Absorption and Stripping
Some important definitions
• In distillation, heat drives the separation of the more volatile from the
less volatile component; this unit op is always counter-current.
• In stripping/absorption, separation is induced by addition of a third
component; these unit ops can be either counter-current or co-current.
stripping: a volatile component of a liquid stream vaporizes into a
carrier gas stream
absorption: a soluble component of a gas stream dissolves in an
extracting liquid stream
- physical absorption: the desired component is soluble in the
-
extracting liquid
chemical absorption: the desired component reacts with the
extracting liquid
• irreversible chemical absorption: generates product/waste
• reversible chemical absorption: solvent is recycled by stripping
Stripping and absorption are often used together.
Ex.: Integrated system for removing CO2 from syn gas
solvent cooler
H2, CO
H2NCH2CH2OH
(MEA)
N2 + CO2
MEA + CO2
heat
exchanger
stripper
absorber
hot feed gas
H2, CO, CO2
syn gas
MEA + CO2
N2
Gases in at the bottom.
Liquids in at the top.
(Why?)
MEA
Key simplifying assumptions
1. stripping gas/carrier gas is insoluble in solvent
2. solvent is non-volatile
- therefore all streams are either pure or binary
3. columns are isothermal and isobaric
4. heat of absorption is negligible
- therefore energy balance is automatically satisfied
Degrees of freedom analysis:
D.o.F. = C – P + 2 = 3 –
2 + 2 = 3
(A,B,C)
(V,L)
When T, P are fixed (assumption 3), can specify only one more
variable: xB or yB
Labeling streams
Vn
yn
xn, yn:
Vn:
Ln:
Ln
xn
H
E
T
HETP
nth stage
Vn+1
yn+1
Packed columns are used more often than tray (plate)
columns in absorption/stripping, because of low mass
transfer efficiencies.
Ln-1
xn-1
HETP ≡ height (of packing) equivalent to a theoretical
plate.
Fractional stages are possible with packed columns.
mole fractions of solute A at equilibrium leaving the nth stage
total gas flow rate = (moles solute A + moles carrier gas B) / time
total liquid flow rate = (moles solute A + moles solvent C) / time
Since A is transferred in one direction only (liq → gas, or gas
are not constant. Therefore CMO is not valid.
→ liq), V and L
Using mole ratios
what is constant?
vapor mole ratio:
G ≡ carrier gas flow rate, moles B/time
since B is presumed insoluble, Gn = Gn+1 = G
S ≡ solvent flow rate, moles C/time
since C is presumed non-volatile, Sn = Sn-1 = S
yA
moles A in gas stream y A
YA =
=
=
moles B in gas stream y B 1- y A
moles A moles B moles A
YAG =
´
=
in gas stream
moles B
time
time
liquid mole ratio:
XA =
x
moles A in liquid stream xA
=
= A
moles C in liquid stream xB 1- xA
X AS =
moles A moles C moles A
´
=
in liquid stream
moles C
time
time
McCabe-Thiele analysis of stripping
feed
S, X0
G, Y1
stage 1
CMB:
GYj+1 + SX0 = GY1 + SXj
operating line equation:
Yj+1 = (S/G)Xj + [Y1 – (S/G)X0]
slope = S/G
stage j
Yint = [Y1 – (S/G)X0]
analogous to operating line for stripping section
of distillation column
G, Yj+1
S, Xj
usually specified: X0, YN+1, S/G, XN
stage N
stripping gas
G, YN+1
S, XN
fast plotting of operating line:
• the point (XN, YN+1) lies on the operating line
• calculate Y1 from CMB
• the point (X0, Y1) also lies on the operating line
Ex.: Analysis of counter-current stripper
Given X0, XN, YN+1 and S/G, find N.
1. Plot VLE data as mole ratios
(unless x0 < 0.05)
Note: y = x line has no use here.
•X0
1•
2. Plot (XN, YN+1) and (X0, Y1)
and draw operating line.
It will be below the VLE line.
3. Step off stages (use
Murphree efficiencies if
available).
