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

  • D. Camargo-TrillosEmail author
  • F. Chejne
  • J. Alean
Original
  • 41 Downloads

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.

Abbreviations

C

Gas concentration, mmol m−3

D

Diffusion, m2 s−1

Hc

Henry constant by adsorption

HMTZ

Height Mass Transfer Zone, cm

K

Henry adsorption constant, mol/g

kd

Micropore kinetic adsorption, s−1

Kf

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

ρL

Microparticle density, g cm−3

T

Time, Min

V

Volume, cm3

v

Interstitial velocity, m/s

W0

Total standard micropore volume, cm3 g−1

ϕ

Fractional capacity

δ

Boundary layer thickness

σ

Kinetic diameter

Subscript

BET

Brunauer–Emmett–Teller

B

Bed

ip

Intraparticle

Meso

Mesopore

Micro

Micropore

MTZ

Mass Transfer Zone

Notes

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.

Compliance with ethical standards

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Universidad Pontificía BolivarianaMonteríaColombia
  2. 2.Facultad de MinasUniversidad Nacional de ColombiaMedellínColombia
  3. 3.Facultad de IngenieríasUniversidad de La GuajiraRiohachaColombia

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