Mathematical modeling of arsenic(V) adsorption onto iron oxyhydroxides in an adsorption-submerged membrane hybrid system

The adsorption of arsenic (V), As(V), on two porous iron oxyhydroxide-based adsorbents, namely, micro-sized tetravalent manganese feroxyhyte (μTMF) and granular ferric hydroxide (μGFH), applied in a submerged microfiltration membrane hybrid system has been investigated and modeled. Batch adsorption tests were carried out to determine adsorption equilibrium and kinetics parameters of As(V) in a bench-scale slurry reactor setup. A mathematical model has been developed to describe the kinetic data as well as to predict the As(V) breakthrough curves in the hybrid system based on the homogeneous surface diffusion model (HSDM) and the corresponding solute mass balance equation. The kinetic parameters describing the mass transfer resistance due to intraparticle surface diffusion (D_s) involved in the HSDM was determined. The fitted D_s values for the smaller (1–63 μm) and larger (1–250 μm) diameter particles of μGFH and μTMF were estimated to be 1.09 × 10⁻¹⁸ m²/s and 1.53 × 10^-16 m²/s, and 2.26 × 10⁻¹⁸ m²/s and 1.01 × 10^-16 m²/s, respectively. The estimated values of mass transfer coefficient/ kinetic parameters are then applied in the developed model to predict the As(V) concentration profiles in the effluent of the hybrid membrane system. The predicted results were compared with experimental data for As(V) removal and showed an excellent agreement. After validation at varying adsorbent doses and membrane fluxes, the developed mathematical model was used to predict the influence of different operation conditions on As(V) effluent concentration profile. The model simulations also exhibit that the hybrid system benefits from increasing the amount of adsorbent initially dosed and from decreasing the membrane flux (increasing the contact time).