The goal of this research is to make predictions for the relationship among the operating variables (pressure drop, gas flux, and solid flux) in solid transfer lines. These predictions will be generated from fundamental hydrodynamic models comprising mass, momentum, and energy balances for the two phases. Representation of fluid-fluid, particle-particle, and fluid-particle interactions will be investigated in the model development, as well as proper formulation of boundary conditions. Computer simulation of transient two-dimensional gas-solids flow will be preformed, and the model will be extensively tested with a full range of available experimental data. The results from lead to improved design and operation of pneumatic systems.