Fractal-like Vermeulen kinetic equation for the description of diffusion-controlled adsorption dynamics

In this paper, we validated the applicability of a new fractal-like Vermeulen equation for the analysis of Cd2+ kinetic adsorption data on fly ashes both as received and as treated by means of mechanical sieving and CO2/steam gasification. The modeling results showed a better agreement between theoretical and experimental data in the whole time range for the fractal-like equation, with respect to its classic counterpart, the latter generally underestimating the capture outcomes for short adsorption times. In the case of the raw ash, the nonfractal adsorption pattern was linked to its more homogeneous pore structure while the widening of the pore size distribution induced by the mechanical sieving determined a time-dependent intraparticle diffusivity. In the case of the gasified samples, the occurrence of a significant fraction of smaller pores (<50 nm) further emphasized the fractal nature of the diffusion process. The proposed model can also be applied to fluid-solid processes that involve a chemical conversion of the porous matrix (e.g., flue-gas desulfurization with Ca-based sorbents), with a resulting modification of the solid microstructural properties determining a time-variable intraparticle transport coefficient for the diffusing species.