Size Limitation of fuel Bundle in a nuclear reactor

[Ashok]

TL;DR Summary

Size Limitation of fuel Bundle in a nuclear reactor

What is the limitation of length of a fuel bundle in a nuclear reactor. Can we increase the length of bundle consequently reducing the number of bundles in a fuel channel?

 

[anorlunda]

Summary:: Size Limitation of fuel Bundle in a nuclear reactor

Can we increase the length of bundle consequently reducing the number of bundles in a fuel channel?

You can change any dimension in theory, but there will be many secondary consequences that must be evaluated. That makes it an analysis project that could take many man-years to evaluate an answer of "better or worse."

 

[Astronuc]

Summary:: Size Limitation of fuel Bundle in a nuclear reactor

Can we increase the length of bundle consequently reducing the number of bundles in a fuel channel?

CANDU, AGR or RBMK?

LWRs use a plurality of single assemblies in a square array, and the core is designed for a height of the fuel zone (pellet stack, or fuel column) to approximately match the width of the core (H/D ~ 1). Most LWR assemblies themselves use square lattice/array of fuel rods and guide tubes/instrument tube.

VVER (Russian PWR) and fast reactors use hexagonal (or triangular) lattices/arrays and assembly array in the core.

The dimensions of the assemblies and core are sized based on energy/power generation and nuclear considerations, subject to constraints on mechanical and thermal limits, as well as expected dynamic response when the assembly and core would be subject to a seismic event (earthquake), loss of coolant accident (LOCA), or reactivity insertion accident (RIA) event. There are also considerations for the core support structure and reactor pressure vessel (RPV).

 

[rpp]

If you are designing a reactor from scratch, yes, you can increase the length to whatever you can make work. The trick is finding something that will work.

For an LWR reactor, you have to consider how much heat you can remove from the fuel assembly and safely make sure that you do not reach departure from nucleate boiling (DNB) or critical power. The coolant comes in at a certain inlet temperature, and you must be able to remove a certain amount of heat before reaching the limits. Given the inlet temperature and power density of modern LWRs, the maximum fuel height is about 12-12.5 feet tall. However, if you lower the inlet temperature or reduce the power density, you can make the bundle taller.

Other reactor types will have similar limitations. In the end, the core size is going to be limited to being able to safely and effectively being able to remove the heat generated and remain in the limits of the materials.

 

[artis]

@Astronuc please correct if possible, I liked this question because it made me think from a neutronics point of view. I had the idea in my mind that the shape is somewhat influenced by the neutron economy and balance of the resulting critical mass once assembled and formed but then I thought and...
In a bomb the shape has to be spherical in order to achieve homogeneous reaction rate during explosion is what I understand , neutron mean free path in U235/238 is about 16cm for an uncompressed sphere that probably goes down as the mass is compressed during the firing of the implosion charges.

Anyway for a reactor this doesn't change because the density of materials largely stays the same, but what about the shape of a reactor in terms of it's neutron economy?
When tried to refresh my memory I recall hydrogen aka light water is a very good neutron scatterer and for example for a 2MeV neutron needs only about 18 collisions on average to get down to 0.025eV.
The mean free path for neutrons in water around fuel rods are a few cm right? Does it change with neutron energy, as they get lower in energy after each scatter does the path length also decrease?

Anyway this made me think and as a question, if the neutrons emitted by fission within fuel rod (those that get out of the rod at all) never make far away from the rod before they get either absorbed or down scattered to thermal energy where they cause fission in an adjacent rod, then does a reactor (purely from a neutronics point of view) has to be spherical or any specific shape at all?
I mean shouldn't in theory (again from a neutronics viewpoint) one have a reactor that is like a long thin noodle or a twisted spring or whatever shape ?
Because from what I recall the vast majority of neutrons ever get to interact close to the point they are born?
Also from the same viewpoint would a reactor be more efficient if the fuel was in the form of tiny particles mixed with the moderator like in "soup" somewhat like the molten salt reactors thereby one could have a homogeneous chamber of a given amount of fuel/moderator mixture instead of having solid fuel rods with lots of adjacent space filled with moderator as well as structural material

 

[Astronuc]

from a neutronics point of view. I had the idea in my mind that the shape is somewhat influenced by the neutron economy and balance of the resulting critical mass once assembled and formed but then I thought and...
In a bomb the shape has to be spherical in order to achieve homogeneous reaction rate during explosion is what I understand , neutron mean free path in U235/238 is about 16cm for an uncompressed sphere that probably goes down as the mass is compressed during the firing of the implosion charges.

A bomb is very different from a power reactor. The mean free path of a neutron decreases as one increases the density of fissile material.

