A hybrid stochastic/fixed-sectional method for solving the population balance equation

Alexandre Bouaniche (1) , Luc Vervisch (1) , Pascale Domingo (1)

1 CORIA - Complexe de recherche interprofessionnel en aérothermochimie

The dynamics of flowing non-inertial particles undergoing nucleation, surface growth/loss, agglomeration and sometimes breakage, is usually characterised by the particle size distribution function. This distribution evolves according to a population balance equation. A novel approach combining Monte Carlo and fixed-sectional methods is proposed to minimise the discretisation errors when solving the surface growth/loss term of the population balance equation. The approach relies on a fixed number of stochastic particles and sections, with a numerical algorithm organised to minimise errors even for a moderate number of stochastic particles and sections. Canonical test cases featuring nucleation, agglomeration, and surface growth/loss are simulated. Results against the analytical solutions confirm the improvement in accuracy of the novel approach compared with fixed-sectional methods for the same computational effort. The hybrid method is thus of particular interest for simulating problems where surface growth/loss dominates the particles physics.

Mots clés: Aerosol modelling; Sectional method; Stochastic method; Hybrid modeling; Particle Size Distribution; Population Balance Equation; Probability Density Function; Monte Carlo solution

Domaines: Sciences de l'ingénieur [physics]; Milieux fluides et réactifs

Alexandre Bouaniche, Luc Vervisch, Pascale Domingo. A hybrid stochastic/fixed-sectional method for solving the population balance equation. Chemical Engineering Science, 2019, 209, pp.115198. ⟨10.1016/j.ces.2019.115198⟩. ⟨hal-02313897⟩