A process for producing a hydrogen-containing product gas comprising: (a) introducing a process stream comprising steam and at least one hydrocarbon selected from the group consisting of methane, ethane, propane, butane, pentane and hexane into a first reactor containing a first reforming catalyst, the process stream having an initial molar flow rate of steam, F s, and a initial molar flow rate of hydrocarbon-based carbon, F C, the steam being provided in the process stream, in one or more steam-containing streams, or in a combination of the process stream and the one or more steam-containing streams, to provide a steam-to-carbon molar ratio, S/C, of between 1.5 and 2.4; (b) introducing the one or more steam-containing streams (20, 22, 24), when present, into the process stream (12, 14, 16), the one or more steam-containing streams (20, 22, 24) having a molar flow rate of steam, W s, ranging from 0 to 5 F s, and having a molar flow rate of methane-based carbon, W c, ranging from 0 to 1 F c to provide the steam-to-carbon molar ratio, S/C, where S C = F s + W s F C + W C (c) reacting the at least one hydrocarbon and steam in the process stream in the presence of the first reforming catalyst under adiabatic conditions at a first temperature ranging from 425°C to 600°C and a first pressure ranging from 5 to 55 atmospheres to form reaction products comprising hydrogen and carbon dioxide in the process stream; (d) heating the process stream to a second temperature ranging from 425°C to 730°C; (e) reacting methane and steam in the process stream (12, 14) in the presence of a second reforming catalyst in a second reactor at the second temperature ranging from 425°C to 730°C and a second pressure ranging from 4 to 55 atmospheres to form additional reaction products comprising hydrogen and carbon dioxide in the process stream; (f) withdrawing the process stream from the second reactor at an exit temperature ranging from 510°C to 730°C; (g) subsequent to withdrawing the process stream from the second reactor, introducing the process stream comprising methane and steam into a plurality of catalyst-containing reformer tubes in a reformer furnace having a ceiling, a floor and side walls, and reacting methane and steam in the process stream inside the plurality of catalyst-containing reformer tubes at a third temperature ranging from 500°C to 1000°C and a third pressure ranging from 2 to 50 atmospheres to form the hydrogen-containing product gas; and (h) combusting a fuel gas in the reformer furnace external to the plurality of catalyst-containing reformer tubes by introducing the fuel gas and an oxidant gas through burners mounted in the ceiling of the reformer furnace to supply energy for reacting methane and steam inside the plurality of catalyst-containing reformer tubes, and withdrawing a flue gas from the reformer furnace. (a) introducing a process stream comprising steam and at least one hydrocarbon selected from the group consisting of methane, ethane, propane, butane, pentane and hexane into a first reactor containing a first reforming catalyst, the process stream having an initial molar flow rate of steam, F s, and a initial molar flow rate of hydrocarbon-based carbon, F C, the steam being provided in the process stream, in one or more steam-containing streams, or in a combination of the process stream and the one or more steam-containing streams, to provide a steam-to-carbon molar ratio, S/C, of between 1.5 and 2.4; (b) introducing the one or more steam-containing streams (20, 22, 24), when present, into the process stream (12, 14, 16), the one or more steam-containing streams (20, 22, 24) having a molar flow rate of steam, W s, ranging from 0 to 5 F s, and having a molar flow rate of methane-based carbon, W c, ranging from 0 to 1 F c to provide the steam-to-carbon molar ratio, S/C, where S C = F s + W s F C + W C (c) reacting the at least one hydrocarbon and steam in the process stream in the presence of the first reforming catalyst under adiabatic conditions at a first temperature ranging from 425°C to 600°C and a first pressure ranging from 5 to 55 atmospheres to form reaction products comprising hydrogen and carbon dioxide in the process stream; (d) heating the process stream to a second temperature ranging from 425°C to 730°C; (e) reacting methane and steam in the process stream (12, 14) in the presence of a second reforming catalyst in a second reactor at the second temperature ranging from 425°C to 730°C and a second pressure ranging from 4 to 55 atmospheres to form additional reaction products comprising hydrogen and carbon dioxide in the process stream; (f) withdrawing the process stream from the second reactor at an exit temperature ranging from 510°C to 730°C; (g) subsequent to withdrawing the process stream from the second reactor, introducing the process stream comprising methane and steam into a plurality of catalyst-containing reformer tubes in a reformer furnace having a ceiling, a floor and side walls, and reacting methane and steam in the process stream inside the plurality of catalyst-containing reformer tubes at a third temperature ranging from 500°C to 1000°C and a third pressure ranging from 2 to 50 atmospheres to form the hydrogen-containing product gas; and (h) combusting a fuel gas in the reformer furnace external to the plurality of catalyst-containing reformer tubes by introducing the fuel gas and an oxidant gas through burners mounted in the ceiling of the reformer furnace to supply energy for reacting methane and steam inside the plurality of catalyst-containing reformer tubes, and withdrawing a flue gas from the reformer furnace.