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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 5:21 am 
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Quote:
How would you feel about a 10mm thick vessel for a 10m diameter core? To floppy to weld together?


Not at all. My company has done equipment services for petroleum tanks this size, with wall thickness down to 5 mm (the minimum required per API650). That's with crappy structural steel. Hastelloy N is much stronger than the standard grades structural steel.

From my talking to welders, 10 mm is considered a near ideal welding thickness. Much thinner, and it gets tricky to use thin electrodes. Much thicker, and the plates become unwieldy, costly, and quality control becomes more difficult (and expensive if you screw up a weld). With Hastelloy N there will be much more of a reason to reduce materials quantities (structural steel is pretty cheap).


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 9:28 am 
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Ok, so corrugated tanks are commonly used to store water, apparently:

http://www.bhtank.com/corrugated.php

Quote:
Corrugated steel has nine (9) times the tensile strength of flat steel and is superior in resistance to compressive loads. Corrugated steel is especially resistant to the buckling and "mushrooming" that can affect flat metal tanks during an earthquake.


That sounds very good.

Joining the corrugated plates together obviously could be a problem for high temperature applications.


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 1:42 pm 
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Lars,

Shoot. Those numbers are way off mine, and mine are in a spreadsheet... with a bunch of numbers just typed in. Grrr. I was pretty sure I had validated these numbers against one of your earlier postings, where you'd given %full power at 1 hour, 1 day, 30 days, 1 year, etc. But now I can't find that post, and Kirk may have deleted it.

(BTW, I'm pissed about those deletions. Maybe they fixed an IP problem of Kirk's. I archive email forever and use those archives. I'm used to using my prior posts and others responses to supplement my fading memory. If anyone has a suggestion for how to get back those posts, or how to archive these discussions in a way that isn't a PITA, please let me know.)

I reviewed that chapter, thank you. I do not understand the units of the vertical scale in Figure 5.

Where did you get 0.066 from? It looks like this is the equation (9) from this chapter, which gives Pdecay/Pfull_power = 6.48e-3*((t-t0)^-0.2 - t^-0.2), where reactor operating time in days is t0, and time after shutdown is t-t0. That's almost the same as your number, but not quite. Is yours a correction for a Th-232 fission chain?

I've updated my spreadsheet with your numbers, and it's way better, thus invalidating my earlier results entirely. I need to rerun everything, but now I'm willing to believe that a 0.5% loss path from a reasonably large core would be sufficient.

Here's the AHTR PRACS/DRACS paper: http://pb-ahtr.nuc.berkeley.edu/papers/ ... onse_C.pdf

I'm not sure reading this correctly, but it looks like they have two loops to remove heat from the core. The first loop pumps core coolant from the top of the reactor, through an intermediate heat exchanger to their secondary loop, back to the bottom plenum. The pump for this first loop normally forces enough salt through the core that the bottom plenum is higher pressure than the top, by more than the gravity head would normally make it. The second loop passively connects the top and bottom plenums through the PRACS heat exchanger. Nominal conditions would tend to push salt upward through this HX. A fluidic diode causes the flow to be small. When the pump stops on the first loop, the heat of the core causes the pressure at the bottom plenum to be lower than the isothermal gravity head would normally make it, which pushes salt downward through the PRACS HX. The fluidic diode has low resistance in this direction, and convection drives the loop.

This system has a lot of out-of-core volume, so it's not directly applicable to a molten salt fuelled reactor. As Cyril notes, that PRACS HX is also safety critical.


Last edited by iain on Nov 19, 2012 4:19 pm, edited 1 time in total.

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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 2:18 pm 
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I dont think PWR or the other types in Rageb are the applicable
decay heat profile.
I use ORNL 4541, Figure 3.25, page 43.
If you look at this figure, you will see that
a surprising amount of the decay heat ends up
in the offgas system and, if you assume ORNL 4541
style fuel processing, in the fuel processing stream,
rather than being stored up in fuel pins.
For drain tank calcs, ORNL 4541 claims a a significant amount
stays in the moderator and the PHX internals,
when the salt drains.

The overall decline is very un-exponential.

