Chapter 4. Absorption and Stripping of Dilute Mixtures

Spring, 2012

Comparison with Distillation

Opposite Processes

Stripping is opposite process to absorption Sometimes they work together as a whole

process In absorption, the solvent should be

nonvolatile Otherwise, it will contaminate the product – gas

stream In stripping, the carrier gas should be

insoluble Otherwise, it will contaminate the product – liquid

stream

Physical and Chemical

Physical absorption • no significant chemical reaction occur between the absorbent

and solid

Chemical absorption (reactive absorption) • Reversible (or irreversible) reaction take place in the liquid

phase • Chemical reactions increase the rate of absorption

(Example) Absorption of an acid gas with sodium hydroxide (a strong base) Absorption of CO2 and H2S with aqueous solution of MEA

(monoethanolamine) or DEA (diethanolamine)

Equipment for absorption and stripping

(a) Trayed tower (b) Packed column (c) Spray tower (d) Bubble column (e) Centrifugal contactor

Details of contacting tray in trayed tower

Possible vapor-liquid flow regimes for a contacting tray

(a) Spary (b) Froth (c) Emulsion (d) Bubble (e) Cellular foam

Oclusion : Liquid carries vapor bubbles Entrinment : Vapor carries liquid droplets Weeping : liquid fall down to the tray holes

Three types of tray openings and passage of vapor up into liquid

(a) Perforation (b) Valve cap (c) Bubble cap (d) Tray with valve caps

Turn down ratio = Maximum / minimum vapor capacity

Details of internals used in packed column

Prevent channeling when the depth of packing is more than 20 ft

Typical materials used in packed column

Random packing and structured packing

Structured packing materials

Calculation Method

Equilibrium based method Rate-based method

Graphical Equilibrium Stage Method for Trayed Tower

Countercurrent-flow, trayed tower • Absorption (Solute : Gas Liquid) • Stripping (Solute : Liquid Gas )

Assumption • Isobaric, Isothermal • Continuous, Steady state • Equilibrium is assumed • Only one component transferred (!)

For n1 R1 + n2 R2 + …. → m1 P1 + m2 P2 + …. ∆Grx= ∆Grx°+ RT ln{∑aPi - ∑ aRj} = ∆Grx°+ RT ln(K), where K = {aP1

n1 aP2n2..}/{aR1

m1 aR2m2…..}

For the solvent extraction of Uraium nitrate by TBP in the nitric acid medium UO2

2+ + 2 NO3- + 2 TBP ⇒ UO2(NO3)2․2TBP

where, the aquous phase is in blue and the organic phase is in red ∆Grx= ∆G[U_TBP-(U+2HNO3+2TBP)]°+ RT ln{aU_TBPi – (aU + aHNO3

2 +aTBP

2 )} = ∆Grx°+ RT ln(K) where K = {aU_TBP}/{aU aHNO3

2 aTBP2 } and [TBP total] = aU_TBP + aTBP(free)

Let x = aU and y = aU_TBP, then K = (y/x) /(aHNO3

2 aTBP2 )

if [HNO3] is large (ex:3 N), then most of U in organic phase and verse versa HNO3 is called an salting out agent

Equilibrium Line and Operating Line

L’ = molar flow rate of solute-free absorbent G’ = molar flow rate of solute-free gas (carrier gas) X = mole ratio of solute-free absorbent in the liquid Y = mole ratio of solute-free gas in the vapor

Symbols

Equilibrium Relation

)1/()1/(

nn

nn

n

nn XX

YYxyK

++

==

Calculated from thermodynamics

X0, L’ Y1, G’

YN+1, G’ XN, L’

N

1

An Absorber

Advantage of using solute-free basis : L’ and G’ is always constant

X

Y

Equilibrium Line and Operating Line - Absorber

X0, L’ Y1, G’

YN+1, G’ XN, L’

N

1

n

Mass balance

'''' 110 GYLXGYLX nn +=+ +

)'/'()'/'( 011 GLXYXGLY nn −+=+

)1/()1/(

nn

nn

n

nn XX

YYxyK

++

==

Equilibrium Relation

X

Equilibrium Line

Operating Line Y

Gas Liquid Transfer : Equilibrium line lie lower than operating line

Equilibrium Line and Operating Line - Stripper

XN+1, L’ YN, G’

Y0, G’ X1 , L’

1

N

n

Mass balance

'''' 101 GYLXGYLX nn +=++

)'/'()'/'( 101 GLXYXGLY nn −+= +

)1/()1/(

nn

nn

n

nn XX

YYxyK

++

==

Equilibrium Relation

X

Equilibrium Line

Operating Line Y

Liquid Gas Transfer : Operating line lie lower than equilibrium line

L = L’ + solute in the liquid and G = G’ + solute in the organic x = X/(1 + X) and Y/(1 + Y)

Minimum Absorbent Flow Rate

X0, L’ Y1, G’

YN+1, G’ XN, L’

N

1

n

X

Y Decreasing absorbent rate

X0 (liquid in)

Y1 (gas out)

YN+1 (gas in)

XN (Liquid out for Lmin)

infinite Lmin

Minimum Absorbent Flow Rate

Mass balance

'''' 110 GYLXGYLX NN +=+ +

)()(''

