A process for producing a hydrogen-containing product and a steam product, the process comprising: (a) introducing a reformer feed gas mixture into a plurality of catalyst-containing reformer tubes in a reformer furnace, reacting the reformer feed gas mixture in a reforming reaction to form a reformate comprising H 2, CO, CH 4, and H 2 O, and withdrawing the reformate from the plurality of catalyst-containing tubes; (b) combusting a fuel with a heated oxidant gas in a combustion section of the reformer furnace external to the plurality of catalyst-containing reformer tubes to form a combustion product gas and generate heat to supply energy for reacting the reformer feed gas mixture inside the plurality of catalyst-containing reformer tubes, and withdrawing the combustion product gas from the combustion section; (c) heating an oxidant gas by indirect heat transfer with the combustion product gas from the combustion section thereby forming the heated oxidant gas and cooling the combustion product gas; (d) heating a first water feed stream by indirect heat transfer with the combustion product gas thereby further cooling the combustion product gas, wherein heat is extracted from the combustion product gas to heat the oxidant gas prior to extracting heat from the combustion product gas to heat the first water feed stream; (e) heating a second water feed stream by indirect heat transfer with the reformate withdrawn from the plurality of catalyst-containing tubes; (f) passing the first water feed stream and the second water feed stream to a deaerator, the first water feed stream being passed to the deaerator after being heated by the combustion product gas, the second water feed stream being passed to the deaerator after being heated by the reformate, introducing steam into the deaerator or forming steam in-situ by heating or flashing, stripping dissolved gases from the first water feed stream and from the second water feed stream in the deaerator, withdrawing a vent stream from the deaerator, the vent stream comprising steam and gases formed from the dissolved gases stripped from the first water feed stream and from the second water feed stream, and withdrawing a boiler feed water stream from the deaerator, the boiler feed water stream comprising at least a portion of the first water feed stream and at least a portion of the second water feed stream; (g) forming the hydrogen-containing product from the reformate after the reformate has heated the second water feed stream; and (h) forming the steam product from at least a portion of the boiler feed water stream withdrawn from the deaerator. (a) introducing a reformer feed gas mixture into a plurality of catalyst-containing reformer tubes in a reformer furnace, reacting the reformer feed gas mixture in a reforming reaction to form a reformate comprising H 2, CO, CH 4, and H 2 O, and withdrawing the reformate from the plurality of catalyst-containing tubes; (b) combusting a fuel with a heated oxidant gas in a combustion section of the reformer furnace external to the plurality of catalyst-containing reformer tubes to form a combustion product gas and generate heat to supply energy for reacting the reformer feed gas mixture inside the plurality of catalyst-containing reformer tubes, and withdrawing the combustion product gas from the combustion section; (c) heating an oxidant gas by indirect heat transfer with the combustion product gas from the combustion section thereby forming the heated oxidant gas and cooling the combustion product gas; (d) heating a first water feed stream by indirect heat transfer with the combustion product gas thereby further cooling the combustion product gas, wherein heat is extracted from the combustion product gas to heat the oxidant gas prior to extracting heat from the combustion product gas to heat the first water feed stream; (e) heating a second water feed stream by indirect heat transfer with the reformate withdrawn from the plurality of catalyst-containing tubes; (f) passing the first water feed stream and the second water feed stream to a deaerator, the first water feed stream being passed to the deaerator after being heated by the combustion product gas, the second water feed stream being passed to the deaerator after being heated by the reformate, introducing steam into the deaerator or forming steam in-situ by heating or flashing, stripping dissolved gases from the first water feed stream and from the second water feed stream in the deaerator, withdrawing a vent stream from the deaerator, the vent stream comprising steam and gases formed from the dissolved gases stripped from the first water feed stream and from the second water feed stream, and withdrawing a boiler feed water stream from the deaerator, the boiler feed water stream comprising at least a portion of the first water feed stream and at least a portion of the second water feed stream; (g) forming the hydrogen-containing product from the reformate after the reformate has heated the second water feed stream; and (h) forming the steam product from at least a portion of the boiler feed water stream withdrawn from the deaerator.