A regeneratively cooled fixed bed reactor, shown in Figure 1, consists of two sections alternating roles as reactor and heat regenerator by periodic flow reversals. The reactor can have any desired diameter because the cooling "Occurs strictly by regeneration. The system possesses four control variables that can be adjusted for optimal operation. The first is the temperature profile in the reacting section at the beginning of each cycle and is implemented during regeneration. The second is the temperature of the feed to the reacting section as a function of time. The third is the catalyst activity profile and can be implemented by mixing the catalyst with an inert solid. The last is the period of cycling, that is, the time interval between flow reversals. These four variables are not available in steady state designs.