Jack


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 2:24 pm 
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iain wrote:
I'm not sure reading this correctly, but it looks like they have two loops to remove heat from the core. The first loop pumps core coolant from the top of the reactor, through an intermediate heat exchanger to their secondary loop, back to the bottom plenum. The pump for this first loop normally forces enough salt through the core that the bottom plenum is higher pressure than the top, by more than the gravity head would normally make it. The second loop passively connects the top and bottom plenums through the PRACS heat exchanger. Nominal conditions would tend to push salt upward through this HX. A fluidic diode causes the flow to be small. When the pump stops on the first loop, the heat of the core causes the pressure at the bottom plenum to be lower than the isothermal gravity head would normally make it, which pushes salt downward through the PRACS HX. The fluidic diode has low resistance in this direction, and convection drives the loop.

This system has a lot of out-of-core volume, so it's not directly applicable to a molten salt fuelled reactor. As Cyril notes, that PRACS HX is also safety critical.


That's how it works, yes. The PRACS is safety critical, but the normal HX no longer is (but it can be used as defense in depth, not that that's necessary).

As I've suggested twice already, a MSR version of PRACS could use a seperate KF-ZrF4 or other fluoride coolant for the PRACS. There would then be tubes inside the reactor vessel - perhaps conveniently cooling the permanent outer reflector - and outside it, filled with KF-ZrF4. This eliminates the need for a fluidic diode as well. More heat is transferred normally, but that's no problem; the buffer salt has its own HX feeding the power cycle.

Added advantage here is that we prevent delayed neutrons from entering the buffer salt (this would happen in a direct PRACS a la PB-AHTR).


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 2:35 pm 
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Posts: 5057
djw1 wrote:
I dont think PWR or the other types in Rageb are the applicable
decay heat profile.
I use ORNL 4541, Figure 3.25, page 43.
If you look at this figure, you will see that
a surprising amount of the decay heat ends up
in the offgas system and, if you assume ORNL 4541
style fuel processing, in the fuel processing stream,
rather than being stored up in fuel pins.
For drain tank calcs, ORNL 4541 claims a a significant amount
stays in the moderator and the PHX internals,
when the salt drains.

The overall decline is very un-exponential.

Jack


It's table 3.11.

"at shutdown" I would infer as being 10e2 seconds, rather than 1 second, but that doesn't matter much for the integrated decay heat.

For some reason the table 3.11 stops giving processing plants heat rate beyond "at shutdown". So I'm going to guess that part and add it up in the following.

The decay heat after 10e3 seconds (17 minutes) is around 23 MWt for a 2250 MWt MSBR. The rest is in the offgas and processing systems, but these will be outside the vessel (maybe in separate tanks, pipes etc. in the buffer salt). If we assume a DMSR with some processing systems not included, and no Pa separation, then we’d be talking about ~30 MWt decay heat that you are generating inside the vessel at 1000 seconds.

12.6 MW in the salt, metal and graphite at 10e4 seconds (2.8 hours). Adding Pa and salt seekers (for a DMSR decay heat) gets you around 18 MWt in the vessel at 2.8 hours. There is also 5 MW in Pa decay.

6.4 MW at 10e5 seconds (28 hours). Plus Pa and salt seekers, maybe around 12 MWt in the vessel.

Clearly, the heat profile is different for the thorium cycle.


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 2:59 pm 
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Cyril,

I should have said that I don't believe a heat exchanger with 100 C delta-T in the metal will survive many cycles. It's turns out I'm going to have to eat even those words (see below). Are coal-fired heat exchangers approaching 100 C just in the metal?

I know that some coal-fired HX actually rely on the operating temperature to anneal some of the strain out of the metal, which is why the rate of load change (not exactly temperature) is limited. For reasons I don't understand, sometimes the metal creeps, and sometimes it spalls. These heat exchangers are actually designed for that environment -- they know the rate at which the metal creeps at operating temp, there are operating constraints that ensure the metal is at that temp before they change load, and the pressure stresses are somehow small enough not to cause creep-swelling of the tubes.

PWR claddinig does not creep (much). I just figured this out, btw, it's not like this was my argument all along. Figure 8 in the chapter 8 of Lamarsh, which Lars attached earlier in this thread, shows the drop across an operating PWR clad of around 100 C. Wow. That said, zircaloy at 600 F has a linear CTE of 6.17e-6/K and a Young's modulus of 75 GPa. Combine those and 100 C of delta-T makes 46 MPa of delta stress. 23 MPa is a lot less than zircaloy's 125 MPa yield strength at the same temperature. (Numbers here.) Zircaloy can take 3 times the delta-T that Hastelloy can take at the same fraction of it's yield strength, with about the same thermal conductivity.

