Dimethyl ether is typically produced from synthesis gas by conversion to methanol and subsequent etherification. Compared to this classical approach, the direct synthesis has the advantage of higher equilibrium conversion and a simpler single-stage process. The heat release of the strongly exothermic reactions requires a careful thermal reactor design. Pure axial models are not sufficient, as they neglect the important radial heat transport resistance. Therefore, a 2D model including axial and radial gradients was implemented and used for design optimization.