Multiscale modelling of oxygenic photogranules.

This work presents a mathematical model which describes both the genesis and growth of oxygenic photogranules (OPGs) and the related treatment process. The photogranule has been modelled as a free boundary domain with radial symmetry, which evolves over time as a result of microbial growth, attachment and detachment processes. A system of hyperbolic and parabolic PDEs has been considered to model the advective transport and growth of sessile biomass and the diffusive transport and conversion of soluble substrates. The reactor has been modelled as a sequencing batch reactor (SBR) through a system of first order IDEs. Phototrophic biomass has been considered for the first time in granular biofilms, and cyanobacteria and microalgae are taken into account separately to model their differences in growth rate and light harvesting and utilization. To describe the key role of cyanobacteria in the photogranules formation process, the attachment velocity of all suspended microbial species has been modelled as a function of the cyanobacteria concentration in suspended form. The model takes into account the main biological aspects and processes involved in OPGs based systems: heterotrophic and photoautotrophic activities of cyanobacteria and microalgae, metabolic activity of heterotrophic and nitrifying bacteria, microbial decay, EPS secrection, diffusion and conversion of soluble substrates (inorganic and organic carbon, ammonia, nitrate and oxygen), symbiotic and competitive interactions between the different microbial species, day-night cycle, light diffusion and attenuation across the granular biofilm and photoinhibion phenomena. The model has been integrated numerically, investigating the evolution and microbial composition of photogranules and the treatment efficiency of the OPGs-based system. The results show the consistency of the model and confirm the effectiveness of the OPGs technology.