Catalytic reactor having a shell which extends about a reactor centre axis and having at least one reactor module (A, B) which comprises a gas distribution chamber connected to a shell-side gas feed, a gas collection chamber connected to a shell-side gas discharge, and, between the gas distribution chamber and the gas collection chamber, a catalyst bed which extends transversely to the reactor centre axis, wherein the gas distribution chamber and the gas collection chamber are each bounded by the catalyst bed and an associated reactor wall (8a, 8b), wherein the gas feed either - opens into the gas distribution chamber on the shell side, or - is connected to a pipe length which extends towards the reactor centre axis and opens into the gas distribution chamber in the region of the reactor centre axis, wherein a height (h), determined parallel to the reactor centre axis, of the gas distribution chamber reduces towards the reactor centre axis starting from a mouth of the gas feed in the case of a shell-side connection or reduces towards the shell starting from the pipe length which opens into the region of the reactor centre axis, and in that the gas discharge either - opens into the gas collection chamber on the shell side or - is connected to a pipe length which extends towards the reactor centre axis and opens into the gas collection chamber in the region of the reactor centre axis, wherein a height (h), determined parallel to the reactor centre axis, of the gas collection chamber reduces towards the reactor centre axis starting from a mouth of the gas discharge in the case of a shell-side connection or reduces towards the shell starting from the pipe length which opens into the region of the reactor centre axis, characterized in that - the reactor module as a module which receives inflow on the shell side is constructed such that the height (h), determined parallel to the reactor centre axis, of the gas distribution chamber and of the gas collection chamber reduces towards the reactor centre axis starting from the shell and the reactor walls (8a, 8b) which are arranged on both sides of the catalyst bed of the module which receives inflow on the shell side have a concave shape, in particular a conical shape, starting from the reactor centre axis, in relation to the catalyst bed, or the reactor module as a module which receives central inflow is constructed such that a pipe length (9a, 9b) which extends towards the reactor centre axis and respectively opens into the gas distribution chamber and the gas collection chamber in the region of the reactor centre axis in each case adjoins the shell-side gas feed and the shell-side gas discharge, wherein the height (h), determined along the reactor centre axis of the gas distribution chamber and of the gas collection chamber reduces towards the shell starting from the reactor centre axis and the reactor walls (8a, 8b) which are arranged on both sides of the catalyst bed of the module which receives inflow on the shell side have a convex shape, in particular a conical shape, starting from the reactor centre axis, in relation to the catalyst bed. - opens into the gas distribution chamber on the shell side, or - is connected to a pipe length which extends towards the reactor centre axis and opens into the gas distribution chamber in the region of the reactor centre axis, - opens into the gas collection chamber on the shell side or - is connected to a pipe length which extends towards the reactor centre axis and opens into the gas collection chamber in the region of the reactor centre axis, - the reactor module as a module which receives inflow on the shell side is constructed such that the height (h), determined parallel to the reactor centre axis, of the gas distribution chamber and of the gas collection chamber reduces towards the reactor centre axis starting from the shell and the reactor walls (8a, 8b) which are arranged on both sides of the catalyst bed of the module which receives inflow on the shell side have a concave shape, in particular a conical shape, starting from the reactor centre axis, in relation to the catalyst bed,