Concurrent and Countercurrent Cooling in Tubular Reactors with Exothermic Chemical Reactions

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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.
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Contributed by: Clay Gruesbeck (March 2017)
Open content licensed under CC BY-NC-SA
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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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