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 Post subject: Running your reactor
PostPosted: Jan 04, 2014 4:05 pm 
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So the objective is to get to k=1 and criticality, this is done with a specific combination of fissile material, moderator and control elements in a PWR for instance. When criticality is reached, the power level can be adjusted by making the reactor slightly supercritical to increase the power output and slightly sub-critical to reduce the power.

My question is, what's going on when the reactor is running at a stable power setting. If the reactor was operating at k=1 with just the fissile material present in the fuel, there isn't time to reacte to power transients so delayed neutrons are used produced by a fission product.

What isotope is producing those delayed neutrons and how are they used to control the reactor?


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 Post subject: Re: Running your reactor
PostPosted: Jan 04, 2014 4:39 pm 
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Here you go. Check out the wiki explanation of delayed neutrons.


Attachments:
delayed neutron parameters.xlsx [9.15 KiB]
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 Post subject: Re: Running your reactor
PostPosted: Jan 04, 2014 8:00 pm 
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It's important to note that there is a significant difference in reactor controllability when using different fuel types in reactors.

For example, the delayed neutron fraction of U233 is small relative to the U235 we normally use: 0.67% versus 1.62%.

On top of that, unlike the *pure* U233 used in LFTRs, U235 is typically used as a small fraction in a mix with U238.
While not fissile, U238 does actually fission by fast neutrons to some extent – providing a delayed neutron yield of 4.4%.

Besides that, there may also be important sources of delayed neutrons that do not come from fission product decay.
For example, when heavy water moderator is used, we get some delayed neutrons from gamma ray hits on deuterium nuclei.
The yield is not very large (small x-section) but the effective neutron precursor halflife is much longer than for fission products: Since delayed neutrons are weighted by precursor halflife, it makes these D(g,n)H neutrons quite important -- giving Candu reactors a nice slow response to reactivity changes.


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 Post subject: Re: Running your reactor
PostPosted: Jan 04, 2014 10:08 pm 
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Quote:
how are they used to control the reactor


I am not an expert so if I made mistakes I apologize and I hope someone will correct me.

The idea is to be slightly subcritical with prompt neutrons and reach a steady power with delayed neutrons.

Imagine a reactor running at stable power k=1. In that case one fission will produce neutrons and this neutrons will produce exactly one other fission.

So 100 000 fissions will give you exactly an other new 100 000 fissions (k=1, steady power). These fissions give you "instantaneously" some prompt neutrons and fission products ( I note Np the number of prompt neutrons generated by 100 000 fissions). Later some of the fissions products will give you the delayed neutrons ( I note Nd the number of delayed neutrons generated ). The total amount of neutrons generated by these 100 000 fissions is N. We have N = Np + Nd

The delayed neutron fraction is defined by B = Nd / N

For example, we imagine that the reactor is a thermal reactor with only pure U235 as a fissile material. The total number of neutrons released by one fission
is v = 2.42

So the total amount of neutron released by 100 000 fissions is roughly 242 000 neutrons. For U235 you have B = 0.679 % = 679 pcm

The number of delayed neutrons produced by this 100 000 fissions is roughly Nd = B*N = 1643 delayed neutrons ( of course the precision is not at one neutron but let's forget it)

And the number of prompt neutrons : Np = N-Nd = 240 357 prompt neutrons.

The delayed neutrons are emitted with not the same energy of the prompt neutrons, so their probability of inducing fission is different than the prompt neutrons, we manage this with the "effective fraction of delayed neutron".
The effective fraction of delayed neutron is noted Beff.

Beff depends of your reactor design. Let say that we have Beff = 0.69 % = 690 pcm. The delayed neutrons will induce Beff = 0.69 % of the new 100 000 fissions. So they will induce 690 new fissions.

The prompt neutrons will induce 99.31 % of the new fissions so they will induce 99 310 fissions, this is less than 100 000 so the reactor is subcritical with only prompt neutrons, and the delayed neutrons fill the gap until 100 000 fissions.

When you change the power of your reactor you must always be subcritical with prompt neutrons in order to control the reactor.


