Conversion from weight leak rate to volume leak rate

In vacuum technology, the leak rate in general is described as volume leak rate (mbar.l/s). But there are industries which define the leak rates in loss of weight per year (g/a). The following example shows the conversion from loss of weight to volume leak rate (for constant pressure and temperature). Change to a different type of gas is also considered.

In an example from the refrigerator industry, the calculation for molecular flow leak rate becomes clear. Let us assume, that a refigerator manufacturer wants to check his products for a leakrate equal to or less than 0.01 g loss of the gas (R-12) per year. The correspondig volume leak rate is calculated via the mol:.

The relative mass of an R-12 refrigerant molecule is 121.

121 g of R-12 corresponds to 22.414 litre of gas at 1013 mbar und 00C, so that 0.01 gm R-12 = 1.85.10-3 bar.l that is 1.85 mbar.l R-12 per year.

1 year has 3.1536 . 107 seconds, then the R-12 volume leak rate is:

q_{R-12} = \frac{1,85 mbar \cdot l}{3,1536 \cdot 10^7 s} = 5,86 \cdot 10^{-8} \, mbar \cdot l/s

But this is not quite correct, because the mol is specified for the conditions of 0°C and 1.013 bar. The test takes place at room temperature, say 20°C. So we have to correct this result according to Charles´ Law (the pressure stays constant at both tests):

q_{R-12} = \frac{1,85 mbar \cdot l \cdot 293 K}{3,1536 \cdot 10^7 \, s \cdot K} = 6,3 \cdot 10^{-8} \, mbar \cdot l/s

At molecular flow, when pressure and temperature stay constant, the corresponding helium leak rate is calculated as follows:

\textup{helium leak rate qA} = \, ?

\textup{R-12 leak rate qB} = \, 6,3 \times 10^{-8}

\textup{relative mass of Helium} = \, 4

\textup{relative mass of R-12} = \, 121

We remember: The dependency of the leak rate at molecular flow in relation to the type of gas, is inversely proportional to the square root of the relative mass of molecules.

q_A = \frac{q_B \cdot \sqrt{M_B}}{\sqrt{M_A}} = \frac{6,3 \cdot 10^{-8} \cdot \sqrt{121}}{\sqrt{4}} = 3,5 \cdot 10^{-7} mbar \cdot l/s

This example is rarely used in practice. It was only chosen as a case of molecular flow. It shows that the helium leak rate in this case is factor 5.7 times higher than the R-12 leakrate. In practice, the required leak rates for refrigerators are in the range of 1 to 5 gm per year. These leakrates are already in the range of transition or laminar flow.