The partial differential equations for modeling gas-solid flows using computational fluid dynamics are compared for different coordinate systems. The numerical results of 2D and 3D simulations for both cylindrical and rectangular domains are presented in Part I (N. Xie, F. Battaglia, S. Parmala, Effects of using two- versus three-dimensional computational modeling of fluidized beds: Part I, Hydrodynamics (2007-this volume), doi:10.1016/j.powtec.2007.07.005), comparing the hydrodynamic features of a fluidized bed. The individual terms of the governing equations in 2D and 3D simulations with the cylindrical and Cartesian coordinate systems are evaluated in this study through a budget analysis. The additional terms appearing in the 3D equations can be used to explain the discrepancies between 2D and 3D simulations. The values of the additional terms is shown to increase as inlet gas velocity increases. This explains the good agreement between 2D and 3D simulations that is observed for bubbling regimes with low gas velocity, and why the differences between 2D and 3D simulations increases for slugging and turbulent regimes. (C) 2007 Elsevier B.V. All rights reserved.