A mathematical model for anaerobic digestion in plug-flow reactors is proposed on the basis of mass balance considerations. The model consists of a system of parabolic partial differential equations for the variables representing the concentrations of the bio-components constituting the waste matrix and takes into account convective and diffusive phenomena. The plug-flow reactor is modelled as a one-dimensional domain; the waste matrix moves in the direction of the reactor axis and undergoes diffusive phenomena which reproduce the movement of the bio-components along the reactor axis due to a gradient in concentration. The velocity characterizing the convection of the waste matrix is not fixed a priori but it is considered as an additional unknown of the mathematical problem. The variation in the convective velocity allows to account the mass variation occurring along a plug-flow reactor due to the conversion of solids. The equation governing the convective velocity is derived by considering the density of the waste matrix within the reactor constant over time and the sum of the volume fractions of the bio-components constituting the waste matrix constrained to unity. The waste matrix undergoes biochemical transformations catalyzed​ by anaerobic microbial species which lead to the production of gaseous methane, the final product of the anaerobic digestion process. Biochemical processes are modelled using a simplified scheme and a differential equation is used to describe the dynamics of the produced gaseous methane. A finite difference scheme is used for the numerical integration. Model consistency is showed through numerical simulations which investigate the effect of the variation of some operating parameters on process performance. The model is then applied to a real case scenario of engineering interest. Simulations produce results in good agreement with experimental observations.

### A modelling and simulation study of anaerobic digestion in plug-flow reactors

#### Abstract

A mathematical model for anaerobic digestion in plug-flow reactors is proposed on the basis of mass balance considerations. The model consists of a system of parabolic partial differential equations for the variables representing the concentrations of the bio-components constituting the waste matrix and takes into account convective and diffusive phenomena. The plug-flow reactor is modelled as a one-dimensional domain; the waste matrix moves in the direction of the reactor axis and undergoes diffusive phenomena which reproduce the movement of the bio-components along the reactor axis due to a gradient in concentration. The velocity characterizing the convection of the waste matrix is not fixed a priori but it is considered as an additional unknown of the mathematical problem. The variation in the convective velocity allows to account the mass variation occurring along a plug-flow reactor due to the conversion of solids. The equation governing the convective velocity is derived by considering the density of the waste matrix within the reactor constant over time and the sum of the volume fractions of the bio-components constituting the waste matrix constrained to unity. The waste matrix undergoes biochemical transformations catalyzed​ by anaerobic microbial species which lead to the production of gaseous methane, the final product of the anaerobic digestion process. Biochemical processes are modelled using a simplified scheme and a differential equation is used to describe the dynamics of the produced gaseous methane. A finite difference scheme is used for the numerical integration. Model consistency is showed through numerical simulations which investigate the effect of the variation of some operating parameters on process performance. The model is then applied to a real case scenario of engineering interest. Simulations produce results in good agreement with experimental observations.
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2022
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11588/866517`
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