Time to Design Pressure equations, need help.

[Wiggin]

I JUST got invited to work with a nuclear plant in Texas based on my completing my Nuclear Engineering Technology degree. I am in the final class and am scheduled to finish August 15. With this class it is based on writing a paper about Fukushima Daiichi/ lessons learned and design corrections you would make, while incorporating various "Outcomes" to prove you learned something.
Specifically we have to write a math problem and the one I am working on is determining how much time it would take to exceed design pressure of the primary containment in a BWR mark II plant versus a PWR and show that even though the PWR is up to 8 times larger than BWR's primary containment, that the design pressure would have still been exceeded. Even though the containment is larger, being with SBO for 10 or 14 days (depending on the unit) is still too much time for no operator action.

with this in mind, I know I need to get the volume of the BWR mark I or mark II primary containment vessels, and for ease of comparison multiply by 8 for PWR. and I know I'll need the steam tables to derive the temp and pressure changes based on density of water and steam and the rate of water expansion with temp increase. My problem I'm having are from this starting point where do I go... Which equations do I use and what are they called so I can google them. I have ideas and know it is possible to do this, I am just at the end of this 30 page monster and can't think as clearly anymore.

Any help would be greatly appreciated.

[thenuttyneutron]

This is not an easy question to answer.  I am going to point out that I am bothered that you have the conclusion of "even though the PWR is up to 8 times larger than BWR's primary containment, that the design pressure would have still been exceeded" prior to gathering the facts or making any calculations. 

Not all containment systems are the same.  A large dry ambient containment system would take longer to pressurize than an Ice condenser containment.  The ambient losses to atmosphere and the ground would be very different than what a small Mark II containment would have.   

You also have to ask the question about the integrity of the RCS.  During a long SBO event where the RCS is intact, you would lose the ability to operate many components.  If the PWR uses Terry turbine driven auxiliary feed pumps, the concern would not be the lack of cooling.  It would be an over cooling.  If the operators get control of the aux feed system by throttling the flow correctly and establish a way to dump the steam to atmosphere in a controlled way, you will have bought yourself a lot of time.  All that steam being dumped into the air are BTUs of decay heat being removed from containment which is a good thing.  I am not going to say "no operator action" because the Japanese operators were able to perform a few actions before they lost access to the plant.  They also had RCIC running on a unit for a long time after the event.  What is not known is what caused it to fail.  Did it fail because the bearings wiped or did it fail because the back pressure of the turbine exhaust got too high?

The next concern would be when the RCS loses sub-cooling margin.  With no electricity, the pressurizer will cool off and the RCS will become saturated.  If you have proper aux feed cooling from steam driven pumps, you would still cool the reactor.  If it has been long enough for the decay heat generation rate to have dropped off, saturated cooling may be enough to prevent fuel damage.

You then have to consider the RCP seals packages.  Not all plants use the same seal packages and some are better than others.  You will lose inventory through the seals.  What is more important to know is what is the rate of inventory loss.  If the loses are smaller, your in a much better situation.  Eventually the RCS would depressurize and the Core Flood Tanks will empty into the RCS.  With all of that extra inventory and boiler condenser cooling, how long would it take to uncover the core?

With all of the factors listed above, would pressurizing containment beyond the design pressure even occur?  It all depends on the ambient losses of containment compared to what the decay heat generation rate is.  What if the end point is a voided RCS with the core covered at 0 psig and 212 F with the steam generators full of water and open to atmosphere?  What if dumping the BWST or RWST into containment prior to it getting pressurized is enough to submerge the vessel and the decay heat generation rate of the core is within the capacity of ambient heat losses from containment?

[Rerun]

Uh it isnt a volume issue ..

[Rerun]

And yes given long enough you will over pressurize a PWR containment but honestly I dont see you losing the terry turbine provided you have an operator to operate it locally and provided you have a make up source. A BWR is a hell of a lot different

[thenuttyneutron]

Uh it isnt a volume issue ..

