Mat-1.3656 Seminar on numerical analysis and computational science

Monday, Feb 14, 2011, room U322 at 14.15, Eirola & Stenberg

Ville Alopaeus,
Population balance models


Population balance models are integro-partial differential equations describing evolution of distributed property densities. In the mathematical physics, these equations are traditionally referred as to the Smoluchowski equations. The most typical chemical engineering applications are predictive models for particle, bubble, or droplet size distributions.

In this presentation a class of high-order numerical methods is proposed for solving these models. The solution is based on discretization of internal coordinate (size in this case). Numerical solution of the discretized domain is carried out by using a moment-conserving method, where in principle any number of moments can be set to be conserved. Conservation of a number of first integer moments is especially attractive since the moments in many cases inherently describe real physical conserved properties, such as total mass.

Similar moment methods are also applied to other problems, such as prediction of state variables in dynamic plug flow reactors or continuous-contact separation devices. In these applications, polynomial state profiles are assumed instead of spatial discretization. It can be shown that the proposed method has some attractive features compared to some traditional weighted residual methods.