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Highlights • A novel model that integrates mixing and biochemical reactions in AD is presented. • This is the first fully Lagrangian computational model for this type of processes. • A diffusion equation is used to link the mixing and the biochemical reactions. • The biological properties are advected by the SPH particles following the fluid flow. • Lagrangian nature of SPH is an asset in wastewater treatment process studies. Abstract The impact of mixing on biochemical reactions is of high importance in anaerobic digestion (AD). In this paper, a novel 2D fully Lagrangian computational model for the integration of mixing and biochemical reactions in AD is developed and presented. The mixing-induced fluid flow is modeled by smoothed particle hydrodynamics (SPH). The computational domain is discretized by SPH particles, each of which carries the information of biologically active compounds and follows the flow field. In this natural way, advection is reproduced, which is the main advantage of SPH for this type of problems. A mathematical model that governs the biochemical reactions is integrated in time for each particle, which allows to spatially resolve the biological concentrations. Mass transfer interactions between particles are reproduced by the diffusion equation to directly link mixing to biochemical reactions. The total biogas production is obtained by integrating over all the particles. Both SPH and biochemical models are verified against existing data in the literature and the integrated model is then applied to a real world anaerobic digester. The application of a novel fully Lagrangian method to AD is a stepping stone to future possible developments. However, in the simulation of such problems, SPH is still uncompetitive if compared to other mainstream methods and industrial application of the model depends on the computational efficiency of future SPH solvers. [ABSTRACT FROM AUTHOR]