Modelling and simulation of crystallisers under non-perfect micromixing conditions

Abstract

A mathematical model, formulated in terms of interacting populations under perfect macromixing conditions, is presented and analysed for describing micromixing in crystallisation processes. The model consists of two population balance equations, describing the changes of fluid elements of solution and crystals, respectively. The kinetics of micromixing is described by the coalescence–dispersion model, and is characterised by a constant coefficient of coalescence of fluid elements as the parameter of the mixing intensity. The rates of nucleation and growth of crystals are expressed as the expected values over the randomly interacting fluid elements. A closed moment equation model is derived and used to analyse the effects of micromixing on the dynamic and steady-state properties of crystallisers, and on the properties of the crystalline product. The steady-state value of the mean concentration of fluid elements decreases, while the yield of crystallisers increases by increasing segregation level. In steady states, a crystalliser with segregated solution phase produces more mass of smaller crystals than the corresponding crystalliser with solution mixed perfectly on microlevel. In well mixed microlevel states, the mean size of the crystalline product increases with increasing mean residence time, while in segregated states this tendency reverses. In segregated states, higher standard deviation of concentration of fluid elements is induced with increasing residence time.