A Monte Carlo methods for identification and sensitivity analysis of coagulation processes

A stochastic simulation algorithm is presented to calculate parametric derivatives of solutions of a population balance equation. The dispersed system is approximated by an N-particle stochastic weighted ensemble. The derivatives are accounted for through infinitesimal deviation of the statistical weights that are recalculated at each coagulation. Thus, all the parametric derivatives can be calculated along one trajectory of the process, given N sufficiently large. We use an operator-splitting technique to account for surface growth of the particles. The obtained solution is in good agreement with the available analytical solutions. As soon as the parametric derivatives are known the gradient-based methods can be applied to the control and identification of the coagulation process. The extension of the proposed technique to a multi-dimensional case is straightforward.