Effects of process-generated hydrogen on RPV walls

6. Hydrogen concentration in PWR wall

where a H is the activity of hydrogen in steel, k S is the solubility or Sieverts’ constant for the system and f H 2 is the fugacity of hydrogen gas. As the fugacity is the thermodynamic equivalent of a pressure, the activity is the thermodynamic equivalent of a concentration. A similar relation exists: a = γx (6.17) where γ is the activity coefficient and x is the physical concentration. As for the fugacity, the difference between the activity and the concentration only becomes important for high concentrations. This is according to Henry’s law for activities, valid at low concentrations. The temperature dependence of Sieverts’ law has been investigated intensively over time and it is agreed to be valid up to at least a few thousand K. [77] However, the validity of Sieverts’ law in the pressure domain has had less attention. Therefore it is not known whether one can use Sieverts’ law for very high hydrogen fugacities as encountered here. However, for the interest of this calculation Sieverts’ law will be assumed to be valid. Chapter 3 discussed in depth the solubility of hydrogen in steel and the influence of hydrogen traps on this solubility. It was found that the experimental scatter for the solubility or Sieverts’ constant and diffusion constant was very high. Variations of 1 order of magnitude for the Sieverts’ constant and up to 4 orders of magnitude for the diffusion constant at low temperatures have been found. These variations have been explained by the attractive forces between the hydrogen traps and the dissolved hydrogen. Therefore, finding values for both of these constants is difficult. However, it can be expected that the solubility constant for hydrogen will be at the high end of the experimental range as the concentration of hydrogen traps will be high, due to the presence of radiation induced defects like vacancies. Similarly, the diffusion coefficient for hydrogen in steel can be expected to be in the low range of the experimental values as the high concentration of hydrogen traps will attract the hydrogen atoms and therefore reduce their mobility and thus the diffusion coefficient. The following temperature dependent Sieverts’ and diffusion constant will be used in the following of these calculations.

− 1418 T

+1 . 628 ppm Pa -1/2 [78]

k S = 10

T 2 !

(6.18)

1 . 0831 · 10 6

2320 . 3 T

D = 10 − 9 exp

m 2 /s [44]

−

where in both equations T is given in K. One can see in Figure 6.9, that the Sieverts’ constant is very temperature dependent. Using Sieverts’ constant, one can find the equilibrium concentration of H. At 300 ◦ C, Sieverts’ constant is found to be k S = 10 − 1418 573 +1 . 628 ppm Pa -1/2 = 0 . 1425 ppm Pa -1/2 (6.19) 72