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[KEML]

I want to use the Levenspiel Plot to size chlorine disinfection tanks for CSTR and PFR, but I don't really understand what I'm doing and my lecturer was no help. I'm an enviro eng student so some of this chemistry stuff is a bit confusing as we only do bits and peices of it. I haven't been able to find a worked through example that applies to water disinfection.

 

Here is the process I want to apply:

 

http://ocw.mit.edu/c..._03072007_w.pdf

 

But I'm not sure what -rA is?

 

Is it just the reaction rate? I've assumed a k value of 2 per hour. Is this the same thing as rA?

 

And is XA the ratio of chlorine that has reacted to the initial chlorine?

 

How does XA and -rA relate to CT and k? If someone could explain those first 2 equations in the link relating to disinfection that would be super awesome.

 

Is there a way to actually calculate k without experimental data? I couldn't find any raw experimental data for residual chlorine decay that I could use to calculate k. I've just used 2 per hour because a couple of text book questions assumed that value, I would like something that has a bit more justification behind it but I can't seem to find anything.

 

Also we were given a CT value for 3log removal of Giardia and a target free residual chlorine value. So using this I was able to calculate dosages of chlorine and basic tanks volumes for PFR and CSTR.

 

But then we were also given a graph of Residual Chlorine against chlorine dosage. When I find the dosage required for the free chlorine target on the graph, the dosage derived from the CT and free residual target does not even get close to passing the breakpoint on the graph.

 

What is going on there? Does that mean that the 3log removal of Giardia occurs before the breakpoint, from the combined residual Chlorine? That doesn't seem right.

 

Thanks!

[shantanuk100]

Hi KEML,

 

Let's take things conceptually for better understanding.

a. Consider a well mixed tank, with the reaction having a rate constant rA.

b. Now, primarily, we need to see at what rate A is being generated/consumed.

c. So, for this consider this equation

 

(Flow of A into system - Flow of A out of system)  + Rate of Any A generated through reaction =    Rate of Total A accumulation in System

 

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1. Let us consider Flow rate of A into reactor system as Fao, and flow rate of A out of reactor system as Fa.

2. Consider ra as rate or reaction of formation/depletion of A (moles/vol/time), and V as total reactant feed rate into system.

3. As we have already included the reaction generation of A, total accumulation rate of A in the overall system must be conserved (=0)

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4. So we get

 

Fao - Fa + ra*V  =  Accumulation of A (dNa / dt) = 0

Fao - Fa + ra*V  =  0

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5. Upon rearranging, we get,

 

V = (Fao - Fa) / (-ra)

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6. Now, conversion (X) of any species/ reactant in a given reaction or reaction set is defined as

Rate of moles leaving (Fa)  =  Rate of moles fed (Fao)  - Rate of Moles Reacted  (Fao * X)

Fa = Fao - Fao*X

 

Fa = Fao * (1-X)

 

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7. From 5, 6 we get,

V = Fao * X / (-ra)

 

where,

V = Volume or reactant feed entering system

-ra = Rate of reaction of formation/depletion of A (Sign changes based on that)

X = Conversion of A in the Reactant system

Fao = Inlet Feed Rate of A into Reactant System

 

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8. What the author is saying in the graph in the first section is that :

 

a. As time increases, the Conversion of A (Xa) will increase since the reaction is going on

 

b. As time increases and conversion of A goes on, the Concentration of A present in the Feed (Ca) will decrease since more and more A is getting converted

 

c. The volume of reactor required for A will always be lesser for a PFR type reactor than a CSTR, because,

mathematically speaking, 

 

--- The area under graph represents the volume of reactor required

--- This area is calculated by discrete addition in case of CSTR, while it is calculated by continuous integration in PFR and the integration area always will be lower than areas calculated by discrete addition methods like Trapeziodal rule etc.

 

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Regards,

Shantanu

Edited by shantanuk100, 20 April 2016 - 12:00 AM.