In process engineering applications numerical models are needed to make extensive analysis for the design and operation of unit operations. In the present work, a transversal granular flow model and two numerical models for the description of the granular bed of a rotary kiln are developed for the analysis of a Calcium Aluminate rotary kiln from an industrial partner. From the transversal granular flow model it is concluded that the kiln from the industrial partner is probably not in rolling mode. This hints the possibility that there is a non-optimized mixing in the kiln which could bring adverse consequences in the production and current modelling of the studied rotary kiln. A validated one-dimensional rotary kiln model is developed taking into account different approaches from literature. Simplified sintering reactions are proposed by considering experimental X-Ray Diffraction data. The one-dimensional model is successfully used to describe the properties of the product when changing air to gas ratio of the combustion gasses in the kiln from the industrial partner. Furthermore, a two-dimensional transversal model for granular bed heat transfer is developed to explore whether a full granular flow model is necessary in order to have a sufficiently accurate description of the granular material properties of the kiln from the industrial partner. It is concluded that due to the low loading of the analyzed CAC kiln, a one-dimensional is sufficient to make a sensitivity analysis on the operating conditions and design varaibles of the kiln if the bed has a rolling mode with an active layer of 5 to 20 percent of the bed height. Further research must be done in order to characterize the transversal flow of the analyzed kiln in order to develop more complex kiln models.