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 theextracting 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

stripper

MEA + CO2

N2

N2 + CO2

MEA

H2, CO

MEA + CO2

Gases in at the bottom. Liquids in at the top.

(Why?)

solvent cooler

absorber

H2NCH2CH2OH(MEA)

hot feed gasH2, CO, CO2

syn gas

heat exchanger

Key simplifying assumptions

1. stripping gas/carrier gas is insoluble in solvent2. solvent is non-volatile

- therefore all streams are either pure or binary3. columns are isothermal and isobaric4. 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

nth stage

Packed columns are used more often than tray (plate) columns in absorption/stripping, because of low mass transfer efficiencies.

HETP ≡ height (of packing) equivalent to a theoretical plate.

HET

HETP

Ln-1

xn-1

Vn

yn

Ln

xn

Vn+1

yn+1

xn, yn: mole fractions of solute A at equilibrium leaving the nth stage

Vn: total gas flow rate = (moles solute A + moles carrier gas B) /

timeLn: total liquid flow rate = (moles solute A + moles solvent C) /

time

Fractional stages are possible with packed columns.

Since A is transferred in one direction only (liq → gas, or gas → liq), V and L are

not constant. Therefore CMO is not valid.

Using mole ratios

what is constant? 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 = Svapor mole ratio:

liquid mole ratio:

McCabe-Thiele analysis of stripping

feedS, X0

stripping gasG, YN+1

G, Y1

S, XN

stage 1

stage N

stage j

S, XjG, Yj+1

CMB: GYj+1 + SX0 = GY1 + SXj

operating line equation:

Yj+1 = (S/G)Xj + [Y1 – (S/G)X0]

slope = S/G Yint = [Y1 – (S/G)X0]

analogous to operating line for stripping section of distillation column

usually specified: X0, YN+1, S/G, 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

VLE (m

ay be cu

rved)

1. Plot VLE data as mole ratios (unless x0 < 0.05)Note: y = x line has no use here.

2. Plot (XN, YN+1) and (X0, Y1) and draw operating line. It will be below the VLE line.

N = 3

•(X0,Y1)

3. Step off stages (use Murphree efficiencies if available).

Given X0, XN, YN+1 and S/G, find N.

(S/

G) max

operati

ng line

slo

pe = S/G

•(XN,YN+1)

•

•

•1

•2

•3

To find minimum stripping gas flow rate (Gmin):1. Plot X0 on VLE line (watch for earlier pinch point, if VLE is curved).

•X0

2. Calculate Gmin = S / (S/G)max Rule-of-thumb: (S/G)opt ≡ 0.7 (S/G)max

Estimating fractional stages

Y

XXN

•

(X3, Y4)(X4, Y4) ••

VLEop. line

X3

XN

X4•

•

•

fractional stage requirement

McCabe-Thiele analysis of absorber

SolventS, X0

feedG, YN+1

G, Y1

S, XN

stage 1

stage N

stage k

S, Xk-1G, Yk

CMB: GYN+1 + SXk-1 = GYk + SXN

operating line equation:

Yk = (S/G)Xk-1 + [YN+1 – (S/G)XN]

slope = S/G Yint = [YN+1 – (S/G)XN]

analogous to operating line for rectifying section of distillation column

usually specified: X0, YN+1, S/G, Y1

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

VLE (m

ay be cu

rved)1. Convert VLE data to mole

ratios (unless x0 < 0.05)Note: y = x line has no use here.

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).

N = 3

(XN,YN+1)•

3. Step off stages (use Murphree efficiencies if available).

Given X0, Y1, YN+1 and S/G, find N.

(S/G

) min

oper

ating l

ine

sl

ope = S/

G

(X0,Y1)•

• •

•

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

1

3 •

YN+1 •

Ex.: Analysis of counter-current absorber

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

1

N

xA,0

xD,0

yA,N+1

yD,N+1

yA,1

yD,1

xA,N

xD,N

VLE(A

)

Separation of A requires N = 3.

(xA,N,yA,N+1)•

oper

ating l

ine

sl

ope = L/

V(xA,0,yA,1)•

• •

•

•

2

3

1 •

Specify yA,N+1, yD,N+1, xA,0, xD,0

Specify L/V and yA,1. Find N and yD,1

VLE(D)

Separation of D must also use N = 3 and same L/V.Trial-and-error: guess yD,1(xD,0,yD,1)•

• •

•

• •

2

3

1

(xD,N,yD,N+1)•

slope =

L/V

Probably a good idea to use a different graph for each component…

y

x

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: xA ≅ 0 and yA ≅ 0

Equation of the VLE line: yA = 0

Ex. Irreversible absorption

1

N

C + Rx0 = 0

A + ByN+1

By1 = 0

C + R•AxN = 0

yN+1

•

operati

ng line

slo

pe = L/V

(x0,y1)•

Specify yN+1, x0, L/V.Required: xN = y1 = 0

VLE

Only one theoretical equilibrium stage required …

(x1,y1) •

(A + R•A)

y

x

Ex.: Irreversible absorption with low efficiency

1

N

C + Rx0 = 0

A + ByN+1

By1 ≠ 0

A + R•AxN = 0

yN+1

•

(x0,y1)•

Specify yN+1, x0, L/V, y1 ≠ 0

VLE

More than one actual equilibrium stage required …

(A + R•A)

•

•

••

•

•

••2

6

5

4

3

1•

•

operati

ng line

slo

pe = L/V • EMV = 0.25y

x

pseudo-VLE

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

(x1,y1)•

Specify y0, x0 = 0, xN, yN = 0

(A + R•A)

L, x0

V, yN

V, y0

L, xN

j

L, xjV, yj

(x0,y0)•

VLE

operating line

slope = -L/VOnly one theoretical equilibrium stage required, if the reaction is irreversible and mass transfer is fast …

y

x

VLE for dilute streams

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.

When streams are dilute, VLE data can be approximated by a straight line.

y = mx

Analytical solution, when both VLE and op. line are straight

VLE: y

= mx

Op. line

(x0,y1)• •(x1,y1)

(x1,y2) • •(x2,y2)

(Δy)1 = y2 - y1

(x2,y3) •

(Δy)2

change in vapor composition between adjacent stages:

special case: if L/V = m, then (Δy)j = Δy. Δy1 + Δy2 + Δy3 + … = yN+1 – y1 = NΔy

CMB:

VLE:

OR

general case: L/V ≠ m, then (Δy)j ≠ (Δy)j+1

Kremser equation: L/V ≠ m

use VLE:

where A = L/mV ≡ absorption factor

where y0 = mx0

Kremser equation:

➠

Other forms of Kremser equation

More forms shown in Wankat, chapter 12.4

where S = mV/L ≡ stripping factor, and xN+1 = yN+1/m

For liquid phase compositions (stripper columns):

For gas phase compositions (absorber columns):

solve for N:

include Murphree vapor efficiency:

Counter-current column sizing

Height: 1. measure HETP2. 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 column3. calculate D using same procedure as distillation column