# Souders-Brown equation

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The Souders-Brown equation[1][2] has for many decades been the chemical engineering tool for obtaining the maximum allowable vapor velocity in vapor-liquid separation vessels (variously called flash drums, knockout drums, knockout pots, compressor suction drums and compressor inlet drums). It has also been used for the same purpose in designing trayed industrial distillation columns, trayed absorption (chemistry) columns and other vapor-liquid contacting columns.

## Description of a vapor-liquid separator

(GNU) Image: Milton Beychok
Typical Vapor-Liquid Separator

A vapor-liquid separator is a most often a vertical vessel used in many industrial applications to separate a vapor-liquid mixture. Gravity causes the liquid to settle to the bottom of the vessel, where it is withdrawn.[3][4][5][6] The vapor travels upward at a design velocity which minimizes the entrainment of any liquid droplets in the vapor as it exits the top of the vessel.

The feed to a vapor-liquid separator may also be a liquid that is being partially or totally flashed into a vapor and liquid as it enters the separator.

When used to remove suspended water droplets from streams of air, a vapor-liquid separator is often called a demister.

Some vapor-liquid separators are horizontal vessels and, in such cases, the following methodology for using the Souders-Brown equation must be adjusted to be applicable.

## Using the Souders-Brown equation

The diameter a vapor-liquid separator drum is dictated by the expected volumetric flow rate of vapor and liquid from the drum. The following sizing methodology is based on the assumption that the flow rates of vapor and liquid entering the separator vessel are known.

Use a vertical vessel with a length-to-diameter ratio of about 3 to 4, and size the vessel to provide about 5 minutes of liquid inventory between the normal liquid level and the bottom of the vessel (with the normal liquid level being somewhat below the feed inlet).

Calculate the maximum allowable vapor velocity in the vessel by using the Souders-Brown equation:

${\displaystyle V=\left(k\right){\sqrt {\frac {\rho _{L}-\rho _{V}}{\rho _{V}}}}}$

${\displaystyle V}$ where: = maximum allowable vapor velocity, m/s = liquid density, kg/m³ = vapor density, kg/m³ = 0.107 m/s (when the drum includes a de-entraining mesh pad)

Then the cross-sectional area of the drum (A) is obtained from:

A, in m² = (vapor flow rate, in m³/s) ÷ (vapor velocity V, in m/s)

And the drum diameter (D) is:

D, in m = [ (4) (A) ÷ (3.1416) ] 0. 5

The drum should have a vapor outlet at the top, liquid outlet at the bottom, and feed inlet at about the half-full level. At the vapor outlet, provide a de-entraining mesh pad within the drum such that the vapor must pass through that mesh before it can leave the drum. Depending upon how much liquid flow is expected, the liquid outlet line should probably have a liquid level control valve.

As for the mechanical design of the vessel (i.e., materials of construction, wall thickness, corrosion allowance, etc.), use the same criteria as for any pressure vessel.

### Recommended values of k

The GPSA Engineering Data Book[7] recommends the following k values for vertical drums with horizontal mesh pads (at the denoted operating pressures):

• At a gauge pressure of 0 bar: 0.107 m/s
• At a gauge pressure of 7 bar: 0.107 m/s
• At a gauge pressure of 21 bar: 0.101 m/s
• At a gauge pressure of 42 bar: 0.092 m/s
• At a gauge pressure of 63 bar: 0.083 m/s
• At a gauge pressure of 105 bar: 0.065 m/s

GPSA Notes:

1. k = 0.107 at a gauge pressure of 7 bar. Subtract 0.003 for every 7 bar above a gauge pressure of 7 bar.
2. For glycol or amine solutions, multiply above k values by 0.6 - 0.8
3. Typically use one-half of the above k values for approximate sizing of vertical separators without mesh pads
4. For compressor suction scrubbers and expander inlet separators, multiply k by 0.7 - 0.8

## Where vapor-liquid separators are used

Vapor-liquid separators are very widely used in a great many industries and applications, such as:

## References

1. M. Souders and G. G. Brown (1934). "Design of Fractionating Columns, Entrainment and Capacity". Industrial & Engineering Chemistry, 38 (1): pages 98-103.
2. Analytical Study of Liquid/Vapour Separation Efficiency, study developed by W.D. Monnery, Chem-Pet Process Technology Ltd. and W.Y. Svrcek, University of Calgary, Calgary, Canada, 2005, for Petroleum Technology Alliance Canada
3. William D. Baasel (1990). Preliminary Chemical engineering Plant Design, 2nd Edition. Van Nostrand Reinhold. ISBN 0-442-23440-6.
4. David H.F. Liu (1997). Environmental Engineers' Handbook, 2nd Edition. CRC Press. ISBN 0-8493-9971-8.
5. Stanley S. Grossel (June 2004). "Design and sizing of knock-out drums/catchtanks for emergency relief systems". Plant/Operations Progress (AIChE) 5 (3): 129-135. ISSN 0278-4513.
6. Stanley M. Walas (1988). Chemical Process Equipment:Selection and Design. Butterworth- Heinemann. ISBN 0-409-90131-8.
7. Gas Processing Suppliers Association (GPSA) (1987). Engineering Data Book, 10th Edition, Vol. 1. Gas Processing Suppliers Association, Tulsa, Oklahoma.