Modeling of cement clinker production in a rotary kiln incorporating melting and aggregation of particles

Cement clinker is produced in rotary kilns operating at high temperature. The harsh internal conditions in the kiln prevent direct measurements of key process variables. Digital twins that use mathematical models to mimic and emulate the process in real time are viable alternatives to track equipment performance and product quality. Building on the past modeling efforts for rotary kilns, this work brings in two important and interacting phenomena of melting and aggregation that have often been ignored in the literature. Some of the components that form in the solid phase, melt due to the high temperature in the kiln. The melt aids smaller particles to aggregate and grow to form large clinker chunks. In this work, a core-shell model is used to capture the melting process along with a population balance model to track the particle size distribution of the aggregates. The model predicts melting and aggregation to take place nearly after 75\% of the kiln length from the feed end. The model is first validated with published chemical analysis of clinker in an industrial kiln. Simulations reveal that as melting lowers the bed temperature, it reduces $\rm C_{3}S$ production and increases $\rm C_{2}S$ production. Aggregation somewhat reverses the trend, bringing out the interactions among particle size, melting and reaction kinetics.