Euler-Euler two-phase model simulations are usually performed with mesh sizes larger than the small-scale structure size of gas-solid flows in industrial fluidised beds because of computational resource limitation. Thus, these simulations do not fully account for the particle segregation effect at the small scale and this causes poor prediction of bed hydrodynamics. An appropriate modelling approach accounting for the influence of unresolved structures needs to be proposed for practical simulations. For this purpose, computational grids are refined to a cell size of a few particle diameters to obtain mesh-independent results requiring up to 17 million cells in a 3D periodic circulating fluidised bed. These mesh-independent results are filtered by volume averaging and used to perform a priori analyses on the filtered phase balance equations. Results show that filtered momentum equations can be used for practical simulations but must take account of a drift velocity due to the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and particle sub-grid stresses due to the filtering of the non-linear convection term. This paper proposes models for sub-grid drift velocity and particle sub-grid stresses and assesses these models by a priori tests. (c) 2013 Elsevier Ltd. All rights reserved.