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Elsewhere on this website Fast Neutron Reactors (FNRs) have been identified as the primary source of energy for sustainably meeting mankind's future energy needs. Today we can reliably forecast that failure to promptly pursue FNR deployment will result in an energy supply catastrophe for mankind later in this century.
This web page focuses on the issue of providing FNRs sufficient fissile start fuel. The immediate problem is displacement of fossil fuels. However, if too much of the natural fissile fuel inventory is consumed in the existing "burner" type reactors there will not be enough fissile fuel left to start the "breeder" type reactors which are required for long term fuel sustainability.
Some uncertain factors which complicate this tradeoff calculation are:
1) What is the fraction of natural uranium in sea water that is economically recoverable?
2) What is the fraction of U-235 in natural uranium that is actually consumed in a light water power reactor? Part of the U-235 is lost during the enrichment process and part of the U-235 remains in the used fuel.
3) What is the actual breeding gain of a power FNR?
4) What is the actual breeding gain of a liquid fuel molten salt reactor that converts thorium (Th-232) into uranium (U-233)?
5) Will new reactors be located in cities or must they deliver heat via electricity?
6) What is the average rate of erosion of the ocean floor?
7) What is the uranium fraction of ocean floor rock?
8) How fast will the total thermal power load grow during the transition period from fossil fuels to non-fossil fuels?
9) How much additional reactor thermal power capacity is required to meet reliability requirements and load fluctuations?
10) What will be the load growth due to both increases in human population and increases in average thermal power per person?
11) Can real Th-232 - U-233 fueled reactors actually breed more fissile fuel than they consume? There are a number of parasitic neutron absorbing processes that have not been properly taken into account. In sodium cooled U-238 to Pu-239 FNRs there are enough spare neutrons to ensure that more fissile is bred than is consumed. That may not be the case for Th-232 - U-233 breeding cycles.
Another author has addressed this matter in the paper titled: Long Term Sustainability of Nuclear Fuel Resources.
We will start this analysis by finding the approximate average thermal power output obtained from fossil fuels in 2019.
WORLD COAL PRODUCTION:
During the year 2019 the total world coal production, obtained by summing the productions from the major coal producers was;
8.13 billion tonnes
= .813 X 10^10 tonnes/year
The corresponding carbon mass that entered the atmosphere in 2019 was about:
0.8 X .813 X 10^10 tonnes / year = .6504 X 10^10 tonnes carbon / year.
The average thermal power liberated by world combustion of coal during 2019 was about:
.813 X 10^10 tonnes coal / year X 32,494 X 10^6 J / tonne coal X 1 year / 8766 hour X 1 hour / 3600 s
= 8.371 X 10^12 watts
WORLD OIL PRODUCTION:
The world oil production in 2019 as obtained by summing producers outputs was about 35 billion barrels / year. The corresponding annual carbon output is:
35 X 10^9 barrels /year X .137 tonnes/barrel X .86 tonne carbon / tonne oil
= 0.412 X 10^10 tonne carbon / year
Not all of this carbon immediately goes into the atmosphere because a small fraction of it is used to produce asphalt, which may take as much as 50 years to oxidize into CO2.
The average thermal power liberated by world combustion of oil is about:
35 billion barrels / year X (5.8 X 10^6 BTU / barrel) X 1055.06 J / BTU X 1 year / 8766 hour x 1 hour / 3600 s
= 6.786 X 10^12 Wt
WORLD NATURAL GAS LIQUIDS PRODUCTION:
The world natural gas liquids production in 2004 as obtained by summing producers outputs was about 7,393,210 barrels per day. The corresponding annual carbon output is:
7,393,210 barrels / day X 365 days/year X .137 tonnes/barrel X .86 tonne carbon / tonne NG liquid
= .03179 X 10^10 tonne carbon / year
Not all of this carbon goes into the atmosphere because part of the carbon related to NG liquid production is used to produce resins. However, the non-atmospheric carbon amount is likely off set by unreported fossil fuel production, especially unreported coal.
The thermal power liberated by world combustion of natural gas liquids in 2004 is about:
7,393,210 barrels / day X 5.8 X 10^6 BTU / barrel X 1055.06 J / BTU X 1 day / 24 hour x 1 hour / 3600 s
= 0.5236 X 10^12 Wt
WORLD DRY NATURAL GAS PRODUCTION:
The world dry natural gas production during 2019, as obtained by summing the producers outputs was:
4100 billion m^3 / year.