From a purely neutronics point of view, a sphere is the most economical form. One can do a criticality calculation and determine that, and show that a right circular cylinder is somewhat less efficient for the same volume. For a power reactor however, one usually settles for a core that is close to cylindrical as possible. This obviously is not the case where assemblies are discrete lattices of fuel rods on a given square pitch. In a light (LWR) or heavy (HWR) water reactor, the coolant channels between adjacent fuel rods provide both moderation and cooling.

The mean free path for neutrons in water around fuel rods are a few cm right? Does it change with neutron energy, as they get lower in energy after each scatter does the path length also decrease?

The mean free path depends on the neutron energy as does the macroscopic cross-section. Fission neutrons are born in the MeV range, and in an LWR, they are slowed to energies in the 0.02 to 0.1 eV range, where the fissile cross section for ²³⁵U is much larger than for neutrons at greater energies. Keep in mind, that fast neutrons can induce fission in ²³⁵U and ²³⁸U with something like 8-10% of fissions coming from fast neutrons.

Fast neutrons may travel some distance from their birth, while many don't, due to moderation or absorption. In general, initial cores are loaded with varying enrichments, with lower enrichments toward the outside, which act more as a reflector. Also, some fraction of the fuel (typically 1/3 of the core) will be replaced at the end of the first cycle. Higher enrichment assemblies will remain in the core, and those of lower enrichment moved to the outside (periphery), where the power falls due to increased leakage, and the fact that toward the edge of the core, one does not have a source of neutrons entering from outside the core.

Also from the same viewpoint would a reactor be more efficient if the fuel was in the form of tiny particles mixed with the moderator like in "soup" somewhat like the molten salt reactors thereby one could have a homogeneous chamber of a given amount of fuel/moderator mixture instead of having solid fuel rods with lots of adjacent space filled with moderator as well as structural material

There are concepts of molten salt-cooled reactors, but a molten salt moderator is rather limited. One is limited to light elements like Li or Be, with some amount of U involved. Usually, however, there is some graphite-type moderator. One current design considers TRISO-type particles/pebbles (fuel/PyC/(SiC or ZrC)/PyC) in a molten salt mixture.

https://kairospower.com/technology/
https://www.nrc.gov/docs/ML1833/ML18337A040.pdf
https://www.nrc.gov/docs/ML2018/ML20182A830.pdf

Flouride salts are used in thermal (neutron spectrum) reactors, while chloride-based salts are used in fast reactor systems.

The OP was not clear on the type of reactor, but simply asked, "Can we increase the length of bundle consequently reducing the number of bundles in a fuel channel?" This would imply a system like CANDU, RBMK, Magnox or AGR in which fuel elements are loaded in channels. CANDUs have horizontal fuel channels, and each of 12 or 13 fuel assemblies have a fuel length of ~1 m. RBMKs, MagnoxRs and AGRs have vertical channels, and the fuel rods are also short.

Ostensibly, the fuel rods/assemblies could have been longer, but there various engineering and performance aspects that resulted in the shorter lengths.

As for longer fuel assemblies, e.g., 3.66 m to 4.27 m fuel stack length, or 4 to 4.5 m fuel assembly length/height, besides cooling and thermal hydraulic considerations (a longer fuel assemby has a greater pressure drop (drag) for a given flow rate), there are other considerations such as structural stability (assembly bow and vibration/oscillation), dimensional stability (due to differential growth due to flux/thermal gradients), reactivity control (how fast can control rods be inserted into a core to shutdown a reactor), fuel rod internal pressure, and fuel handling before and after service.

 

[artis]

In a light (LWR) or heavy (HWR) water reactor, the coolant channels between adjacent fuel rods provide both moderation and cooling.

Well that was my question, in a bomb the sphere is small in size and a neutron born at any place within said sphere could in theory reach any other place within the sphere and cause a fission event or be absorbed or scattered or escape. But the point was that anyhow each part can affect any other part of the sphere. But in a power reactor given neutrons quickly become thermal outside of a fuel rod their mean free path becomes small and before (fission, absorption,) they don't get far from their birth place within their birth fuel rod?
I talk only about those neutrons that get out of the fuel rod at all and don't even consider the ones that end their life at the very fuel rod they were born to cause that

8-10% of fissions coming from fast neutrons

because I assume that once a neutron leaves a fuel rod within a "thermal" LWR reactor it is not longer fast but quickly becomes thermal.
With all of this I'm asking is that unlike for a bomb sphere it seems to me that in a reactor only adjacent fuel rods can impact one another via neutrons? It seems to me the whole reactor simply works as if it were many smaller reactors put together?

Let me ask differently , imagine a typical PWR stack of fuel bundles, from the perspective of a bundle located at the center or few bundles away from center would the neutron flux change if I removed say 30% of the outer bundles in a symmetrical fashion evenly around the periphery?
It seems to me it shouldn't change because those neutrons from the outer bundles never make it to the center or close to it anyway, is that true?

