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Multi-scale mathematical model of mass transference phenomena inside monolithic carbon aerogels

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Abstract

A phenomenological basis model was developed to describe behavior of gas adsorption at multi-length scales; from the macroscale (fixed bed scale) to mass transport, into the mesopores and micropores (microscale). The multiscale mass transport model is based on partial differential equations of adsorbate in the gas phase; where an additional adsorption flux on interface was implemented as a boundary condition (BC). Therefore, parallel contributions of kinetic adsorption and diffusive mass transference at BC were considered. The model allows a good fit between experimental and simulated results for fixed bed (FB) concentration profile, height of mass transport, and total adsorption capacity by carbon aerogels, with mesopores to micropores volume relation from 0.3 to 3.4. Both the experimental setup date and multi-scale model identify volume relation (Vmeso/Vmicro) as a key parameter on the design and optimization of adsorption technologies.

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Abbreviations

C :

Gas concentration, mmol m−3

D :

Diffusion, m2 s−1

Hc :

Henry constant by adsorption

H MTZ :

Height Mass Transfer Zone, cm

K :

Henry adsorption constant, mol/g

k d :

Micropore kinetic adsorption, s−1

K f :

Transfer external constant, cm s−1

Kn :

Knudsen number

J :

Mass flux, mmol m−2 s−1

Nsc:

Schmidt number

Nsh:

Sherwood number

q :

Adsorption capacity, mmol/g-MCA

r :

Radial axis

Rp :

Characteristic monolithic particle radio, Cm

S:

Specific surface area, m2 g−1

T :

Temperature, K

ρ L :

Microparticle density, g cm−3

T :

Time, Min

V :

Volume, cm3

v :

Interstitial velocity, m/s

W 0 :

Total standard micropore volume, cm3 g−1

ϕ :

Fractional capacity

δ :

Boundary layer thickness

σ :

Kinetic diameter

BET:

Brunauer–Emmett–Teller

B:

Bed

ip :

Intraparticle

Meso:

Mesopore

Micro:

Micropore

MTZ:

Mass Transfer Zone

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Acknowledgements

Authors are thankful with the COLCIENCIAS (Ph.D. scholarship program number 528 and 617) for providing funding, for the successful completion of this study. Diego Camargo is grateful with CIDI-Universidad Pontifícia Bolivariana for supporting this work. Farid Chejne and Jader Alean wish to thank to the project “Strategy of transformation of the Colombian energy sector in the horizon 2030” funded by the call 788 of Colciencias Scientific Ecosystem. Contract number FP44842-210-2018.

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Authors and Affiliations

  1. Universidad Pontificía Bolivariana, km 8 via Cerete, Montería, Colombia

    D. Camargo-Trillos

  2. Facultad de Minas, Universidad Nacional de Colombia, Medellín, Colombia

    D. Camargo-Trillos, F. Chejne & J. Alean

  3. Facultad de Ingenierías, Universidad de La Guajira, Riohacha, Colombia

    J. Alean

Authors
  1. D. Camargo-Trillos
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  2. F. Chejne
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  3. J. Alean
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Correspondence to D. Camargo-Trillos.

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Highlights

• A multi scale mathematical model which relates external and internal behavior of the monolithic particle.

• Ratio of mesoporous and microporous volumes allows to predict adsorption behavior in fixed bed.

• The mathematical model developed links different scales without considering the instantaneous adsorption hypothesis.

• Border condition includes a singularity based on the adsorption surface.

• This model allows to link mass transport between macro and micro scale in fixed bed of porous particles, that required more knowledge of material surface morphology such as particle porosity, real and apparent density and effective diffusivity into meso and micropores.

• The model also allows to represent the complex effect of mesopores/micropores volume relation of monolithic carbon aerogels on macroscopic adsorption behavior at fixed bed.

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Camargo-Trillos, D., Chejne, F. & Alean, J. Multi-scale mathematical model of mass transference phenomena inside monolithic carbon aerogels. Heat Mass Transfer 55, 3317–3325 (2019). https://doi.org/10.1007/s00231-019-02654-6

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  • DOI: https://doi.org/10.1007/s00231-019-02654-6

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