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

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.