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# Scale-Up of a Batch Reactor

This Demonstration shows why a batch reactor with a cooling jacket cannot be scaled up geometrically. That is, as the diameter and height of the reactor increases, the surface area for heat transfer divided by the volume decreases, and thus the maximum temperature increases.
This example is for an exothermic, liquid-phase, first-order reaction. The diameter and height of the reactor are equal. A cooling jacket around the outside of the reactor transfers heat away from the reactor. As the reactor size increases, the maximum temperature approaches the adiabatic limit. Adiabatic reactor behavior is shown by selecting the adiabatic checkbox. This is independent of the reactor size.

### DETAILS

In this Demonstration, the height of the batch reactor is equal to the inner diameter, so reactor volume and surface area can be simplified to
,
,
,
,
.
Mass and energy balances:
surface area for heat transfer ()
height (and diameter) of reactor (cm)
volume of reactor ()
rate of reaction (mol )
pre-exponential factor ()
activation energy (J )
ideal gas constant (J )
temperature of reaction (K)
concentration of reactant (mol )
initial reactant concentration (mol )
moles of reactant (mol)
moles of reactant initially (mol)
heat capacity of (J )
heat of reaction (J )
heat transfer coefficient (J )
temperature of cooling liquid (K)

### PERMANENT CITATION

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