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Absorption in packed towers: Rich gases case

Rich gas case: Vconst, Lconst

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Consider an absorption column;

Consider a mass transfer process in a section ofthe column dZ (cross-section of the column is S)

La,xa

Va,ya

Vb,yb Lb,xb

Z

dZ

SdZyyaKy

VdydN yA *)(1

*

S

Absorption in packed towers: Rich gases case

yxy k

y

k

m

K

)1(1*

i

i

y

y

yyy

1

1ln

]1[]1[1

Rich gas case: Vconst, Lconst

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La,xa

Va,ya

Vb,yb Lb,xb

Z

S

b

a

y

y yaKyyy

Vdy

SZ

**))(1(

1

Absorption in packed towers: Rich gases case

Example:McCabe, Smith, Harriott: Chapter 18Seader Hanley: Chapter 6

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Absorption in packed towers: Rich gases case

Prescriptive design process

1) Establish equilibrium relation y*=mx

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Absorption in packed towers: Rich gases case

Prescriptive design process

1) Establish equilibrium relation y*=mx

2) Operating line. In case of rich gases both V and L change andit is more convenient to work in terms of pure carrier

gas V and pure solvent stream L

)1(' xLL

)1(' yVV

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Absorption in packed towers: Rich gases case

Prescriptive design process

1) Establish equilibrium relation y*=mx

2) Operating line. In case of rich gases both V and L change andit is more convenient to work in terms of pure carrier

gas V and pure solvent stream L

plot y vs x

y

y

y

yV

x

x

x

xL

b

b

b

b

11'

11'

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Absorption in packed towers: Rich gases case

y

x

(mole fraction of A in L)

(mole fraction of A in V)

xa xb

y

yb

equilibrium line

x*b

3) For several values of y onthe operating line find:

y*

y1*y

*1 y

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Absorption in packed towers: Rich gases case

y

x

(mole fraction of A in L)

(mole fraction of A in V)

xa xb

y

yb

equilibrium line

x*b

3) For several values of y onthe operating line find:

y*

akak

xx

yy

y

xi

i

i

y i

i

y

y

yy

y

1

1ln

]1[]1[

1

iy

ak

y

ak

m

aK yxy

)1(1

*

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Absorption in packed towers: Rich gases case

3) Continued:

4) Find the term:

)1(

'

y

V

V

aKyyy

V

y

**))(1(

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Absorption in packed towers: Rich gases case

5) Integrate

aKyyy yVSZ y**))(1(1

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Absorption in packed towers:

Seader, Hanley

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P

GVlog

dry

Loading point

Flooding point

Design considerations: Pressure drop and flooding

G mass flow per unit area (GV-gas, GL-liquid)

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Liquid inlet

Liquid outlet Gas inlet

Gas outlet

Some flooding description

A visual build-up of liquid on the uppersurface of the packed bed

A rapid increase in liquid hold-up withincreasing gas rate

Formation of a continuous liquid phase abovethe packing support plate

A considerable entrainment of liquid inthe outlet vapour

Filling of the voids in the packed bed with liquid

Design considerations: Pressure drop and flooding

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(McCabe, Smith, Harriott)

Design considerations: Pressure drop and flooding

GV

GL

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Pressure drop analysis: Eckert graph

)(

1.02

VLV

p vFGVC

Pressure drop in

inH2O/ft of packing(brackets: mm H20/m of packing)

Flooding line

Design considerations: Diameter of packed towers

L/V=GL/GV

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Design considerations: Diameter of packed towers

Sinnott

McCabe, SmithHarriott

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* Moderate to high pressure distillation =0.4 to 0.75 in water / ft packing= 32 to 63 mm water / m packing

* Vacuum Distillation =0.1 to 0.2 in water / ft packing

= 8 to 16 mm water / m packing

* Absorbers and Strippers =0.2 to 0.6 in water / ft packing= 16 to 48 mm water / m packing

Design considerations: Diameter of packed towers

Given L, V (mass flow rates) Select pressure drop)(

)( 1.02

VLV

p vFGVC

select packingGV D

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Design considerations: Diameter of packed towers

Given L, V (mass flow rates))(

)( 1.02

VLV

p vFGVC

GV=GV(flooding)/2 D

at flooding velocity

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Example of using pressure drop correlations to estimategeometrical parameters of the packed column

Specify the packing type and column dimensions for a column that will beused to remove chlorine from a gas stream using an organic solvent.The vapor flow is 7000 kg/h, the average vapor density is 4.2 kg/m3.

The liquid flow is 5000 kg/h, the average liquid density is 833 kg/m3.The liquid's kinematic viscosity is 0.48 centistokes (4.8 x 10-7 m2/s)

Design considerations: Diameter of packed towers

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First, we evaluate the x-axis of the graph above:(L/V)(vapor density/liquid density)0.5 = (5000/7000)(4.2/833)0.5 = 0.0507

5.1

)(

1.02

VLV

p vFGVC

* Moderate to high pressure distillation =0.4 to 0.75 in water / ft packing

= 32 to 63 mm water / m packing

* Vacuum Distillation =0.1 to 0.2 in water / ft packing= 8 to 16 mm water / m packing

* Absorbers and Strippers =0.2 to 0.6 in water / ft packing= 16 to 48 mm water / m packing

Design considerations: Diameter of packed towers

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5.1)(

1.02

VLV

p vFGVC

Fp packing factor,

accounts for structure ofpacking and decreaseswith increasing void fraction

Fp=24 for 2 inch Pallrings

Design considerations: Diameter of packed towers

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Correlations for HTU

LGOG HL

mVHH

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Sinnott

Correlations for HTU

Cornell

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Sinnott

Correlations for HTU

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Correlations for HTU

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Correlations for HTU

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Design of packed towers

1) Calculate NTU

distillation/absorption from dilute gas

b

a

y

yyy

dy* y

yy ab

absorption from rich gas

b

a

y

yyyy

dyy*))(1(

)1(

2) Select packing: defines size, packing factor Fp, specific surface area, voidfraction etc

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Design of packed towers

3) Pressure drop, diameter of the column

4) HTU from Cornell, or Onda methods

5)

D

OGOGNHZ At this stage, height, diameter of the column andthe type of packing is known