An error analysis on the nonlinear biosorption kinetic models of biowaste adsorbent in an aqueous solution

Abstract

The adsorption kinetic experimental data were utilized to capture the intricate relationships behind the mechanism involving the biosorptive capability of a biowaste material to remove toxic substances from an aqueous solution using batch adsorption under specified experimental conditions. Several nonlinear models, such as the pseudo-first order, pseudo-second order, Elovich, intraparticle diffusion, and MacArthur-Wilson were compared. The model parameters were estimated using the Gauss-Newton iterative method of nonlinear regression analysis. Results showed that the removal uptake increases with an increase in adsorbent dose and longer contact time. Removal uptake reflects a relatively slow initial and terminal increase rates against contact time with an overall kinetic process behaving under a pseudo-second order equation. Elovich model suggests higher initial adsorption rate, extent of surface coverage, and activation energy are favored at a lower adsorbent dose, while the intraparticle diffusion is noted to be relatively faster at a higher adsorbent dose. Analysis of the differential forms and the second degree derivatives of the Elovich and MacArthur-Wilson models revealed that it is negative over the entire range of contact time. Error analysis supports that intraparticle diffusion, Elovich, and McArthur-Wilson are possible nonlinear models which can optimally describe the nonlinear behavior of the kinetic processes presented in this study.