In the present study heat and mass transfer related to the chemical conversion of limestone to quicklime in a shaft kiln are investigated by means of a coupled numerical scheme for gas and solid phase transport. The three-dimensional transport of mass, momentum and energy in the gas phase is modelled by computational fluid dynamics (CFD), while a discrete element method (DEM) is employed for the mechanical movement and the conversion reactions of the solid material. The DEM simulation readily describes the mechanical and thermal particle-to-particle interactions of a large number of differently sized particles. Novel aspects addressed in this work are the simultaneous effects of inner particle heat-conduction and pore-diffusion of the gaseous product of the calcination reaction (CO2) modelled by a shrinking core approach. Simulations of laboratory scale experiments of single reacting spheres show good agreement with the measured conversion rates. Simulations of an idealised vertical shaft kiln including pressure drop calculations demonstrate the suitability of the proposed approach for the modelling of industrial scale systems. (C) 2010 Elsevier Ltd. All rights reserved.