Thermochemical phenomena involved in cement kilns are still not well understood because of their complexity, besides technical difficulties in achieving direct measurements of critical process variables. This article addresses the problem of their comprehensive numerical prediction. The presented numerical model exploits Computational Fluid Dynamics and Finite Difference Method approaches for solving the gas domain and the rotating wall, respectively. The description of the thermochemical conversion and movement of the powder particles is addressed with a Lagrangian approach. Coupling between gas, particles and the rotating wall includes momentum, heat and mass transfer. Three-dimensional numerical predictions for a full-size cement kiln are presented and they show agreement with experimental data and benchmark literature. The quality and detail of the results are believed to provide a new insight into the functioning of a cement kiln. Attention is paid to the computational burden of the model and a methodology is presented for reducing the time-to-solution and paving the way for its exploitation in quasireal-time, indirect monitoring.