Kinetic and equilibrium adsorption parameters estimation based on a heterogeneous intraparticle diffusion model

• Autor(a) principal: Silva, Luís M. S.
• Data de Publicação: 2021
• Outros Autores: Muñoz-Peña, Maria J., Domínguez-Vargas, Joaquín R., González, Teresa, Cuerda-Correa, Eduardo M.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.22/20292
• topic: Parabens adsorption; Intraparticle diffusion model; Partial differential equation; Method of lines; Parameter estimation; Sensitivity analysis

In this work, a commercial resin with a well-developed internal pore structure was chosen to adsorb four parabens used as probe molecules. The main novelty was to propose and validate a phenomenological transient adsorption model based on conservation law in both phases coupled with Langmuir’s equilibrium law and Fick’s mass transfer rate law inside the pores. With such an aim, a heterogeneous three-parameter intraparticle diffusion model, IPDM, was formulated, and its numerical solution was fitted to time-dependent concentration data by minimizing the sum of squared residuals. Equilibrium constants were also predicted by fitting Langmuir isotherm to equilibrium data. A monolayer capacity of 0.81 mmol/g was calculated for the four parabens regardless of the number of carbons in the ester group. With the optimal parameters values from the IPDM fitting process, a system of ODEs comprising local sensitivity coefficients as dependent variables was solved to compute the parameters’ variance-covariance matrix and infer their ranges for a 95% marginal confidence interval. In order to test the validity of the proposed model, an attempt to crosscheck between the parameters obtained by the estimation of the equilibrium related parameter, κ, and the modified capacity parameter, and the ones obtained by fitting the Langmuir’s isotherm to equilibrium data was carried out. As far as equilibrium related parameters concern, there is a relative agreement inside the limits of the confidence range between the estimated values of the amount adsorbed in equilibrium with initial bulk solution concentration, q0, and Langmuir’s equilibrium constant, K, adjusted to kinetic and equilibrium data, independently. Additionally, the order of magnitude of pore diffusivity obtained in this work is in accordance with the one predicted by Wilke-Chang correlation and is inversely proportional to the van der Waals volume raised to the power 0.53 in close agreement with the literature.