COREX is a promising alternative to blast furnace ironmaking. It includes two main reactors: a reduction shaft (RS) for the direct reduction of iron ore and a melter gasifier for the melting reduction of directly reduced iron. This work uses a two-dimensional slot model to investigate the gas-solid flow in the RS by a combined computational fluid dynamics and discrete element method approach. The three-dimensional flow of cohesive solids is then examined for three RS designs by the discrete element method. The effects of gas flow, the stickiness between particles, the rotational speed of screws, and different designs are depicted in terms of gas-solid flow pattern, overall bed pressure drop and solid flowrate. The results show that the effect of gas flow is insignificant on gas-solid flow pattern due to the small gas-solid interaction forces under the considered conditions. Solid flow varies in a complex manner with the rotational speed of screws and the sticking force, and a correlation is formulated for predicting the solid flowrate based on the simulated results. It is also shown that the effect of geometrical design on solid flow is complicated and significant. Caution should be taken for any changes in the design. The findings should be useful for the design, control and optimization of the RS operation.