The scientist is interested in the right answer, the engineer in the best answer now.
I read an interesting article today about the natural nuclear reactors of Oklo, Gabon. I had first read about these reactors in a Scientific American article back in 2005. The article I read today was interesting because it did a good job presenting some of the key numbers related to uranium isotope ratios on Earth, how the uranium got here, and how natural nuclear reactors could have formed ~2 billion years ago, but probably not today.
To help me understand the isotope ratios presented in this article, this post will develop an expression for how the isotope ratio of 235U to 238U has varied over time and this expression will be used to explain how conditions in Oklo two billion years ago were just right to form a natural nuclear reactor. In addition, I will use this model to estimate when the uranium was formed in a supernova explosion prior to the formation of our solar system.
French researchers discovered the reactors in 1972 while performing an isotope analysis on rock samples from the Oklo site. The 235U-to-238U isotope ratio is normally very close to 0.72%, but at Oklo the ratio is 0.717%. While this may seem like a small deviation, the natural isotope ratio normally has little variance and the Oklo measurement were significantly outside the normal range. Detailed measurements of isotope residues conclusively showed that Oklo's 235U-to-238U isotope ratio was low because a nuclear reaction had consumed some 235U.
Figure 2 shows a video briefing on the Oklo reactors that provides useful background information.
|Figure 2: Video Briefing on Oklo Natural Reactors.|
Figure 3(a) shows the location of the Oklo reactors on the African continent. Figure 3(b) shows the appearance of one of the reactors when a tunnel was dug through it.
|Figure 3(a): Location of Gabon's Natural Nuclear Reactors (Link)||Figure 3(b): Appearance of the Underground Strata at Oklo.|
Figure 4 is an illustration that shows how the natural reactors are positioned in the strata.
The following Wikipedia quote gives a good description of the number of reactors and their power level.
Oklo is the only known location for this in the world and consists of 16 sites at which self-sustaining nuclear fission reactions took place approximately 1.7 billion years ago, and ran for a few hundred thousand years, averaging 100 kW of thermal power during that time.
The following excerpt from the Wikipedia describes how the reactors would turn off and on periodically.
The natural nuclear reactor formed when a uranium-rich mineral deposit became inundated with groundwater that acted as a neutron moderator, and a nuclear chain reaction took place. The heat generated from the nuclear fission caused the groundwater to boil away, which slowed or stopped the reaction. After cooling of the mineral deposit, the water returned and the reaction started again. These fission reactions were sustained for hundreds of thousands of years, until a chain reaction could no longer be supported.
.... The concentrations of xenon isotopes, found trapped in mineral formations 2 billion years later, make it possible to calculate the specific time intervals of reactor operation: approximately 30 minutes of criticality followed by 2 hours and 30 minutes of cooling down to complete a 3-hour cycle.
Stated Isotope Ratios
The article that I read presented the following numbers:
Uranium Isotope Ratio when the Solar System Was Formed
The article stated that the 235U to 238U ratio at the time of the solar system formation was ~17%. Here is the quote:
The most useful uranium isotope for nuclear power is uranium-235, which today accounts for just 0.7202% of any given natural sample of uranium. When the solar system first formed, that number would have been more like 17%, falling steadily until it reached the modern day value.
Uranium Isotope Ratio when Oklo Reactor was Operating
The article stated that the 235U to 238U ratio at the time the Oklo reactors were active was 3.6%, which was about 2 billion years ago. Here is the quote.
And 2 billion years ago? Scientists estimate the Oklo reactors would have had samples with roughly 3.6% uranium-235 — that’s close to the enrichment threshold of modern nuclear reactors. However, just packing the right material into a closed space does not a power plant make.
Today's 235U to 238U ratio of 0.72% is much lower than the 3.6% of 2 billion years ago and creating a natural nuclear reactor would be very difficult. You can create a nuclear reactor using natural uranium, but it is not easy (example). However, there is a fringe theory in geophysics today about a natural nuclear reactor at the Earth's core.
My plan is to show that we can compute these ratios using the standard formula that describes radioactive decay using time and half-life. To perform our calculations, we will need to make a few assumptions:
- All the uranium isotopes in our solar system were created during a supernova explosion that occurred long before the Earth came into being.
- The 235U to 238U ratio after a supernova explosion is 1.65 to 1 (source).
- The article states that the 235U to 238U ratio was 17% "when the solar system formed". For this post, "when the solar system formed" means 4 billion years ago, which was the time the late heavy planetesimal bombardment stopped (source).
Given these assumptions, we can now perform the calculations shown in Figure 5. As part of my isotope ratio calculations, I also estimated that the supernova that created our solar system must have occurred ~6.5 billion years ago, which agrees with the value given by this source.
I was able to duplicate the article's results for the 235U to 238U isotope ratios of:
- 17% for the early Earth.
- 3.6% for the time when the Oklo reactor was active.
As a bonus, I was able to use the same model to compute that a supernova occurred 6.5 billion years ago that produced the material for our solar system.
Nice little problem.