Solução numérica de modelos de transferência de massa difusivos em sistemas de adsorção

Abstract

The present work develops in detail the numerical solution of diffusion mass transfer models in the adsorption process of cationic dyes. The diffusive models are developed based on the mass transfer phenomena in a porous solid: (i) external mass transfer, (ii) intraparticle diffusion, and (iii) diffusion at the active sites. Thus, intraparticle diffusion can occur through pore volume diffusion (PVDM), surface diffusion model (SDM), or a combination of both (PVSDM – Pore Volume and Surface Diffusion Model). The numerical method of finite difference approximation was used to solve the partial differential equations derived from the model. The non–linear least squares estimation technique was used for fitting the model to the experimental data. In the first article introduced in this work, the details of the numerical solution were deduced and elucidated in the modeling of the malachite green onto bentonite adsorption system. In addition, the characterization of bentonite is addressed. As a result, the external mass transfer and the intraparticle diffusion act simultaneously in the adsorption and the PVSDM model were more able to explain the adsorption phenomenon. In the second article, statistical tests were performed and it was verified that the mean and the variance of the PVSDM model corresponded to the experimental data of the adsorption of malachite green onto bentonite. Finally, the last article presents the modeling and statistical analysis of the diffusion models for the adsorption of crystal violet and methylene blue onto bentonite. As a result, surface diffusion was the controlling mechanism in the adsorption of crystal violet, it being possible to neglect the effects of diffusion in the pore volume. In contrast, both intraparticle mechanisms are necessary to explain the phenomenon of adsorption of methylene blue onto bentonite. Further,the hindered diffusion effects were significant since the molecular size of the methylene blue was very close to the basal space of the bentonite. Therefore, the results presented in this research showed that the finite difference approximation technique within the nonlinear parameter estimation techique is a suited tool for numerical solution of the mass transfer diffusion models.