Population Balance Solution Using Fixed Point Convergence Acceleration for Steady-State Reactor Networks

Abstract

The simulation of industrial crystallizers needs the implementation of multi-compartment models to handle the spatial heterogeneities at lower cost. In this context the study of recycle streams appears as an intermediate step to solve complex reactor networks. In this work, an accelerated fixed-point algorithm is applied to the solution of the crystal size distribution and the liquid phase composition in a structure including two compartments and one recycle stream. The numerical strategy, including fixed-point formulation, acceleration method, initial condition and convergence criteria, is introduced. One of the strengths of the proposed algorithm is that it does not depend on the numerical method used to solve the population balance equation in each compartment. As a case study, the numerical method is performed on the uranium oxalic precipitation. Thanks to this approach, local values of crystallisation kinetics, mass transfer and crystal size distribution are obtained. The evolution of the actinide concentration and the average crystal size follow the theory of the crystallisation mechanisms. Finally, the very satisfactory numerical performances open the way to simulate more complex and demanding reactor network structures.