How to choose a pump size - evacuation of a vacuum system

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Basically, two independent questions arise concerning the size of a vacuum system:

What effective pumping speed must the pump arrangement maintain to reduce the pressure in a given vessel over a given time to a desired value?
What effective pumping speed must the pump arrangement reach during a vacuum process so that gases and vapors released into the vessel can be quickly pumped away while a given pressure (the operating pressure) in the vessel, is maintained and not exceeded?

During the pumping-out procedure of certain processes (e.g., drying and heating), vapors are produced that were not originally present in the vacuum chamber, so that a third question arises:
What effective pumping speed must the pump arrangement reach so that the process can be completed within a certain time?

The effective pumping speed of a pump arrangement is understood as the actual pumping speed of the entire pump arrangement that prevails at the vessel. The nominal pumping speed of the pump can then be determined from the effective pumping speed if the flow resistance (conductances) of the baffles, cold traps, filters, valves, and tubulations installed between the pump and the vessel are known (see the page on conductance). In the determination of the required nominal pumping speed it is further assumed that the vacuum system is leaktight; therefore, the leak rate must be so small that gases flowing in from outside are immediately removed by the connected pump arrangement and the pressure in the vessel does not alter (for further details, see Leak detection). The questions listed above under 1., 2. and 3. are characteristic for the three most essential exercises of vacuum technology

Evacuation of the vessel to reach a specified pressure.
Pumping of continuously evolving quantities of gas and vapor at a certain pressure.
Pumping of the gases and vapors produced during a process by variation of temperature and pressure.

Initial evacuation of a vacuum chamber is influenced in the medium, high, and ultrahigh vacuum regions by continually evolving quantities of gas, because in these regions the escape of gases and vapors from the walls of the vessel is so significant that they alone determine the dimensions and layout of the vacuum system.

Evacuation of a vacuum chamber (without additional sources of gas or vapor)

Because of the factors described above, an assessment of the pump-down time must be basically different for the evacuation of a container in the rough vacuum region from evacuation in the medium and high vacuum regions.

Evacuation of a chamber in the rough vacuum region

In this case the required effective pumping speed S_eff, of a vacuum pump assembly is dependent only on the required pressure p, the volume V of the container, and the pump-down time t.

With constant pumping speed S_eff and assuming that the ultimate pressure p_end attainable with the pump arrangement is such that p_end << p, the decrease with time of the pressure p(t) in a chamber is given by the equation:

(2.32)

Beginning at 1013 mbar at time t = 0, the effective pumping speed is calculated depending on the pump-down time t from equation (2.32) as follows:

(2.33a)

(2.33b)

(2.34)

Introducing the dimensionless factor

(2.34a)

into equation (2.34), the relationship between the effective pumping speed Seff, and the pump-down time t is given by

(2.35)

The ratio V/Seff is generally designated as a time constant τ. Thus, the pump-down time of a vacuum chamber from atmospheric pressure to a pressure p is given by:

(2.36)

The dependence of the factor from the desired pressure is shown in Fig. 2.75. It should be noted that the pumping speed of single-stage rotary vane and rotary piston pumps decreases below 10 mbar with gas ballast and below 1 mbar without gas ballast. This fundamental behavior is different for pumps of various sizes and types but should not be ignored in the determination of the dependence of the pump-down time on pump size. It must be pointed out that the equations (2.32 to 2.36) as well Fig. 2.75 only apply when the ultimate pressure attained with the pump used is by several orders of magnitude lower than the desired pressure.

Fig 2.75 Dependency of the dimensionless factor s for calculation of pumpdown time t according to equation 2.36. The broken line applies to single-stage pumps where the pumping speed decreases below 10 mbar.

Example: A vacuum chamber having a volume of 500 l shall be pumped down to 1 mbar within 10 minutes. What effective pumping speed is required?
500 l = 0.5 m³; 10 min = 1/6 h
According to equation (2.34) it follows that:

For the example given above one reads off the value of 7 from the straight line in Fig. 2.75. However, from the broken line a value of 8 is read off. According to equation (2.35) the following is obtained:

under consideration of the fact that the pumping speed reduces below 10 mbar. The required effective pumping speed thus amounts to about 24 m³/h.

