How Do Levenspiel Plots Determine CSTR Volume for Increasing Reaction Rates?

[gfd43tg]

Hello,

I am having some difficulty with levenspiel plots, in particular when dealing with a CSTR and when the reaction rate is increasing with conversion. I will give an example plot to demonstrate my point.

Assume we are trying to find the volume of a CSTR necessary to reach a conversion of X = 0.5, with the levenspiel plot given below

What I wonder, is how do I figure out what area should be taken, and why? I initially thought it would be the one in green, but I am missing something important here as far as how to use the levenspiel plot. When it is the other way around (reaction rate is decreasing with temperature), I can figure it out usually, but I seem to be missing something subtle.

 

[gfd43tg]

This problem raises more questions yet still, what if X = 0.15? That is 0.15*400,000 = 60,000 m^3. Does that mean this reactor needs to be larger to have less conversion?

 

[Chestermiller]

Maybe this like will help: http://www.umich.edu/~elements/course/lectures/two/

 

[gfd43tg]

From that page, when it is normal plots (i.e. slope is up with X increases) I am good. It's only for the very specific case I gave that I am having some trouble. Why is it that it is the orange box, and not the green box for the area?

 

[Chestermiller]

From that page, when it is normal plots (i.e. slope is up with X increases) I am good. It's only for the very specific case I gave that I am having some trouble. Why is it that it is the orange box, and not the green box for the area?

You need to find $\frac{F}{-r}\times X$. Geometrically (on the graph), that's the area of the orange box.

Chet