Six algorithms following single particle trajectories are used to predict the axial dispersion in rolling or slumping flow in a continuous rotary kiln. Models incorporating different physical phenomena show that axial dispersion is affected by the Froude number, L/D ratio, solid fill level and rolling or slumping layer thickness. The main cause of axial dispersion is segregation of the particles roll or slump distance due to variation of the solid flow properties caused by nonuniform particle size, density and shape. In a rolling bed with uniform particles the rolling layer thickness and the time of roll have to be accounted for in the prediction of the dispersion. The Peclet numbers computed for solid particles with uniform physical properties are of the order of 10(4). The solid segregated motion may lead to Peclet numbers of the order of 10-10(3) a much larger dispersion. The main obstacle for a-priori prediction of the axial dispersion is lack of a reliable relation between the segregated roll or slump distance and the variation in particles properties, as well as the change in segregation as the flow properties of particles are changed during calcination.