Biosorption of binary heavy metal systems: Phenomenological mathematical modeling

- Phenomenological binary biosorption modeling was successfully applied.
- Kinetics and competitive binary equilibrium were evaluated.
- The Cu(II) ions had a higher affinity to the biomass than the Ni(II) ions.
- There was a competition for the active sites of the biosorbent.
- The internal mass transfer resistance was related to the rate of the process.

A phenomenological mathematical modeling approach was applied in order to describe the biosorption of binary heavy metal systems. The mathematical modeling here proposed was verified with the biosorption of Cu(II)-Ni(II) systems onto residue of alginate extraction from Sargassum filipendula. Equilibrium studies were carried out in order to elucidate the competition between the ions in the process. The Cu(II) ions showed a higher affinity with the biosorbent, while the Ni(II) removal was highly dependent on the presence of Cu(II) ions (i.e., the Cu(II) ions inhibit the removal of Ni(II)). According to the Akaike criterion, the equilibrium experimental data was better described by the Langmuir-Freundlich model, which considers the competition among ions for the active sites. The phenomenological mathematical modeling of the kinetics of biosorption was based on binary equilibrium equations, material balances and possible limiting mass transfer steps instead of the empirical models usually applied. The model was then adjusted to the experimental kinetic data and validated by a simulation in a different condition. According to the model, the internal mass transfer resistance (intra-particle diffusion) is the limiting step that controls the kinetics of the process. Therefore, due to its high predictive capacity, the phenomenological approach described in this work can be applied as a tool for design and optimization of binary heavy metal adsorption systems.