Solving a CFSTR Pesticide Problem

[Bradracer18]

Homework Statement

This is for one of my engineering classes. I missed class due to sickness, and can't figure out how to even begin this problem. No numbers are present, so I'm confused. Here is the problem:

Problem 1 (7 points). A conservative (non-reactive) pesticide is injected into the input flow of a CFSTR on continuous basis, beginning at time t = 0 and resulting in a constant input concentration of pesticide = Cin.

(a) Determine C, the reactor output concentration of this pesticide, as a function of time, and

(b) plot the pesticide output response curve (i.e., reactor output (C/Cin) versus the hydraulic residence time. Use C/Cin scale from 0 to 1 and HRT scale from 0 to 10.

(C) What is the ratio of C/Cin for 1 HRT?

(d) How many HRTs are required to reach 95% of input concentration at the reactor output?

(e) How many HRTs are required to reach 99% of input concentration at the reactor output?


---I think it is actually CSTR(continuous Flow/Stiring). The problem is also about mass balance, if that helps.


I understand that these reactors have inflow and outflow(equal I think). They are considered instantaneous and perfect in mixing.

Homework Equations

I understand that these reactors have inflow and outflow(equal I think). They are considered instantaneous and perfect in mixing.

The Attempt at a Solution

I'm not sure if this is even relevant, but in an example problem we showed that C = constant = dC/dt = 0.

Thank you for the help.
Brad

 

[Bradracer18]

Anyone know about these? Any help to get started would be very benificial...or the equations...

 

[berkeman]

As I said in my message to you, it would be helpful if you could give more details about which class this problem is from, and what field of study it pertains to. You are using some acronyms and terms that are probably not familiar to many who have read your post, but if I/we knew more about the subject area, we could ask around to try to find someone who can be of help.

 

[berkeman]

As I said in my message to you, it would be helpful if you could give more details about which class this problem is from, and what field of study it pertains to. You are using some acronyms and terms that are probably not familiar to many who have read your post, but if I/we knew more about the subject area, we could ask around to try to find someone who can be of help.

Oops, I see a couple details that I missed before. I'll try pinging a couple folks elsewhere on the PF to see if they might have any ideas.

 

[Bradracer18]

Thank you Berkeman. I'm very grateful.

This is for an Ag. Engineering class. We do things like figure the "R" value for walls/windows(and other building materials), and now this is a new subject matter. I believe it can be about anything. Some examples were stirring paint, water softener, etc.

Thank you again!
Brad

 

[Integral]

It seems to me that this should be a pretty straight forward DE. You have a constant concentration being fed in so your concentration should be changing at a constant rate.

This would mean something like:

$$\frac {dC} {dt} = kC_{in}$$

Is there any meaning with the term CSTR? Do you have any special knowledge of how this type of reactor function? How does it modify the input? I cannot answer these questions and they may have a big impact on the governing equations.

 

[Bradracer18]

I'm not sure of the right answers to your questions. I think you are right, on your formula. We have something similar in a practice problem, which he did in class.

CSTR = Continuous Flow and Continuous Stirring

I'm pretty sure they are supposed to be "perfect" in that they are always stirring and the Q(flow) in = Qout.

HRT I found to be "mean hydraulic residence time

HRT = V/Q (v = volume).

Not sure if this helps. If not, I can always just ask in class, and turn in late. I will not miss class again, I sure know this...sick or not!

Thank you!

 

[Integral]

What is your Q?

After making my first post I realized that a closer approximation to your DE will be:

$$\frac {dC} {dt} = C_{in} - C_{out}(t)$$

Note that I say that this is an approximation. It cannot be right because the way I have it written here the units are not correct. The LHS is C/t and the RHS is concentration. You need to sort that out. That is the reason for the k in my first post.

edit: Oops I just noticed that Q is flow.

 

[Bradracer18]

Well Integral, I went to class today and out of about 50 of us, he collected only 5 homeworks! Ha. He was like...so I guess this weeks homework was hard? Everyone started moaning and groaning, and asked questions like "where are you getting your information(not the book)?" It was funny, and I think pretty informative to him too.

So, anyways I appreciate your hard work, but he went through it today in class, and now I somewhat understand it. Just to answer part A, was a full page of writing(which included integrals, etc).

You were close with your formula, I think. We started with something similar to it, and integrated a few times, and ended up with a natural log function, and then, finally an exponent(e) function. Too much info to post, or I'd show you the steps.

Thank you for your help though!

Brad