A reactor in the form of a cylinder or prism wherein the interior of the reactor is divided by a cylindrical or prismatic gastight housing G which is arranged in the longitudinal direction of the reactor into an inner region having one or more catalytically active zones, in which in each case a packing composed of monoliths stacked on top of one another, next to one another and behind one another and before each catalytically active zone in each case a mixing zone having solid internals are provided, and an outer region B arranged coaxially to the inner region A, wherein the inner region A is insulated from the outer region B of the reactor by means of a microporous high-performance insulation material having a thermal conductivity 1 at temperatures up to 700° C. of less than 0.05 W/m*K is proposed.