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 Post subject: Re: Running your reactor
PostPosted: Jan 04, 2014 10:52 pm 
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Location: Oak Ridge, TN
In addition to delayed neutrons, reactivity feedback effects are also very important for the stability and controllability of reactor systems. Reactors are designed to have "negative reactivity coefficients" such that when reactor power increases (and fuel temperature and coolant/moderator temperatures increase) result in negative reactivity supporting stability of the system. Even in the case of prompt supercritical reactivity insertions (where delayed neutrons are no longer limiting), the rapid feedback affect of the fuel can prevent serious over-power transients. Of course, reductions in the power (and decreases in temperatures) will add reactivity to the system, so you also need to consider over-cooling events as well.

jaro - note that for CANDU reactors the primary reason why they have slower kinetics is that the neutron lifetime is rather long. Neutron scatter around a lot more in D2O before being absorbed than for light water systems resulting in a neutron lifetime that is about 10x longer than in LWRs (~10-3 vs ~10^-4).


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 Post subject: Re: Running your reactor
PostPosted: Jan 04, 2014 11:09 pm 
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Jess Gehin wrote:
jaro - note that for CANDU reactors the primary reason why they have slower kinetics is that the neutron lifetime is rather long. Neutron scatter around a lot more in D2O before being absorbed than for light water systems resulting in a neutron lifetime that is about 10x longer than in LWRs (~10-3 vs ~10^-4).
This effect is widely known.

The effect of delayed neutrons from D(g,n)H appears to be far less known -- in fact I'm not sure I've ever seen it outside of internal AECL reports: Have you ?
As "fab" explains so well in his (her?) post above, reactors are operated subcritical on prompt neutrons -- so it's the differences in the delayed neutron groups (grouping by half-life) that really make the difference.
Same deal in fast reactors: The prompt neutron lifetime is on the order of microseconds, but with a good supply of delayed neutrons (inluding U238 fission, with an unusually high fraction), they are quite manageable.....


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 Post subject: Re: Running your reactor
PostPosted: Jan 04, 2014 11:32 pm 
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jaro wrote:
The effect of delayed neutrons from D(g,n)H appears to be far less known -- in fact I'm not sure I've ever seen it outside of internal AECL reports: Have you ?


Yes, we considered this in the design analysis of the Advanced Neutron Source reactor at ORNL (a very high flux research reactor with a D2O reflector) in the early 1990s. Both deuterium and beryllium, common moderators for research reactors, can have gamma,n reactions, but I believe that Be has a higher energy threshold.

jaro wrote:
Same deal in fast reactors: The prompt neutron lifetime is on the order of microseconds, but with a good supply of delayed neutrons (inluding U238 fission, with an unusually high fraction), they are quite manageable.....


Right, I didn't say they weren't manageable, just that the reactivity feedback effects are key in the response (in addition to the neutron kinetics parameters). For reactivity insertions that approach or exceed prompt critical, your reactivity control systems cannot respond quickly enough and it the feedback effects that you have to rely on. A good example of this is a control rod ejecting event in a PWR.


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 Post subject: Re: Running your reactor
PostPosted: Jan 05, 2014 10:41 am 
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Quote:
As "fab" explains so well in his (her?)


his.



I wonder what happens if a reactor reach prompt criticality. It depends of your prompt negative temperature coefficient and the lifetime of the neutrons.

I believe that a little TRIGA reactor is designed to resist at this event with his high prompt negative temperature coefficient.

What happens in a big commercial Light Water Reactor ? A meltdown ? A steam explosion if you can not depressurize quickly ?

And in a fast sodium cooled reactor ? I believe that I read on this forum that with a metal fuel the core is melted and dispersed, and with an oxide fuel the core explodes.

Does anyone here know something about this ?


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 Post subject: Re: Running your reactor
PostPosted: Jan 05, 2014 11:02 am 
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The SL-1 went prompt critical.

It is a fairly good example of what happens to a PWR.


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 Post subject: Re: Running your reactor
PostPosted: Jan 05, 2014 11:04 am 
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fab wrote:
Quote:
As "fab" explains so well in his (her?)

I wonder what happens if a reactor reach prompt criticality. It depends of your prompt negative temperature coefficient and the lifetime of the neutrons.

I believe that a little TRIGA reactor is designed to resist at this event with his high prompt negative temperature coefficient.

What happens in a big commercial Light Water Reactor ? A meltdown ? A steam explosion if you can not depressurize quickly ?

