PSI - Issue 36

V. Zapukhlyak et al. / Procedia Structural Integrity 36 (2022) 378–385 V. Zapukhlyak, Yu. Melnychenko , І . Оkipnyi et al./ Structural Integrity Procedia 00 (2021) 000 – 000

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3

repairs. I t should be mentioned, that approximately 90 percent of repair methods can’t avoid using arc welding. Moreover, lately pipelines repair methods using arc welding have been applied most of all whilst the product transportation enabling to increase the economic efficiency of the work due to: it is not necessary to bleed off gas to the atmosphere and there are no fine sanctions in case of gas supply-cutting (Sopilnyk et al., (2019), Poberezhny et al., (2019), Okipnyi et al., (2020)). It is well-known that during welding works on operating pipelines a heated metal zone is being formed around the welded joint having lower strength characteristics. The size and temperature (which can reach the value up to 1000 °С on the inner surface of the pipe wall) of the heated zone are influenced by the welding modes and the size of the welded area, they also depend on the pipe diameter and thickness as well as on the gas flow speed. It is well known that thermal decay of methane (СН 4 → С + 2Н 2 ) starts at (380- 400) °С and partial pressure of molecular hydrogen can reach (1- 1,5) МPа. Under such pressure of hydrogen conditions on should expect considerable hydrogenation of metal on the zone of thermal impact formed on the inner surface of the pipe (Li et al., (2018), Hoyos et al., (2019), Nykyforchyn et al., (2019), Nguyen et al., (2020)). In the general case, to analyze hydrogen re-arrangement in metal, one should solve a nonstationary problem of hydrogen diffusion by dividing the hydrogen absorbed by metal into diffusion-moving and motionless. The differential equation of diffusion looks like ( ) ( ) ( )   e 2 , , , K C x t C t D C x t t C x t − −    =   , 0  t ,    x 0 , (1) where – hydrogen concentration in metal; D – coefficient of hydrogen grain-boundary diffusion in steel; – initial hydrogen concentration of equal weight in metal. The second term in the right-hand side of the equation (1) determines the power of the hydrogen negative source proportional to the hydrogen concentration changes. This source, with specific kinetic coefficient K , takes into account the diffusion hydrogen absorption by different “catchers” (traps) in metal and its removal from the diffusion process (Zhou et al., 2019, Polianskyi et al., 2019). For the case of total desorption of diffusion hydrogen from metal the actual, experimentally measured hydrogen distribution in the wall will be equal to ( ) C x t , p C

(

)

( С C C X C X C   , ( )   ( ) ( −  1 sh sh 1 X   ) − − =   e s , ,



e







(

)



   

   

  = 1 n





(

)

2 exp т  

2

sin 1 

X



−



+

− +



   (2)

)

( )

 1 2 n

т

n

n

 + + − 

(

)

2

2

+

 

n

where C s – surface concentration of hydrogen; h – coefficient of phase transition; 2   Dt = ; D K 2   = ;   h = ;  X x = . According to the results of calculations the curves of hydrogen total concentration distribution on the wall thickness for different time periods are constructed (diffusion and absorbed by traps) (figure 1).