## Transient behaviour in a reactor

Cyril R
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### Transient behaviour in a reactor

In reading up on transient behaviour of various gas cooled and fluoride cooled TRISO fuelled reactors, I ran into a couple question marks.

Assume the PB-AHTR core with a k-eff of 1.1. This is about the lowest they can go with a poisoned deep burn core. This gives a Rho of 0.0909 or 9090 percent milliRho (pcm). 9000 pcm seems like a lot.

In the ATWS transient - failure of pumps without control rod insertion - the temperature of the fuel rose only 100-200 degrees or so. How come this is so low? If you have a total alpha of -10 pcm/K (about the most negative you could possibly get with this core) then the heatup would be 900 degrees Celsius.

In the PB-AHTR ATWS the core fission power increases again, swinging around 1-3% normal core power, then appears to equilibrate to 2% core power (the temperature stops rising because this is the heat flux the DRACS and PRACS can move out). Again this seems very low if your k-eff is 1.1.

Can someone explain to me how this works?

David
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### Re: Transient behaviour in a reactor

Assume the PB-AHTR core with a k-eff of 1.1. This is about the lowest they can go with a poisoned deep burn core. This gives a Rho of 0.0909 or 9090 percent milliRho (pcm). 9000 pcm seems like a lot.
Can you explain this assumption? Are you sure you are not talking about a k inf of 1.1? Also give a reference to where they talk about a pump failure transient? I can't really see why a pump failure increases reactivity since in most cases they had negative temp and void for the salt (but probably studied some cases where it wasn't negative).

A reactivity coeff of -10pcm/K is hugely negative (they often quote FHRs as being 80 times the neg coeff of LWRs) so they can react to almost anything imaginable with small changes in the TRISO temperature. In fact, even the whole issue of positive void was a bit of a red herring since in most of their cases even a full voiding would just mean the TRISO fuel hops up a few tens of degrees to compensate.

David LeBlanc

jaro
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### Re: Transient behaviour in a reactor

In solid fuel reactors, geometry and material make a big difference in reactivity transients.
Ceramic fuel types are poor heat conductors compared to metal or particle dispersions in metal, so it takes longer for the negative reactivity feedback to kick in.
Similarly for thin versus thick fuel elements, for example thin plates (MTR type fuel) versus round rods (LWRs, etc.). Large fuel pebbles with thick graphite outer shells are not particularly good in this respect.
Experiments back in the 50s and 60s have demonstrated that the delay in negative reactivity feedback can lead to powerful and even destructive transients, if enough excess reactivity is added, in solid fuel cores. The Kiwi-TNT explosion was an infamous example of that, as was the Borax destructive test.
Another factor is moderator heterogeneity: A fine mix of fuel & moderator gives quick reactivity feedback, whereas heat transfer in a strongly heterogeneous arrangement, typical of solid fuel cores, is impeded, allowing the transient to ramp up longer, to higher peak power....
Many factors to consider.

Cyril R
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Joined: Jul 14, 2008 3:12 pm

### Re: Transient behaviour in a reactor

David wrote:
Assume the PB-AHTR core with a k-eff of 1.1. This is about the lowest they can go with a poisoned deep burn core. This gives a Rho of 0.0909 or 9090 percent milliRho (pcm). 9000 pcm seems like a lot.
Can you explain this assumption? Are you sure you are not talking about a k inf of 1.1? Also give a reference to where they talk about a pump failure transient? I can't really see why a pump failure increases reactivity since in most cases they had negative temp and void for the salt (but probably studied some cases where it wasn't negative).

A reactivity coeff of -10pcm/K is hugely negative (they often quote FHRs as being 80 times the neg coeff of LWRs) so they can react to almost anything imaginable with small changes in the TRISO temperature. In fact, even the whole issue of positive void was a bit of a red herring since in most of their cases even a full voiding would just mean the TRISO fuel hops up a few tens of degrees to compensate.

David LeBlanc
The main reference is Alain Griveau's M.Sc. report:

http://pb-ahtr.nuc.berkeley.edu/papers/ ... riveau.pdf

The k-inf that they mention is much higher at roughly 1.35. But even with the much lower value for a poisoned core and a really much more negative-than-achievable total alpha of -10 pcm/K still gives a much higher heatup than simply dividing Rho by alpha.

Even substracting leakage (k-eff) doesn't give the result. If you start with k-inf of 1.35 you'll get more than 1.1 for k-eff right? And anyway the figures for different alpha's don't differ linearly in terms of heatup.

So clearly this is not simple to calculate. How can a core with this much reactivity have such a good performance to ATWS? The k-eff is a physical property of the core, so it's there always. Is it assumed that some of the control rods are always in to regulate power and all control rods simply stick to their existing position?

David
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### Re: Transient behaviour in a reactor

I still don't really follow. Keff in my understanding is always right at 1.0 if you are at steady power and you keep it within the delayed neutron factor when you increase (i.e. keff just slightly over 1.0). The PB AHTR has a huge kinf since it is an annular core which is quite leaky.

I couldn't find what you meant about the 200 degree temperature rise upon pump failure but isn't this likely just the temp rise by decay heat when the pumps shut down until the DRACS reach a new equilibrium? Again I am pretty sure a pump failure actually lowers reactivity in the PB AHTR.