And in a fast sodium cooled reactor ? I believe that I read on this forum that with a metal fuel the core is melted and dispersed, and with an oxide fuel the core explodes.

Does anyone here know something about this ?


Yes, reactivity insertion events are part of the design basis of reactors. For prompt supercritical events, the active control systems cannot perform fast enough, so inherent negative feedback mechanism are used. For most reactors this is the Doppler feedback, or negative fuel temperature feedback, that is very fast acting because it is directly related to the fuel temperature. Increasing temperature broadens absorption resonances that capture more neutrons. This is the dominate mechanism for thermal reactors. For fast reactors, the Doppler feedback is not as strong, but thermal expansion plays an important role. The design of the reactor is such that you limit the maximum credible reactivity insertion so that these inherent feedback mechanisms can limit the power excisions to avoid fuel damage. In the case of TRIGA reactors (and a few other times), the feedback mechanism are enhanced to allow the reactor to pulse without fuel damage. This is accomplished in TRIGA reactors through the use of uranium-zirconium-hydride fuel.

You can find more background on this for LWRs in the NRC standard review plan, NUREG800 (http://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr0800), chapter 15. A typical section on this is 15.4.8 related to control rod ejection in PWRs. You can see the range of accidents that must be considered by looking through the section titles of Chapter 15.

For fast reactors, I would recommend NUREG1368 (http://pbadupws.nrc.gov/docs/ML0634/ML063410561.pdf), which includes a discussion of reactivity insertion events that go in to the design considerations of the number of control rods and use of rod stops to prevent accidental rod ejections that would add more than $0.5 of reactivity, thus avoiding prompt critical excursions.


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 Post subject: Re: Running your reactor
PostPosted: Jan 05, 2014 11:24 am 
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E Ireland wrote:
The SL-1 went prompt critical.

It is a fairly good example of what happens to a PWR.



SL-1 is actually not a very good example because it's design was significantly different than currently operating LWRs. Key differences in design that would result in a substantially different response to a control rod ejection event is that SL-1 had very fuel control rods, meaning that each rod had a large reactivity worth. The fuel was used HEU, which would result in less Doppler feedback that LEU fuel. And the fuel was uranium-nickel-aluminum alloy fuel that melt at relatively low temperature compared to UO2, and the rapid melting and dispersal of the the fuel is what resulted in the steam explosion.


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 Post subject: Re: Running your reactor
PostPosted: Jan 05, 2014 11:43 am 
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Thanks a lot, I will see the documents.


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 Post subject: Re: Running your reactor
PostPosted: Jan 06, 2014 5:02 pm 
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Interesting.

So on start-up you take the reactor to slightly below k=1 and allow the buildup of fission products that provide the needed neutron flux to take you over the threshold?

And then monitor the power level and activate control elements as needed to keep the reactor as close to k=1 as possible?


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 Post subject: Re: Running your reactor
PostPosted: Jan 07, 2014 6:19 am 
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Quote:
So on start-up you take the reactor to slightly below k=1 and allow the buildup of fission products that provide the needed neutron flux to take you over the threshold?


I don't really know, they always have a source of neutrons in the reactor, if the reactor is new they use a startup neutrons source :

http://en.wikipedia.org/wiki/Startup_neutron_source

These sources give you a weak flux of neutrons which permit you to measure k and maybe they also replace the delayed neutrons for a safe startup.

If the reactor has not been shut down for a long period, the fission products in the fuel gives you a weak flux of neutrons which is maybe sufficient for a safe startup.


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 Post subject: Re: Running your reactor
PostPosted: Jan 09, 2014 12:28 am 
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Yes, reliable reactor startup requires a source of neutrons, either from an inserted source using materials such as Cf-252 or from spontaneous neutron generation in burned fuel (from alpha,n sources, not delayed neutrons which are long-gone for most shutdown periods). This source of neutrons is negligible at power, so for reactor startup you need k slightly greater than 1 to increase the core power level. If k<1 on reactor startup, it doesn't start up, but you can get subcritical multiplication, its just that the neutron start up sources are too low to amount to much power). Also note that the definition of keff is for steady state operation including the delayed neutrons (the value of nu used in the calculation typically includes both prompt and delayed neutrons). Of course, as the power increases, you also need to add reactivity (typically by withdrawing control rods) to offset the reactivity loss from the increasing fuel and coolant temperatures.


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