Application of The Splitting Approach to Solve Population Balance Equations in Chemical Processes

• Published in: Chemical engineering & technology Vol. 32; no. 12; pp. 1894 - 1900
• Main Authors: Bastani, D., Baghaei, A., Sarrafi, A.
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 01-12-2009; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Applied sciences; Break-up; Chemical engineering; Classes method; Coalescence; Exact sciences and technology; Hydrodynamics of contact apparatus; Particle size distributions; Population balance; Design; Chemical industry; Bubble; Particle size distribution; Multiphase flow; Hydrodynamics; Kinetics; Coalescence; Population balance
• ISSN: 0930-7516; 1521-4125
• DOI: 10.1002/ceat.200900109

Different processes in chemical industries deal with particles and multiphase flow. In such processes, particle or bubble size distribution (PSD) influences the final product quality and also process design. On the other hand, solutions to the dominant hydrodynamic and thermo‐kinetic equations ignoring these distributions will make it impossible to accurately simulate these processes. Solutions to population balance equations (PBE's) are needed to attain the PSD. One of the most common methods for the solution of a PBE is the classes method (CM). However, as this method requires a large number of classes to give a reasonable result, it needs a huge amount of calculations and time. To overcome this problem, in this paper, a variant of the CM is proposed in which particles in different classes are transformed to new classes in two steps with the application of the operator splitting technique. In the first step, the particles are aggregated and broken up to form three parallel types of groups, namely: groups formed from aggregated particles, groups formed from broken‐up particles, and finally, a group formed from non‐altered particles. In the second step, these parallel groups are combined to redefine classes for the next time step. Finally, results of this method, which could be called the parallel groups classes method (PGCM), for different coalescence and breakage kernels are compared with those obtained using the analytical solution and the CM. Excellent agreement of the results from the PGCM with the analytical solution reveals its effectiveness and accuracy; which will give it an advantage over the CM.
Population balance, used in several engineering applications, is a well‐established method used to analyze the particle size distribution (PSD) of the dispersed phase in processes. A novel technique for solving population balance equations was proposed.