**Concurrent and Countercurrent Cooling in Tubular Reactors with Exothermic Chemical Reactions**

Prepared by: C. Gruesbeck

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. Download the CDF file to view the simulation using the free Wolfram CDF player. |

**Details**

Mass balance for A:

where ρ is the average reactants density (kg/m

^{3}), C_{p}is the heat capacity (kg m^{2}/K s), U_{i}is the inner pipe overall heat transfer coefficient (kcal/m^{2}s K), R_{i}is the radius for the inner pipe (m), T_{c}is the coolant temperature (K), and ΔH is the heat of reaction (kcal/mol).Thermal balance for concurrent cooling fluid in 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 ρ

_{c}is the coolant density (kg/m^{3}), C_{PC}is the coolant heat capacity (kg m^{2}/K s), ψ is the ratio of the velocity of the coolant to the reactant fluid, U_{o}is the outer pipe overall heat transfer coefficient (kcal/m^{2}s K), R_{o}is the radius of the outer pipe (m), κ is the ratio R_{i}/R_{o}, and T_{a}is the ambient temperature (K).This split boundary value problem is solved with:

with user-selected direction of coolant and values of TC, ψ, and κ.