0

11

XXYYGL

N

N

−−

= +

)1/()1/(

NN

NNN XX

YYK++

=

Equilibrium Relation

011

11min })]1(/[{

)(''XKKYY

YYGLNNNN

N

−+−−

=++

+

For dilute solution,

01

11min /

)(''

,

XKyyyGL

xXyY

NN

N

−−

=

≈≈

+

+

If pure liquid was used,

N

NN

KGLy-yyX

'' ,0

min

1110

=≈≈ ++

NKLG /''min =Similar Derivation for Stripper

Number of Equilibrium Stages

A similar method as McCabe-Thiele Method Operating Line Material balance equation

Equilibrium line Phase Equilibrium equation

)'/'()'/'( 011 GLXYXGLY nn −+=+

)1/()1/(

nn

nn

n

nn XX

YYxyK

++

==X0

Y1

YN+1

XN

Stage 1 (top)

Stage 2

Stage 3 (bottom)

Rate-based Method for Packed Columns

Using packed column • The required column diameter is less than 2 ft • Pressure drop must be low (ex : vacuum service) • Corrosion consideration ( ex: ceramic or polymer

material) • Low liquid holdup

Analysis Method • Rate based method : mass transfer consideration • Equivalent equilibrium stages

Analysis of Packed Column using Equivalent Equilibrium Stages

Height Equivalent to Theoretical Equilibrium plate (HETP)

HETP data comes from experimental Data Example)

• Number of equilibrium plate : 6.1 example 6.1 • 1.5 in Pal rings are used : HETP = 2.25 ft • lt = (HETP) Nt = (2.25)*(6.1) = 13.7 ft

t

t

NlHETP ==

stages mequilibriu equivalent ofNumber height packed

Rate-based Method

Lin ,xin

Gin ,yin

Gout ,yout

Lout ,xout

x Ll

y Gl

l

Lin ,xin

Gin ,yin

Gout ,yout

Lout ,xout

x Ll

y Gl

l

Material balances

outoutllinin GyxLyGLx +=+

Assuming dilute solution,

LLLLGGGG

outinl

outinl

======

For absorbers

)()(GLxy

GLxy inout −+=

For strippers

)()(GLxy

GLxy outin −+=

Two film theory

Physical equilibrium at the interface Physical equilibrium line is also

important in the rate-based method The method of determining

minimum absorbent liquid or stripping vapor flow rate is identical to the method for trayed towers

Mass transfer coefficient • k : mass transfer on a unit area • ka : mass transfer on unit volume

• a : the area for mass transfer per unit volume

Interface Gas Liquid

Bulk gas phase composition

Bulk liquid phase composition

Film gas composition

Film liquid composition

y or p

xI or cI

yI or pI

x or c

x* c*

y* p*

Two film theory

Steady state absorber • (rate of solute mass transfer across gas phase film) = (rate of solute mass transfer across liquid film)

)()( xxakyyakr IxIy −=−=

akak

xxyy

y

x

I

I =−−

)()(

y

x

equilibrium curve

Operating line

A

B

D

E

F C

y*, x

y, x*

yI, xI

Gas phase driving force

Liquid phase driving force

Mass transfer resistance in gas phase is low yI ≈y Liquid film controlling process

Mass transfer resistance in liquid phase is low xI ≈x Gas film controlling process

Increasing turbulence on gas/liquid phase

Rate-based method

Mass transfer coeff. defined in terms of overall driving force • avoid compositions at interface

• Fictitious compositions

)()( ** xxaKyyaKr xy −=−=

y xxy

with mequilibriu : with mequilibriu :

*

*

)(111

)(111

*

*

I

I

yxx

I

I

xyy

yyxx

akakaK

xxyy

akakaK

−−

+=

−−

+=

Rate-based Method

The equilibrium line is almost straight light through the origin dilute region

y

x

equilibrium curve

Operating line

A

B

D

E

F C

y*, x

y, x*

yI, xI

)(111

)(111

*

*

I

I

yxx

I

I

xyy

yyxx

akakaK

xxyy

akakaK

−−

+=

−−

+= K

1/K

aKkakaK

akK

akaK

yxx

xyy

111

11

+=

+=

Rate-based method

Determination of packed column height • Liquid phase has strong affinity to solute • Commonly involves Kya

Differential mass balance equation S : cross sectional area

Lin ,xin

Gin ,yin

Gout ,yout

Lout ,xout

dl lT

y G

x L

y+dy G

x+dx L

l

SdlyyaKGdy y )( *−=−

∫∫ −== in

out

T y

y

Tyly

yydy

GaSlK

dlGaSK

*0

∫ −= in

out

y

yy

T yydy

aSKGl *

Rate-based Method

Chilton and Colburn

Integration of NTU

∫ −=

=

=

in

out

y

yOG

yOG

OGOGT

yydyN

aSKGH

NHl

*

HTU : Overall height of transfer unit

NTU : Overall number of transfer unit

AAAKxyKxyAAN

KxLKGyyLKGdy

yydyKxy

inoutininOG

y

yinout

y

y

in

out

in

out

/)1()}/1()]/()]}[(/)1ln{[(

)/()/1(*

*

−+−−−

=

−+−=

−

=

∫∫

A : absorption factor = L/KG

Rate-based method

Relation between NTU, HTU and Nt, HETP

AAANN

AAAHHETP

tOG

OG

/)1()/1ln(

/)1()/1ln(

−=

−=

Alternative Mass Transfer Groups