chapter 04 absorption and stripping of dilute mixtures
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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
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