Problem 31: SteadyState Diffusion

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Problem 31Steady-State Diffusion

• Presented by Eric Burkhart
• 14 Feb. 2007

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Problem Statement
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What Type of Diffusion

• Hydrogen moving between neighboring interstitial
  sites in steel
• Interstitial diffusion is often much faster than
  vacancy diffusion

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Where to Start

• Trying to find kg/h of hydrogen diffusing out of
  steel vessel

Where A is the area over which diffusion is
occurring and J is the diffusion flux.

• We can first find A, the surface area of a cube
  from the volume of the cube (1m3)

6 Cube Faces 1m2 per Face 6m2 Surface Area
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How to Find J
Where D is the diffusion coefficient and dC/dx is
the slope of the concentration profile

• Diffusivity is given in the problem statement

WARNING Diffusivity varies with temperature, use
eqn. 6.8 to find D given a specific temperature.

• Okay, but what is a concentration profile?

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Concentration Profiles

• In this case, the denominator is simply the
  thickness of a wall (2mm).
• CA is the concentration of Hydrogen on the
  inside steel wall, and CB is the concentration
  of Hydrogen on the outside steel wall, given by
  the problem statement as zero.

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Concentration and Solubility

• Concentration is in terms of atoms or mass per
  length3.
• Solubility is in mass of Hydrogen per overall
  mass. In this case kg H/ kg Steel assuming
  negligible mass addition from Hydrogen.
• Problem statement says

Solubility
And gives the initial condition that at 300C and
1 atm, solubility is 1 ppm by weight, allowing us
to solve for a.
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Calculating Concentration

• Given pressure of 12.86 atm (189psia), solubility
  on inside wall is

3.586e-6 kg Hydrogen/ kg Steel

• To get concentration, multiply solubility by
  density of steel.

CA 3.586e-6 kg H/kg Steel 7500 kg steel/m3
Steel 0.02690 kg H/m3 Steel
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Back to the Beginning
A6m2
D5e-10 m2/s CA 0.02690 kg H/m3 Steel
CB0 xA-xB2mm
1.453x10-4 kg Hydrogen/hour
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Relevance
Pressure Vessel Design -

• Gas loss (particularly Hydrogen and other small
  gasses) not always insignificant.
• High temperature, high pressure and thin walls
  all increase the rate of loss.

Why is solubility proportional to square root of
pressure?

• Sieverts' Law H2 dissociates into
  monatomic Hydrogen and then passes
  through steel, becoming diatomic again on the
  other side.