In most fluidized beds, both solids flux and gas phase Reynolds number are high and the flow are usually turbulent. It is therefore necessary to consider both the effects of particle-particle collisions and particle phase turbulence in any mathematical model for simulating gas-particle flows. A comprehensive model is developed in the present work in which a two-equation (k-epsilon) turbulence model is used for calculating the gas phase. In addition, a transport equation of particle phase turbulent kinetic energy is proposed and used for modeling the particle phase turbulence (k(p) model). Similar to that of the single gas phase, effective viscosity of the particle phase is the sum of the laminar viscosity caused by particle-particle collisions described by kinetic theory and the turbulent viscosity caused by collections of particles described by the k(p) model. The proposed model is used to predict gas-particle flows in a vertical pipe. Results obtained using this model compare well with experimental data. (C) 2004 Elsevier B.V. All rights reserved.