Discrete Element Method simulations were performed on a horizontally run annular shear cell in order to extract relevant dimensionless quantities necessary for a description of the granular rheology. The change from the usual upright orientation greatly increases the complexity of the equations governing the granular flow dynamics. Volume fraction and velocity distributions were extracted from the simulation outputs, to ultimately be used to calculate shear stress, pressure and power dissipation distributions within the horizontal shear cell. The volume fractions were found to follow a power law distribution within the band of sheared material, while the velocity followed an exponential in the sheared region. Additionally, a clear anisotropy in the velocity distributions exists, dependent on friction between particles and the applied shear rate. Analysis of this anisotropic behaviour resulted in the boundary condition of the velocity distribution at the shearing wall, along with a description of the behaviour of the shear band under differing applied shear rate and particle friction conditions. This simulation work can be used to control the wear patterns in horizontally stirred mills by tuning the shear rate and the material friction.