  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.
