Mathematical modeling of Fe(II), Cu(II), Ni(II) and Zn(II) removal in a horizontal rotating tubular bioreactor

Industrial wastewaters polluted with toxic heavy metals are serious ecological and environmental problem. Therefore, in this study multi-heavy metals (Fe²⁺, Cu²⁺, Ni²⁺ and Zn²⁺) removal process with mixed microbial culture was examined in the horizontal rotating tubular bioreactor (HRTB) by different combinations of process parameters. Hydrodynamic conditions and biomass sorption capacity have main impact on the removal efficiency of heavy metals: Fe²⁺ 95.5–79.0%, Ni²⁺ 92.7–54.8%, Cu²⁺ 87.7–54.9% and Zn²⁺ 81.8–38.1%, respectively. On the basis of experimental results, integral mathematical model of removal heavy metals in the HRTB was established. It combines hydrodynamics (mixing), mass transfer and kinetics to define bioprocess conduction in the HRTB. Mixing in the HRTB was described by structured cascade model and metal ion removal by two combined diffusion–adsorption models, respectively. For Langmuir model, average variances between experimental and simulated concentrations of metal ions were in the range of 1.22–10.99 × 10⁻³ and for the Freundlich model 0.12–3.98 × 10⁻³, respectively. On the basis of previous facts, it is clear that developed integral bioprocess model with Freundlich model is more efficient in the prediction of concentration of metal ions in the HRTB. Furthermore, the results obtained also pointed out that the established model is at the same time accurate and robust and therefore it has great potential for use in the scale-up procedure.