There are three basic methods of measuring pumping speed. Two can be used with pumping stations with either gas transfer pumps (e.g., turbomolecular and diffusion) and gas capture pumps (e.g., cryo and ion). The third is for gas-transfer pumps only.
Method I (applicable to both transfer and capture pumps)
Each atom/molecule follows a random, independent path of wall collisions, and must enter the pumping mechanism before it is removed from the chamber. That is, the system follows first-order reaction kinetics: Nf = No x e-kt. Integrating this formula with respect to time gives:
|S = pumping speed in liter/sec|
|V = chamber volume in liters|
|t = time to go from Po to Pf in sec|
|Po = original pressure in torr|
|Pf = final pressure in torr|
S = V/t x logePo/Pf
While this equation does measure the effective pumping speed from the chamber, there are three cautions to note that strictly limit the range of pressures over which it is useful:
- This formula only works in molecular flow conditions.
- Do not expect the formula to give valid results if Po even edges into transitional flow.
- If the Pf is less than 100x the chamber's base pressure, then the pressure decay time will be distorted by wall outgassing. The distortion increases the closer Pf gets to the base pressure.
Worked Example: Knowing the chamber volume and timing the interval from the starting pressure to the final pressure, gives numbers we can substitute. A 150 L chamber has a fine leak-valve attached. Gas is let in through the valve at a rate that keeps the pressure steady at 4 x 10-4 torr with the pumps operating. The valve is shut and 26 seconds later the chamber pressure is 6 x 10-6 torr. What is the effective pumping speed (EPS)?
EPS = 150/26 x loge(4 x 10-4/6 x 10-6)
EPS = 5.77 x loge66.67
EPS = 5.77 x 4.2
EPS = 24 L/sec
Method II (applicable to transfer and capture pumps)
A few companies, including the Kurt J. Lesker Company, offer calibrated gas leaks of gases other than helium. A leak filled with a pumpable gas (such as N2 or CO2) is attached to the chamber via a valve. With the leak shut off, the chamber's base pressure is determined to ensure it is low compared to the operating pressure. The leak's valve is then opened and the steady state operating pressure measure. Use the throughput/pressure ratio to determine the effective pumping speed.
Worked Example: The chamber's base pressure is 1.7 x 10-8 torr. With the leak open, the working pressure is
5.3 x 10-6 torr. The N2 calibrated leak rate is 7 x10-8 std. atm cc/sec. What is the effective pumping speed?
Leak Rate = 7 x 10-8 std. atm cc/sec
Leak Rate = 7 x 10-8 x 760/1000 T.L/sec
Leak Rate = 5.32 x 10-8 T.L/sec
EPS = 5.32 x 10-8 T.L/sec divided by 5.3 x 10-6 T
EPS = 100 L/sec
Method III (applicable to transfer pumps only)
In this method we physically measure the gas coming out of the mechanical pump's exhaust. For this method to work, the gas leaving the must be:
- not captured in the foreline trap
- not soluble in the pump oil
- a reasonably large mass flow
If the mechanical pump has a gas ballast, shut it off. Note the chamber's steady state pressure under the gas load. Using a rubber bung with a piece of tube through it, block the pump's exhaust port and connect the tube, with a rubber tube, to a bubble flow-meter. Measure the flow rate in cc/sec at atmospheric pressure. (If the flow rate is high, sometimes the volume is measured by stretching a balloon over the tube and the volume measured by the diameter of the resulting “sphere”.) Because the measure system pressure is steady, the gas load must equal the measured throughput.
If more precise numbers are needed, measure the exhaust gas temperature and the barometric pressure and re-calculate the quantity of gas at STP with Boyle's and Charles' law combined:
P1V1/T1 = P2V2/T2
Worked Example: The measured flow of gas at the pump's exhaust is 2.3 atm cc/minute from a chamber at a measured pressure of 1.4 x 10-5 torr. The exhaust gas temperature is 32°C and the barometric pressure is 750 mm Hg. What is the effective pumping speed (EPS) from the chamber?
2.3 atm cc/min = 2.3/60 atm cc/sec
2.3/60 atm cc/sec = 2.3/60 x 760/1000 torr.liter/sec
2.3/60 x 760/1000 T.L/sec at 750 torr and 32°C is
2.3/60 x 760/1000 x 750/760 x 273/305 T.L/sec at standard temperature and pressure
Throughput = 0.0257 T.L/sec
EPS = 0.0257 divided by 1.4 x 10-5 L/sec
EPS = 1838 L/sec