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⟩ I would like to know how to size a partial combustion reactor processing methane and oxygen, as a function of the flowrate and of the pressure.

In your case, you essentially have two reactions: CH4 + 3/2 O2 ---> CO + 2 H2O (incomplete combustion) CH4 + 2 O2 ---> CO2 + 2 H2O (complete combustion) each of these reactions has a specific rate at which it occurs. If you wanted to design a reactor properly, you would need to determine the conversion of methane in each of the above reactions. The upper limit of your flow rate is bound by the rate of reaction. If the flow rate is too high, the reaction simply will not take place (i.e. the flame will burn out). I am not sure that there is a simple relationship between pressure and flow rate in this case. The gases need to spend a certain amount of time in the reactor in order for the combustion to take place (residence time). Once you know the residence time, you could design a reactor for your specific flow rate.

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