Fast Compartmental Monte Carlo Simulation of Population Balance Models: Application to Nanoparticle Formation in Nonhomogeneous Conditions

Abstract

A new compartmental Monte Carlo (CMC) algorithm is introduced for the stochastic simulation of population balance models in spatially heterogeneous systems. The heterogeneities are modeled using a network of compartments. The algorithm is based on a new stochastic procedure called particle bundle flow (PBF) to model the stochastic transfer of particles between compartments in a given time interval (a time-driven algorithm). Different from other time-driven methods, the accuracy of the PBF is independent of the particle concentration. The validity of the PBF method is demonstrated by construction and confirmed with numerical experiments. A new strategy for time step control is developed to set bounds on the calculation of the time steps during the simulation. The CMC algorithm, based on the combination of the PBF algorithm with the τ point ensemble Monte Carlo algorithm, is a general-purpose methodology that can be applied to any network of compartments. The computational speed and the low computational load of this algorithm allow the solution of problems that may be intractable otherwise. A new hybrid strategy for the solution of problems with stochastic fluctuations and disparate time scales is also developed in this work. The CMC is applied to study the formation of nanoparticles in a large reactor utilizing a two-compartment model. The Monte Carlo ability to track single events is utilized to study the impact of turbulence and the stability factor on the generation of large particles.