What is Boron Coefficient – Definition

The boron coefficient is defined as the change in reactivity per the change in the boron concentration. It is expressed in units of pcm/g.kg-1. Reactor Physics

Boron Coefficient

The boron coefficient is defined as the change in reactivity per the change in the boron concentration.

αB = dg/kg

It is expressed in units of pcm/g.kg-1. The value of boron coefficient in PWRs is usually ranges from about -1000 pcm/g.kg-1 to about -2000 pcm/g.kg-1. The boron coefficient usually decreases (becomes more negative) as the fuel burnup increases.

It is obvious this coefficient does not represent any reactivity feedback, but it is commonly used by reactor operators, because it describes the influence of changes in the boron concentration on the reactivity of the reactor.

See also: Boron 10

Boron 10 - (n,alpha) reaction

Natural boron consists primarily of two stable isotopes11B (80.1%) and 10B (19.9%). In nuclear industry boron is commonly used as a neutron absorber due to the high neutron cross-section of isotope 10B. Its (n,alpha) reaction cross-section for thermal neutrons is about 3840 barns (for 0.025 eV neutron). Isotope 11B has absorption cross-section for thermal neutrons about 0.005 barns (for 0.025 eV neutron). Most of (n,alpha) reactions of thermal neutrons are 10B(n,alpha)7Li reactions accompanied by 0.48 MeV gamma emission.

(n,alpha) reactions of 10B

Moreover, isotope 10B has high (n,alpha) reaction cross-section along the entire neutron energy spectrum. The cross-sections of most other elements becomes very small at high energies as in the case of cadmium. The cross-section of 10B decreases monotonically with energy. For fast neutrons its cross-section is on the order of barns.

Boron as the neutron absorber has another positive property. The reaction products (after a neutron absorption), helium and lithium, are stable isotopes. Therefore there are minimal problems with decay heating of control rods or burnable absorbers used in the reactor core.

Boric Acid - Chemical Shim
By chemical shim, we mean that boric acid is dissolved in the coolant/moderator. Boric acid (molecular formula: H3BO3), is a white powder that is soluble in water. In pressurized water reactors, chemical shim (boric acid) is used to compensate an excess of reactivity of reactor core along the fuel burnup (long term reactivity control). At the beginning of specific fuel cycle concentration of boric acid is highest (see picture). At the end of this cycle concentration of boric acid is almost zero and a reactor must be refueled.

In certain cases also fine power changes can be controlled by chemical shim. If it is desired to increase power, then the boric acid concentration must be diluted, removing 10B from the reactor core and decreasing its poisoning effect. When compared with burnable absorbers (long term reactivity control) or with control rods (rapid reactivity control) the boric acid avoids the unevenness of neutron-flux density in the reactor core, because it is dissolved homogeneously in the coolant in entire reactor core. On the other hand high concentrations of boric acid may lead to positive moderator temperature coefficient and that is undesirable. In this case more burnable absorbers must be used.

Moreover this method is slow in controlling reactivity. Normally, it takes several minutes to change the concentration (dilute or borate) of the boric acid in the primary loop. For rapid changes of reactivity control rods must be used.

Theory of Boron Coefficient

↑boron ⇒ ↓keff = η.ε.p.  ↓f  .Pf.Pt

The concentration of boric acid diluted in the primary coolant influences the thermal utilization factor. For example, an increase in the concentration of boric acid (chemical shim) causes an addition of new absorbing material into the core and this causes a decrease in thermal utilization factor.

The thermal utilization factor for heterogeneous reactor cores must be calculated in terms of reaction rates and volumes, for example, by the following equation:

thermal utilisation factor - equation2

where Σa is the macroscopic absorption cross section, which is the sum of the capture cross section and the fission cross section, Σa = Σc + Σf. The superscripts U, M, P, CR, B, BA and O, refer to uranium fuel, moderator, poisons, control rods, boric acid, burnable absorbers and others, respectively. It is obvious, that the presence control rods, boric acid or poisons causes a decrease in the neutron utilization, which, in turn, causes a decrease of multiplication factor.

When compared with burnable absorbers (long term reactivity control) or with control rods (rapid reactivity control) the boric acid avoids the unevenness of neutron-flux density in the reactor core, because it is dissolved homogeneously in the coolant in entire reactor core. On the other hand high concentrations of boric acid may lead to positive moderator temperature coefficient and that is undesirable. In this case more burnable absorbers must be used.

Moreover this method is slow in controlling reactivity. Normally, it takes several minutes to change the concentration (dilute or borate) of the boric acid in the primary loop. For rapid changes of reactivity control rods must be used.

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.

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 also:

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