The effect of Flue Gas Recirculation (FGR) on the decarbonation process during oxy-fuel combustion in a lime (and cement) rotary kiln is analyzed using an unsteady one-dimensional Eulerian-Lagrangian mathematical model. The model considers gas and limestone as continuous phases and the coal particles as the discrete phase. The model predicts limestone decarbonation, temperature and species distribution of gas and solid phases along the kiln. Simulation results of an air-combustion case are successfully validated with reported experimental data. This model is used to study and to compare the conventional air combustion process with oxy-fuel combustion with FGR ratios between 30% and 80% as controller parameter in this process. Changes in decarbonation process due to energy fluxes by convection and radiation with different FGRs were simulated and analyzed. Simulation results indicate a temperature increase of 20% in the gas and solid phases and a higher decarbonation rate of 40% in relation to the air-combustion case, for a given constant fuel consumption rate. However, for a given temperature, the increase of the CO2 partial pressure in the oxy-fuel case promotes a reduction of the decarbonation rate. Therefore, there is a compromise between FGR and decarbonation rate, which is analyzed in the present study. Simulation results of the decarbonation step in low FGR cases, compared to air-combustion case, shows that conversion takes place in shorter distances in the kiln, suggesting that the production rate can be increased for existing kilns in oxy-fuel kilns or, equivalently, shorter kilns can be designed for an equivalent production rate. (C) 2015 Elsevier Ltd. All rights reserved.