This paper deals with the mathematical modelling of a furnace devoted to the limestone processing. The novelty of this reactor is that the energy required by the endothermic reaction of calcination is provided by the combustion of biomass, making it compatible with sustainable development. The model is based on balance equations completed with phenomenological relations for the estimation of heat and mass transfer inside the reactor and for the estimation of the kinetics of the reaction. in a first section, the equations describing the behaviour of a single reacting particle of limestone are derived. The model relies on the assumption that the reacting particle obeys the shrinking core model. Then this model of a single particle is introduced in a more general one-dimensional model describing the whole furnace, where the different relevant properties depend upon the location within the reactor. Some industrial information is compared to numerical predictions, thus validating the model. Also the results provided by the numerical model allow for a better comprehension of the different phenomena occurring within the reactor. (C) 2009 Elsevier Ltd. All rights reserved.