# Scale-Up of a Batch Reactor

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.

### 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 [1] shows how to use this Demonstration. A video at [2] shows a real-life example of the danger associated with the scale-up of a batch reactor.
References
[2] Runaway: Explosion at T2 Laboratories [Video]. (Sept 21, 2009) www.youtube.com/watch?v=C561PCq5E1g.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.