A reactor for partial oxidations of a fluid reaction mixture in the presence of a heterogeneous particulate catalyst, comprising - one or more cuboidal thermoplate modules which are each formed from two or more rectangular thermoplates arranged parallel to each other while in each case leaving a gap 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 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 and hoods (15, 16) which seal it at both ends and whose longitudinal axis is aligned parallel to the plane of the thermoplates, 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 - wherein a gas pressure is applied to the intermediate space between the thermoplate modules and the predominantly cylindrical shell, in that the pressure applied is constant and is effected by pressure-regulated feed and removal of nitrogen or in that the pressure is applied with continuous feeding of a gas which is inert or intrinsic to the process, in particular nitrogen or cycle gas, through the intermediate space, - or wherein, in addition to the application of pressure, the intermediate space between the thermoplate modules and the predominantly cylindrical shell is filled with an inert bulk material composed of a chemically inert material of sufficient mechanical and thermal stability, - wherein, for application of pressure, appropriate nozzles and/or an internal ring line having small drillholes that are preferably directed downward is provided, and wherein the intermediate space between the thermoplate modules and the shell is sealed at the upper end of the thermoplate modules by a sheet metal cover having orifices or a sheet metal cover similar to a valve tray. - one or more cuboidal thermoplate modules which are each formed from two or more rectangular thermoplates arranged parallel to each other while in each case leaving a gap 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 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 and hoods (15, 16) which seal it at both ends and whose longitudinal axis is aligned parallel to the plane of the thermoplates, 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 - wherein a gas pressure is applied to the intermediate space between the thermoplate modules and the predominantly cylindrical shell, in that the pressure applied is constant and is effected by pressure-regulated feed and removal of nitrogen or in that the pressure is applied with continuous feeding of a gas which is inert or intrinsic to the process, in particular nitrogen or cycle gas, through the intermediate space, - or wherein, in addition to the application of pressure, the intermediate space between the thermoplate modules and the predominantly cylindrical shell is filled with an inert bulk material composed of a chemically inert material of sufficient mechanical and thermal stability, - wherein, for application of pressure, appropriate nozzles and/or an internal ring line having small drillholes that are preferably directed downward is provided, and wherein the intermediate space between the thermoplate modules and the shell is sealed at the upper end of the thermoplate modules by a sheet metal cover having orifices or a sheet metal cover similar to a valve tray.