Project: 3rd year design Engineering Calculations By: D....

Project: 3rd year designBy: D. ModyDate: Nov 25 2008

Engineering Calculations

Purpose:

Vertical Separator CalculationThis example shows a difficult to size separator due to the very high liquid flow rates

Method:The method follows that presented in "Applied Process Design, Vol 1" by Ernest Ludwig forimpingment separators

vallow kρL ρv−

ρv⋅=

Assumptions:

Per the method, droplet sizes of less than about 10 microns will be captured. There is acurve of droplet size vs efficiency in the book.

Unit Definition (for Mathcad use):

none used

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Data:

ρL 1033kg

m3⋅:=Liquid Density

ρv 12.12kg

m3⋅:=Vapour Density

k for demister k 1260mhr

⋅:= with a demister

Vapour Flow Rate volflow 558m3

hr⋅:=

Liquid Flow Rate flowliquid 237m3

hr⋅:=

vallow kρL ρv−

ρv⋅:= vallow 1.156 104×

mhr

=

vdesign 0.75 vallow⋅:= vdesign 2.409ms

=

Areavolflowvdesign

:=Area 0.064 m2=

Area πdia2

2⋅=

Vessel Diameter for adequate vapour/liquid separation

dia 2Area

π:=

dia 0.286 m= dia 0.939 ft=

Calculate the Liquid holdup requirements

holduptime 10 min⋅:=

flowliquid 237m3

hr⋅:=

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volholdup holduptime flowliquid⋅:= volholdup 39.5 m3=

Calculate the vessel height for just the liquid holdup portion

heightliquid_holdupvolholdup

Area:= heightliquid_holdup 613.947 m=

This is not a feasible solution. If our diameter were larger more the same amount of liquidcould be held in a shorter vessel. We'll remove the demister and calculate the maximumdiameter

10% of velocity allowable is a typcial minimum velocity (when using a demister) thatensures droplets impact the wire mesh.


=

volflow 558m3

hr⋅:=

Areavolflowvdesign

:=Area 0.483 m2=

Area πdia2

2⋅=

dia 2Area

π:=

dia 0.784 m= dia 2.572 ft=

Now Calculate the Liquid holdup requirements

holduptime 10 min⋅:= flowliquid 237m3

hr=





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Still not feasible; Remove the demister and use 10% of Vel allowable

k 576mhr

⋅:= without a demister

vallow kρL ρv−

ρv⋅:= vallow 5.286 103×

mhr

=


= volflow 558m3

hr=

Areavolflowvdesign

:= Area 1.056 m2=

therefore dia 2Area

π:= dia 1.159 m=Area π

dia2

2⋅=

dia 3.803 ft=

Now Calculate the Liquid holdup requirements

holduptime 2 min⋅:= flowliquid 237m3

hr=





heightliquid_holdup 24.555 ft=

This liquid height is to the normal liquid level. The maximum liquid height isusually twice the normal, therefore total height for the liquid holdup is:

heightliquid_holdup 2 heightliquid_holdup⋅:= heightliquid_holdup 14.969 m=

heightliquid_holdup 49.11 ft=

Still extremely tall, should be split into two vessels, or we need to go below Vmin and weneed to check our correlations (Stokes Law & Impingment separators) to see ifseparation is still going to work.

For illustration purposes of the method, we'll go with this design for now.

Add in the Vapour Liquid disengagement space of 8



Size the Nozzle at 50% of errosional velocity:ρ2phase 316

kg

m3⋅:=

velnozzle 50 %⋅100

ρ2phaselb

ft3

⋅ft

sec⋅:=

velnozzle 11.257ft

sec= velnozzle 3.431

ms

=

Inlet_massflow 2.515 105⋅kghr

⋅:=

Inlet_massdensity 316kg

m3⋅:= this is the density of the 2phase flow stream

Inlet_volflowInlet_massflow

Inlet_massdensity:= Inlet_volflow 0.221

m3

s=

NozzleareaInlet_volflow

velnozzle:=

Nozzlearea 0.064 m2=

dianozzle 2Nozzlearea

π:= say 12 inch

nozzledianozzle 0.94 ft=

dianozzle 12 in⋅:=

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Distance from nozzle to high liquid level

heightLL_to_nozzle 12in12

dianozzle⋅+:= heightLL_to_nozzle 0.457 m=

Distance from nozzle to top of separator

heightnozzle_to_top 36in12

dianozzle⋅+:= heightnozzle_to_top 1.067 m=

Overall height

Heightoverall heightnozzle_to_top heightLL_to_nozzle+ heightliquid_holdup+:=

Heightoverall 16.5 m= Heightoverall 54.11 ft=

L / D ratio is:

Heightoveralldia

14.226=

If we examine splitting this into two vessels, we would have a small separator thatdischarges liquid into a holding tank that we'll assume has an L/D of about 3

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Two Vessels:Separator Dimensions will be per the first iteration of calculations

Liquid Holdup

Separator

k for demister k 1260mhr

⋅:= with a demister

vallow kρL ρv−

ρv⋅:= vallow 1.156 104×

mhr

=


=

Areavolflowvdesign

:=Area 0.064 m2=

Area πdia2

2⋅=

Vessel Diameter for adequate vapour/liquid separation

dia 2Area

π:=

dia 0.286 m= dia 0.939 ft=

Separator height

heightLL_to_nozzle 12in12

dianozzle⋅+:= heightLL_to_nozzle 0.457 m=

Distance from nozzle to top of separator

heightnozzle_to_top 36in12

dianozzle⋅+:= heightnozzle_to_top 1.067 m=

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Heightoverall heightnozzle_to_top heightLL_to_nozzle+:=

Separator dimensions:

Heightoverall 1.5 m= Heightoverall 5 ft=

Should check this against industrially available units - see spirax sarco

Dimensions for liquid holdup

volholdup 7.9 m3= this is to the normal liquid level

volholdup_full volholdup 2⋅:= volholdup_full 15.8 m3= this is full

vol vessel_length π⋅dia2

2⋅= vessel_length 3 dia⋅=

vol 3 dia⋅ π⋅dia2

2⋅= dia 2

volholdupπ 3⋅

1

3

⋅:=

dia 1.886 m= vessel_length 3 dia⋅:= dia 6.187 ft=

check the volume calculation

volumecalc vessel_length π⋅dia2

2⋅:=

volumecalc 15.8 m3= All okay!

Summary, The holdup vessel should be 1.89 m dia (rounded up to nearest 6") = 6.5 ft. The vesselshould be 3x that length, 19.5 ft long.

Separator dimensions 1ft dia x 5 ft high

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Project: 3rd year design Engineering Calculations By: D....

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