  We treat the accurate simulation of the calcination reaction in particles,
where the particles are large and, thus, the inner-particle processes must be
resolved. Because these processes need to be described with coupled partial
differential equations that must be solved numerically, the computation times
for a single particle are too high for use in simulations that involve many
particles. Simulations of this type arise when the Discrete Element Method
(DEM) is combined with Computational Fluid Dynamics (CFD) to investigate
industrial systems such as quick lime production in lime shaft kilns. We show
that, based on proper orthogonal de-composition and Galerkin projection,
reduced models can be derived for single particles that provide the same
spatial and temporal resolution as the original PDE models at a considerably
reduced computational cost. Replacing the finite-volume particle models with
the reduced models results in an overall reduction of the reactor simulation
time by about 60% for the simple example treated here.
