Resonant tubes of a pulse combustor are immersed in a bed of solid particles in a reaction zone to provide indirect heat from the pulsating combustion gases to the solid particles of the bed. The bed is maintained in an agitated state by a gas or vapor flowing through the bed. Reactant materials are introduced into the agitated bed and undergo reaction at enhanced rates resulting from heat transfer coefficients at least about twice as high as those of steady flow combustors and an intense acoustic pressure level propagated from the pulsating combustor into the reaction zone. The apparatus is useful, for example, to steam reform heavy hydrocarbons and to gasify carbonaceous material, including biomass and black liquor to produce combustible gas at relatively low temperatures, with steam being usilized as the bed fluidizing medium. Black liquor gasification, utilizing sodium carbonate as bed solids, results in liquor energy and chemical content recovery without smelt production.