Quoting from PNAS | September 25, 2001 | vol. 98 | no. 20 | 11085-11090
posted at http://www.pnas.orgycgiydoiy10.1073ypnas.201393998 :
In setting forth the fundamental concepts and underlying basis for planetary-scale nuclear fission reactors, Herndon (4-6, 10) recognized that fuel breeding was necessary for reactor functioning over the most recent 2,000 million years. From evidence of fuel breeding in the Oklo reactor, fuel breeding was assumed possible for planetary-scale reactors, but it was not demonstrated quantitatively in previous publications. This communication presents the results of calculations made by using the SCALE code sequence for nuclear reactor fuel-depletion studies (11).
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For the calculations performed in this paper, the initial material compositions and abundances are contained in Table 1.
Table 1. Initial values of the deep-Earth reactor
Isotope Initial mass, Initial density, Relative atom
g g/cm^3 abundances
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235 U 4.867x10^18 8.568 0.233
238 U 1.606x10^19 28.272 0.767
Uranium 2.0927x10^19 36.84 1.0
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Values are those used as input to SAS2. Initial volume of the uranium is 5.6807x10^17 cm^3 . Steady-state fission power: 3.0 TW (3.0x10^19 ergs / s). The uranium values are taken from Herndon (4), based on the uranium concentration of the alloy portion of the Abee enstatite chondrite, corresponding to the Earth's core, multiplied by Earth core mass. The uranium density is from equation of state calculations (4).
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The reason a self-sustaining chain reaction is possible through-out the entire period of geologic time is that 235 U, 239 Pu, and other higher order fissile actinides are produced from 238 U as follows. When 238 U absorbs a neutron, it eventually transmutes to 239 Pu, which is a fissile nuclide. The 239 Pu fissions, decays to 235 U, or absorbs a neutron, forming a higher-mass actinide, which is also fissile. In a long-lived breeding fission reactor, the majority of 238 U is converted to fissile actinides that help sustain the self-sustained chain reaction.
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In the constant-power level geo-reactor simulation, fast neutron fission and fuel breeding reactions keep the 235 U/ 238 U ratio nearly constant after 1.5 billion years and appropriate for critical reactor operation. By contrast, in the absence of fission and breeding, radioactive decay alone decreases the 235 U/ 238 U ratio to such a point that the natural initiation
of nuclear chain reactions for natural uranium in recent geologic times is impossible.
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Jaro
-----Original Message-----
From: Nardi, A. Joseph [<mailto:nardiaj@WESTINGHOUSE.COM>]
Sent: Thursday July 18, 2002 3:10 PM
To: RADSAFE; 'Susan L Gawarecki'
Subject: RE: Nuclear Planet in DISCOVER
I read the article and feel that there is a major problem with the concept.
The % U-235 would have to less than 0.71% to account for the U-235 burnup
over time. At normal conditions it is not be possible for normal uranium to
achieve criticality without the presence of special moderators. Also at
normal conditions it is not possible to have U-238 achieve a fast neutron
critical state. But I am not sure if the conditions at the center of the
earth would be sufficient to achieve a "fast neutron criticality". So it is
not clear to me that the theory proposed in the article has any possible
merit. My impression on reading the article is that Mr. Herndon has only
looked at the issue from heat generation without answering the question of
whether nuclear criticality is possible. I do know that the implosion
design of nuclear weapons achieve nuclear criticality by increasing the
density of the Plutonium. So maybe the conditions at the center of the
earth might permit a nuclear criticality event that we do not encounter
under the normal conditions on the surface.
Does any nuclear criticality specialist out there know of data that would
answer the questions?
What uranium density would have to be achieved to reach a fast
neutron critical state with 0.7% U-235 material?
Is it possible to have U-238 reach a fast neutron critical state at
high densities?
And for the physicists among us:
What would be the density of uranium under the pressure at the
center of the earth?
A. Joseph Nardi
Supervisory Engineer
Environment, Health and Safety
Westinghouse Electric Company
Phone: (412) 374-4652
Email: nardiaj@westinghouse.com