A reactor and process for production of hydrogen gas from a carbon-containing fuel in a reaction that generates carbon dioxide is described. The carbon-containing fuel can be, for example, carbon monoxide, alcohols, oxygenates bio-oil, oil and hydrocarbons. In preferred embodiments, the reactor includes a monolithic structure form with an array of parallel flow channels. Methods of using the reactor are also described. In the reactor apparatus of the present invention, the catalytic reaction for hydrogen formation is conducted in conjunction with a carbonation reaction that removes carbon dioxide that is produced by the reactor. The carbonation reaction involves reaction of the carbon dioxide produced from the hydrogen formation reaction with metal oxide-based sorbents. The reactor apparatus can be periodically regenerated by regeneration of the sorbent. A carbon dioxide sorbent system comprising a solid sorbent and a eutectic, mixed alkali metal molten phase is also described.