### Sample Problem Statement

Design a vertical gas-liquid separator or a Knock Out Drum for separation of liquid droplets entrained in fuel gas flow. The liquid in this case is water and the fuel gas phase can be considered to be mostly ethane.

Flow rate of water = 18 m3/hr

Entrained Flow of fuel gas = 100 m3/hr

Operating temperature of separator = 25 ^{0}C

Operating pressure of separator = 0.2 barg (near atmospheric)

Separation efficiency required is to remove water droplets above the size of 10 microns.

Fuel gas properties can be approximately taken as properties of ethane.

### Step 1

Water density at 25 ^{0}C = 994.72 kg/m3

Water viscosity at 25 ^{0}C = 0.9 cP

For fuel gas properties,

Molecular weight of ethane = 30 gm/gmole

Fuel gas density at 25 ^{0}C = 1.45 kg/m3

Fuel gas viscosity at 25 ^{0}C = 0.0069 cP

### Step 2

The gas liquid separation can be modeled using Stokes law. Where gas bubble terminal velocity is expressed as,

The subscripts L and G stand for liquid phase and vapour phase respectively.

And the gas bubble diameter Dp is described in microns.

Thus, using Dp = 10 micron,

*V _{t} = 0.0078 m/s*

(It should be noted that the use of Stokes law is valid only for Reynolds number lower than 2. EnggCyclopediaâ€™s vertical degasser sizing calculator uses an iterative procedure for calculation of Reynolds number and terminal velocity to make sure that the correct correlation is used. For higher Reynolds number, other equations govern the phase separation)

Here Reynolds number is calculated below,

As Re < 2 Stokes law is valid.

### Step 3

A tentative H/D ratio needs to be fixed for the vessel. Since the diameter of vessel (D) and TL-TL height of the vessel (H) are unknown, it makes it necessary to put a handle between then in the form of H/D ratio. Normally this ratio varies from 3 to 5. Here we select 3.5.

### Step 4

Next the vessel diameter can be calculated based on the allowable gas phase design velocity value obtained using Stokes law equation.

The terminal velocity for gas phase can be expressed as,

V_{t} = 4Ã—Vg/(3600Ã—Ï€d^{2})... where Vg is gas volumetric flow (m^{3}/hr) and 'd' is vessel diameter

Hence,

d = âˆšVg/(900Ã—Ï€Ã—V_{t})

d = âˆš100/(900Ã—Ï€Ã—0.0078) =Â 2.13 m

Considering the L/D ratio requirement,

L = 3.5 Ã—Â 2.13 =Â 7.45 m

This length has to be checked to be compliant with project specification of liquid residence time between HLL and LLL.