Full factorial design and dynamic modelling of silent and ultrasound-assisted lead and cadmium removal by porous biosorbent

Present work aimed to analyse single and competitive lead and cadmium batch adsorption, using experimental studies and mathematical modelling. The experiments were conducted in silent and ultrasound-assisted systems, in aqueous environment, using grinded hazelnut shells as porous biosorbent. The influence of process factors (pH, adsorbent concentration, adsorbent particle size, and initial species concentration in liquid phase) on species removal efficiency was evaluated when process equilibrium was attained. The statistical study, following a 2(4) factorial experimental design, allowed the development of a model to predict variables influence. Based on the obtained results a deeper analysis of the separation efficiency, depending on process factors, was conducted. The dynamic study was performed based on experimentally obtained removal rates, modelled considering species diffusion, with reversible kinetics of sorption inside solid particles. Hence, the dynamics of removal efficiency was determined for several representative experiments. The equilibrium isotherms data, best fitted by an appropriate Langmuir model, were used in the dynamic model to reduce the number of model parameters which normally require experimental identification.