Modelling of laminar multiphase flow is extremely important in a wide range of engineering and scientific applications. The particle phases are often difficult to model, especially when particles display a range of velocities at each location in space. Lagrangian method can be too costly and many Eulerian methods, though often computationally less taxing, suffer from model deficiencies and mathematical artifacts that lead to non-physical results. In particular, efficient Eulerian models that can accurately predict the crossing of multiple streams of non-interacting particles in laminar flow have traditionally been lacking. The goal of this work is to investigate the predictive capabilities of modern techniques from the kinetic theory of gases to a treatment of disperse multiphase flow. In particular, several moment-methods, including a recently proposed fourteen-moment approximation to the underlying kinetic equation describing particle motion, are applied and their abilities to predict particle-stream crossing are assessed. The derivation, mathematical structure, and physical behaviour of the resulting model are explained. A numerical implementation is presented and results for a flow problem that is designed to demonstrate the fundamental behaviour of each model with respect to particle stream crossing is presented. (C) 2019 Elsevier Ltd. All rights reserved.