To put energy production from uranium into context, it is interesting to com­pare the known recoverable resources and current use of uranium with the re­coverable resources and current use of fossil fuels (coal, oil, and natural gas). Figures provided from the 1992 World Energy Congress in Madrid are shown in Tables 1.1 to 1.3.

The estimated total fossil fuel resources (Table 1.2) are 209 x 1021 joules, of which 40.3 x 1021 joules are estimated to be recoverable.

Table 1.1 • Proven Fossil Fuel Reserves and Production Rates ES^MTED) PROVEN! RESERVES IN Ufe at Estimated Current Production to Production Fuel Gtoe‘ 102IJ Date in G^«* Rate in Y^ears Coal (excluding 496 23.5 n/a 197 lignite) lignite 110 5.2 n/a 293 Oil 137 6.5 86 40 Na^tural gas 108 5.1 40 56 Source:’WEC 1992 Su^roey of Energy Resources. "’I Gtoe = energy equivalent to 1012 tons of oil.

Table 1.2 • Ultimately Recoverable Fossil Fuel Resources RESOURCES IN Fuel 102’J ^^ent Coal and lignite 3400 161.6 76 Conventional oil 200 9.5 5 Unconventional oil Heavy crude 75 3.6 2 Nat^al bitten 70 3.3 2 Oil shale 450 21.4 10 Nat^al gas 220 10.4 5 Total (approx.) ^00 209.1 100

Sources: WEC 1992 Su^rvey of Entergy ResourcesWEC 1989 Worid Entergy Horirnns 2000-2020; C. D. Masters et al., World* Resources of C^n. uk Oil and Natural Gas, 13th World Petroled Congress, 1991; C. D. [Masters et al., World* Res^ves of C^rude Oil, Natural Bitumen and Shale Oils, 12th World Petroled Confess, 1987.

Table 1.3 • Uranium Resources Source Amount, M Tons Ene^^ content in R^^tors, 10J’) Ufeat C^rcent Production, Years Ene^rgy Content in Fast R^eactor, 1()2iJ “Known" 3.12 1.37 76 68.5 S^^^tive 8-13 3.5 -5.7 — 175 -285 ^Extraction from seawater ^-40 1760 “ 88,00

Sources: OECD^/IAEA “Red Bok,” 1991;^^^, 1976.

Uranium resources can be similarly estimated, and the results are presented in Table 1.3.

The estimated “known” uranium resources are equivalent to 1.4 x 1021 joules if used in thermal reactors and 70 x 1021 joules if used in fast reactors (the dif­ference between these values is explained in Chapter 2). Taking account of speculative resources, the energy content for utilization in fast reactors is esti­mated to be between 175 and 285 x 1021 joules. Uranium resources would be greatly increased by extracting uranium from seawater, in which it occurs at a concentration of 3 parts per billion. This extraction is not likely to be economi­cally feasible in the foreseeable future, however.

Because “known” reserves will last only 76 years at present usage rates, it is important to utilize the uranium resources more efficiently than by simply burn­ing them in thermal reactors. Efficient utilization of these resources can be ob­tained by using fast reactors. An alternative approach might be to use thermal reactors in which the excess neutrons are employed to convert thorium (placed in the reactor core) to an alternative fissile material, uranium-233. ^thile such re­actors can be made self-sustaining (i. e., they can produce as much fissile material as they consume), they cannot be designed to breed efficiently, i. e., produce enough excess fissile material to start a new reactor within a reasonable time.

Primary energy usage from I960 to 1990 and estimated up to 2100 is given in Table 1.4 in Gtoe/year. It will be seen that nuclear power currently provides just

Table 1.4 • Ene^^ Usage (in gigatonne of oll equivalent per ^anumn) Fuel 1960 1990 2020 (est.) 2050 (est.) 2100 (est.) Coal 1.4 2.3 2-5 Oil 1.0 2.8 3-4.6 8.7-15.6 3-17 Na^tural gas 0.4 1.7 2.5-36 Nuclear — 0.4 0.7-1 1.2-3.8 2.2-12 ^UJ. rge hydro 0.15 0.5 0.7-1 Traditional 0.5 0.9 1.1-1.3 3-4 8-10 “New” renewables — 0.2 0.6-1.3 Total (Gtoe) 3.3 8.8 11-17 15-27 20-42

over 5% of world primary energy demand and this is predicted to grow to be­tween 8% and 30% by 2100.

