NOVELTY - The process comprises introducing a process stream (10) comprising steam and a hydrocarbon into catalyst-containing reformer tubes (104) in a reformer furnace and then reacting the process stream inside the catalyst-containing reformer tubes at a first temperature of 700-1000 degrees C and a first pressure of 2-50 atmospheres to form a reformate stream (12) comprising hydrogen, carbon monoxide, methane and steam and withdrawing the reformate stream from the reformer tubes, and introducing a feed gas comprising a hydrocarbon and optionally steam into the reformate stream.    USE - The process is useful for producing a hydrogen-containing product gas, which is useful as a fuel in a reformer furnace.    ADVANTAGE - The process is capable of energy-efficiently producing the hydrogen-containing product gas with large-scale, reduced carbon dioxide emissions, improved thermal efficiency, high purity and increased throughput.    DETAILED DESCRIPTION - The process comprises introducing a process stream (10) comprising steam and a hydrocarbon into catalyst-containing reformer tubes (104) in a reformer furnace and then reacting the process stream inside the catalyst-containing reformer tubes at a first temperature of 700-1000 degrees C and a first pressure of 2-50 atmospheres to form a reformate stream (12) comprising hydrogen, carbon monoxide, methane and steam and withdrawing the reformate stream from the reformer tubes, introducing a feed gas comprising a hydrocarbon and optionally steam into the reformate stream, introducing an oxygen-rich gas into the reformate stream to partially oxidize the reformate stream, reacting the partially oxidized reformate stream in the presence of a reforming catalyst in a secondary reforming reactor under reaction conditions sufficient to form reaction products comprising carbon monoxide and hydrogen in the reformate stream, reacting the reformate stream in the presence of a shift catalyst at a second temperature of 200-400 degrees C and a second pressure of 2-50 atmospheres to form a second process stream (42) comprising carbon dioxide, hydrogen, carbon monoxide and methane, reacting the second process stream in the presence of a second shift catalyst at a fourth temperature of 190-300 degrees C and a fourth pressure of 2-50 atmospheres to form carbon dioxide and hydrogen in the second process stream, scrubbing the second process stream with a wash stream (64) to form a carbon dioxide-depleted stream (62) and a carbon dioxide-loaded wash stream, separating the carbon dioxide-depleted stream to form the hydrogen-containing product gas and a by-product gas (50-98 vol.%) comprising methane and carbon monoxide, introducing a portion of the by-product gas into the process stream at a location upstream of the catalyst-containing reformer tubes and/or into the reformate stream at a location upstream of the reforming catalyst in the secondary reforming reactor, combusting a fuel gas comprising 30-98 vol.% of a hydrogen-containing product gas, optionally 2-70 vol.% of a by-product gas and optionally a supplementary fuel in the reformer furnace external to the catalyst-containing reformer tubes to supply energy for reacting the process stream inside the catalyst-containing reformer tubes and then withdrawing a flue gas from the reformer furnace, and reacting the process stream in the presence of a second reforming catalyst in an unfired reactor at a third temperature of 425-600 degrees C and a third pressure of 2-50 atmospheres to form carbon dioxide and hydrogen in the process stream before introduction of the process stream. The portion of the by-product gas is introduced into the process stream upstream of the unfired reactor, and is introduced into the reformate stream at the location upstream of the secondary reforming reactor.    DESCRIPTION OF DRAWING(S) - The figure shows a flow diagram of a process for producing a hydrogen-containing product gas.    Process stream (10)    Reformate stream (12)    Second process stream (42)    Carbon dioxide-depleted stream (62)    Wash stream (64)    Catalyst-containing reformer tube. (104)