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# Autothermal Reactor

In this autothermal reactor, an exothermic reaction takes place in a packed bed of catalyst (a plug flow tubular reactor). The feed gas enters an annular region around the packed bed, but flows in the opposite direction from that in the packed bed. Some energy from the reaction in the packed bed is removed by heat transfer through the reactor wall and preheats the gas in the annular region. The feed temperature, , is known, but the temperature at the entrance to the packed bed, , must be guessed in order to obtain initial conditions for the ODEs. This value is correct when the entrance temperature to the annular region equals ; this solution approach is known as a shooting method. In this Demonstration, a slider is used to change the value (the blue circle in the graph) until the correct value (the red circle in the graph) is obtained and the initial conditions are satisfied. The ODE for the annular region is solved by integrating against the direction of flow, and the signs in the ODE are adjusted accordingly. Two solutions are possible, one of which corresponds to essentially no reaction. Which solution is obtained depends on how the reactor is started up.

### DETAILS

Material balance on packed bed:
= cross sectional radius of reactor (m)
= concentration of A (mol )
= activation energy (J )
= molar flow rate of A (mol )
= inlet molar flow rate of A (mol )
= rate constant ()
= pre-exponential factor ()
= pressure (bar)
= ideal gas constant ()
= ideal gas constant (J )
= temperature (K)
= volumetric flow rate ()
Energy balance on packed bed:
= mass heat capacity ()
= heat of reaction ()
= heat transfer rate ()
= temperature in the annular region (K)
= feed temperature to reactor (K)
= feed temperature to packed bed (K)
= heat transfer coefficient (J )
Energy balance on annular region:
The sign of the heat transfer term in the annular region is negative because integration is opposite to the direction of flow.
For the solution in which the reaction rate is nonzero, the feed temperature in the annular region increases as the feed flows to the left and is heated by the packed bed. The temperature increases in the packed bed due to the exothermic reaction and some of the energy transfers to the feed gas in the annular region. As the reactant is used up, the temperature in the packed bed reaches a maximum and decreases as heat is transferred to the feed gas.
Reference
[1] J. G. Ekerdt and J. B. Rawlings, Chemical Reactor Analysis and Design Fundamentals, Madison, WI: Nob Hill Publishing, 2002 pp. 326–332.

### PERMANENT CITATION

(University of Colorado Boulder, Department of Chemical and Biological Engineering)
"Autothermal Reactor"
http://demonstrations.wolfram.com/AutothermalReactor/
Wolfram Demonstrations Project
Published: July 10, 2013
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