Fluid flowing through packed beds of multi-sized spheres is studied by a parallel lattice-Boltzmann (LB) model. The packed beds are generated by means of the discrete element method. First, the LB model is used to study the effects of size ratio and volume fraction on the fluid flow and quantify the drag forces on binary mixtures of particles. Typical flow behaviours are identified in relation to pore geometries. The results suggest that the polydispersity in particle size enhances local structure heterogeneity and flow non-uniformity, resulting in distributed fluid particle interaction forces. Then, based on the simulated data, a new equation is formulated to calculate the mean individual drag force. The equation is extended to multicomponent mixtures of particles. The results show that the new equation is more accurate and reliable than those in the literature, and can be generally used in the modelling of particle fluid flows. (C) 2014 Elsevier Ltd. All rights reserved.