Evacuation of a chamber in the high vacuum region

It is considerably more difficult to give general formulas for use in the high vacuum region. Since the pumping time to reach a given high vacuum pressure depends essentially on the gas evolution from the chamber’s inner surfaces, the condition and pre-treatment of these surfaces are of great significance in vacuum technology. Under no circumstances should the material used exhibit porous regions or – particularly with regard to bake-out – contain cavities; the inner surfaces must be as smooth as possible (true surface = geometric surface) and thoroughly cleaned (and degreased). Gas evolution varies greatly with the choice of material and the surface condition. Useful data are collected in Table X.

Table X Outgassing rate of materials in mbar · l · s–1 · cm–2

The gas evolution can be determined experimentally only from case to case by the pressure-rise method: the system is evacuated as thoroughly as possible, and finally the pump and the chamber are isolated by a valve. Now the time is measured for the pressure within the chamber (volume V) to rise by a certain amount, for example, a power of 10. The gas quantity Q that arises per unit time is calculated from:

(2.37)

(Δp = measured pressure rise)

The gas quantity Q consists of the sum of all the gas evolution and all leaks possibly present. Whether it is from gas evolution or leakage may be determined by the following method:

The gas quantity arising from gas evolution must become smaller with time, the quantity of gas entering the system from leakage remains constant with time. Experimentally, this distinction is not always easily made, since it often takes a considerable length of time – with pure gas evolution – before the measured pressure-time curve approaches a constant (or almost a constant) final value; thus the beginning of this curve follows a straight line for long times and so simulates leakage (see Leak Detection).

If the gas evolution Q and the required pressure p_end are known, it is easy to determine the necessary effective pumping speed:

(2.38)

Example: A vacuum chamber of 500 l may have a total surface area (including all systems) of about 5 m². A steady gas evolution of 2 · 10^-4 mbar · l/s is assumed per m²of surface area. This is a level which is to be expected when valves or rotary feedthroughs, for example are connected to the vacuum chamber. In order to maintain in the system a pressure of 1 · 10^-5 mbar, the pump must have a pumping speed of

A pumping speed of 100 l/s alone is required to continuously pump away the quantity of gas flowing in through the leaks or evolving from the chamber walls. Here the evacuation process is similar to the examples given in the section on rough vacuum above. However, in the case of a diffusion pump the pumping process does not begin at atmospheric pressure but at the forevacuum pressure pV instead. Then equation (2.34) transforms into:

At a backing pressure of p_V = 2 · 10^-3 mbar “compression” K is in our example:

In order to attain an ultimate pressure of 1 · 10^-5 mbar within 5 minutes after starting to pump with the diffusion pump an effective pumping speed of

is required. This is much less compared to the effective pumping speed needed to maintain the ultimate pressure. Pumpdown time and ultimate vacuum in the high vacuum and ultrahigh vacuum ranges depends mostly on the gas evolution rate and the leak rates.

Evacuation of a chamber in the medium vacuum region

In the rough vacuum region, the volume of the vessel is decisive for the time involved in the pumping process. In the high and ultrahigh vacuum regions, however, the gas evolution from the walls plays a significant role. In the medium vacuum region, the pumping process is influenced by both quantities. Moreover, in the medium vacuum region, particularly with rotary pumps, the ultimate pressure pend attainable is no longer negligible. If the quantity of gas entering the chamber is known to be at a rate Q (in millibars liter per second) from gas evolution from the walls and leakage, the differential equation (2.32) for the pumping process becomes

(2.39)

Integration of this equation leads to

(2.40)

where
p₀ is the pressure at the beginning of the pumping process
p is the desired pressure

In contrast to equation 2.33b this equation does not permit a definite solution for Seff, therefore, the effective pumping speed for a known gas evolution cannot be determined from the time – pressure curve without further information.

In practice, therefore, the following method will determine a pump with sufficiently high pumping speed:
a) The pumping speed is calculated from equation 2.34 as a result of the volume of the chamber without gas evolution and the desired pump-down time.
b) The quotient of the gas evolution rate and this pumping speed is found. This quotient must be smaller than the required pressure; for safety, it must be about ten times lower. If this condition is not fulfilled, a pump with correspondingly higher pumping speed must be chosen.

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