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.