REraRENCES

Armstead, H. C.H. (1978). Geothermal Energy, Chapman & Hall, London. Cowan, G. A. 0976). “A Natural Fission Reactor.” Sci. Am., July, 36-47.

Dorf, R. C. 0978). Energy Resources and Policy. Addison-Wesley, Reading, Mass.

Duffie, J. A., and W. A. Beckman 0980). Solar Engineering of Thermal Processes. Wiley, New York.

Gass, I. G. (1971). Understanding the Earth. Artemis Press.

Hawking, S. 0988). A BriefHistory of Time, Bantam, New York.

NEAIIAEA 0991). Uranium, Resources, Production and Demand. Joint report by OECD and IAEA.

Newson, H. E., and J. H. Jones 0990). Origin of the Earth OUP/Lunar and Planetary Institute, Houston.

U. K. Atomic Energy Authority 0976). Uraniumfrom Seawater.

Wetherill, G. W. 0990). “Formation of the Earth.” Ann. Rev. Earth Planet. Sci. 18:205-56.

——— (1980). “Formation of the Terrestrial Planets” Ann. Rev. Astron. Astrophys.

18:77-113.

World Energy Conference 0992). Survey of Energy Resources.

EXAMPLES ^AND PROBU-MS

1 Chemical energy release

Example: Liquid within a chemical reaction vessel releases chemical energy at the rate of 1.5 kW. The stirrer requires a further power input of 1 kW. If the vessel is cooled by water flowing in a jacket surrounding the vessel, what must the water flow rate be to limit the temperature rise across the jacket to 1 0°C?

Solution: The energy gained by the cooling water must equal that liberated by the chemical reaction and the heat put in by the stirrer. Let W be the water flow rate in kilograms per second. The specific heat of water is 4187 kJ/kg0C Therefore,

W X lOx 4187 = 1500 + 100OJ I s
W = 0.06kg /s

Problem: For the chemical reaction described in the above example, calculate the rise in cooling-water temperature that will occur if the flow rate of water in the cooling jacket is set at 0. 1 kg/s.

2 Pumped storage scheme

Example: A massive pumped storage scheme in North Wales has an upper reservoir containing 67 million m3 of water 500 m above the lower reservoir. The scheme can supply 1800 MW(e) to the electricity grid. Assuming there are no losses, how long can the plant remain in operation at maximum output?

Solution: The total mass of water in the upper reservoir is the volume of water (6.7 x 106 m3) multiplied by the density of water (100 kg! m3), or 6.7 x 109 kg. The total potential en­ergy is this mass times the head (in meters) times the acceleration due to gravity, or

Total potential energy = 6.7 x 109 x 500 x 9.81 = 32.8 X 1012 J

The power output is 1800 MW(e) = 1.8 x 109

= 1.8×109 J/s

Therefore, the plant can remain in operation for

= 5h

Problem. Suppose that the scheme described in the example is to be extended to sup­ply 2000 MW(e) for a period of 7 h. Assuming a conversion efficiency of 95%, calculate the volume of the upper reservoir now required.

3 National fast reactor policy

Example: It is sometimes stated that the introduction of the fast reactor allows a coun­uy to be independent of uranium imports. Why does this statement need considerable qualification? A country has a nuclear power program based on thermal reactors of 10GW by the year 2020. The demand for electric power is growing at 3% per year, and it is decided to introduce fast reactors capable of breeding sufficient plutonium for a further fast reactor in 40 years (the doubling time). What are the consequences? Solution. Let us assume that sufficient plutonium is available from the operation of the thermal reactors (for about 20 years) to allow 10 GW of fast reactors to be installed in 2020. However, the fast reactor capacity can then increase only at the rate at which plu­tonium becomes available to provide fuel for further fast reactors. This rate is 1/40 per year, or 2.5%/yr. Thus the rate at which fast reactors can be installed is lower than the electric power demand growth rate (3%/yr). The difference must (presumably) be made up by installing further thermal reactors, which will increase the counuy’s need for imported uranium. Even if a fast reactor with a shorter doubling time (say, 30 years) is available, a finite time will still be needed to replace thermal reactors by fast reactors. Thus it will take about twice the doubling time, i. e., 60 years, for the counuy to be free from uranium imports.

Problem. Suppose the counuy described in the example decided on an intensive pro­gram of energy conservation to reduce its growth in demand for electric power to 2%. How would this reduction affect the scenario for introducing fast reactors?

2