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I wanted to know what is the minimum critical mass of natural uranium (99.28% U-238) when moderated by beryllium and light water, when in a optimumally designed lattice.
As can be seen in this article (google Plutonium Production Using Natural Uranium) criticality is attained at about 10 tons of U on graphite and 800Kg of U on heavy water. Maybe those are not optimally yet but seem close by the articles text.
With beryllium it should be an amount inbetween heavy water and graphite.
Now here (google Volume 1, Issue 2, 2007 Burn-Up Profiles for a New Beryllium) there is a reactor design that uses both beryllium and light water but it takes 300 tons of natural uranium. It is not the minimum design for critical mass but it is used for power production.
The article also says that a mixture of uranium, beryllium and water has a smaller critical mass then uranium with either beryllium or water alone. So that must be part of the solution too.
If you can think of a technically and economically easier way to achieve critical mass with natural uranium please tell us. Particle aceleration driven systems are too expensive and technical. Heavy water seems much more technical to manufacture and manage then beryllium, although you would use less uranium it doesn't offset the costs. Also beryllium seems a better neutron reflector then heavy water.
One way would be to make a subcritical pile that would breed plutonium fast enough to increase reactivity to become critical, but how long does that take? Maybe it would need to be too close to critical size to do such breeding in a reasonable time (5 years maybe) so it would be utterly futile to have to wait that long to spare 100kg of uranium.
By recent prices, you would need 3300t of graphite, maybe $39.6 mil plus $11mil for the uranium , but beryllium in the natural uranium reactor (that I think is not optimized) would be $51mil (204t) so with $28mil (303t) from uranium you would potentially be $28mil more expensive.
Can someone help us to figure how small can the beryllium reactor be? I guestimate 55.5t of Uranium and 144t of Be. Anyone with reactor physics knowlegde would please help?
Here goes some info for who knows the formulas:
Notice that adding some light water and less beryllium, the minimum mass could be smaller still. Anyone that can help?
This articles cited on Hayes (Burn-Up Profiles for a New Beryllium Moderated Water Cooled Natural Uranium Reactor) seem to have the answer but I couldn't get a hold on them:
As can be seen in this article (google Plutonium Production Using Natural Uranium) criticality is attained at about 10 tons of U on graphite and 800Kg of U on heavy water. Maybe those are not optimally yet but seem close by the articles text.
With beryllium it should be an amount inbetween heavy water and graphite.
Now here (google Volume 1, Issue 2, 2007 Burn-Up Profiles for a New Beryllium) there is a reactor design that uses both beryllium and light water but it takes 300 tons of natural uranium. It is not the minimum design for critical mass but it is used for power production.
The article also says that a mixture of uranium, beryllium and water has a smaller critical mass then uranium with either beryllium or water alone. So that must be part of the solution too.
If you can think of a technically and economically easier way to achieve critical mass with natural uranium please tell us. Particle aceleration driven systems are too expensive and technical. Heavy water seems much more technical to manufacture and manage then beryllium, although you would use less uranium it doesn't offset the costs. Also beryllium seems a better neutron reflector then heavy water.
One way would be to make a subcritical pile that would breed plutonium fast enough to increase reactivity to become critical, but how long does that take? Maybe it would need to be too close to critical size to do such breeding in a reasonable time (5 years maybe) so it would be utterly futile to have to wait that long to spare 100kg of uranium.
By recent prices, you would need 3300t of graphite, maybe $39.6 mil plus $11mil for the uranium , but beryllium in the natural uranium reactor (that I think is not optimized) would be $51mil (204t) so with $28mil (303t) from uranium you would potentially be $28mil more expensive.
Can someone help us to figure how small can the beryllium reactor be? I guestimate 55.5t of Uranium and 144t of Be. Anyone with reactor physics knowlegde would please help?
Here goes some info for who knows the formulas:
"infinite reapeating slab geometries, Be and NU(Natural Uranium) had a maximum reactivity (kinf=1.08) at about 16 cm Be and 0.6 cm NU"
[tex]R_{crit}\cong\frac{\pi*M}{\sqrt{k-1}}[/tex]
M is the migration lenght, the square root of the migration area.
Beryllium migration area=582cm2
Beryllium density=1.85g/cm3
Uranium density=19.05g/cm3
[tex]R_{crit}\cong\frac{\pi*M}{\sqrt{k-1}}[/tex]
M is the migration lenght, the square root of the migration area.
Beryllium migration area=582cm2
Beryllium density=1.85g/cm3
Uranium density=19.05g/cm3
Notice that adding some light water and less beryllium, the minimum mass could be smaller still. Anyone that can help?
This articles cited on Hayes (Burn-Up Profiles for a New Beryllium Moderated Water Cooled Natural Uranium Reactor) seem to have the answer but I couldn't get a hold on them:
Hayes R.B. A light-water-cooled nuclear reactor of natural uranium and beryllium. Journal of
ASTM International, Vol. 3, No.8 Published on line, Paper ID JAI00274. DOI:
10.1520/JAI100274
Green R. Nuclear criticality safety concerns related to transport of U-BeO waste. Trans. Amer.
Nucl. Soc 76:256, 1997.
Miller B. A., Busch R. D. Minimum enrichments of uranium for criticality in homogenous and
heterogeneous systems. Proceedings of ICNC ’99, 6th International Conference on Nuclear
Criticality Safety.
ASTM International, Vol. 3, No.8 Published on line, Paper ID JAI00274. DOI:
10.1520/JAI100274
Green R. Nuclear criticality safety concerns related to transport of U-BeO waste. Trans. Amer.
Nucl. Soc 76:256, 1997.
Miller B. A., Busch R. D. Minimum enrichments of uranium for criticality in homogenous and
heterogeneous systems. Proceedings of ICNC ’99, 6th International Conference on Nuclear
Criticality Safety.
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