The corresponding amount of carbon released to the atmosphere was:
4100 X 10^9 m^3 /year X 1000 lit / m^3 X 1 mole / 22.4 lit X 273/288 X 16 gm / mole X 1 tonne/10^6 gm X .75
= 4.1 X 10^15 lit / year X (1 mole / 22.4 lit) X (273/288) X 16 g / mole X 10^-6 tonne / gm X .75
= 2.082 X 10^9 tonnes carbon / year
=0.2082 X 10^10 tonnes carbon / year
Almost all of this carbon enters the atmosphere.
The average thermal power liberated by world combustion of natural gas in 2019 was:
4100 X 10^9 m^3 / year X 1000 ft^3 / 28.328 m^3 X 1000 BTU / ft^3 X 1055.06 J / BTU X 1 year / 8766 hour X 1 hour / 3600 s
= 4.839 X 10^12 Wt
WORLD AVERAGE FOSSIL FUEL THERMAL POWER PRODUCTION IN 2019:
[8.371 + 6.786 + 0.5236 + 4.839] X 10^12 Wt
= 20.52 X 10^12 Wt
= 20.52 X 10^3 GWt
This quantity is the minimum thermal power that nuclear reactors must supply to completely displace fossil fuels. If the reactors are to be located remote from urban centers this number must be tripled because the heat must be delivered to the load via electricity.
WORLD AVERAGE FOSSIL FUEL THERMAL POWER PER PERSON:
The world average fossil fuel thermal power per person in 2019 was about:
20.52 X 10^12 Wt / 7.8 X 10^9 people
= 2.63 kW / person
By comparison in Canada and the USA the average fossil fuel thermal power is about 9 kWt / person and the average electrical power per person is about 1.2 kWe.
In the Province of Ontario the average thermal power per person is about 7 kWt per person but the Canadian average is higher, in large part due to energy intensive fossil fuel extraction in the province of Alberta.
REQUIRED FISSILE MASS CONSUMPTION:
The fissile mass / unit time that must be consumed to displace present fossil fuel consumption on a simple thermal basis is:
(20.52 X 10^3 GWt) X (10^9 Wt / GWt) X (1 fission / 200 MeV) X (1 MeV / 10^6 eV)
X (1 eV / 1.602 X 10^-19 J) X (1 J / Wt-s) X (1 atom fissile / fission)
X (238 gm / 6.023 X 10^23 atom) X (3600 s / hour) X (8766 hour / year)
= (20.52 / 200) X (1 / 1.602) X [(238 X 3600 X 8766) / 6.023] X 10^2 gm / year
= 79,964,171 X 10^2 gm fissile / year
= 7,996,417 kg fissile / year
= 8000 tonne fissile / year
Assume that the entire world is powered by FNRs.
The fissile inventory required to start the most efficient FNRs is about:
40 tonne fissile / GWt
The required world fissile inventory dedicated to FNR start fuel is:
40 tonne / GWt X 20.52 X 10^3 GWt
= 821 X 10^3 tonnes
= 8.21 X 10^5 tonnes.
At the expense of much more fuel reprocessing, the FNR fissile inventory can be reduced to about 20 tonnes / GWt, which allows approximate doubling of the number of FNRs that one can start.
The rate of growth of the fissile inventory, once economic mining is exhausted, is set by the number of neutrons yielded per fission which sets an upper limit on the fissile fuel breeding rate.
Note that if thermal energy is delivered to the load via electricity instead of via heat the required nuclear power capacity triples. Thus it is essential that the largest possible fraction of the reactors have urban siting.
FIND OCEAN FISSILE CONTENT:
Ocean volume = 1.332 X 10^9 km^3 which contains 1.332 X 10^18 m^3.
Mass of ocean water = 1.332 X 10^18 tonnes.
Weight fraction of ocean water which is natural uranium = 2.8 X 10^-9
Mass of natual uranium dissolved in the ocean is:
1.332 X 10^18 tonnes X 2.8 X 10^-9
= 3.73 X 10^9 tonnes
Mass of U-235 fissile dissolved in the ocean is:
(0.7 / 100) X 3.73 X 10^9 tonnes = 2.61 X 10^7 tonnes
The problem is that if only 10% of the U-235 in the ocean is recoverable the ocean resource drops to 2.61 X 10^6 tonnes. If LWRs only fission (1 / 4) of the fissile in the mined natural uranium then the effective fissile consumption rate rises to 32,000 tonnes / year. That allows powering civilization for:
2.61 X 10^6 tonnes/ 32,000 tonnes / year = 81.5 years with LWRs without allowing construction of any FNRs. However, if the heat is delivered to the load via electricity instead of via heat the working life of the LWRs drops by about a factor of three.
