Energy From Thorium Discussion Forum

It is currently Feb 20, 2018 12:34 pm

All times are UTC - 6 hours [ DST ]




Post new topic Reply to topic  [ 23 posts ]  Go to page 1, 2  Next
Author Message
PostPosted: Nov 28, 2013 4:28 am 
Offline

Joined: Mar 16, 2010 1:48 am
Posts: 68
Location: Guangdong, China
I found many papers mentioned graphite has positive temperatur coefficient of reactivity, it is caused by heating effect, but I don't understand this mechanism very much. And I also found some calculated result showed the negative temperature coefficient (I also get the same conclusion by calculation).

Does anyone know the tmperature effect of graphite moderator? Except the scattering cross section, how it impact the reactivity in reactor?


Top
 Profile  
 
PostPosted: Nov 28, 2013 5:43 am 
Offline

Joined: Jul 14, 2008 3:12 pm
Posts: 5057
I think it has to do with fission resonances. In a well moderated reactor the neutrons will be slower than the lower U233 fission resonances. Hence a heatup of graphite causes a reduction in moderation which results in the neutron population creeping up slightly to concentrate in the lower fission resonances. I wanted to add this in the Wiki LFTR article but it is too technical and too much detail.

The effect occurs in U233, it is not clear if it occurs in other fissiles. You'd have to check their lower fission resonances. And also check the fertile resonances for non-fission capture.

The graphite effect is not very strong unless the reactor uses loads of graphite to produce an overmoderated spectrum. Still it is a design (geometry) issue. MSBR had a slightly positive coefficient so that's bad.


Top
 Profile  
 
PostPosted: Nov 28, 2013 5:04 pm 
Offline

Joined: Oct 28, 2013 12:24 am
Posts: 256
Thanks, I was also wondering why the graphite causes a positive feedback on MSRs and not in other reactors. I have read that in some reactors (like pebble bed helium cooled reactor or the LEADIR-PS100 lead cooled reactor if I am correct), the graphite gives a strong negative temperature coefficient and I didn't understand it. So I guess it's because those reactors use mainly U235 as a fuel.

In that case, a DMSR running only with low enriched uranium will maybe not have this problem.


Top
 Profile  
 
PostPosted: Nov 29, 2013 3:41 am 
Offline

Joined: Mar 16, 2010 1:48 am
Posts: 68
Location: Guangdong, China
Cyril R wrote:

The graphite effect is not very strong unless the reactor uses loads of graphite to produce an overmoderated spectrum. Still it is a design (geometry) issue. MSBR had a slightly positive coefficient so that's bad.


You are right, MSBR has positive temperature effect, it is mentioned in: "Impact of the MSBR concept technology on long- lived radio-toxicity and proliferation resistance "

Other papers talked about the reason of graphite positive effect,
"Molten salt reactors: A new beginning for an old idea"
"Core Analysis, Design and Optimization of a Deep-Burn Pebble Bed Reactor"
Does anyone have a systematic discussion paper for graphite temperature effect?


Top
 Profile  
 
PostPosted: Nov 29, 2013 6:27 am 
Offline

Joined: Jul 14, 2008 3:12 pm
Posts: 5057
I've checked the nuclear databases for fission resonances.

U-233 has a spike from 1 eV to about 2 eV peak, where the cross section rises from 100 barns or so (1 eV) to about 800 barn (2 eV). That is a big increase in fission probability in this region.

I think this means that an attractive mean neutron energy would be around 2 eV or higher, but not much lower.

U-235 does not have any big resonance peaks, rather the opposite, it drops off quickly at higher than thermal energies.

I think this indeed means that U-235 would not have a problem with positive graphite feedback even for very well thermalized spectra with loads of graphite.

There is a "but" to that last statement: Pu-239 has a big fission resonance peak at 0.35 eV. So a well thermalized spectrum with a lot of U-238 would get lots of energy from Pu-239 and could still get a positive contribution from graphite here. However the peak is more thermal than the peak of U-233 so it is unlikely to be a problem with graphite in any practical amounts for a power reactor....


