Metallurgical and Materials Transactions A

, Volume 25, Issue 4, pp 723–731 | Cite as

Modeling hydrogen entry and exit in metals exposed to multiple charging processes

  • S. L. Amey
  • G. M. Michal
  • J. H. Payer
Transport Phenomena
Received:

Abstract

A model is presented to evaluate hydrogen entry or exit in metals exposed to an aqueous environment. The model may be used to analyze data obtained from hydrogen permeation experiments through metal membranes. The model takes advantage of the ideal behavior predicted from the Nernst Equation and Sievert’s Law. It provides a single parameter,κ, to quantify the deviation from Sievert/Nernstian behavior. It is sufficiently general to allow arbitrary chemical potentials of hydrogen on both sides of a sheet, in addition to an arbitrary initial hydrogen distribution within a metal sheet. Simulated permeation curves are presented to show the influence of the model parameters upon permeation behavior. The model is applied to solution agitation during permeation of a low-carbon steel sheet as an illustration. By curve-fitting the model to experimental data, the diffusivity, surface solubilities, andκ on both sides of a metal sheet may be obtained for a given electrochemical charging condition. When compared to other popular models, the model presented by this article fit the experimental data well. The parameters obtained by the model may be used to characterize a given charging process. As such, the effect of one or more processes may be evaluated by using the model to calculate hydrogen distributions in a metal sheet.

Keywords

Material Transaction Metal Sheet Hydrogen Concentration Hydrogen Permeation Exit Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

A

reduced parameter from Eq. [12]

Βn

transcendental parameter from Eq. [15]

C(x, t)

concentration of hydrogen at position x and time t

Cn

the effective hydrogen concentrations (fugacity) in the environment on either side of the sheet

c(0, ∞)

the steady-state hydrogen concentration just underneath the entry surface

c(L, ∞)

the steady-state hydrogen concentration just underneath the exit surface

D

the diffusion coefficient of hydrogen in the metal

E

reduced parameter from Eq. [17]

Ew

the working electrode potential

en

reduced parameters from Eq. [18]

f(x, t)

an initial distribution of hydrogen in a sheet

fH2

the fugacity of hydrogen on a metal surface that is in equilibrium with an equivalent partial pressure

F

Faraday’s Constant (96,500 C/eq)

hn

a reduced, convective mass transfer coefficient

i∞

the steady-state permeation current density

i

the current density at a particular time t and position x = xo

J

the hydrogen flux through the sheet surface

J∞

the hydrogen flux through the exit surface of the sheet

Kn

the convective mass transfer coefficient

kn

a reduced variable for Eq. [10]

L

sheet thickness

T

reduced parameter from Eq. [12]

u(x, t)

the steady-state solution of Eq. [11]

w(x, t)

the non-steady-state solution of Eq. [1]

Z

reduced parameters from Eq. [12]

z

the number of electrons passed for the reduction and oxidation of hydrogen (eq/mole)

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Copyright information

© The Minerals, Metals and Materials Society, and ASM International 1994

Authors and Affiliations

  • S. L. Amey
    • 1
  • G. M. Michal
    • 2
  • J. H. Payer
    • 2
  1. 1.Master Builders, Inc.Cleveland
  2. 2.Department of Materials Science andEngineeringCase Western Reserve UniversityCleveland

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