pressure

p a (Pa):

Ambient pressure

p c (Pa):

Critical pressure

p 0 (Pa):

Adsorbate saturation pressure

\(\dot{Q}_{el}\) (W):

Rate of heat generation (equal to electric power)

Q el (J):

Heat generation (equal to electric energy)

q (mol/g):

Adsorbate concentration in the solid phase

R g (J/mol/K):

Gas constant

r (cm):

Radial coordinate

r 1 (cm):

Adsorber dimension—radius of the central tube (Fig. 2)

r 2 (cm):

Adsorber dimension (Fig. 2)

r 3 (cm):

Adsorber dimension (Fig. 2)

r 4 (cm):

Adsorber dimension—radius of the adsorber vessel (Fig. 2)

S w (cm2):

Surface are of the outer wall of the adsorber vessel

T a (K):

Ambient temperature

T g (K):

Gas phase temperature

T c (K):

Critical temperature

T R (K):

Referent temperature

T s (K):

Solid phase temperature

T sw (K):

Switch temperature (from desorption to adsorption)

T w (K):

Wall temperature

t (s):

Time

U (V):

Electric potential

U 0 (V):

Supply voltage

u (cm/s):

Radial superficial gas velocity

VP A , VP B , VP C , VP D :

Wagner constants (Wagner equation)

v (cm/s):

Axial superficial gas velocity

W 0 (cm3/g):

Total volume of micropores (D-R equation)

z (cm):

Axial coordinate

α p :

Purification factor

α s :

Separation factor

ΔH ads (J/mol):

Heat of adsorption

ΔH cond (J/mol):

Heat of condensation

ε b :

Bed porosity

μ (Pa/s):

Dynamic viscosity

ρ (Ωcm):

Electric resistivity

ρ 0 (Ωcm):

Electric resistivity at referent temperature T R

ρ g (mol/cm3):

Gas phase density

ρ b (g/cm3):

Adsorbent bed density

ρ A (g/cm3):

Adsorbate density

τ (s):

Time period

A:

Adsorption

b :

Bed

D:

Desorption

g :

Gas

in :

Inlet

out :

Outlet

p :

Previous (initial)

r :

In the radial (r) direction

s :

Solid phase

ct :

Central tube

as :

Annular space

z :

In the axial (z) direction

〈 〉:

Time average value

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Author notes

  1. Ana Markovic

    Present address: Max-Planck Institute for Dynamics of Complex Technical Systems, Sandtorstr. 1, 39106, Magdeburg, Germany

Authors and Affiliations

  1. Department of Chemical Engineering, Faculty of Technology and Metallurgy, University of Belgrade, Belgrade, Serbia

    Menka Petkovska, Danijela Antov-Bozalo & Ana Markovic

  2. Air Force Research Laboratory, Tyndall AFB, FL, USA

    Patrick Sullivan

Authors
  1. Menka Petkovska
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  2. Danijela Antov-Bozalo
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  3. Ana Markovic
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  4. Patrick Sullivan
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Corresponding author

Correspondence to Menka Petkovska.

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The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the U.S. Government.

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Petkovska, M., Antov-Bozalo, D., Markovic, A. et al. Multiphysics modeling of electric-swing adsorption system with in-vessel condensation. Adsorption 13, 357–372 (2007). https://doi.org/10.1007/s10450-007-9028-2

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  • DOI: https://doi.org/10.1007/s10450-007-9028-2

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