A Revision of Population Balance Equation Applied to Microalgae with Birth, Growth, and Death

A revised population balance equation (PBE) is proposed to handle problems with the population growth, birth, death, and division of particles. Different to conventional models, the revised PBE deducts dead cells from the growing population, thus making this new version much more stable and accurate than existing methods such as the “traditional” upwind scheme. In addition, the obtained numerical solution is further improved by considering the “compound effect” caused by discretization. With the implementation of a simple guideline setting the time and size intervals, the revised PBE is able to obtain a high-quality solution. Also, unlike sectional methods, diffusion can be avoided even when the growth term is present. Compared to the analytical solution, the quality of the solution from the new approach is as good as the moving size interval approach but without the limitation caused by the moving size ranges. As a case study, the new methodology is utilized to simulate microalgae growth, and includes birth, death, division, and size-dependent growth rates. This allows the possibility to evaluate parameters that may be very challenging to collect directly from experiments.