Top
 Profile  
 
PostPosted: Nov 29, 2013 8:09 am 
Offline

Joined: Jul 14, 2008 3:12 pm
Posts: 5057
It appears that Pu-241 has a similar low energy resonance as Pu-239 (near 0.3 eV).

It would appear then, that the U/Pu cycle in MSRs have no issues with large positive graphite feedback.


Top
 Profile  
 
PostPosted: Nov 29, 2013 4:37 pm 
Offline

Joined: Oct 28, 2013 12:24 am
Posts: 256
I have just realized that fission resonances occur at the same energies than capture without fission resonances, so It's more complicated than I thought.

For example with Pu239 the fission cross section rises from 474 barns (0.1 eV) to 3260 barns (0.3 eV)

and the neutron capture without fission cross section rises from 221 barns (0.1eV) to 2195 barns (0.3 eV),

maybe the effect here is to decrease k and gives you a negative feedback (but i don't know).

There is also a very big capture/fission resonance for Pu240 at 1 eV.

I guess that only a proper neutronic simulation of the system can give us the answers.


Last edited by fab on Nov 29, 2013 7:29 pm, edited 1 time in total.

Top
 Profile  
 
PostPosted: Nov 29, 2013 5:54 pm 
Offline

Joined: Jul 14, 2008 3:12 pm
Posts: 5057
Good point, Pu is a bit of an exception with its great thermal capture cross section.

The increase in fission cross section is still bigger (faster) than the increase in capture.

So there should still be a net increase in reactivity on spectrum shift from thermal, right?


Top
 Profile  
 
PostPosted: Nov 29, 2013 7:10 pm 
Offline

Joined: Oct 28, 2013 12:24 am
Posts: 256
Quote:
So there should still be a net increase in reactivity on spectrum shift from thermal, right?


I really don't know, I think that only a neutronic simulation with all parameters of the system considered (geometry, exact fuel composition) can give us a good result.

After all, the conceptors of the MSBR have made a mistake in the temperature coefficient and they were not amateurs like me.
But they have an excuse, in the 70's they lacked of good computers and simulation softwares.

I just know one formula to calculate k in an unrealistic case :mrgreen:

- if you consider a system with only pure Pu239
- if you consider the system is infinit (no neutron leakage)
- if you consider that all the neutrons have the same energy (unrealistic but allows you to use only one value of cross section)
- I note v the average number of neutrons released per fission ( i take v = 2.88 for Pu239 ) , f the fission cross section and c the capture cross section you have :

k = v*f / (f+c)

at 0.1 eV you have k = 1.96

at the resonance 0.3 eV you have k = 1.72

It's a little ridiculous but that why I was wondering if the effect of this resonance is a negative feedback.


Top
 Profile  
 
PostPosted: Nov 29, 2013 8:45 pm 
Offline

Joined: Oct 28, 2013 12:24 am
Posts: 256
In fact the effect of this resonance is low ( and we are already on this resonance in normal operation, around 0.1 eV and 0.3 eV).

The effect of the resonance capture of Pu240 is much more important, in this paper, the author discuss of the graphite temperature coefficient in the AHTR :

http://www.icenes2007.org/icenes_proceedings/powerpoints.ppt/Session%207A/NEUTRONICS%20OF.pdf

Graphite reactivity coefficient :

For Pu fueled reactor : -6.53 pcm/K (very nice)

For a low enriched uranium fueled reactor : -0.21 pcm/K

Graphite (or other solid moderators) seems to be a problem only in thorium fueled reactors.


Top
 Profile  
 
PostPosted: Nov 30, 2013 3:42 am 
Offline

Joined: Jul 14, 2008 3:12 pm
Posts: 5057
If fission produces 2.88 neutrons and capture only takes out 1, wouldn't that shift the balance towards fission in reactivity?

The Pu240 I think has to do with all resonances that broaden due to overheating of the actinide atom in question (Doppler). Which is of course a different effect than the indirect graphite heating effect that comes from a spectrum shift itself (less moderation) rather than Doppler broadening through fuel overheating. But it's good to know that Pu doppler outrules any possible graphite heatup effect (even if it is positive for Pu, which now seems in question).

