In section 2 it was stated that there is sufficient uranium in the U.S. to power fleets of breeder reactors supplying basically the entire nation’s energy needs for thousands of years. The purpose of this appendix is to provide the basis for that statement.
First, as was also stated in section 2, the breeder reactor makes use of uranium fuel at least twenty times more efficiently than a LWR. A corollary to this statement would be that one LWR would provide sufficient feed stock for twenty equivalently sized LMFBRs. That feed stock would be in the form of the tailings from the enrichment plants needed to enrich the fuel for the LWRs and the LWR spent fuel itself. With all of the tailings and spent fuel from the world’s fleet of LWRs, it would be a long time before it would become necessary to mine additional uranium to support a growing number of LMFBRs.
Nonetheless, the question of limitations must ultimately be addressed. The world has so much oil, so much natural gas, and so much coal. All of it will be exhausted at some point – doesn’t the same argument apply to nuclear power with the breeder reactor? How much uranium is there in the world and how long would it last if it were to be relied upon to supply a sizeable fraction of the world’s energy needs?
The authoritative reference for uranium resource supply and demand is a document referred to as the “red book” that is published approximately biennially. It is a joint report of the OECD Nuclear Energy Agency and the IAEA.1 On the resource side of the equation, the red book quotes resources as a function of cost of extraction. Costs of extraction are expressed in US dollars per kilogram uranium metal and categorized as shown in the table below.
| Resource category | Estimated resource, 1000 MTU |
| $40/kgU | 680.9 |
| $80/kgU | 3078.5 |
| $130/kgU | 5327.2 |
| $260/kgU | 7096.6 |
Table 13 World uranium resources
On the demand side, the red book reported that the 440 reactors operating worldwide in 2010 represented an installed capacity of 375.2 GWe, generated 2623 TW-hr of electricity and required 63,875 MTU. The red book also projects demand out to 2035 expecting it to increase to between 97,645 and 136,385 MTU/yr. At high resource utilization, consumption will exhaust supply in less than 70 years. Since nuclear plants now being built are expected to have a useful operating lifetime of at least 60 years, one wonders where the uranium will come from. The answer of course is that more expensive sources of uranium will be called upon.
Nature’s vehicle for the manufacture of uranium is the supernova. Thus, the only source of uranium on earth is space detritus originating from various galactic supernova, which only occur about once every 500 years in our milky way galaxy. Uranium is therefore a rather rare substance. Nonetheless a great deal of uranium has managed to accumulate on the planet. The oceans, for example, contain about 3 ppb of dissolved uranium in its hexavalent state. While 3 ppb doesn’t sound like much, when multiplied by the mass of the planet’s oceans this puny concentration adds up to a total of 5.9 ∙ 109 MTU. There are various mechanisms for reducing (reducing here used in the context of decreasing the valence state of the ion) the dissolved uranium in the oceans that involve decaying organic material and hydrogen sulfide from its hexavalent state to its quadravalent state which leads to its precipitation. That is the reason why most of the so-called marine black shales which contain petrochemicals also contain fairly generous amounts of uranium.
Earlier in this monograph it was stated that the Marcellus shale contains about 25 ppm of uranium. Assuming an average thickness of 300 ft. over its 90,000 sq. mi. extent, there are over 1.3 ∙ 109 MTU in the Marcellus shale. Other shales offer more promising sources because of their higher concentrations of uranium. For example, the Chattanooga shales that run through eastern Tennessee contain 80 ppm of uranium. The Chattanooga shales are far less extensive than the Marcellus shales, covering about 1000 square miles and having an average thickness of about 20 ft. Nonetheless, these shales contain about 6.5 ∙ 106 MTU, about the same as the total world resource quoted in the red book.
Yet another shale formation that has been much in the news recently is the Bakken formation, which has so enriched the state of North Dakota in the past several years. The Bakken formation is actually primarily sandstone with relatively thinner layers of shale both above and below. There is relatively little uranium in the sandstone, but the upper shale formation averages 6 ft in thickness and contains an average of 42 ppm uranium while the lower shale formation averages 13 ft in thickness and contains an average of 62 ppm uranium.2 Given that the extent of the Bakken formation is about 200,000 square miles, the lower shale formation contains 1.6 ∙ 109 MTU with another 0.5 ∙ 109 MTU from the upper shale.
If one uses the current consumption and production figures in the red book, LWRs require about 25 MTU/TW-hr. Accounting for their better fuel utilization (the factor of 20 quoted above) and their higher thermodynamic efficiency, LMFBRs can reasonably be expected to require just 1 MTU/TW-hr. Actually this number is probably way too high. The well known relationship between uranium consumption and power production of 1 gram = 0.95 MWth-days = 22.8 MWth-hr would imply that for a 40% thermodynamic efficiency and a 60% fuel utilization rate, 1 gram should yield 5.5 MWe-hr. Thus a TWe-hr of production would consume only 0.2 MTU, about a hundredth of current LWR consumption rate. At this rate of consumption, the cost of uranium extraction can be measured in the thousands of dollars per kilogram and the plants would still be economic from a fuel utilization point of view. $10,000/kg U would translate into about $20/lb of coal so even at such a high price it would still be a bargain.
A thousand 1000MWe plants would come close to supplying all the U.S. electric power requirements for many years to come. At the uranium consumption rates described above, such a fleet of reactors would consume about 1750 MTU per year. At this consumption rate, the Chattanooga shale alone would be a 3700 year supply. The Marcellus shale would be good for millions of years. One could argue that over such lengthy periods other sources of energy such as fusion should certainly have been developed to the point that they can be used as reliable sources of power production. Such arguments miss the point. The point is that resource limitations cannot be used as an argument for continuing the halt on nuclear power development. Moreover, while the environmental impact of nuclear power is known and is capable of being significantly reduced, there is no knowledge – just speculation – of the environmental impact of any future technology that might be offered to replace it.
Endnotes
1 Uranium 2011: Resources, Production, and Demand, OECD 2012, NEA No. 7059
2 The Uraniferrous Bakken Shales of North America, IAEA presentation, November 12, 2009
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