The loop reactor, in the form composed of several units, with feed and exit ports switching, is investigated for a reversible exothermic reaction like the synthesis of methanol. Unlike applications, of VOC combustion, which have been extensively investigated and experimentally tested, the maximal temperature here is limited by equilibrium conditions and the advantage gained is due to the effectively periodic boundary conditions that describe the system: due to the rotating nature of the system, the stream undergoes cooling as it leaves the system, which in turn yields increasing conversions at an extent that depends on the parameters. We show that the system exhibits the slow-switching asymptote and the complex many-domains pattern that was identified for the irreversible case. The dynamic features within these domains are analyzed. Conversions are comparable to those in the commercially applied reactor with interstage cooling. Control procedures are suggested and tested.