A method of operating a catalytic steam-hydrocarbon reformer, the method comprising: introducing a reformer feed gas mixture comprising at least one hydrocarbon and steam into a catalyst-containing reformer tube in a reformer furnace, the reformer feed gas mixture having a hydrocarbon-based carbon flow rate, C, and a steam flow rate, S op, where the steam flow rate, S op, relative to the hydrocarbon-based carbon flow rate, C, in the reformer feed gas mixture can be changed, reacting the reformer feed gas mixture in a reforming reaction under reaction conditions effective to form a reformate comprising H 2, CO, CH 4, and H 2 O wherein the reformer feed gas mixture is reacted as a process gas in the catalyst-containing reformer tube, and withdrawing the reformate from the catalyst-containing tube; combusting a fuel (35, 82) with an oxidant gas in a combustion section of the reformer furnace external to the catalyst-containing reformer tube under conditions effective to combust the fuel (35, 82) to form a combustion product gas and generate heat to supply energy for reacting the reformer feed gas mixture inside the catalyst-containing reformer tube, and withdrawing the combustion product gas from the combustion section; determining a steam flow rate, S det, at which carbon forms on an inner wall segment of the catalyst-containing reformer tube at a first hydrogen production rate wherein determining the steam flow rate, S det, comprises: measuring a temperature of the process gas at a first location inside the catalyst-containing reformer tube proximate the inner wall segment; measuring a temperature on an outer wall of the catalyst-containing reformer tube at a second location proximate the inner wall segment; and evaluating the temperature of the process gas at the first location and the temperature on the outer wall at the second location for temperatures indicative of carbon formation on the inner wall segment of the catalyst-containing reformer tube wherein the temperatures indicative of carbon formation on the inner wall segment of the catalyst-containing reformer tube comprise a wall temperature exceeding a process gas temperature by greater than a selected difference while the process gas temperature is less than a selected value; and controlling the steam flow rate, S op, responsive to determining the steam flow rate, S det, at which carbon forms on the inner wall segment of the catalyst-containing reformer tube wherein the steam flow rate, S op, is controlled to be greater than the steam flow rate, S det, at which carbon forms on the inner wall segment of the catalyst-containing reformer tube so that less or no carbon is formed on the inner wall segment of the reformer tube at the steam flow rate, S op. introducing a reformer feed gas mixture comprising at least one hydrocarbon and steam into a catalyst-containing reformer tube in a reformer furnace, the reformer feed gas mixture having a hydrocarbon-based carbon flow rate, C, and a steam flow rate, S op, where the steam flow rate, S op, relative to the hydrocarbon-based carbon flow rate, C, in the reformer feed gas mixture can be changed, reacting the reformer feed gas mixture in a reforming reaction under reaction conditions effective to form a reformate comprising H 2, CO, CH 4, and H 2 O wherein the reformer feed gas mixture is reacted as a process gas in the catalyst-containing reformer tube, and withdrawing the reformate from the catalyst-containing tube; combusting a fuel (35, 82) with an oxidant gas in a combustion section of the reformer furnace external to the catalyst-containing reformer tube under conditions effective to combust the fuel (35, 82) to form a combustion product gas and generate heat to supply energy for reacting the reformer feed gas mixture inside the catalyst-containing reformer tube, and withdrawing the combustion product gas from the combustion section; determining a steam flow rate, S det, at which carbon forms on an inner wall segment of the catalyst-containing reformer tube at a first hydrogen production rate wherein determining the steam flow rate, S det, comprises: measuring a temperature of the process gas at a first location inside the catalyst-containing reformer tube proximate the inner wall segment; measuring a temperature on an outer wall of the catalyst-containing reformer tube at a second location proximate the inner wall segment; and evaluating the temperature of the process gas at the first location and the temperature on the outer wall at the second location for temperatures indicative of carbon formation on the inner wall segment of the catalyst-containing reformer tube wherein the temperatures indicative of carbon formation on the inner wall segment of the catalyst-containing reformer tube comprise a wall temperature exceeding a process gas temperature by greater than a selected difference while the process gas temperature is less than a selected value; and controlling the steam flow rate, S op, responsive to determining the steam flow rate, S det, at which carbon forms on the inner wall segment of the catalyst-containing reformer tube wherein the steam flow rate, S op, is controlled to be greater than the steam flow rate, S det, at which carbon forms on the inner wall segment of the catalyst-containing reformer tube so that less or no carbon is formed on the inner wall segment of the reformer tube at the steam flow rate, S op.