a multi - tubular reactor system for catalytically reacting a fluid reactant mixture to form a fluid product comprising a shell and a plurality of reactor tubes housed therein . the reactor system is adapted to allow heat - exchange fluid to flow between the shell and the external surface of the reactor tubes . a reactor tube comprises a reaction zone , and also a heating zone and / or a cooling zone . the reaction zone is positioned downstream of the heating zone . the cooling zone is positioned downstream of the reaction zone . the reactor tube contains a bed of solid particulate catalyst in the reaction zone . the reactor tube additionally contains a heat - exchanging essentially rod - shaped insert having a length of from 1 to 20 %, preferably 1 to 5 %, of the total length of the reactor tube in the heating zone and / or the cooling zone .