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.