Samarium Equilibrium – Promethium Equilibrium

Samarium Equilibrium – Promethium Equilibrium

When the rate of production of promethium equals the rate of removal of promethium equilibrium exists. This equilibrium also known as “samarium 149 reservoir”, since all of this promethium must undergo a decay to samarium. In equilibrium, the promethium concentration remains constant and is designated NPm(eq). The following equation for the promethium equilibrium concentration can be determined from the preceding equation by setting the dNPm/dt =0.

promethium equilibrium - equation

Since the equilibrium promethium concentration is proportional to the fission reaction rate, it is also proportional to reactor power level.

When the rate of production of samarium equals the rate of removal, equilibrium exists also for samarium. The samarium concentration remains constant and is designated NSm(eq). The following equation for the samarium equilibrium concentration can be determined from the preceding equation by setting the dNSm/dt =0. For samarium to be in equilibrium, promethium must also be in equilibrium. Substituting the expression for equilibrium promethium concentration into the equation for equilibrium samarium results in the following equation:

samarium equilibrium - equation

This expression for equilibrium samarium 149 concentration during reactor operation illustrates that equilibrium samarium 149 concentration is independent of neutron flux and power level. It follows the time of saturation is dependent upon the neutron flux level. The equilibrium concentration usually produces negative reactivity (samarium worth) of about -600 pcm.

 
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. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

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:

Samarium