Modelagem da adsorção de manganês em carvão de ossos bovinos

Abstract

In the present study, a mathematical model was developed to describe the dynamics of manganese adsorption onto bovine bone char. The model was developed in two steps and validated using experimental data obtained by Sicupira (2012): (i) Modeling of batch adsorption in a finite batch volume, and (ii) Modeling of the continuous adsorption in a fixed bed column. In the first step, two mathematical formulations were used to describe the intraparticle diffusional process: diffusion model and shrinking core model. The first formulation consists of a partial differential equations system, while the second consists of an ordinary differential equations system (initial value problem). Both formulations adequately described the experimental adsorption behavior of manganese onto bone char in operating conditions evaluated experimentally (R² > 0.97 and relative error < 15%). The metal adsorption was enhanced when smaller particles were used, due to the increase in the contact area and easier manganese access to the active sites, and when larger solid-liquid ratios were used, due to the increase in the number of active sites available. Particularly the diffusion model best described the batch operation when small particles were employed (dp 0.147mm), while the shrinking core model best described the operation when larger adsorbent particles were used (dp > 0.147mm). In the second step of the work, the shrinking core model was chosen to describe the kinetic-diffusive intraparticle process and the backmixing model was chosen to describe the hydrodynamics of the column, resulting in an ordinary differential equations system (initial value problem). The model was used to simulate the experimental conditions evaluated, namely, the feed flow of the column (3.0 to 7.5ml/min) and the bed column height (8-16cm). The model adequately described the experimental behavior expected (R² > 0.99 and relative error < 15%). Hydrodynamic and kinetic-diffusive parameters were obtained by data fitting using the developed models. In all studied conditions, the intraparticle diffusion represented the slowest step of the process, and consequently controlled the overall manganese adsorption process. This work contributed to the development of a relatively simple mathematical model to describe the dynamics of adsorption of metals in fixed bed columns, without using partial differential equations and keeping the rigorous description of the main phenomena that occur simultaneously during operation.