PSI - Issue 13

Zahreddine Hafsi et al. / Procedia Structural Integrity 13 (2018) 210–217 Hafsi et al. / Structural Integrity Procedia 00 (2018) 000–000

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6

Figure 6 shows a 2D plot of the concentration of hydrogen in the pipe wall for unnitrided API X52 at the end of the simulation i.e. at t=24h as well as a line plot of the concentration over a cut line along the thickness of the pipe wall (from r=0.5D to r=0.5D+e ).

Fig. 6. Hydrogen concentration (in mol/m 3 ) in unnitrided X52 steel at t=24h (a) 2D plot; (b) Line plot

To validate the modelling results, the line plot of the numerically obtained concentration is compared with the analytical solution of Fick’s second law (equation (3)). Actually for a one dimensional diffusion phenomenon, using appropriate boundary conditions, equation (3) has been extensively studied to be solved numerically and analytically in several litterature references. For the studied model, assuming that the diffusion is radial and only r dependent, the solution of one dimensional diffusion along radial direction r through the thickness of the wall and by denoting x=r 0.5*D is written (Frederiksen, J.M. et al., 2008)

   

   

   

   

D t x c

  C x t C t ,   

(8)

1

erf



i

2

where C i is the surface concnetration and erf stands for Gaussian error function. The term D c t is known as the characteristic diffusion length. In Fig.7, the evolution of hydrogen concentration along a cut line on the wall of the X52 steel pipeline is plotted. A good agrrement between the numerical and the anlytical solutions is observed through Fig.7 which allows to extend the COMSOL model to test hydrogen diffusion after a nitriding process of X52 and on another material used also for gas transportation networks viz.API X80 steel.

Fig. 7. Numerical and analytical solutions of hydrogen concentration (in ppm ) at t=24h for unnitrided API X52 steel