A multiscale mathematical model is presented to describe the de novo granulation and the evolution of multispecies granular biofilms within a continuous reactor. The granule is modelled as a spherical free boundary domain with radial symmetry. The equation which governs the free boundary is derived from global mass balance considerations and takes into account the growth of sessile biomass and the exchange fluxes with the bulk liquid. Starting from a vanishing initial value, the expansion of the free boundary is initiated by the attachment process, which depends on the microbial species concentrations within the bulk liquid and their specific attachment velocity. Nonlinear hyperbolic PDEs model the growth of the sessile microbial species, while quasi-linear parabolic PDEs govern the dynamics of substrates and invading species within the granular biofilm. Nonlinear ODEs govern the evolution of soluble substrates and planktonic biomass within the bulk liquid. The model is applied to an anaerobic granular-based system and solved numerically to test its qualitative behaviour and explore the main aspects of de novo anaerobic granulation: ecology, biomass distribution, relative abundance, dimensional evolution of the granules and soluble substrates and planktonic biomass dynamics within the reactor. The numerical results confirm that the model accurately describes the ecology and the concentrically-layered structure of anaerobic granules observed experimentally, and is able to predict the effects of some significant factors, such as influent wastewater composition, granulation properties of planktonic biomass, biomass density and hydrodynamic and shear stress conditions, on the process performance.
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