This passive core heat leak might transfer about the same amount of heat in idle and at full power. If so, it's really not going to change stress every time the reactor load changes. So maybe there is an argument there.

I'm a lot less worried about the issue now that Lars has fixed my nonunderstanding of afterheat rates. When I get some time I'll look at it again, but I'm hoping that a simple 10mm thick 10m cylinder will in fact be able to leak 0.5% heat and that'll be fine.

Seems like we need to get a better model for the afterheat rates from the core as well as the offgas system. A nice table of numbers over time in a shared Google Spreadsheet that I can look at, along with totals from the two that match up to PWR afterheat rates.


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 4:13 pm 
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iain wrote:
Lars,
I reviewed that chapter, thank you. I do not understand the units of the vertical scale in Figure 5.
Neither do I. From the code preceding it I expected it to be the natural log of the power but still could not make sense of it.
Quote:
Where did you get 0.066 from? It looks like this is the equation (9) from this chapter, which gives Pdecay/Pfull_power = 6.48e-3*((t-t0)^-0.2 - t^-0.2), where reactor operating time in days is t0, and time after shutdown is t-t0. That's almost the same as your number, but not quite. Is yours a correction for a Th-232 fission chain?
No just a different source (wikipedia) - but they are close enough that it doesn't change the rough design.
Quote:
I've updated my spreadsheet with your numbers, and it's way better, thus invalidating my earlier results entirely. I need to rerun everything, but now I'm willing to believe that a 0.5% loss path from a reasonably large core would be sufficient.


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 4:38 pm 
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Location: Ottawa
Great discussion, keep up the good work. Just a little point to make sure isn't being missed is that while we like to take a 1000 MWe reactor as a guideline (like the big 10 m diameter DMSR of ORNL) that the ratio of surface area to volume goes way up for smaller total power (since one is R squared the other cubed). Thus if one is planning for smaller reactors, more likely for first generation at least then you get a lot more surface area per MW of heat. As well, since most simple graphite reactors will have a similar radial and axial graphite reflector zone the ratio changes even more rapidly.

For example the DMSR wanted an average of 5MWth per m3 of core so they needed a 8.3 meter wide and tall core but then with 0.85 meters added all around for reflector and salt gap. This gave the resulting 10 m wide and tall vessel. Surface area of a right cylinder is 6pieR2 so about 471 m2 for 2250 MWth. If however one was planning a similar core power density but only 1/10th the output or 100 MWe (225 MWth) then the core is only 3.85 m wide and with a similar reflector you get a 5.55 m wide vessel which has 145 m2 of surface area. This has 3 times the ratio of surface area to power of the big DMSR.

I used to only like to think big but there are a surprising amount of benefits from lower total power that are sometimes not obvious on the surface.

David LeBlanc


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 4:45 pm 
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iain wrote:
Figure 8 in the chapter 8 of Lamarsh, which Lars attached earlier in this thread, ...

Just to clarify. I used several information sources. One was a graph in Lamarsh 3rd edition figure 8.3. A separate source was the chapter - unknown book - that I squirreled away after it had been posted to the forum. A third source was wikipedia. These three agreed and also agreed with the decay heats I saw in my simulations using fission yields from Kirk. I saw little difference between the decay heat of u235 and u233 except in the very long run where the u233 path produces much more 238Pu than the U235 path does. This impacts the decay heat load after several decades and through several centuries.

For the purpose of emergency cooling I think we can use the results from U235 just fine.

The processing system will move heat loads around. The most significant ones are off-gas and Pa isolation. Since I'm generally assuming no Pa isolation I haven't thought about that one. The offgas load (~20 MW) is a significant portion but does not dominate the total decay heat (150-160MW). I haven't plotted the post shutdown decay heat versus time. Cyril's concept of keeping it all (off-gas, processing, and storage of isolated fission products) in the buffer salt makes it mostly a mute point anyway. If we just assume all the decay heat is in the core then we are a little bit conservative in the beginning and quite conservative years into the accident. But it is the first months that are challenging so I don't think things will change much by going into more detail now.


