There are presented the results of simulations concerning reverse-flow reactors for the catalytic combustion of methane present in mine ventilation air, with two modes of the recovery of the heat of reaction. The objective of the simulations was to find such a method for cooling the reaction gases that would make it possible to recover the maximum amount of the heat via production of high-pressure steam during stable operation of the reactor. The simulations revealed that these requirements are met only by withdrawing some 30% of the reaction gas from the central part of the reactor and feeding it to a boiler in which the gas undergoes cooling to about 473 K.