Methods and apparatus relate to both generating steam for injection into a wellbore and capturing carbon dioxide (CO2) produced when generating the steam. A direct steam generator (DSG) makes the steam by contacting water with a combustion area for hydrogen and oxygen. Quantity of the steam made exceeds quantity of water input into the steam generator since the steam includes vaporized water resulting from combustion of the hydrogen and oxygen mixed with the water inputted and heated. Steam-methane-reforming or autothermal-reforming produces the hydrogen stripped of the CO2 prior to introduction into the steam generator. Further, an air separation unit supplies the oxygen to the steam generator.