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 19, 2012 6:16 pm 
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David wrote:
Great discussion, keep up the good work. Just a little point to make sure isn't being missed is that while we like to take a 1000 MWe reactor as a guideline (like the big 10 m diameter DMSR of ORNL) that the ratio of surface area to volume goes way up for smaller total power (since one is R squared the other cubed). Thus if one is planning for smaller reactors, more likely for first generation at least then you get a lot more surface area per MW of heat. As well, since most simple graphite reactors will have a similar radial and axial graphite reflector zone the ratio changes even more rapidly.

For example the DMSR wanted an average of 5MWth per m3 of core so they needed a 8.3 meter wide and tall core but then with 0.85 meters added all around for reflector and salt gap. This gave the resulting 10 m wide and tall vessel. Surface area of a right cylinder is 6pieR2 so about 471 m2 for 2250 MWth. If however one was planning a similar core power density but only 1/10th the output or 100 MWe (225 MWth) then the core is only 3.85 m wide and with a similar reflector you get a 5.55 m wide vessel which has 145 m2 of surface area. This has 3 times the ratio of surface area to power of the big DMSR.

I used to only like to think big but there are a surprising amount of benefits from lower total power that are sometimes not obvious on the surface.


One of those advantages in terms of decay heat removal through the vessel, is that minimum required vessel thickness reduces rapidly with smaller vessel diameters.

225 MWt though is very small. You get 10x lower output but still need a vessel over half the diameter as the 1000 MWe machine! The economics of the plant will take a big hit. This is also what I worry about with all the small modular reactors.

Another hit is in the neutron leakage and breeding ratio. Those same volume/area scalings that help to remove heat, hurt here. It's fun to look at ORNL's numbers. The 500 MWe MSBR for example had 3.89% leakage and a BR of 1.043. This is already much lower than the standard 1000 MWe MSBR at 2.44% leakage and a BR of 1.065. But David would be planning on a DMSR where a CR of 0.05 more or less won't be frowned upon. But be prepared for a bigger fissile startup per MWe. There'll be more fissile in the virtual blanket, generating much less power there than in the core.

Another hit is in the cycle efficiency. A 100 MWe supercritical steam cycle doesn't exist, you'll have to settle on superheated. That won't break any hearts I suppose, but it costs in efficiency, in addition to the lower efficiency you get with smaller turbines. It could mean only a 40% net efficiency in stead of 44%. If you're planning on process steam then there is no disadvantage here, only advantages.

But for a DMSR power reactor, maybe a better compromise is 2x the core power density, 1/4 the power. This way you can scale everything down a factor of 2, except the reflector. The vessel becomes 5.85 meters ID with a 4.15 meter core. This also allows us to use ORNL's HX design. They use 4 HXs and 4 pumps, so we'd need one such HX and one such pump. Simple design.


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 Post subject: Re: Meltdown Risk?
PostPosted: Nov 23, 2012 2:18 pm 
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Cyril R wrote:
djw1 wrote:
I dont think PWR or the other types in Rageb are the applicable
decay heat profile.
I use ORNL 4541, Figure 3.25, page 43.
If you look at this figure, you will see that
a surprising amount of the decay heat ends up
in the offgas system and, if you assume ORNL 4541
style fuel processing, in the fuel processing stream,
rather than being stored up in fuel pins.
For drain tank calcs, ORNL 4541 claims a a significant amount
stays in the moderator and the PHX internals,
when the salt drains.

The overall decline is very un-exponential.

Jack


It's table 3.11.

"at shutdown" I would infer as being 10e2 seconds, rather than 1 second, but that doesn't matter much for the integrated decay heat.

For some reason the table 3.11 stops giving processing plants heat rate beyond "at shutdown". So I'm going to guess that part and add it up in the following.

The decay heat after 10e3 seconds (17 minutes) is around 23 MWt for a 2250 MWt MSBR. The rest is in the offgas and processing systems, but these will be outside the vessel (maybe in separate tanks, pipes etc. in the buffer salt). If we assume a DMSR with some processing systems not included, and no Pa separation, then we’d be talking about ~30 MWt decay heat that you are generating inside the vessel at 1000 seconds.

