Numerical simulation of population balance equations and lime shaft kilns

The numerical simulation of a one-dimensional mathematical model is developed describing the lime calcination process in different types of shaft kilns. The model comprises a system of ordinary differential equations derived from mass and energy balances. A particle model for the chemical reaction is used and is connected to the energy balance equations for the gas and the solid inside the kiln taking into account the size distribution of solid particles.

This mixed initial value problem leads to a very unstable behavior of the existing numerical methods for boundary value problems. A stable numerical scheme for the solution of the equations is developed and analyzed. With this the influence of several parameters on the lime calcination process can be investigated. The results of this study can be transferred directly to the praxis for design, operation, regulation and optimization of normal shaft kilns.