An exothermic gas atmosphere can prevent surface oxidation during the heat treatment of metals. This column shows how to calculate the composition of an exothermic atmosphere in each stage of preparation and the atmosphere’s oxidation potential with respect to iron. Details are shown in downloadable Excel workbook ExoCalc.xlsx.


    Equation 1 shows the methane combustion reaction with less than stoichiometric air. The value of X must be such that the reaction heat is sufficient to sustain a chamber temperature between 1000˚C and 1400˚C (1800-2600˚F). The evolution of heat produced for this purpose accounts for the name “exothermic” applied to this class of atmospheres.[1,2]


          CH4 + XO2 +3.76XN2 ® MCO + DCO2 + YH2 + WH2O + 3.76XN2    [1]

    The composition of the combusted gas mixture can be calculated by a material balance plus the equilibrium constant of equation 2, the water-gas shift (WGS) reaction:


                        CO2 + H2 ® CO + H2O; Kequil = M´W  [2]


Exothermic Atmosphere Generation

An exothermic gas generator burns natural gas (NG) in the presence of a catalyst to a near-equilibrium condition, thereby consuming all of the oxygen and virtually all of the CH4. The hot gas is tempered by cooling it to remove most of the water vapor. Figure 1 illustrates the flow diagram. Exothermic atmospheres are classified as “lean” when produced at air/NG ratios between about 85% and 95% of stoichiometric and “rich” when the air/NG ratio is between about 50% and 85% of stoichiometric.


Calculational Procedure

The example here is for a rich atmosphere that is burning methane with 57% of the stoichiometric air (air/CH4 molar ratio of 5.43) at 1120˚C (2048˚F). The exogas is prepared by condensing water from the hot gas at 20˚C, then using it to anneal steel at 1050˚C (1922˚F). Here’s how to calculate the furnace atmosphere’s composition and its tendency to oxidize steel.

    First, use the FREED database[3] to obtain equations for heat content, dew point, log Kequil and DH°form of substances at 25˚C. This is the same procedure used in previous “Combustion Concepts[4,5]” columns.

    Next, write a material balance and set up an equilibrium relationship. There are four unknowns (M, D, Y and X), so we need four equations. Equation 1 stoichiometry gives: M + D = 1, W + Y = 2 and M + 2D + W = 2X = 0.21(5.43) = 1.14. Equation 2 equilibrates the four gas species according to the value of Kequil for the WGS.

    Workbook ExoCalc, which can be found on our website at, shows how to solve these four equations to give the hot gas composition at 1120˚C. Cooling the hot gas to 20˚C (pH2O = 0.0226 atm) removes 0.825 moles of water, lowering the value of W to 0.146. Heating the exogas in the heat-treat furnace re-equilibrates the gas via the WGS. Table 1 shows the furnace gas and exogas composition.

    Equation 3 expresses the oxidizing potential of the exogas (oxygen partial pressure, or pO2). Equation 4 shows iron’s oxidation tendency by the pO2 for iron/wustite equilibrium. Table 2 shows the oxidation situation for the hot burner and exogas conditions.


        2CO2 ® 2CO + O2; pO2=Kequil ´ (pCO2)2            [3]




        2Fe.947O ® 1.894Fe(aust) + O2; pO2 = Kequil                  [4]


1. ASM Committee on Furnace Atmospheres, Furnace Atmospheres and Carbon Control, Metals Park, Ohio [1964].

2. Neményi, Rezso, Controlled Atmospheres for Heat Treatment, edited by G.H.J. Bennett; [translated from the Hungarian by B. Gebora], Pergamon Press, [1984].


4. Arthur Morris, “Calculating the Heat of Combustion of Natural Gas,” Industrial Heating, September 2012.

5. Arthur Morris, “Making a Heat Balance,” Industrial Heating, December 2012.