Asian Research Journal of Mathematics

Background: Anaerobic digestion (AD) is a proven technology for renewable bio-methane production, but digester efficiency is often limited by poor hydrodynamic mixing rather than by microbial kinetics alone; most existing models, however, assume idealised, fully homogeneous reactors.

Objective: This study investigates the influence of hydrodynamics on mixing efficiency and bio-methane production potential in anaerobic digesters using mathematical modelling.

Methods: A two-dimensional incompressible Navier–Stokes model was coupled with a tracer advection–diffusion equation to simulate slurry flow and mixing behaviour. The governing equations were non-dimensionalised using the Reynolds and Péclet numbers, discretised using the finite difference method, and solved numerically in MATLAB. An optimisation framework that treated inlet velocity as the control variable, together with an adjoint sensitivity analysis, was used to evaluate and improve mixing efficiency.

Results: At a Reynolds number of 2100, the flow exhibited transitional characteristics, with a dead zone fraction of approximately 35.1%. Velocity contours revealed limited circulation, whereas the tracer distribution showed a non-uniform concentration pattern across the domain. The dead zone fraction declined exponentially as Re increased, with values above 4000 projected to reduce it below 15%. At Pe = 10,000, transport was strongly advection-dominated, and the adjoint sensitivity analysis identified the inlet/impeller region as offering the greatest leverage over mixing performance.

Conclusion: Hydrodynamic conditions play a critical role in determining mixing efficiency and, consequently, bio-methane production potential. The developed model provides a computationally efficient framework for analysing and optimising anaerobic digester performance and offers a foundation for future integration with biochemical reaction models.