A modeling 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 catalysed 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.

• The paper proposes a novel convection-diffusion-reaction model for dry anaerobic digestion in plug-flow reactors that dynamically adjusts convective velocity based on internal mass changes.
• The study employs finite difference methods to simulate key biochemical processes, showing that reactor length and inlet velocity significantly impact methane yields.
• Numerical simulations validated the model against lab-scale data, highlighting the importance of optimizing reactor design parameters for efficient biogas production.

Anaerobic Digestion in Plug-Flow Reactors

Introduction

The study investigates the dynamics of anaerobic digestion (AD) in plug-flow reactors (PFR), a topic of significant interest for optimizing biogas production from organic waste. The paper presents a new mathematical model specifically tailored to dry AD processes, taking into account convection, diffusion, and biochemical reactions. Unlike previous models, this approach treats the convective velocity as a variable influenced by the reactor's internal mass changes.

Mathematical Model

Model Formulation

The proposed model is an adaptation of the classic convection-diffusion-reaction framework. It uses parabolic partial differential equations (PDEs) to represent mass balances on key biocomponents along the reactor's length. This model distinguishes itself by dynamically calculating the convective velocity based on variations in the reactor's mass, a method justified by the assumption of constant waste matrix density.

The equations are derived under the assumption that the mass of volatile solids (VS) and other biomass components is conserved across the reactor. This assumption leads to an equation for convective velocity, dependent on changes in biocomponent concentrations due to microbial activity.

Biochemical Kinetics

The reaction kinetics simplify the complex biochemical processes into key stages: disintegration, hydrolysis, acidogenesis, acetogenesis, and methanogenesis, with disintegration and methanogenesis being the rate-limiting steps. A finite difference method is applied to solve these equations, ensuring numerical stability and enabling simulation of realistic reactor scenarios.

Numerical Simulations and Results

Simulation Setup

Simulations were carried out under various conditions, altering parameters such as reactor length, inflow velocity, HRT, and the diffusion coefficient to study their effects on system performance metrics like VS conversion efficiency, methane yield, and microbial biomass distribution.

Key Observations

1. Reactor Length and Inlet Velocity: Maintaining constant HRT across different reactor lengths revealed that longer reactors with lower inlet velocities had improved methane production due to increased microbial contact time with substrates.
2. Diffusion Effects: High diffusion coefficients resulted in uniform concentration profiles akin to a CSTR, thus reducing substrate availability for methanogenesis, unlike low diffusion setups which maintained a PFR's biological stratification advantage.
3. Process Dynamics: The model captured the expected diminishing returns on methane yield when operating under increasing OLRs, emphasizing the balance needed between reactor dimensions and operational loadings for stable operation.

Real-World Application

The model's validity was further ratified through application to lab-scale reactor data, simulating a series of operational scenarios with varying OLRs. The model demonstrated an impressive congruence with empirical results regarding methane production and VS reduction, although slight discrepancies in methane yield were noted at higher loadings.

Conclusion and Future Directions

The study provides a robust framework for predicting the performance of PFRs under various operating conditions. Given its impressive alignment with experimental data, this model serves as a potent tool for reactors' design and management. Future enhancements to this model may include integration with the ADM1 framework for more detailed biochemical substrate interactions, consideration of variable waste density, and expansion to multidimensional analysis to capture complex flow and reaction dynamics in industrial-scale applications. Other potential improvements encompass real-time pH monitoring to prevent microbial inhibition and optimizing in-situ biogas tapping strategies for more energy-efficient operations.