A mathematical model for a bubbling fluidized bed has been developed to simulate the performance of the fuel-reactor in chemical-looping combustion (CLC) systems. This model considers both the fluid dynamic of the fluidized bed and freeboard and the kinetics of reduction of the oxygen-carrier, here CuO impregnated on alumina. The main outputs of the model are the conversion of the carrier and the gas composition at the reactor exit, the axial profiles of gas concentrations and the fluid dynamical structure of the reactor. The model was validated using measurements when burning CH4 in a 10 kW(th) prototype using a Cu-based oxygen-carrier. The influence of the circulation rate of solids, the load of fuel gas, the reactor temperature and size of the oxygen-carrier particles were analyzed. Combustion efficiencies predicted by the model showed a good agreement with measurements. Having validated the model, the implications for designing and optimizing a fuel-reactor were as follows. The inventory of solids for a high conversion of the fuel was sensitive to the reactor's temperature, the solids' circulation rate and the extent to which the solids entering to the reactor had been regenerated. The optimal ratio of oxygen-carrier to fuel was found to be 1.7-4 for the Cu-based oxygen-carrier used here. In this range, the inventory of solids to obtain a combustion efficiency of 99.9% at 1073 K was less than 130 kg/MWth. In addition, the model's results were very sensitive to the resistance to gas diffusing between the emulsion and bubble phases in the bed, to the decay of solids' concentration in the freeboard and to the efficiency contact between gas and solids in the freeboard. Thus, a simplified model, ignoring any restriction to gas and solids contacting each other, will under-predict the inventory of solids by a factor of 2-10. (C) 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.