Applying the Bayesian Technique, Statistical Analysis, and the Maximum Adsorption Capacity in a Deterministic Way for Caffeine Removal by Adsorption: Kinetic and Isotherm Modeling

Abstract

The present work evaluates the Bayesian statistical method in adsorption, kinetic, and isotherm studies for estimation of the parameters along with the experimental data of the solid's maximum adsorption capacity. For the experimental data, the removal of caffeine (CAF) on granular activated carbon (GAC), previously characterized, was evaluated in five different temperatures (288, 298, 308, 313, and 323 K), and the following operational conditions were investigated: pH; adsorbent concentration (C GAC ), and contact time (t). The maximum adsorption capacity was estimated in the models, the usual approach in the literature, and not by applying its experimental value (deterministic: kinetic, q e ; isotherm, q max ). The kinetic models applied were pseudo-first order (PFO), pseudo-second order (PSO), and Elovich, and for the isotherms, Langmuir, Freundlich, Redlich−Peterson, and Sips, which were selected through five statistical metrics (classical and Bayesian). The results showed that it was possible to obtain a CAF removal of 90% (residual concentration of 0.978 mg•L −1 ) at room temperature by applying pH = 6, t = 120 min, and C GAC = 10 g•L −1 . The proposed method, with the maximum adsorption capacity used deterministically and five statistical metrics, is a more reliable and accurate resolution approach for both kinetic and isotherm studies because the values of q e and q max were over-or underestimated in all temperatures evaluated in this work; the selection of the models was altered and only possible through the Bayesian metrics due to the proximity of the values obtained for R 2 . The kinetic study showed that the Elovich model fitted the experimental data more adequately for the temperatures of 288, 298, 303, and 313 K and the PFO for 323 K. For the equilibrium isotherms, the Langmuir model best fitted the system at 288 K, while the Redlich−Peterson model was more adequate at the remaining temperatures (298, 303, 313, and 323 K), leading to the conclusion that the kinetics and equilibrium of CAF adsorption onto GAC is directly affected by the temperature, being enhanced in higher temperatures, which obtained an experimental q max = 24.85 mg•g −1 at 323 K; in addition, the incorporation of caffeine occurs, mainly, on the surface of the solid.

Immobilization of Marbofloxacin for Water Treatment by Adsorption in Batch Scale and Fixed-Bed Column: Applying of Monte Carlo Bayesian Modeling

“…Moreover, the GAC pH PCZ value is 8.04, which suggests a positively charged solid surface at lower pH values; it can be concluded that the adsorbent is mostly alkaline, facilitating the adsorption of MBX. According to de Oliveira et al when the solution in contact with the adsorbent solid has pH < pH PCZ , the surface is positively charged, favoring the adsorption of anions; however, when the solution has pH > pH PCZ , the surface of the adsorbent is negatively charged. Consequently, the adsorption of cations is favored.…”