A reaction-diffusion-growth framework for anaerobic granule formation and stability in high-rate wastewater reactors

Abstract

High-rate anaerobic wastewater reactors rely on dense microbial granules to retain biomass and sustain elevated volumetric conversion rates. Within these aggregates, microorganisms are embedded in a porous matrix where substrate transport occurs primarily through diffusion. As a result, the substrate concentration experienced by microbial populations varies spatially within the granule, and the reaction rates observed at the reactor scale differ from the intrinsic microbial kinetics governing metabolism. This work develops a reaction-diffusion-growth framework for analyzing microbial activity, pathway selectivity, and structural stability in granular anaerobic systems. A spherical reaction-diffusion model with Monod kinetics and external film transport was solved numerically to evaluate intragranular substrate distributions and effectiveness factors. The analysis demonstrates that diffusion limitations can bias kinetic parameters inferred from reactor measurements and modify the apparent activity and selectivity of competing metabolic pathways. Dimensionless analysis identifies the reaction-diffusion parameter and the mass-transfer Biot number as the primary variables governing transport regimes within granular biomass. Coupling the transport model with a biomass growth-detachment balance reveals stability boundaries linking granule size and hydrodynamic conditions. These results demonstrate that granular anaerobic reactors can be interpreted as transport-limited reacting particles in which apparent microbial kinetics, pathway selectivity, and structural stability emerge from the coupled reaction-diffusion-growth system governing substrate transport and microbial metabolism within the aggregate.