# Technical Report 28 c4e-Preprint Series, Cambridge

## Population balance modelling of droplet size distribution in a RDC: inverse problem approach

ref: Technical Report 28 c4e-Preprint Series, Cambridge

Associated Theme: Numerics

An inverse problems method is applied to a two-phase liquid-liquid system in a Rotating Disc Contactor (RDC). The dispersed phase is modelled by population balance equations, which are solved by a Monte Carlo method together with the equations for the parametric derivatives of the solution with respect to the parameters of the model. The best fitting problem is solved by a gradient search method. Since the inverse problem is ill-posed, the iteration procedure is augmented by an appropriate termination criterion to stabilize the calculations. The parametric derivatives of the solution can be used to quantify the relative importance of different parameters of the model. It is shown that the model's parameters, which are identified on one set of the experimental data describe adequately the behavior of the system under another unfitted operation condition, i.e., the proposed method can be applied to scale up problems.

Material from this preprint has been published in: AIChE Journal 52, 1441-1450, (2006)

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