A PDF modelling of precipitation reactors

Abstract

Efforts to model precipitation processes in chemical reactors need to combine fluid mechanics with precipitation processes description. The main difficulty is to consider together micromixing phenomena, which are known to play an important role, with complex reactions kinetics and particles size distribution in the flow. In the present study, a probability density function (PDF) method is presented to calculate the evolution of the particles size distribution. The main advantage of the method is to include a micromixing model based on a Lagrangian frame where chemical reactions are treated without modelling and which requires minimal computational resources. The micromixing model considered is the interaction and exchange with the mean (IEM). Precipitation reactions are nucleation, growth and aggregation. Because of the nature of the powerful numerical technique used, based on Monte-Carlo simulations, the method is able to produce, at any point in the flow, reactants concentration and supersaturation fields, and the particles size distribution field, by simple moments method. The main advantage of the method over traditional population balance solvers is its capability to treat multi-dimensional (e.g. size, crystal morphology, chemical properties, etc.) population balances just as efficiently as it treats high-dimensional PDF. The PDF code is coupled with the commercial CFD package FLUENT which is used for the turbulent calculation of the flow (classical k– ε turbulence model), where the presence of the solid phase is assumed not to affect the flow field. An example is presented in the case of silica particles aggregation. The influence of initial reactants concentration and hydrodynamics parameter are investigated.