Helium as Moderator: Neutron Absorption & Travel Distance

[snorkack]

Helium has the only stable nucleus which does not absorb neutrons.

At practical reactor conditions, say 300 atmosphere pressure and +300 Celsius temperature, how far would a fission spectrum neutron at say 5 MeV average, travel until it is thermalized?

Under the same conditions, how far would the neutron travel by Brownian motion in 1000 seconds?

 

[Astronuc]

Helium has the only stable nucleus which does not absorb neutrons.

At practical reactor conditions, say 300 atmosphere pressure and +300 Celsius temperature, how far would a fission spectrum neutron at say 5 MeV average, travel until it is thermalized?

Under the same conditions, how far would the neutron travel by Brownian motion in 1000 seconds?

300 atm = 4410 psia, which would be problematic for a pressure vessel - i.e., it would require a very expensive pressure vessel. Try using the ideal gas law to determined the mass and atomic density under the cited conditions, and then determine the potential scattering cross-section for He, and see what the mean distance is for the first collision (and compare the results to those of graphite).

5 MeV is a bit high. The most probably energy for a fission neutron is about 1 MeV.

1000 seconds is a very long time for a neutron in a reactor. That's 16.66 minutes, which is greater than one half-life (~10.2 min). Lifetimes of neutrons in a fission reactor are measured in micro-seconds.

Gas(He)-cooled reactors generally use graphite for moderation.

 

[snorkack]

300 atm = 4410 psia, which would be problematic for a pressure vessel - i.e., it would require a very expensive pressure vessel.

I see that typical pressures of pressurized water reactors are 150...160 atm.
Is 300 Celsius a plausible number for temperature in a working reactor?

 

[Astronuc]

I see that typical pressures of pressurized water reactors are 150...160 atm.
Is 300 Celsius a plausible number for temperature in a working reactor?

Yes - 300 °C is less than the hot leg temperature to the steam generator in a PWR. Typical inlet temperatures are in the range of 280 to 294°C, and hot leg temperatures are on the order of 320 to 330 °C.

Gas-cooled reactors can run hotter using a Brayton cycle, which could conceivably reject heat to a steam (Rankine) cycle - as in a combined cycle plant.

However, the higher the steam temperature, the higher the pressure, and one has to balance temperature/efficiency against the structural requirements (strength and creep resistance) and corrosion resistance (and generally resistance to degradation).

There has been consideration given to supercritical water cycles for nuclear plants. Supercritical water systems have been used in coal plants.

http://www.gen-4.org/Technology/systems/scwr.htm

http://power4georgians.com/supercritical.aspx

http://www.aep.com/environmental/climatechange/advancedtechnologies/docs/SuperCriticalFactsheet.pdf

http://www.worldcoal.org/coal-the-environment/coal-use-the-environment/improving-efficiencies/

Special steels must be used for SCW power plants.

 

[snorkack]

300 atm = 4410 psia, which would be problematic for a pressure vessel - i.e., it would require a very expensive pressure vessel. Try using the ideal gas law to determined the mass and atomic density under the cited conditions, and then determine the potential scattering cross-section for He, and see what the mean distance is for the first collision (and compare the results to those of graphite).

Fine...
Ideal gas would be 1 mole about 22,4 l at 273 K and 1 bar, so about 47 l at 300 C and 1 bar. From ideal gas law, about 0,32 l at 150 bar... though gases are no longer ideal at 150 bar. So, guess 3,2 mol/l. Which is about 1,9*10^24 nuclei.

With cross-section, from http://www.nndc.bnl.gov/sigma/index.jsp?as=4&lib=endfb7.1&nsub=10 being 7,05 barns at 1 MeV, the mean distance for first collision would be in the region of 75 cm.

For graphite, solid density about 2200 g/l means about 180 mol/l nuclei. Cross-section 2,6 barns means about 2 cm distance for first collision.

Right?

 

[snorkack]

For graphite, solid density about 2200 g/l means about 180 mol/l nuclei. Cross-section 2,6 barns means about 2 cm distance for first collision.

Right?

My error - about 3,5 cm.

 

[Astronuc]

Those numbers are about right as a rough estimate (i.e., excluding other materials such as fuel). For He, I calculated 33 cm, but I assumed compressing the gas to 300 atm. The larger the mean free path, the larger the core, or higher the enrichment requirement for criticality for a given core size. One also has to consider the accumulation of fission products and their impact on the fuel integrity, criticality and power distribution in the core.

Note the steep drop off of the cross-section for He as the neutron energy decreases, so the mean free path increases.

In a fission reactor, one has to have fuel (some fissile material dispersed in some matrix), some structural material (which retains fission products and maintains a relatively constant geometry), and a coolant. A moderator may be present depending on whether or not one wishes to use a thermal or epi-thermal neutron spectrum.

The temperature of the fuel is important with repect to fission product retention, fuel-structure chemical interaction, and controlled geometry. Controlled geometry is critical for controllability and coolability of the fuel - both technical and legal requirements for reactors.

 

[snorkack]

Those numbers are about right as a rough estimate (i.e., excluding other materials such as fuel). For He, I calculated 33 cm, but I assumed compressing the gas to 300 atm. The larger the mean free path, the larger the core, or higher the enrichment requirement for criticality for a given core size. One also has to consider the accumulation of fission products and their impact on the fuel integrity, criticality and power distribution in the core.

Note the steep drop off of the cross-section for He as the neutron energy decreases, so the mean free path increases.

I see...
Some common light nuclei for comparison (the tables are hard to read each time to consult):
H - scattering 4,24 barns at 1 MeV, 20,4 barns thermal, capture 332 millibarns thermal
D - scattering 2,87 barns at 1 MeV, 3,4 barns thermal, capture 0,5 millibarns thermal
He - scattering 7,06 barns at 1 MeV, 0,77 barns thermal, capture impossible
C - scattering 2,58 barns at 1 MeV, 4,74 barns thermal, capture 3,86 millibarns thermal
O-16 - scattering 8,15 barns at 1 MeV, 3,85 barns thermal, capture 0,19 millibarns thermal
Correct?

 

[snorkack]

1000 seconds is a very long time for a neutron in a reactor. That's 16.66 minutes, which is greater than one half-life (~10.2 min). Lifetimes of neutrons in a fission reactor are measured in micro-seconds.

Yes - 1000 seconds is more than e-life, but the correct order of magnitude.

I considered He-4 because the lifetimes if neutrons are in microseconds in any condensed matter except He-4.

So what could be the distance a neutron covers in He-4 by diffusion in its half-life of 10 minutes?

 

[ZoomStreak]

Are we assuming an infinitely large reactor vessel containing no fuel?