A system for modernizing exothermic heterogeneous reactors used in the synthesis of ammonia, methanol and the like, which include a pressure shell, a wall for forming an airspace, a wall or cartridge for containing a catalyst bed, and catalyst-containing basket. An airspace-forming wall is formed of a single piece substantially the whole axial length of the reactor. A bed forming wall is distinct from, and unconnected to, the airspace forming wall, and it constitutes independent modules, each module containing at least one catalyst bed and each module resting either on an underlying module or on an extension of an inside gas distribution collector. The bed forming walls contain the catalyst and distribute gas therethrough. A portion of the catalyst contacts the airspace-forming wall.