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# Vapor Pressure Of Insoluble Mixture Runaway Reaction

6 replies to this topic
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### #1 Na3BrO

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Posted 14 June 2018 - 07:52 AM

I have a need to determine the adiabatic temperature and pressure of a runaway polymerization (emulsion) reaction for worst-case scenario evaluations for relief design of a batch reaction. The main constituents can be assumed to be water, ethyl acrylate, and methyl methacrylate, at a ratio of 1.5/1/0.53.

Given a known quantity and heats of polymerization, I've calculated the total heat evolved from the reaction. I've also estimated the heat capacity of the emulsion during the process (a bit tricky, as the heat capacity changes slightly when going from monomer -> polymer), and estimated a final temperature of the solution.

This estimation was done assuming a small vapor space, such that the enthalpy of vaporization did not absorb very much of the overall heat generated.

My problem comes when trying to estimate vapor pressure. EA and MMA are poorly soluble in water, so I don't think typical fugacity calculations apply. All three components have similar vapor pressures (MMA and EA boil at 1 atm at 213 F and 211 F, respectively).

I also don't think Raoult's law would apply, as it assumes a mixture of components, i.e. P = x1*psat1 +x2*psat2 + ...

I'm thinking this system may behave like the following: it would be as if each component were separated into individual containers with a shared vapor space, and are heated up to the same temperature. The EA and MMA would be in one container, such that "P(sat of EA and MMA) = x1*psat1 +x2*psat2" applies", and water in the other container.

Edit: Looked at VLLE calculations (doh!), and for pure, insoluble components, it does seem like like the sum of the vapor pressures are correct (activity coefficients are near 1 due to insolubility).

So, for this system, all components have near equal vapor pressure at 100 C. Thus the total pressure of the system at 100 C would be ~30 psig. Am I missing something?

Edited by Na3BrO, 14 June 2018 - 11:41 AM.

### #2 latexman

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Posted 14 June 2018 - 08:37 AM

Don't forget, as the monomer polymerizes there is less monomer to have a vapor pressure, and at the end (100% conversion), water will be the only component with a vapor pressure.  So it is a dynamic situation and you need to look at the total pressure as time progresses from t=0 to 100% conversion.

### #3 Saml

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Posted 14 June 2018 - 11:43 AM

Unless you have a complete thermodynamic description of what is going on inside the vessel, plus the physical condition of the relief (it is foamy?, will be only gas?)  the safest thing is to do a bench testing according to DIERS.

Just google for "diers calorimetry testing" to find  possible suppliers of this service.

Runaway reactions are not your "friendly" blocked outlet case from API 521

### #4 Na3BrO

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Posted 14 June 2018 - 02:36 PM

We are having an outside company do this runaway testing as the final word on the pressure/temperature development. This testing will serve as the basis for the relief design, not my calculations. However, I wanted to do these rough calculations to see if they corresponded to an actual scenario - more for my own benefit and understanding of what is going on during a runaway reaction.

I'm not considering the relief scenario right now (yes, 2-phase foamy flow will exist when this relieves), just final temp/pressure to determine if the reactors have sufficient pressure rating to withstand the pressure. The relief conditions will have to be determined experimentally (emulsion polymers are shear-thinning, and these batches have a good amount of surfactant in them that will create foam).

On the calculation side of thing: Given the assumption of a relatively small vapor space, diminishing monomer content isn't going to change the vapor pressure as long as some liquid remains. VLLE calcs only care about relative fractions of each component in each phase, not the total amount present.

### #5 breizh

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Posted 14 June 2018 - 05:09 PM

Hi ,

Make sure the nozzle connected to the safety device is always free of latex ( dry material) which can affect the integrity of your system .

Cleaning the sky of a reactor is not always easy .This happens in the real life !

A bit off , to be considered , my view.

Breizh

Edited by breizh, 15 June 2018 - 01:31 AM.

### #6 Saml

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Posted 14 June 2018 - 05:51 PM

Edit: Looked at VLLE calculations (doh!), and for pure, insoluble components, it does seem like like the sum of the vapor pressures are correct (activity coefficients are near 1 due to insolubility).

So, for this system, all components have near equal vapor pressure at 100 C. Thus the total pressure of the system at 100 C would be ~30 psig. Am I missing something?

You are right. Adding the vapor pressure of both phases will give you the most conservative (higher) vapor pressure.  So, for having a "feeling" of what to expect I would say is right.

As a side, activity coefficient of near 1 means almost perfect solubility.  What is near 1 is the activity.

### #7 Na3BrO

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Posted 15 June 2018 - 09:25 AM

Edit: Looked at VLLE calculations (doh!), and for pure, insoluble components, it does seem like like the sum of the vapor pressures are correct (activity coefficients are near 1 due to insolubility).

So, for this system, all components have near equal vapor pressure at 100 C. Thus the total pressure of the system at 100 C would be ~30 psig. Am I missing something?

You are right. Adding the vapor pressure of both phases will give you the most conservative (higher) vapor pressure.  So, for having a "feeling" of what to expect I would say is right.

As a side, activity coefficient of near 1 means almost perfect solubility.  What is near 1 is the activity.

Au contraire! The activity coefficient of EA/MMA in water is certainly very much above one. However, the VLLE equation  of y(i,a) * x(i,a) * P(i,sat) = y(i, * x(i, * P(i,sat) = y(i) * P, so the activity coefficients are for each phase (a and . Since the EA/MMA are practically insoluble (1.5 wt% for both) in water, they are present as pure and separated components. Thus, the activity coefficient of the water phase component is 1 (because it is nearly a pure substance), and the activity coefficient of EA and MMA in the organic phase should also both be near 1 because they are almost perfectly soluble in each other.

I suppose I should have better defined which activity coefficient I was talking about!

Re Breizh: Yes, we have a PM to clean the nozzles on the relief line. The current reliefs are rupture discs, so no need to worry about polymerization in the inlet of a PSV or anything.