A New Approach to Solve Population Balance Equations in Chemical Processes

Nowadays, population balance is used as a powerful engineering tool in design issues. Different processes in chemical, petrochemical, biotechnology, pharmaceutical industry, etc. deal with particles. In such processes particle or bubble size distribution (PSD) influences the final product quality and also process design. On the other hand solution to the dominant hydrodynamic and thermo-kinetic equations ignoring this distribution will make it impossible to accurately simulate these processes. Solution to population balance equations (PBE’s) is needed to attain the PSD. Since 1940’s many researchers have proposed different methods for easier and also more accurate solution of PBE’s. One of the most common and famous of these methods 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 new variant of CM is proposed in which particles in different classes are transformed to new classes in two steps. In the first step, the particles are agglomerated and broken up to form three parallel types of groups, namely: groups formed from agglomerated 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 next time step. Finally, results of this method, which could be called Parallel Groups Classes Method (PGCM), for different coalescence and breakage kernels are compared with those obtained using analytical solution and CM. Excellent agreement of results of PGCM with analytical solution reveals its effectiveness and accuracy; which will give it an advantage over CM.

Keywords:

Population balance , Classes method , Particle size distribution , Agglomeration , Break-up