Agreed that this is not a volume issue.

[Rerun]

Btw Fukushima calcs are not releasable

[Wiggin]

Originally I had the conclusion that this type of accident could not occur in a PWR because of the volume and because of the difference in designs, but after reading more into it, I learned that the significant delays and lapse in communications as well as extended loss of power with no help, would likely have any design of plant not recover. There are many variables and angles that could be used to approach this topic, but I chose to use volume specifically for the reason that it makes for a decently involved math problem which is required for the paper.

[Rerun]

Good then prove it

[Wiggin]

working on it. Still looking for the volume of primary containment in any one of the units. Not sure why that is as difficult to find as it is.

[Rerun]

Use 2.6 million cubic feet for the PWR. Use 163000 for the drywell in a Mark I BWR and this is PUBLIC KNOWLEDGE. Do some research

[thenuttyneutron]

working on it. Still looking for the volume of primary containment in any one of the units. Not sure why that is as difficult to find as it is.

You need to step back for a moment and look at the PWR vs the BWR.

The BWR is very close to being a closed system.  You have a bunch of water in containment that is used to feed the ECCS system and quench the steam coming out of the SRVs.  The isolation condenser can be used as a way to reject decay heat to atmosphere but this is not a design feature used at every plant. 

PWR behave more like an open system as long as they have a feed source and water to pump into the steam generators.  One pound of water will absorb lots of energy by becoming a pound of steam.  This energy gets rejected to atmosphere easily by simply dumping it to atmosphere.  The SGs being able to reject steam to atmosphere is a design feature that every PWR has.

The way that I would attack this problem would be to look at the UFSAR of your PWR and see how how much inventory the CST has.  I would then break the time after the start of the accident event into blocks of time (30 minutes per block of time?).  Figure out the decay heat rate for each block of time based on time after shutdown and how much inventory is needed to remove all that heat.  This will give you an approximation of how long the steam driven AFP will be able to supply water to the steam generators.  Figure out what the decay heat rate of the reactor is at the time that the CST is expected to be depleted and then treat the PWR as a closed system like the BWR. 

The UFSAR also has total volume of CTMT.  You can also look at chapter 15 of the UFSAR to maybe give you some ideas on how to attack this problem.

I would also make some basic assumptions to make it more simple.

1) I would expect that the steam generators would lose coupling to the primary even if you had an infinite supply of water to feed the SGs.  Without the ability to make up water to the RCS from leaks through the seals you will eventually start running low on RCS inventory.  The question that needs to be answered is; will I run out of water in the CST first or will I run out of inventory in the RCS needed to have adequate natural circulation cooling?

2) Assume that the the SGs remain intact (no SGTR).  Figure out how much inventory you have in CTMT that is not inside the SGs from the original RCS inventory (include the Core Flood Tanks) and any inventory that was able to be gravity dumped in before CTMT pressure gets above the shutoff head of your water source. 

Based on the answers to your assumptions; you have a total mass of water inside CTMT, the average starting temperature of that water, and the decay heat generation rate.  You then need to pretend that CTMT is a homogeneous system.  You should then be able to figure out the rate that it is pressurizing and then extrapolate from there when CTMT reaches the design pressure. 

[Wiggin]

nutty neutron, thank you for you assistance and ideas, I will consider these when writing this equation. Rerun, thank you for the data, I sifted through a dozen sources and manuals looking for the specific values but came up short, so not sure where you got those numbers but it's definitely a start. I just literally had no idea how big these containment were and I'm used to numbers in the 1000m3 range.

[tr]

Check out:

http://www.sandia.gov/spe3/docs/NUREG_CR-6906-ContSum.pdf

Page 24 has typical containment  volumes  and design pressures.    For r what it's worth the containment volume at San Onofre was 2.3 x10(6) cubic feet.

[Rerun]

An Ice Condenser PWR is going to be about 400,000 cubic feet for lower containment and 250000 cubic feet for upper containment

[Rerun]

And given the exact info is on the NRC website...