Monte Carlo simulation for the solution of the bi-variate dynamic population balance equation in batch particulate systems

This paper presents a study on the solution of the bi-variate population balance equation (PBE) in batch particulate processes using stochastic Monte Carlo (MC) simulations. Numerical simulations were carried out over a wide range of variation of particle aggregation and growth rate models. The PBE was numerically solved in terms of the number density function, n(V,x,t)n(V,x,t), for the prediction of the dynamic evolution of the two-dimensional (with respect to particle volume, VV, and a second internal property, xx) particle size distribution (PSD), as well as for the calculation of the leading moments of the distribution. The performance of the method was assessed in terms of accuracy via a direct comparison of the calculated PSDs and the respective leading moments to available analytical solutions. The comparisons showed that the MC algorithm was capable of predicting the dynamic evolution of the bi-variate distribution with high accuracy, while its computational requirements were relatively low.