[ permeation ]
A simplified view on Fick ’ s laws of diffusion
Let us consider a cross-section of the pipe wall . None of the hydrogen molecules within the pipe wall have a preferred direction of movement . Some molecules move closer to the inside of the pipe , others move closer to the outside of the pipe . But the closer to the inside of the pipe , the more hydrogen molecules are present , due to the steady hydrogen supply from the transported gas , and the lack of hydrogen molecules in the air surrounding the pipe . So close to the inside of the pipe a high amount of hydrogen moves closer to the outside , while on the outside of the pipe a low amount of hydrogen moves closer to the inside of the pipe . Therefore , a net transport of hydrogen molecules from the inside to the outside of the pipe occurs . This is schematically shown in the figure below .
The hydrogen molecules ( blue dots ) move through the material ( black arrows ) and as a result move closer to either the inside of the pipe or the outside of the pipe ( green dotted arrows ). In the leftmost compartment , four hydrogen molecules move closer to the outside , compared to the rightmost compartment where only one hydrogen molecule moves closer to the inside . On the whole , the molecules move from the inside to the outside of the pipe .
A higher pressure of hydrogen inside the pipe will result in a higher concentration of hydrogen molecules ( more blue dots ). This will result in a higher rate of hydrogen movement through the pipe wall , and thus a higher permeation rate .
Inside of the pipe Pipe wall
Outside of the pipe
Movement of the permeant molecule
Net movement to either the inside of the pipe or the outside of the pipe
Hydrogen molecule Pipe wall ( cross section )
as thick , the permeation rate is decreased by half . Also , if the pipe is twice as long , the overall permeation rate is doubled due to an increase of the effective surface area .
The above-mentioned interactions manifest themselves in the following equation :
Q is the rate at which the permeate moves through the barrier material , often expressed as volume of permeate over time . P C is the permeability coefficient , the resistance of a material against the permeation of a permeate . A is the surface area , Δp is the partial pressure difference , and e is the wall thickness . Once the P C is known , it is possible to calculate the permeation rate using this equation of various pipes with different thicknesses and surface areas for different pressures at which the hydrogen is transported .
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Hydrogen Tech World | Issue 8 | February 2023