Neutron interactions radiological experiments

The mean free path depends on the neutron energy as does the macroscopic cross-section

But I assume it's the cross section that determines the mean free path as when neutron energy decreases the cross sections for scattering increase so it interacts more and therefore manages to travel shorter distances before events?

with lower enrichments toward the outside, which act more as a reflector.

the outer assemblies act more as reflectors you say but in the light of what I asked earlier, don't they just reflect the very neutrons that were born within their direct vicinity? If so I would assume this gradual lowering of enrichment should happen over multiple circular layers as one moves toward periphery so that each next layer has an increment lower enrichment therefore less and less neutrons are born within the peripheral assemblies and therefore less of them leak out?

 

[Astronuc]

they don't get far from their birth place within their birth fuel rod?

Let's assume that a neutron doesn't go far, perhaps 1 cm, but that is enough for one fuel rod to affect (cause fission) in the adjacent fuel rods, so each fuel rod will cause fissions in neighbors, which cause fissions in their neighbors (in some cases shared neighbors), and so on. It doesn't take long for a fission event to have propagated through successive fuel rods (like dominoes) until the effect is felt several meters away.

It seems to me the whole reactor simply works as if it were many smaller reactors put together?

Yes and no. Each fuel rod or group of fuel rods (an assembly) is coupled to it's neighbors. In other words, each fuel rod or assembly will immediately affect four face-adjacent assemblies (or fuel rods in square lattice), and four corner assemblies (or rods in the lattice), or in the case of hexagonal assemblies, 6 face-adjacent assemblies.

Fuel rods (and assemblies) can self-irradiate, i.e., a fission neutron can cause a fission in the fuel rod (or assembly) in which it is born, or can travel a short distance to a neighbor and cause a fission (or not). For each 2 or 3 (on average about 2.2 to 2.3) neutrons released from a fission event, only one neutron is necessary to cause another fission. The remaining neutrons can be absorbed by other U (or Pu) fuel atoms and not cause fission, absorbed by various fission products, absorbed by the various structural materials in the core, absorbed by neutron poisons (soluble ¹⁰B in the coolant) or control rods, or simply leave the core, if they are born close enough to the edge to 'leak out'.

O O O
O O O If the center rod emits neutrons, it can self-irradiate, or affect each neighbor, which affect others.
O O O

If the lifetime of a neutron from fast to thermal energy is about 1 msec, then in 1 second, it's effect can be experienced 1 m away. A flux gradient implies that more neutrons are diffusion in a given direction than in the opposite direction, and we see flux gradients between assemblies, especially where one assembly is operating at higher power than neighboring assemblies, which is particularly the case with assemblies near the periphery of the core, or in the case of BWRs, where assemblies operate adjacent to a control blade.

If one removes the outer row of assemblies, then the remaining adjacent assemblies become the outer row, and they would leak neutrons out of the core, and very likely, the core would become subcritical sooner, it wasn't already subcritical. In general, smaller cores require greater enrichment to be critical. If a core is not critical, or rather subcritical, the power continues to decrease, until it shuts down.

Consider a 0.82 cm fuel pellet operating in a fuel rod generating a linear power of 10 kWft (~330 W/cm). That means a power density of ~625 W/cm³. At 200 MeV per fission, that implies 1.95 E13 fissions/cm³-s, or about 4.3 E13 fast neutrons per cm³-s, which is a lot of neutrons.

If so I would assume this gradual lowering of enrichment should happen over multiple circular layers as one moves toward periphery so that each next layer has an increment lower enrichment therefore less and less neutrons are born within the peripheral assemblies and therefore less of them leak out?

Not exactly. In PWRs, fuel rods tend to have the same enrichment at beginning of life (BOL), or as-fabricated. However, there are designs that might use reduced enrichments, placed in the corner cells of the assembly, or symmetrically within the assembly, and often with a burnup absorber material for reactivity control. If the assembly operates in the interior of the core, where the power is relatively flat, i.e., little or no gradient, then the fuel rods of the same enrichment deplete (lose enrichment) at about the same rate. On the other hand, if an assembly sits near the periphery of the core (outer row, or next to outer row), then the inboard fuel rods will deplete at a greater rate than the outboard fuel rods, and so the assembly experiences a flux/fluence and burnup gradient. Such 'gradient' assemblies would then be moved to the opposite side of the core if they remain in the core in order to reverse the gradient and balance the burnup (cumulative energy generation).

In core with free standing assemblies (like those in LWRs), one usually does not stack assemblies for a number of reasons. CANDUs, RBMKS, Magnox and AGRs are different animals.