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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.  I need only a rough evaluation of the relation volume-flowrate at a certain P.

                   

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'd need to determine the conversion of methane in each of the above reactions. The upper limit of your flowrate is bound by the rate of reaction. If the flowrate is too high, the reaction simply won't take place (ie. the flame will burn out). I'm not sure that there is a simple relationship between pressure and flowrate 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 flowrate. I expect that the residence time for a combustion reaction of this sort would be very small, although I cannot find an estimate anywhere. I recommend contacting the following people who should certainly be of more assistance:

1. Combustion and Fuels Research Laboratory
Department of Mechanical Engineering
Texas A&M University
College Station, TX 77843-3123
(409) 845-4705

2. Naval Research Laboratory
Dr. Ronald S. Sheinson
Washington, DC 20375
(202) 404-8101
**Uses 28 m3, 56 m3, and 840 m3 fire test compartments

3. Dr. David T. Pratt
**Specializes in computational modeling of combustion processes
http://www.me.washington.edu/faculty/pratt.html

                Good Luck