# Chemical Reactor Design Optimization

1. Nov 16, 2013

### Woopydalan

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

For this problem, my group is having difficulty figuring out how much Styrene is reacting, since we don't know the molecular weight of polystyrene, we can't find the moles of polystyrene, which would be used to aid in finding the moles of styrene entering the reactor. We know there is 1000 kg of polystyrene coming out of the PFR, but also without knowing any molar ratios of the initiator or styrene, cannot find anything on a molar basis.

I included the matlab code for problem 46 that we wrote, and the 2nd matlab code was given to us by the instructor for our own use.

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• ###### Polymerization_PFR.m
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2. Nov 17, 2013

### Staff: Mentor

A web search would turn up the chemical formula for the styrene "unit cell" of polystyrene. Add up the atomic masses!

3. Nov 17, 2013

### Woopydalan

The problem is that the molecular weight of polystyrene depends on the concentration of the monomer

4. Nov 17, 2013

### Staff: Mentor

My understanding was that polystyrene consists of linked styrene "cells", so that the monomer in this case is styrene which has a fixed molecular weight. 1000 kg of pure polystyrene should consist of a fixed number of moles of styrene.

So, I guess I don't understand your concern about "concentration of the monomer". Then again, I will admit that it's been a long while since I did any organic chemistry

5. Nov 17, 2013

### Woopydalan

It's in the problem statement of problem 46

6. Nov 17, 2013

### Staff: Mentor

Ah. Unfortunately I'm not able to read the docx format files in a way that gives me any more to work with. Much of the text is resolved, but the equations are not being rendered intelligibly. I blame it on the antiquated software I'm running. Sorry about that. Perhaps another Homework Helper will be able to provide some insight.

7. Nov 18, 2013

### Staff: Mentor

According to the problem statement, the density of the mixture is identical to the density of the polystyrene, and also to the density of the polystyrene. You know the amount of polystyrene being produced, and you know the conversion, so you know the mass flow rate of mixture exiting the reactor. If you divide by the density, you get the volumetric rate of flow, which is constant through the reactor. You know the density of monomer, so you know the mass concentration of monomer in the inlet stream. Since you know the molecular weight of monomer, you also know the molar concentration of monomer in the feed.

You have a plug flow reactor. If t represents the cumulative residence time through the reactor, then the kinetic balance equations for a plug flow reactor are, in terms of t, the same as a batch reactor. Set up the balance equations for the concentrations of the species in the reactor as a function of the cumulative residence time.

8. Nov 18, 2013

### SteamKing

Staff Emeritus
I've taken the liberty of printing Woody's files as acrobats so that everyone who is interested can read them:

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• ###### DesignV4.pdf
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9. Nov 18, 2013

### Woopydalan

The molecular weight expression for the polystyrene has been modified as of today, apparently something was wrong with the previous expression, and the initial concentration of the initiator has been changed. When I get home I will post the modified document, this design project is a living document.

Ultimately the goal is to find the conversion that will be the most cost effective

10. Nov 18, 2013

### Woopydalan

The equation for the molecular weight of styrene has been modified, the initial concentration of the initiator has been modified, and the 95% purity constraint has been removed, and the recycle ratio is now 1.

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• ###### Design - PFR.pdf
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11. Nov 18, 2013

### Staff: Mentor

You know the density of the reactor feed. The feed is essentially pure styrene monomer. From this, you should be able to calculate the initial concentration of monomer in moles/liter. What is that initial concentration C0? You have the kinetic equations for the rates of disappearance of initiator and monomer. So, you should be able to write equations for the time derivatives of the initiator concentration and monomer concentration, where the time parameter in these equations is the cumulative residence time through the reactor. What are those two ordinary differential equations?

12. Nov 19, 2013

### Woopydalan

As of today, the feed cost is now \$15 kg/hr for the feed, and here is our MATLAB code. The problem is that the cost is not making a U shape, so it appears that the cost just goes down as you increase the conversion, which doesn't make sense. There should be some intermediate value of conversion where it is a minimum. Just choose an nrange=[.2,.5];

If single pass conversion is 50%, then the overall conversion is 100%, which should not be the least expensive conversion

Should come as Fig. 16, haven't gotten it to be more efficient and not have multiple plots that are the same generated

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• ###### cost_plots.m
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Last edited: Nov 19, 2013