Pu240 is also a great "burnable poison" to regulate reactivity over burnup. It captures to make Pu241, an excellent fuel.


Top
 Profile  
 
PostPosted: Nov 30, 2013 8:49 am 
Offline

Joined: Oct 28, 2013 12:24 am
Posts: 256
Quote:
If fission produces 2.88 neutrons and capture only takes out 1, wouldn't that shift the balance towards fission in reactivity?


I am not sure but I think the ratio c/f (capture to fission ratio) plays a role. One fission always gives you 2.88 neutrons but in order to have an other fission you must use at minimum 1 + c/f neutrons : 1 neutron is absorbed and induces the fission
and c/f neutrons are just captured ( whithout fission )

So it takes you 1 + c/f neutrons just to sustain a steady power. That left you 2.88 - ( 1 + c/f ) neutrons, so if c/f is high you have fewer neutrons surplus. But I am maybe wrong so I prefer stop here, someone on this forum can maybe tell us.

Quote:
The Pu240 I think has to do with all resonances that broaden due to overheating of the actinide atom in question (Doppler). Which is of course a different effect than the indirect graphite heating effect that comes from a spectrum shift itself (less moderation) rather than Doppler broadening through fuel overheating.


It seems that Pu 240 is mainly responsable of the 2 effects, in the paper

http://www.icenes2007.org/icenes_proceedings/powerpoints.ppt/Session%207A/NEUTRONICS%20OF.pdf

the author separates the two effects :

He discuses of the graphite reactivity coefficient at pages 30; 31 and 32 :

page 31 :
Quote:
Increasing the graphite temperature causes a spectral shift to the higher energies.

At 1200 K spectral shift passes through, the peak of the cf (capture to fission) ratio of 240 Pu

Operational tmp (1200 K)
Pu: - 6.53 ± 0.12 pcm/K
U: - 0.21 ± 0.08 pcm/K


(In fact the author speaks about the capture to fission ratio, but he considers ALL the fuel ( he uses macroscopic cross sections rather than microscopic ones) and not one isotope, just looking at c/f of only one isotope like I did before doesn't make sense.)

He discuses about Doppler effect in page 33 :

Quote:
Doppler broadening : Broader peaks are “visible” to more neutrons
Operational tmp (1500 K)
Pu: - 1.24 ± 0.12 pcm/K
U: -2.26 ± 0.08 pcm/K


The composition of the fuels (Pu and U) is given page 7.


Top
 Profile  
 
PostPosted: Dec 01, 2013 12:11 am 
Offline

Joined: Mar 16, 2010 1:48 am
Posts: 68
Location: Guangdong, China
I searched a paper "The Thorium Molten Salt Reactor :Moving On from the MSBR", it discussed the sub-coefficient of temperature of graphite. I got a conclusion from this paper: graphite heating---temperature change---spectrum shift----cross section of fuel change---reactivity affected. Is it right?
the paper download website: http://arxiv.org/abs/nucl-ex/0506004


Top
 Profile  
 
PostPosted: Dec 01, 2013 12:12 am 
Offline

Joined: Mar 16, 2010 1:48 am
Posts: 68
Location: Guangdong, China
longwei1221 wrote:
I searched a paper "The Thorium Molten Salt Reactor :Moving On from the MSBR", it discussed the sub-coefficient of temperature of graphite. I got a conclusion from this paper: graphite heating---temperature change---spectrum shift----cross section of fuel change---reactivity affected. Is it right?
the paper download website: http://arxiv.org/abs/nucl-ex/0506004


So the coefficient of graphite could be negative or positive, right?


Top
 Profile  
 
PostPosted: Dec 01, 2013 5:33 am 
Offline

Joined: Jul 14, 2008 3:12 pm
Posts: 5057
So could someone explain how this works?

Suppose there's an arbitrary spectrum shift. This pushes the plutonium fission cross section up 1 barn and the capture cross section (nonfission) also increases 1 barn.

What happens to the reactivity in this case?


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 23 posts ]  Go to page 1, 2  Next

All times are UTC - 6 hours [ DST ]


Who is online

Users browsing this forum: No registered users and 3 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB® Forum Software © phpBB Group