Consider a straightforward backfill system as shown in the figure consisting of a supply line at a pressure Pl with a filter, a valve and a flow limiter, L. L has a rating that its flow is Qs at a pressure equal to (Pl - dPf ), where dPf is the pressure drop across the filter. With the chamber at a vacuum the gas will flow at Qs when the valve opens. Assuming (Pl - dPf) is at least 15 PSIG the flow L will be a constant Qs until the chamber reaches atmospheric pressure. Assuming there is no loss of gas from the chamber during backfill, the time is given simply by:
Time = V / Qswhere V is the volume of the chamber. More generally, the time to fill the chamber to a pressure P2 is given by:
Time = (V / Qs ) x (P2 /14.7)
Where P2 is in PSIA.
The equations above are valid for 0 < P2 < (Pl - dPf)/2. Practically, this is always the case for typical values of Pl and dPf. For calculating time to pressurize the chamber to a P2 greater than (Pl - dPf)/2 one has to add a term equal to integrating the flow for sub-sonic conditions. (See Technical Reports).
Values of dPf are published by the filter manufacturer and depend up flow and Pl. For example with the TEM Filter 3775 with a 30 PSIG value for Pl and a flow of 25 slm the pressure drop is 5 PSI. At 25 PSIA a Universal Microsystems’ Model B-900-VS-11 flow limiter flows 25 slm (see table in
section). Consequently, a 5 liter chamber would fill in 12 secs.
Universal Microsystems and TEM filter offer an Ultrapure filter with a built-in flow limiter. (See
Flow Control Filter
Designers must also be aware that line pressures can vary considerably if there are multiple users on the supply line. In order to assure accurate and repeatable backfill times consider adding a pressure regulator before the filter.