Concurrent and Countercurrent Cooling in Tubular Reactors with Exothermic Chemical Reactions

The object of this Demonstration is to observe thermal runaway in a tubular reactor and identify the critical parameters that represent the crossover from a thermally well-behaved reactor to one that exhibits thermal runaway.
Consider a chemical reactant that is converted irreversibly and exothermically to products in a tubular catalytic reactor. The reactive mixture in the inner pipe flows from left to right and is cooled using a concentric double-pipe heat exchanger. The cooling fluid in the annular region can flow either concurrently or countercurrently with respect to the reactive fluid.

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DETAILS

Mass balance for reactant :
,
where is the initial concentration of , is the dimensionless variable, (s) is the residence time of the reactive fluid, stands for the pre-exponential rate factor , is the activation energy , is the gas constant , and is the temperature of the reactants .
Thermal balance for reactive fluid within the inner pipe:
,
where is the average reactants density , is the heat capacity , is the inner pipe overall heat transfer coefficient , is the radius for the inner pipe , is the coolant temperature , and is the heat of reaction .
Thermal balance for concurrent cooling fluid in the annulus:
.
The equation for countercurrent cooling differs from the above equation by a negative sign because integration is opposite to the direction of flow. Here is the coolant density , is the coolant heat capacity , is the ratio of the velocity of the coolant to reactant fluid, is the outer pipe overall heat transfer coefficient , is the radius of the outer pipe , is the ratio , and is the ambient temperature .
This split boundary value problem is solved with:
, .
, , , , , and ,
with user-selected direction of coolant and values of , and .
Reference
[1] L. A. Belfiore, Transport Phenomena for Chemical Reactor Design, Hoboken, NJ: John Wiley & Sons, 2003.
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