Matter consumption in a nuclear reactor

Matter consumption in a nuclear reactor

In general, the nuclear fission results in the release of enormous quantities of energy. This energy comes from the nuclear binding energy which holds nuclei together. The binding energy per nucleon is higher for fission fragments than for uranium nuclei. It was found the sum of the rest masses of products of fission is measurably smaller than the rest mass of uranium nucleus.

Mass Defect

It is due to the fact during the nuclear fission some of the mass of the nucleus gets converted into these huge amounts of energy and thus this mass is removed from the total mass of the original particle, and the mass is missing in the resulting nuclei.

According to the Einstein relationship (E = mc2) this binding energy is proportional to this mass difference and it is known as the mass defect.

The annual mass defect of a typical 3000MWth reactor  can be calculated directly from the Einstein relationship (E = mc2) as:

Δm = ΔE/c2

Δm = 3000×106 (W = J/s) x 31.5×106 (seconds in year) / (2.9979 x 108)2 = 1.051 kg

E=MC2

Summary:

Consumption of a 3000MWth (~1000MWe) reactor (12-months fuel cycle)

It is an illustrative example, following data do not correspond to any reactor design.

  • Typical reactor may contain about 165 tonnes of fuel (including structural material)
  • Typical reactor may contain about 100 tonnes of enriched uranium (i.e. about 113 tonnes of uranium dioxide).
  • This fuel is loaded within, for example, 157 fuel assemblies composed of over 45,000 fuel rods.
  • A common fuel assembly contain energy for approximately 4 years of operation at full power.
  • Therefore about one quarter of the core is yearly removed to spent fuel pool (i.e. about 40 fuel assemblies), while the remainder is rearranged to a location in the core better suited to its remaining level of enrichment (see Power Distribution).
  • The removed fuel (spent nuclear fuel) still contains about 96% of reusable material (it must be removed due to decreasing kinf of an assembly).
  • Annual natural uranium consumption of this reactor is about 250 tonnes of natural uranium (to produce of about 25 tonnes of enriched uranium).
  • Annual enriched uranium consumption of this reactor is about 25 tonnes of enriched uranium.
  • Annual fissile material consumption of this reactor is about 1 005 kg.
  • Annual matter consumption of this reactor is about 1.051 kg.
  • But it corresponds to about 3 200 000 tons of coal burned in coal-fired power plant per year.
 
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533
  7. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  8. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  9. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Fuel Consumption