A reactor for performing a reaction between two immiscible fluids of different density, comprising an interior formed by a cylindrical, vertically oriented elongate shell, a bottom and a cap, wherein the interior is divided by internals into a backmixed zone, a zone of limited backmixing preferably arranged below the backmixed zone and a plug-flow zone which are at least consecutively traversable by one of the fluids, wherein the backmixed zone comprises at least one inlet and the plug-flow zone comprises an outlet and the backmixed zone comprises at least one mixing apparatus selected from a stirrer, a jet nozzle and means for injecting the fluid of lower density, a first cylindrical internal element which in the interior extends in the longitudinal direction of the reactor, which delimits the zone of limited backmixing from the plug-flow zone and which comprises a first passage to the backmixed zone and a second passage to the plug-flow zone, a second internal element which delimits the backmixed zone from the plug-flow zone such that there is no direct fluid connection between the backmixed zone and the plug-flow zone, and backmixing-preventing third internal elements in the form of random packings, structured packings or liquid-permeable trays arranged in the zone of limited backmixing. The reactor allows an optimal residence time distribution in the reaction of the two immiscible fluids of different density. The invention further relates to a process for performing a continuous reaction in the reactor.