A process and apparatus for oxidizing components of a feed gas mixture in a heat regenerative reactor are provided. The heat regenerative reactor comprises a vessel having a two ends, the interior of which defines an unfired heat exchange/reaction zone containing a gas-permeable bed comprising heat exchange material in which the components of the feed gas mixture are oxidized. A gas handling system selectively introduces the feed gas mixture into one end of the vessel and discharges reacted gas through the other end of the vessel such that the direction of gas flow through the vessel may be reversed. At the time of flow reversal, a bypass system introduces the feed gas mixture into the vessel at a point intermediate the two ends of the vessel so that the feed gas mixture bypasses a portion of the gas-permeable bed. During bypass, a purging system purges unreacted feed gas mixture from the heat exchange/reaction zone. The process and apparatus described herein provides for continuous processing of the feed gas mixture while avoiding the discharge of unreacted feed gas at the time of flow reversal.