(395u) Model Adsorption On Fixed Bed of Monolithic Carbon Aerogels, a Comparative Study Between Models of Barrier Resistance/Diffusion (CBRD) and Linear Driving Force (LDF)

A base phenomenological model was developed to describe the behavior of adsorption systems at low and moderate concentrations. The model is based on partial differential equation of energy and mass balance to represent the kinetic adsorption and mass transfer at different space scales into the bed and porous material. The carbon aerogels were prepared previously by resorcinol-formaldehyde polymerization (RF), using acid and basic catalyst. Characterization of porous structure and morphology of the materials was obtained by N₂ (-196 ° C) and CO₂ (0 °C) gas adsorption. The specific surface areas BET up to 890 m²/g and 850m²/g were obtained for catalyst acid and basic respectively. The aerogels samples presented a high homogeneous mesopore and micropore size distribution.

Transient balance equations of gas phase into free mean of bed and particle were implemented to model the mass transport into the fixed bed of porous material. A comparative study between two adsorption kinetic models into the monolithic carbon aerogels was realized. 

The first one, linear driving force model (LDF).  This is based in that the rate of mass transfer is expressed through the global transfer coefficient k_pand the difference between the amount adsorbed q (mmol- adsorbed/g- adsorbent) in the particle and your equilibrium condition q^* (mmol- adsorbed/g- adsorbent)[1]. The mass transfer coefficient k_p was estimated by mutual addition of the mass transfer resistance like resistance to diffusion in the outer film in the particle, transport resistance by diffusion across the macropores and mesopores and kinetic adsorption on the micropores 

The second one, model of barrier resistance/diffusion (CBRD). This model describes the mass transfer through of macropore and mesopore by introduction of the transient mass balance equation of gas at spherical particle porous.  An unique mass flux at the interface of particle, that considered both the effect of kinetic adsorption on the outer surface and external film mass transfer was proposed. The kinetic adsorption in micropores of particle was represented through of Linear Driving Force model that introduced an additional transfer coefficient “k_d” for represent the specific rate adsorption by micropores.

The dynamic equations for the balance of material, absorption kinetics, and energy balance of the bed are solved simultaneously with the finite volume method. The model was developed in the MATLAB software, using the function ODE23s and ODE23tb, which implement a numerical differentiation and implicit Runge-Kutta method respectively. The models were validated with experimental adsorption data of hexane on fixed bed of carbon aerogels, implemented the breakthrough curve methodology.

The two adsorption kinetic models allows obtaining a good fit with the experimental uptake data of adsorption Breakthrough curve of hexane on the samples of carbon aerogels. The LDF model presented a good fit with an experimental data of Breakthrough, when only the effects external mass transfer and interparticle  transport diffusion on porous over the mass transfer coefficient k_p was considered. Similar results have been presented for activated carbon[2]. The mass transfer boundary condition implemented at CBDR model represent suitable adsorption process with experimental data that allow a very good mass conservation and good representation of mass flux between the mean free of bed and pores of particle. The CBDR model presents a larger sensibility with the textural change of the monolithic carbon aerogels and the effect over adsorption process than the LDF.    

References.

1.            Suzuki, M., Adsorption Engineering. 1990, Tokyo: Elsevier Science Publishers B. V.

2.            Malek, A. and S. Farooq, Kinetics of hydrocarbon adsorption on activated carbon and silica gel. AIChE Journal, 1997. 43(3): p. 761-776.