Baker-Just Correlation – Zirconium Oxidation Rate

As was written in previous section, the oxidation of zirconium alloys is one of the most studied processes in all of the nuclear industry. While many of these reports are written to address the reaction of fuel and steam with zirconium alloys in the case of a nuclear accident, there are still a substantial number of reports dealing with the oxidation of zirconium alloys at moderate temperatures of about 800 K and below. The aggressive agent in this respect is primary circuit water, at a temperature of some 300° C. This oxidizes zirconium according to the reaction:

Zr + 2H2O→ZrO2 + 2H2

resulting in formation of solid oxide on the metal’s surface. The reaction is always exothermic, and the heat of reaction is similar for all types of zirconium-based alloys. The rate of reaction increases smoothly, although strongly, with temperature.

At high temperatures, the exothermic reaction of Zr-base alloys with steam is much more intensive and hazardous for the safety of nuclear power plants during accidents like a loss-of-coolant accident (LOCA). The main problem of high temperature oxidation is that zirconium cladding rapidly reacts with water steam at high temperature. The oxidation kinetics of relevant zirconium alloys appears to be parabolic in the temperature range of 1000-1500°C for many Zr-based alloys. Above 1577°C, the oxide layer transforms from tetragonal to cubic and the oxidation rate even increases. Moreover, oxidation of zirconium by water is accompanied by release of hydrogen gas. This oxidation is accelerated at high temperatures, e.g. inside a reactor core if the fuel assemblies are no longer completely covered by liquid water and insufficiently cooled. Metallic zirconium is then oxidized by water/steam to form hydrogen gas according to the following redox reaction:

Zr + 2H2O→ZrO2 + 2H2   (Q = 190 kJ/mol; Baker and Just)

Baker-Just Correlation

In 1973, the Baker-Just correlation was selected as the best correlation available and was included as a requirement in Appendix K of 10 CFR 50.46 for calculation of the heating rate due to oxidation, hydrogen generation and the Effective Cladding Reacted (ECR) because it was available in 1973. The Baker-Just equation, as well as more recent correlations, can be represented as an Arrhenius relation (e-Q/RT) with an activation energy Q and an exponential dependence on temperature T (R is the universal gas constant). Thus, the oxidation rate and, hence, the heat generation rate increase rapidly as temperature increases. The integrated form of the Baker-Just correlation (BJ) for weight/surface-area (w) of zirconium consumed during steam oxidation is

w2 = 33.3×106 t exp(-45500/RT), (mg/cm2)2

where t is time in seconds, T is temperature in K and R = 1.987. This equation applies to isothermal oxidation in steam for fresh cladding with no protective, pre-transient oxide layer. However, this correlation has the least significant database and justification of all those reviewed. Oxidation kinetics studies on a variety of zirconium alloys conducted since 1962 – particularly in the 1970s – have demonstrated that the Baker-Just correlation over-predicts weight gain and zirconium consumed by as much as 30% at the peak cladding temperature (1204°C) allowed by 10CFR50.46. USNRC Regulatory Guide 1.157 (May 1989) allows the use of a best-estimate correlation (e.g., Cathcart-Pawel) for temperatures greater than 1078°C.

Special Reference:  Baker, L., Just, L.C., Studies of Metal Water Reactions at High Temperatures, III. Experimental and Theoretical Studies of the Zirconium-Water Reaction, ANL-6548, page 7, May 1962

Special Reference: M.C. Billone, H.M. Chung and Y. Yan. STEAM OXIDATION KINETICS OF ZIRCONIUM ALLOYS. Argonne National Laboratory, June 4, 2002.

Special Reference: F.C. Iglesias, B.J. Lewis, C. Desgranges, C. Toffolon. Clad-coolant chemical interaction. NEA/NSC/R-2015-5. NEA, OECD, 2015.

 

References:
Nuclear and Reactor Physics:
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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.
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      4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Fuel Cladding