David L.

Cyril R
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### Re: Transient behaviour in a reactor

David wrote:I still don't really follow. Keff in my understanding is always right at 1.0 if you are at steady power and you keep it within the delayed neutron factor when you increase (i.e. keff just slightly over 1.0). The PB AHTR has a huge kinf since it is an annular core which is quite leaky.

I couldn't find what you meant about the 200 degree temperature rise upon pump failure but isn't this likely just the temp rise by decay heat when the pumps shut down until the DRACS reach a new equilibrium? Again I am pretty sure a pump failure actually lowers reactivity in the PB AHTR.

David L.
Yes, I also thought that k-eff would be 1 under normal operation. But with a k-inf of 1.35 your k-eff will be larger than 1 even for a leaky core, without any control rods inserted. So here's what I think is going on. The reactor core, being a solid fuelled reactor, has large excess reactivity. This is kept down by inserting control rods during normal operation, as required to keep k-eff at 1. They don't mention this in the report from Alain Griveau. But it seems this is the definition of ATWS for them, control rods stuck as-is, with some or all of them partially or fully inserted.

The LOFC with scram within 3 seconds gives a temperature rise of around 40 degrees C, that's clearly from decay heat and almost nothing from fission. Without scram it becomes about 100 degrees C higher than with scram. So that's mostly to do with fission power.

So what happens if the pumps fail and all control rods are accidentally removed? What kind of temperature will be see? Can it simply be calculated by dividing the Rho at fully withdrawn control rods by the alpha?

David
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### Re: Transient behaviour in a reactor

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``Yes, I also thought that k-eff would be 1 under normal operation. But with a k-inf of 1.35 your k-eff will be larger than 1 even for a leaky core, without any control rods inserted. So here's what I think is going on. The reactor core, being a solid fuelled reactor, has large excess reactivity. ``
Remember though, this is a pebble bed so almost no excess reactivity is needed since they add and subtract pebbles continuously (unlike the prismatic cores that use lots of burnable poisons). I don't think either though rely on slowly removing control rods with time (I could be wrong). Again, k-eff will of be 1.0 or extremely close while the reactor is operating so if they say a pump failure without scram gives more heat rise then it is either that in their case they do have a minor positive temp reactivity of the salt (not fuel) or more likely it is just that even with a negative temp coefficient the power will coast down slower than with a scram so more heat goes into the core before it is really near zero fission power.
So what happens if the pumps fail and all control rods are accidentally removed? What kind of temperature will be see? Can it simply be calculated by dividing the Rho at fully withdrawn control rods by the alpha?
Again, I should know this for sure, but I don't think they or the prismatic use rods to control reactivity with burnup. But yes, if I'm mistaken and they do have them (not just fine control or shutdown rods which are a different story) and are accidentally all removed then you just can take their total worth in pcm and divide by the temp reactivity coefficient to get an idea on the temperature jump. Usually what are called control rods are just to make sure the reactor stays below critical when it is shutdown and allowed to cool and of course for changing Xenon levels. In the thousands of reactors years of operation has their ever been a case of complete accidental removal? The one famous exception of course the SR1 but even there it may have been a murder-suicide as it was pulled out by hand (bad design too if it was even possible to pull it out by hand too far).

David L.

http://en.wikipedia.org/wiki/SL-1

Cyril R
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### Re: Transient behaviour in a reactor

Well, even with fast circulating pebbles you'd still have some excess reactivity need. Maybe only a few days worth, perhaps a little more (you don't want to have to shut down the reactor every time there's a minor problem with the fuelling machine).

I'm not sure if full control rod withdrawal has ever occurred at a power reactor, Chernobyl is probably the worst example (I think they manually overrode the control rod system or something). Lots of the more severe accidents have never happened. A few years ago a long term station blackout had never occurred either, then came Fukushima. LBLOCA has never happened either, but it has happened at coal plants with their poorer quality control and inspections.

One funny thing with the PB-AHTR analysis is that the fission power never drops to zero, it's always higher than 40 MWt even very long term. The passive decay heat removal system can remove this so fission power simply adapts to heat removal.

More recent PB-AHTR designs also use lots of burnable poison, to get lower initial core reactivity and lower swing over the lifetime, plus a negative coolant coefficient. These should do even better in ATWS.

A big remaining question is whether they have inserted control or fine control rods assumed for the ATWS.

jaro
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### Re: Transient behaviour in a reactor

Cyril R wrote:More recent PB-AHTR designs also use lots of burnable poison, to get lower initial core reactivity....
why don't they simply load the core with fewer pebbles, or more pebbles containing only fertile material ??

Cyril R
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### Re: Transient behaviour in a reactor

jaro wrote:
Cyril R wrote:More recent PB-AHTR designs also use lots of burnable poison, to get lower initial core reactivity....
why don't they simply load the core with fewer pebbles, or more pebbles containing only fertile material ??
Good question! Perhaps to get the same power per pebble - with regards to keeping certain safety, thermal, and thermalhydraulic aspects as constant as possible?

In terms of void coefficient, adding burnable poison would make sense at the beginning, because it gives negative coolant coefficient. With fewer pebbles there could be higher leakage but I imagine it would be a weaker effect than the poison could give you.