# Technical Report 33, c4e-Preprint Series, Cambridge

## Two methods for sensitivity analysis of population balance equations by a Monte Carlo method

ref: Technical Report 33, c4e-Preprint Series, Cambridge

Associated Theme: Numerics

We consider two stochastic simulation algorithms for the calculation of parametric derivatives of solutions of a population balance equation, namely, forward and adjoint sensitivity methods. The dispersed system is approximated by an N-particle stochastic weighted ensemble. The infinitesimal deviations of the solution are accounted for through infinitesimal deviation of the statistical weights that are recalculated at each coagulation. In the forward method these deviations of the statistical weights immediately give parametric derivatives of the solution. In the second method the deviations of the statistical weights are used to calculate a infnite-mode approximation of the linearized version of the population balance equation. The linearized equation allows for the calculation of the eigenmodes and eigenvalues of the process, while the parametric derivatives of the solution are given by a Lagrange formalism.

Material from this preprint has been published in: Chemical Engineering Science 61 (15), 4966-4972, (2006)

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