12.6 MW in the salt, metal and graphite at 10e4 seconds (2.8 hours). Adding Pa and salt seekers (for a DMSR decay heat) gets you around 18 MWt in the vessel at 2.8 hours. There is also 5 MW in Pa decay.

6.4 MW at 10e5 seconds (28 hours). Plus Pa and salt seekers, maybe around 12 MWt in the vessel.

Clearly, the heat profile is different for the thorium cycle.

The "at shutdown" power level is approximately the same as at 10 seconds from the formula. It takes a few seconds for fission to stop so it wouldn't surprise me to use 10 seconds as "at shutdown". The level at 1000 seconds is 35.13MW which agrees pretty close to the equation at 36.62MW. A couple of differences that may be hidden. The equation assumes the reactor functions at 100% capacity forever, while generally MSBR is assumed to operate for 30 years at 80% capacity. This difference will make a few MW difference for the longer post shutdown times. Second Pa decay isn't present in LWR reactors from which the equation is derived. The 239U/239Np decay power is around the same as the Pa decay power initially. But it's half-life is only 2.4 days versus 27 days for 233Pa so this will increase the decay power for a thorium reactor versus a uranium reactor over a period from a couple of days to a year by a few MW per GWe. Bottom line - there are too many uncertainties around the assumptions that went into these charts to conclude that the decay heat from a LFTR is significantly different than an LWR.


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 Post subject: Re: Meltdown Risk?
PostPosted: Dec 10, 2013 3:53 pm 
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This was really a great discussion. Some of you said that the ground is an excellent insulator and can not be use as a heat sink, but in a paper Charles Forsberg (one of the major people involved in the FHR developpement) talks about the possibility of conducting heat to the ground for a large power Fluoride Salt cooled High Temperature Reactor.

The paper is here :

http://www.jaif.or.jp/ja/wnu_si_intro/document/2012/1.2-3%20Forsberg,%20Charles_Fluoride-Salt-Cooled%20HTGRs%20for%20Power%20and%20Process%20Heat.pdf

He talks about heat conduction to the ground in slides 18 and 55.

Maybe it's just a little part of the decay heat which is transferred to the ground with that system. He uses a beyond design basis salt and an iron ring silo to transfer heat to the ground. Maybe if he uses a lot of BDBA salt he has sufficient heat capacity to reach a level of decay heat sufficiently low for being transferred to the ground (the BDBA salt is frozen at normal condition, so with the heat capacity between the BDBA salt phase changes, the melting heat and a part of the boiling heat ... it seems that a part of the BDBA salt boils and recondenses in the containment, so the entire containment becomes a heat sink too.)

Soil properties vary greatly depending on location, so he can maybe only use some kinds of soils.

What do you think of that ? Is this really feasible ? Can you use this in complement of your buffer salt tank in your pool-ype MSR ?


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 Post subject: Re: Meltdown Risk?
PostPosted: Dec 10, 2013 5:00 pm 
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From my limited thermo modelling it is impossible to use the ground as the primary heat sink for a large reactor. In fact, even for a small reactor, that has a lot (like a week or so) of buffer capacity in the system, the heatup after that period with just the ground to soak up heat is unacceptable (fuel salt boiling), if there are no other heat losses.

Heat loss to the air works well after some time for a small reactor, and a LOT of time for a larger reactor. But you need a lot of interface area with the outside air to make that happen, so it requires design provisions (for example if we insulate everything it won't work at all). We'll need to put some effort in things like accepting heat losses, not insulating large areas on purpuse, and the like.

Perhaps you'll recall from geologic repository documents, that heat load is a limiting factor for repositories, and its why it can't accept fresh fuel. In fact, even 5 year cooldown spent fuel assemblies are problematic. What happens is, the first layers of rock around the repository heat up, acting like an somewhat efficient short term heat sink, and then when those layers have heated up, the rock becomes an insulator.


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 Post subject: Re: Meltdown Risk?
PostPosted: Dec 10, 2013 5:25 pm 
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Thanks Cyril, I guess Charles F. was maybe too optimistic, unless its concept has really a great quantity of BDBA salt. Moving heat into the atmosphere is the most convenient way to remove decay heat I suppose. The properties of the ground are very complicated and depending of the location, composition, water content, season, etc ...


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