A reactor is proposed for partial oxidations of a fluid reaction mixture in the presence of a heterogeneous particulate catalyst, comprising one or more cuboidal thermoplate modules (1) which are each formed from two or more rectangular thermoplates (2) arranged parallel to each other while in each case leaving a gap (3) which can be filled with the heterogeneous particulate catalyst and is flowed through by the fluid reaction mixture; the heat of reaction being absorbed by a heat carrier which flows through the thermoplates (2) and thus at least partly evaporates, and also having a predominantly cylindrical shell (4, 15, 16) which releases the pressure at the thermoplate modules, completely surrounds them and comprises a cylinder jacket (4) and hoods (15, 16) which seal it at both ends and whose longitudinal axis is aligned parallel to the plane of the thermoplates (2), and also having one or more sealing elements (7, 23) which are arranged in such a way that the fluid reaction mixture, apart from flowing through the reactor interior spaces bounded by the hoods (15, 16), only flows through the gap (3).