2•
3•
•(X0,Y1)
•
•
N=3
•(XN,YN+1)
To find minimum stripping gas flow rate (Gmin):
1. Plot X0 on VLE line (watch for earlier pinch point, if VLE is curved).
2. Calculate Gmin = S / (S/G)max
Rule-of-thumb:
(S/G)opt ≡ 0.7 (S/G)max
Estimating fractional stages
Y
VLE
op. line
(X4, Y4)
•
X4
•
•(X , Y )
3 4
•
XN
X
X3
•
•
XN
XN - X3
fractional stage
=
requirement
X 4 - X3
McCabe-Thiele analysis of absorber
Solvent
S, X0
G, Y1
stage 1
G, Yk
CMB:
GYN+1 + SXk-1 = GYk + SXN
operating line equation:
Yk = (S/G)Xk-1 + [YN+1 – (S/G)XN]
S, Xk-1
slope = S/G
Yint = [YN+1 – (S/G)XN]
analogous to operating line for rectifying section
of distillation column
stage k
usually specified: X0, YN+1, S/G, Y1
stage N
feed
G, YN+1
S, XN
fast plotting of operating line:
• the point (X0, Y1) lies on the operating line
• calculate XN from CMB
• the point (XN, YN+1) lies on the operating line
Ex.: Analysis of counter-current absorber
Given X0, Y1, YN+1 and S/G, find N.
1. Convert VLE data to mole
ratios (unless x0 < 0.05)
Note: y = x line has no use here.
(XN,YN+1)•
2. Plot (X0, Y1) and (XN, YN+1) and
draw operating line.
It will be above the VLE line
(because mass is transferred in
opposite direction, gas → liq).
3. Step off stages (use
Murphree efficiencies if
available).
•
•
(X0,Y1)•
•
1
YN+1 •
•
3
•2
N=3
Find minimum extracting solvent flow rate (Smin) for given G:
1. Plot YN+1 on VLE line (watch for earlier pinch point, if VLE is curved).
2. Calculate Smin = G • (S/G)min
Rule-of-thumb:
(S/G)opt ≡ 1.4 (S/G)min
Multiple non-interacting solutes
Multiple soluble components (A, D, E…) in solvent C, to be stripped using gas B,
OR
Multiple components (A, D, E…) in carrier gas B, to be absorbed using solvent C.
If streams are dilute and components do not interact with each other, assume VLE for
each component is independent.
Treat each as a single-component problem, and solve sequentially.
For dilute streams,
Yi = yi / (1 - yi) ≈ yi
Xi = xi / (1 - xi) ≈ xi
S/G ≈ L/V
Ex.: 2-component absorber
Specify yA,N+1, yD,N+1, xA,0, xD,0
Specify L/V and yA,1. Find N and yD,1
(xD,N,yD,N+1)•
xA,0
xD,0
yA,1
yD,1
Separation of A requires N = 3.
1
y
(xA,N,yA,N+1)•
• •
N
yA,N+1
yD,N+1
xA,N
xD,N
(xA,0,yA,1)•
(xD,0,yD,1)•
•
•
•3
•3
•2
•
2
•1
•
1
Separation of D must also
use N = 3 and same L/V.
Trial-and-error: guess yD,1
x
Probably a good idea to use a different graph for each component…
Irreversible absorption
Add reagent R to solvent. R reacts essentially irreversibly with
solute A to form non-volatile products
R + A(g) → R•A(l)
e.g., NaOH + H2S(g) → Na2S + H2O
Equilibrium lies far to the right:
Equation of the VLE line:
xA ≅ 0
yA = 0
and
yA ≅ 0
Ex. Irreversible absorption
Specify yN+1, x0, L/V.
Required: xN = y1 = 0
C+R
x0 = 0
B
y1 = 0
Only one theoretical
equilibrium stage required …
1
y
yN+1
•
N
A+B
yN+1
C + R•A
xN = 0
(x0,y1)•
(x1,y1)
VLE
•
x (A + R•A)
Ex.: Irreversible absorption with low efficiency
Specify yN+1, x0, L/V, y1 ≠ 0
C+R
x0 = 0
B
y1 ≠ 0
More than one actual
equilibrium stage required …
1
yN+1
•
y
•
•
•
N
A+B
yN+1
A + R•A
xN = 0
• •3
• •2
(x0,y1)• •1
•6
EMV = 0.25
•5
•4
VLE
x (A + R•A)
Co-current cascade
• can use higher vapor velocity to increase mass transfer rate
• can use smaller diameter column without risk of flooding
• generally used for irreversible absorption
Specify y0, x0 = 0, xN, yN = 0
V, y0
L, x0
(x0,y0)•
Only one theoretical
equilibrium stage required, if
the reaction is irreversible
and mass transfer is fast …
j
V, yj
L, xj
Vy 0 + Lx0 = Vy j + Lx j
y=-
V, yN
L, xN
æ
L
L ö
x + ç y 0 + x0 ÷
V
V ø
è
(x1,y1) VLE
•
x (A + R•A)
VLE for dilute streams
When streams are dilute, VLE data can
be approximated by a straight line.
