How to Convert Leak Rate to Flux for Permeability Coefficient Calculation?

[AlexN07]

Hi,

I am performing a helium leak experiment in which the detector outputs a number in mbar.L/s which is the amount of helium permeating through a specimen at a given pressure per unit of time.

I am interested in obtaining a permeability coefficient (K) for this specimen for the given pressure with helium as the working fluid.

My equation is: -K = J . delta x / delta P (rearrange Fick's 1st Law)

I know delta x (thickness) and delta P (pressure), however I am having trouble converting the mbar.L/s (leak rate) to a flux J (which I believe is in (mol /m^2 . s) for the equation.

Can somebody please help.

Alex

 

[Zefram]

,

I am happy to assist you with your experiment and the calculation of the permeability coefficient (K).

Firstly, let's define the terms in your equation. The flux J represents the amount of substance that passes through a unit area per unit time, and it is usually expressed in units of mol/m^2.s. The delta x is the thickness of the specimen, and the delta P is the pressure difference across the specimen.

To convert the leak rate from mbar.L/s to mol/m^2.s, we need to use the ideal gas law. The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. Rearranging this equation to solve for n, we get n = PV/RT.

In your experiment, the volume (V) is constant, so we can rewrite the equation as n = P/RT. Since you are using helium as the working fluid, we can assume that the gas constant (R) is 8.314 J/mol.K. The temperature (T) should also be constant throughout your experiment.

Now, we can calculate the number of moles of helium using the leak rate (mbar.L/s) and the pressure (mbar) at a given time. Let's say the pressure is 100 mbar and the leak rate is 10 mbar.L/s. We can convert the pressure to Pa (1 mbar = 100 Pa) and the volume to m^3 (1 L = 0.001 m^3), and then use these values to calculate the number of moles of helium.

n = (100 Pa)(0.001 m^3) / (8.314 J/mol.K)(constant temperature)

Once we have the number of moles, we can use this value to calculate the flux J using the equation J = n/A, where A is the area of your specimen.

Now, you can plug in the values for J, delta x, and delta P into your equation -K = J . delta x / delta P (rearranged Fick's 1st law) to calculate the permeability coefficient (K) for your specimen at the given pressure.

I hope this helps you in your experiment. If you have any further questions or need clarification, please feel free to reach out. Good luck