PSI - Issue 13

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

212

3

H s

   

  

(4)

 S S p exp 0

RT

where  s is the dissolution enthalpy. In general, the relationship between gas concentration and pressure is given through Henry’s law via the solubility known as Henry’s solubility S H

p gas C gas

(5)

S H 

For diatomic molecules, such as hydrogen, Henry’s law is modified to be known as Sieverts’ law. Actually, Sieverts, an early scientist deeply involved in research on solubility of hydrogen in metals, stipulated that hydrogen solubility in metals is a function of the half-power of pressure. Hence Sieverts’ law is written (Steward, S.A., 1983)

C H

(6)

2

S H 

2

p H

2

In what follows, the subscript H 2 in equation.(6) is dropped for sake of simplicity. Combining equations (4) and (6), the concentration of hydrogen is written as function of the pressure

H s

   

  

(7)

 C S p 0 exp

RT

The latter equation coupled with equations (1) and (2) for gas flow in a pipeline permits to study pressure enhanced diffusion of hydrogen through the pipeline wall under steady and transient states. 3. Numerical modeling and results The set of equations describing embrittlement of steel material by hydrogen diffusion due to transient gas flow in a pipeline is solved using COMSOL Multiphysics software by coupling both physics related to pipe flow of compressible fluids governed by equations (1) and (2) as well as mass transfer considering only diffusion phenomenon described through equation (3). 3.1. Transient hydrogen gas flow simulation For modelling transient flow of hydrogen in a relatively long pipeline, an API X52 pipe of a length L= 80 km and an internal diameter D=0.6 m is considered (Fig.1). An upstream pressure (compressor delivery) of 70 bar is maintained and an isothermal hydrogen gas flow under a temperature T=278 K is assumed.

Fig. 1. Hydrogen gas installation