Pseudo-first order kinetic model (PFO), pseudo-second order kinetic model (PSO) for K2CO3 carbonation

https://doi.org/10.1016/j.ccst.2021.100011

“The widely reported models such as the pseudo-first order kinetic model (PFO), pseudo-second order kinetic model (PSO), the Avrami fractional kinetic model and the modified Avrami fractional kinetic model had been employed to depict the gas-solid adsorption process over potassium-based adsorbents (Balsamo et al., 2016; Guo, B. et al., 2020a; Wang et al., 2020; Zhao, C. et al., 2017).”

“where, qt and qe are the time-dependent CO₂ sorption capacity and the equilibrium CO₂ uptake, k1, k2, k3 and k4 are the kinetic constants in the four kinetic models, respectively, m and n are constants in the Avrami fractional kinetic model and the modified Avrami fractional kinetic model.”

“The PFO model was proposed with the assumption that adsorption rate was dependent on the number of unoccupied sites, and adsorption only occurred on localized sites, and adsorbates showed monolayer adsorption Eq. 18) (An, 2020; Largitte and Pasquier, 2016). The proposal of the PSO model was based on the assumption that chemical adsorption was the rate-limiting step (Eq. 19) (Qiu et al., 2009). As a result, the PFO and PSO kinetic models could only well predict the CO₂ uptakes of potassium-based adsorbents in the initial and final stages of CO₂ adsorption, respectively. In contrast, CO₂ uptakes of the adsorbents in different stages of CO₂ adsorption could be precisely predicted by the Avrami fractional kinetic model and the modified Avrami fractional kinetic model (Eqs. 20 and (21). Particularly, the latter showed promise in well describing the kinetic behaviors of CO₂ adsorption over porous potassium-based adsorbents, since the modified Avrami fractional kinetic model had involved the multiple adsorption pathways such as film diffusion, intra-particle diffusion and the interaction between CO₂ and active sites (Guo, B. et al., 2020c; Guo et al., 2019; Wang et al., 2015; Zhao, C. et al., 2017). The experimental CO₂ uptakes were fitted to the modified Avrami fractional kinetic model to demonstrate the effects of operating parameters on CO₂ sorption kinetic behaviors of the silica aerogel and silica-alumina aerogel supported K₂CO₃ adsorbents (Guo, B. et al., 2020a; Wang et al., 2020; Zhao, C. et al., 2017). These results will offer guidance for designing efficient potassium-based adsorbents and better chemical reactor configurations. In addition, the developed kinetic models and the obtained parameters can be employed as inputs for the modelling and simulation of full-scale reactor systems, and this will further guide the reactor operation in practice.”