After desulfurizing a hydrocarbon feedstream using an alkali metal reagent, the hydrocarbon feedstream can include particles of spent alkali metal salts. The spent alkali metal salts can be separated from the hydrocarbon feedstream and regenerated to form an alkali metal reagent, such as a alkali hydroxide or alkali sulfide. The regeneration process can pass through an intermediate stage of forming an alkali carbonate by successive reactions with carbon dioxide and calcium oxide. The calcium oxide can also be regenerated.