 # Scale-Up of a Batch Reactor Requires a Wolfram Notebook System

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This Demonstration shows the temperature-time behavior for an exothermic, liquid-phase, first-order reaction in a batch reactor that is scaled up geometrically. A cooling jacket around the reactor transfers heat to a heat transfer fluid. Use sliders to vary the temperature of the heat transfer fluid and the reactor height and diameter (diameter = height). As they increase, the (surface area for heat transfer)/volume decreases, and thus the maximum temperature increases. This shows why geometric scale-up is not appropriate for this system. Check "adiabatic" to view the temperature-time behavior for an adiabatic reactor; this behavior is independent of the reactor size.

Contributed by: Rachael L. Baumann (October 2013)
Additional contributions by: John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA

## Snapshots   ## 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: , ,

where us the reactor surface area ( ), is reactor volume ( ), and and are the height and diameter of the reactor where (cm).

Mass and energy balances are done to get the temperature of the reactor and moles in the reactor: , , , , ,

where are moles of (mol), is the concentration of ( ), the subscript refers to the initial condition, and are the reaction and cooling liquid temperatures (K), is time (min), is the rate of reaction ( ), is heat capacity of (J/[mol K]), is the heat of reaction (J/mol), is the heat transfer coefficient ( ), is the pre-exponential factor (1/min), is activation energy (J/mol), and is the ideal gas constant (J/[mol K]).

A screencast video at  shows how to use this Demonstration. A video at  shows a real-life example of the danger associated with the scale-up of a batch reactor.

References

 Scale-Up of a Batch Reactor. www.colorado.edu/learncheme/kinetics/BatchReactorScaleUp.html.

 Runaway: Explosion at T2 Laboratories [Video]. (Sept 21, 2009) www.youtube.com/watch?v=C561PCq5E1g.

## Permanent Citation

Rachael L. Baumann

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