Mathematical Modeling of Batch Adsorption of Manganese Onto Bone Char

Abstract

The present study investigated the dynamics of batch adsorption of manganese onto bone char by using two distinct mathematical formulations: the diffusion model and the shrinking core model. Both models assumed spherical particles and adequately described the transient behavior of metal adsorption under changing operating conditions. Comparatively, the diffusion model described the manganese adsorption better at distinct particle sizes even when small particles were used (d p ≤ 0.147 mm); the shrinking core model proved to be more reliable when larger adsorbent particles were used (d p > 0.147 mm), and it described experimental data better at changing solid-liquid ratios. Manganese adsorption was favored when: (i) smaller adsorbing particles were used due to the increase in the contact area and easier access to reacting sites of the char; however, such an effect proved to be limited to d p ≤ 0.147 mm, and (ii) higher solid-liquid ratios were used due to the increase in the available reacting sites. External and intraparticle mass transfer dependences on particle size and solid-liquid ratio were also investigated, and results corroborated with prior investigations found in the literature.

Mathematical modeling of manganese adsorption onto bone char in a continuous fixed bed column incorporating backmixing and shriking core approaches

“…g) The adsorption of manganese on the bone char particles is described by the shrinking core model, which proved to be adequate in a prior study (Maria and Mansur, 2016). According to this model, adsorbing spherical particles are surrounded by an external aqueous film.…”

“…The proposed model was evaluated to describe the dynamic behavior of manganese adsorption onto bone char in a continuous fixed bed column, using experimental data available in prior literature (Sicupira et al, 2015). The model incorporates two mathematical approaches: (i) the backmixing model to describe the fluid flow within the fixed bed column and (ii) the shrinking core model (Levenspiel, 1999;Arévalo et al, 1997), which proved adequate to reproduce batch experimental data for manganese adsorption onto bone char (Maria and Mansur, 2016). The following operational variables investigated were feed flow rate and bed column height.…”

Variable diffusivity homogeneous surface diffusion model and analysis of merits and fallacies of simplified adsorption kinetics equations

“…and the adsorption of dyes on rice husk ash [77]. Maria and Mansur [94] studied the removal of manganese on bone char and applied a modified form of the SCM based on the PDM, with…”