According to one or more embodiments presently disclosed, a method for processing a chemical stream may include contacting a feed stream with a catalyst in a reactor portion of a reactor system that includes a reactor portion and a catalyst processing portion. Contacting the feed stream with the catalyst may cause a reaction forming an effluent. The method may include separating the effluent stream from the catalyst, passing the catalyst to the catalyst processing portion, and processing the catalyst in the catalyst processing portion. Processing the catalyst may include passing the catalyst to a combustor, combusting a supplemental fuel stream in the combustor to heat the catalyst, and treating the heated catalyst with an oxygen-containing gas. The supplemental fuel stream may include at least 1 mol % of one or more hydrocarbons, and a weight ratio of catalyst to hydrocarbons in the combustor may be at least 300:1.