y = mx
Obtain the slope, m, from Henry’s Law:
PB = HB xB
where yB = PB/Ptotal
PB is the partial pressure of B, and HB is the Henry’s Law constant.
Note: HB = HB(T), like an equilibrium constant.
Analytical solution, when both VLE and op. line are straight
change in vapor composition between
adjacent stages:
(x2,y3) •
(y)2
(x1,y2) •
•(x2,y2)
(y)1 = y2 - y1
(x0,y1)•
•(x1,y1)
( Dy )
j
= y j +1 - y j
CMB:
æ
L
L ö
y j +1 = x j + ç y1 - x0 ÷
V
V ø
è
VLE:
y j = mx j
general case: L/V ≠ m, then (y)j ≠ (y)j+1
special case:
if L/V = m, then (y)j = y.
y1 + y2 + y3 + … = yN+1 – y1 = Ny
OR
N=
x0 - xN
( V)
xN - L
-1
y N+1
Kremser equation: L/V ≠ m
use VLE:
( Dy )
( )
Dy
( )
Dy
( )
- Dy
j +1
j
j
y j = mx j
æL
ö yj æ
ö
æ
L ö æ L
L ö
= ç - m÷ + ç y1 - x0 ÷ = ç
-1 y + y - x
V ø è mV ÷ø j çè 1 V 0 ÷ø
èV
øm è
æ L
ö
æ
L ö
=
1
y
+
y
çè mV ÷ø j +1 çè 1 V x0 ÷ø
j +1
æ L
ö
æ L
ö
=ç
- 1÷ y j +1 - y j = ç
- 1÷ Dy
è mV ø
è mV ø
( )
Dy
(
)
æ L ö
=
çè mV ÷ø Dy
j +1
( )
j
( )
( )
= A Dy
j
where A = L/mV ≡ absorption factor
j
( )(
) ( )
1- AN
y N+1 - y1 = Dy 1 + Dy 2 + Dy 3 + Dy 4 + ... = Dy 1 1+ A + A + A + ... = Dy 1
1- A
Kremser equation:
( ) ( ) ( ) ( )
y N+1 - y1
( Dy )
1
=
y N+1 - y N
( )
A Dy
0
1- AN
=
1- A
➠
2
3
y N+1 - y1 A - AN+1
=
y1 - y 0
1- A
where y0 = mx0
Other forms of Kremser equation
For gas phase compositions
(absorber columns):
For liquid phase compositions
(stripper columns):
y N+1 - y1 A - AN+1
=
y1 - y 0
1- A
xN - xN+1
1- S
=
x0 - xN+1 1- S (N+1)
where
and
S = mV/L ≡ stripping factor,
xN+1 = yN+1/m
solve for N:
é
ù
æ y - y0 ö
-1
ln ê 1- A-1 ç N+1
+
A
ú
÷
y
y
è
ø
ê
úû
1
0
N= ë
ln A
(
)
N=
é
lnê 1- S -1
êë
(
)
ù
æx -x ö
-1
0
N+1
çç
÷÷ + S ú
úû
è xN - x N+1 ø
lnS
include Murphree vapor efficiency:
é
ù
æ y N+1 - y 0 ö
-1
-1
ln ê 1- A ç
÷+A ú
y
y
è 1
ê
úû
0 ø
N=- ë
ln éë1+ EMV A-1 - 1 ùû
(
)
(
)
More forms shown in Wankat, chapter 12.4
Counter-current column sizing
Height:
1. measure HETP
2. measure EMV
3. obtain N
Diameter:
1. key parameter is V, total gas flow rate (not constant)
2. Vj is largest at the top of a stripper column, or at the
bottom of an absorber column
3. calculate D using same procedure as distillation column