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Question 10.6: Design a horizontal separator to separate 10,000 kg/h of liq...

Design a horizontal separator to separate 10,000 kg/h of liquid, density 962.0 kg / m ^{3}, from 12,500 kg/h of vapour, density 23.6 kg / m ^{3}. The vessel operating pressure will be 21 bar.

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u_{t}=0.07[(962.0-23.6) / 23.6]^{1 / 2}=0.44 m / s

 

Try a separator without a demister pad.

 

u_{a}=0.15 \times 0.44=0.066 m / s

 

\text { Vapour volumetric flow-rate }=\frac{12,500}{3600 \times 23.6}=0.147 m ^{3} / s

 

\text { Take } h_{v}=0.5 D_{v} \text { and } L_{v} / D_{v}=4

 

\text { Cross-sectional area for vapour flow }=\frac{\pi D_{v}^{2}}{4} \times 0.5=0.393 D v^{2}

 

\text { Vapour velocity, } u_{v}=\frac{0.147}{0.393 D v^{2}}=0.374 D_{v}^{-2}

 

Vapour residence time required for the droplets to settle to liquid surface =h_{v} / u_{a}=0.5 D_{v} / 0.66=7.58 D_{v}

 

Actual residence time = vessel length/vapour velocity =L_{v} / u_{v}=\frac{4 D_{v}}{0.374 Dv ^{-2}}=10.70 D_{v}^{3}

 

For satisfactory separation required residence time = actual.

 

\text { So, } 7.58 D_{v}=10.70 D_{v}^{3}

 

D_{v}=0.84 m \text {, say } 0.92 m (3 ft \text {, standard pipe size })

 

Liquid hold-up time,

 

\text { liquid volumetric flow-rate }=\frac{10,000}{3600 \times 962.0}=0.00289 m ^{3} / s

 

\text { liquid cross-sectional area }=\frac{\pi \times 0.92^{2}}{4} \times 0.5=0.332 m ^{2}

 

\text { Length, } L_{v}=4 \times 0.92=3.7 m

 

\text { Hold-up volume }=0.332 \times 3.7=1.23 m ^{3}

 

Hold-up time = liquid volume/liquid flow-rate =1.23 / 0.00289=426 s =7 \text { minutes. }

 

This is unsatisfactory, 10 minutes minimum required.

Need to increase the liquid volume. This is best done by increasing the vessel diameter. If the liquid height is kept at half the vessel diameter, the diameter must be increased by a factor of roughly (10 / 7)^{0.5}=1.2.

 

\text { New } D_{v}=0.92 \times 1.2=1.1 m

 

Check liquid residence time,

 

\text { new liquid volume }=\frac{\pi \times 1.1^{2}}{4} \times 0.5 \times(4 \times 1.1)=2.09 m ^{3}

 

new residence time = 2.09/0.00289 = 723 s = 12 minutes, satisfactory

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