Vacuum outlet

From ChroMatters Wiki

For those readers who are interested, here is some theory that pertains to the effects that placing the column exit at vacuum have on the movement of carrier gas through the column. This is supplementary material to the January, 2011, "GC Connections" column in LC/GC North America.^[1]

The pressure drop $Δ p$ across a column is the difference between the inlet and outlet absolute pressures, $p_\mathrm{i}\,$ and $p_\mathrm{o}\,$ :

$\Delta p = p_\mathrm{i} - p_\mathrm{o} \,$

When the outlet of the column is at the ambient atmospheric pressure then the pressure drop is equal to the control point of a split inlet pressure controller that maintains its set pressure in reference to the atmospheric pressure. For example, if the absolute inlet pressure were 44.1 psia (303 kPa) and the outlet pressure were 14.7 psia (101 kPa) then the pressure drop would be the difference, 29.4 psig (202 kPa), and an EPC split inlet controller would read this value for the inlet pressure. This is the normal situation when using an FID or most other non-MS detectors.

The pressure drop across a column produces an average linear gas velocity ū through the column that can be expressed as follows:

$\bar u = \frac{\Delta p j' d^2_\mathrm{c}}{32 L \eta}$

Here, d_c is the column inner diameter, L is the column length, η is the carrier gas viscosity at the column temperature, and j' is a pressure correction factor:

$j' = \frac{3}{4} \cdot \frac{P^2 + 2P + 1}{P^2 + P + 1}$

This factor, termed “j-prime,” adjusts for the influence of carrier gas compressibility on the flow of gas through the column, specifically its influence on the average velocity. Don't confuse it with the “j” factor which relates the average velocity to the outlet velocity on the basis of the volumetric expansion of gas as it transits the column from the inlet to the outlet pressure. The variable P is the pressure ratio of the column:

$P = p_\text{i} / p_\text{o} \,$

In the example above with the column outlet at atmospheric pressure, P equals 3.0 and j' equals 0.9231. At this modest pressure ratio the influence of j-prime on the average velocity predicted from the pressure drop is less than 10%: it means that about 10% higher pressure would be required to achieve the desired velocity than predicted without this factor. This influence exceeds 10% as the pressure ratio goes higher than 4.0, and it is incorporated into EPC systems that calculate the apparent average linear velocity of a column from the pressure drop and other variables.

When the column exit is placed under vacuum, the pressure drop across the column essentially is equal to the absolute inlet pressure: the pressure drop in our example case increases from 29.4 psi (202 kPa) to 44.1 psi (303 kPa). Most EPC pressure controller displays, and all mechanical controller readouts, will continue to show 29.4 psig (202 kPa), however, because the pressure controller operates relative to ambient pressure and not in relation to a vacuum. EPC systems determine the absolute pressure drop by adding the ambient atmospheric pressure (from a separate sensor) to the controller's pressure level and then use it to estimate the column average linear velocity and flow using similar equations. Any discrepancies between the actual column dimensions and the values entered into the EPC system will cause the flow and velocity readouts to deviate from the true values as measured by independent means such as with a flow meter or from the unretained peak time.

The pressure ratio approaches infinity as the outlet pressure approaches zero, and the limit of j-prime approaches 0.75:

$\lim_{P \to \infty} j' = 0.75$

so for vacuum outlet operation:

$\bar u = 0.75 \cdot \frac{\Delta p \cdot d^2_\mathrm{c}}{32 L \eta}$

This equation is used to calculate the average velocity under vacuum conditions.

References

↑ John Hinshaw, LC/GC North America, 29 (1), (2011).

[0] John Hinshaw, LC/GC North America, 29 (1), (2011).

[1]

Vacuum outlet

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