An unsteady model is developed for the particle size distribution in fluidized-bed reactors including fragmentation, abrasion, elutriation and the chemical reactions of wood gasification. Based on the assumption of constant conditions (gas composition, temperature, velocity) of the surrounding atmosphere, an analytical solution is developed for the distribution of sizes belonging to the classes of mother and fine particles. It is found that for the typical feed sizes (minimum above 3 x 10 (2) mm) and the usual maximum size of fine particles (2.4 x 10 (3) mm), the behavior of fine particles is quasi-steady with respect to mother particles. The numerical solution of the quasi-steady formulation of particle population balances is also coupled with a two-phase (bubble and emulsion), three-zone (bed, splash zone and freeboard) model for a bubbling fluidized-bed reactor, giving predictions of the producer gas composition in agreement with measurements for air gasification of wood. (C) 2014 Elsevier Ltd. All rights reserved.