Method and system for preparing dimethyl ether

The invention relates to a method for synthesizing dimethyl ether, in which a feed gas mixture (E) containing carbon dioxide and/or carbon monoxide and hydrogen is conducted through a reaction tube (1) of a cooled shell-and-tube reactor (10), said reaction tube being equipped with a first catalyst and a second catalyst, wherein the carbon dioxide present in the feed gas mixture (E) and/or the carbon monoxide present in the feed gas mixture (E) is at least partially reacted over the first catalyst with the hydrogen present in the feed gas mixture to obtain methanol, and wherein in the same shell and tube reactor (10), the methanol is at least partially converted to dimethyl ether over the second catalyst. It is envisaged that the reaction tubes (1) are equipped with the first and second catalysts in the form of a structured bed, where the structured bed has two to four zones (11, 12, 13), where the first and second catalysts are provided in different physical mixtures, where the zones (11, 12, 13) are arranged