Novel three-stage kinetic model for aqueous benzene adsorption on activated carbon

We propose a novel kinetic model for adsorption of aqueous benzene onto both granular activated carbon (GAC) and powdered activated carbon (PAC). The model is based on mass conservation of benzene coupled with three-stage adsorption: (1) the first portion for an instantaneous stage or external surface adsorption, (2) the second portion for a gradual stage with rate-limiting intraparticle diffusion, and (3) the third portion for a constant stage in which the aqueous phase no longer interacts with activated carbon. An analytical solution of the kinetic model was validated with the kinetic data obtained from aqueous benzene adsorption onto GAC and PAC in batch experiments with two different solution concentrations (C₀ = 300   mg L^-1, 600 mg L^-1). Experimental results revealed that benzene adsorption for the two concentrations followed three distinct stages for PAC but two stages for GAC. The analytical solution could successfully describe the kinetic adsorption of aqueous benzene in the batch reaction system, showing a fast instantaneous adsorption followed by a slow rate-limiting adsorption and a final long constant adsorption. Use of the two-stage model gave incorrect values of adsorption coefficients in the analytical solution due to inability to describe the third stage.