Particulate systems can be readily modeled and simulated with the discrete element method (DEM). Large ranges in grain sizes, however, pose a serious challenge: The number of particles per volume increases significantly and computational time steps need to be reduced. Especially large systems require an efficient treatment of the smallest particles present. We derive and discuss models for two limiting cases. (a) For clearly separated size distributions, we consider the smaller particles as continuous fields. This corresponds, for example, to fines transport through a coarse granular bed including their deposition and release and is validated against measurements on such a system (approx. 10(5) particles, fine-to-particle-diameter ratio 0.105, up to 200% increase in pressure drop). (b) For less strongly separated distributions, e.g. one broad range of sizes, we introduce effective parcels consisting of sub-scale particles with various diameters. This model is applied to numerical experiments with a horizontal gas jet penetrating packed beds with bi- and monodisperse compositions and forming cavities as found in blast furnaces. The results show a good agreement with what one would expect from the full size distribution at fractions of the actual particle number (N-bi approximate to 3.10(5), N-eff approximate to 7.10(4)). Finally, we discuss how these models might be generalized for the application to a wide range of particulate systems. (C) 2017 Elsevier B.V. All rights reserved.