If we build the very minimum required number of FNRs they will require 0.821 X 10^6 tonnes of fissile for start fuel. Hence the maximum number of years of full power LWR operation drops to:
1.8 X 10^6 tonnes / (32,000 tonnes / year) = 56 years
There are the further problems of load variation and reactor capacity factor. The reactor plate capacity likely has to be increased by 100% to meet load variations and to allow for maintenance.
If we double the number of FNRS to account for load variation and reactor capacity factor the FNRs will require:
1.642 X 10^6 tonnes of fissile for start fuel. Hence the maximum number of years of full power LWR operation drops to:
(2.61 X 10^6 tonnes - 1.642 X 10^6 tonnes) / (32,000 tonnes / year)
= 30.25 years
The problem becomes much worse if the heat is delivered to the load from LWRs via electricity instead of directly via heat. Then the aforementioned LWR working lives all drop by about a factor of three.
REPLINISHMENT OF THE URANIUM DISSOLVED IN THE OCEAN:
In principle the uranium concentration dissolved in the ocean should be replenished over time by further erosion of the ocean floor rock.
a) If this rock is primarily silicate it will erode at about 1 um / year.
b) This rock likely has an average density of about 3 tonnes / m^3.
c) The average uranium weight fraction of ocean floor rock is likely about:
4 X 10^-6
d) The area of the ocean is about 361.1 X 10^6 km^2.
Hence the number of tonnes of natural uranium added to the ocean per year by erosion of ocean floor rock is:
3 tonnes rock / m^3 X 10^-6 m / year X 4 X 10^-6 tonnes U / tonnes rock
X 361.1 X 10^6 km^2 X 10^6 m^2 / km^2
= 4333.2 tonnes natural uranium / year
The number of tonnes of U-235 added to the ocean per year is about:
(0.7 / 100) X 4333.2 tonnes = 30.33 tonnes / year. Even if the ocean floor erodes 100X as fast as assumed herein, in any practical time frame erosion of the sea floor will not replace the uranium dissolved in the ocean water.
REQUIRED FISSILE INVENTORY FOR EFFICIENT FISSILE BURNING CANDU REACTORS:
One CANDU fuel load is:
20 kg natural uranium / bundle X 12 bundles / fuel tube X 380 fuel tubes
= 91.2 tonnes.
The fissile content is:
(0.7 / 100) X 91.2 tonnes = 0.6384 fissile tonnes
The fissile / GWt is 0.6384 fissile tonnes / 2 GWt = 0.319 tonnes / GWt
However, if electricity is being generated that heat is almost worthless, so a better figure of merit is:
0.6384 fissile tonnes / 0.700 GWe = 0.912 fissile tonnes / GWe
This figure compares to about 20 fissile tonnes / GWt for a practical FNR. There are two main sources of this large difference. One is the smaller fission cross section in FNRs as compared to thermal CANDU reactors. The other issue is that in FNRs about (2 / 3) of the neutrons are dedicated to fuel breeding rather than supporting the fission chain reaction.
To sustain the present human population at the present average thermal power consumption requires an absolute minimum of 20,000 GWt of average new reactor power capacity.
However, there are a number of factors such as load variation, load growth and reactor siting that could easily increase that capacity requirement to as much as 100,000 GWt. Even with sensible reactor siting, no load growth and minimum allowance for load variation and capacity factor almost certainly 40,000 GWt of reactor capacity will be required. The available supply of natural fissile will be strained to the limit unless almost all new reactors are FNRs which can grow the fissile inventory as the reactor construction procedes. A key issue will be harvesting 50% rather than 10% of the fissile dissolved in the oceans.
The number one issue for young people to understand is that failure to invest in the extra cost of liquid sodium cooled breeding reactors now will doom them to catestrophic energy shortages in their old age, regardless of anything else that they or society might do. To meet this challenge it is necessary to build about 40,000 X 1 GWt of liquid sodium cooled breeder reactor capacity over the next 50 years.
There is some hope of relief of this situation via Liquid Fuel Thorium Reactors (LFTRs), but to date no LFTRs with the necessary breeding capability have ever been built. Even the chemistry of LFTRs, in terms of the necessary corrosion resistant materials, is uncertain. Another uncertainty is whether LFTRs can actually breed more fissile than they consume. The number of excess neutrons provided by U-233 fission is very small and this excess may be absorbed by non-reacting fuel salt elements, by moderator elements and by reactor structural elements. Hence at the end of the day thorium reactors may still require liquid sodium cooled reactors to provide ongoing fissile fuel supplements.
This web page last updated February 1, 2021.
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