The present study deals with pneumatic conveying of spherical particles in a six meter long horizontal channel with rectangular cross-section from a numerical perspective. Calculations are done for spherical glass beads of different sizes with a mass loading of 1.0 kg particles/kg gas. Additionally, different wall roughnesses are considered. Air volume flow rate is kept constant in order to maintain a fixed gas average velocity of 20 m/s. The numerical computations are performed by the Euler/Lagrange approach in connection with a Reynolds stress turbulence model accounting for two-way coupling and inter-particle collisions. For the calculation of the particle motion, all relevant forces (drag, slip-shear and slip-rotational lift and gravity), inter-particle collisions and particle-rough wall collisions are considered. The agreement of the computations with the findings or earlier experiments are found to be satisfactory for mean and fluctuating velocities of both phases as well as for the normalized particle mass flux.