4.1 Gas Liquid Separation - Mass Transfer

CHG 3111

Unit Operation

Chapter 10

Gas-Liquid Separation and Operations

4.1 Mass Transfer

CHG 3111/B. Kruczek

Approach

2

Mass Transfer Thermodynamics (Equilibrium)

Mass and Energy Balances

Size of Equilibrium

Stage

Number of Equilibrium

Stages

Operating Conditions

Complete Design

CHG 3111/B. Kruczek 3

Introduction Separation by Phase Contact

Many chemical processes and biological substances occur as mixtures of different components in the gas, liquid or solid phase.

To separate or remove one or more of the components from its original mixture, it must be contacted with another phase.

The two phase pair can be gas-liquid, liquid-liquid or liquid-solid.

When different phases are brought into contact, a solute or solutes can diffuse from on phase to the other.

The phases are then separated by physical methods, where one phase is enriched while the other is depleted in one or more components.

Contact

Phase 2

Phase 1

Separation

Phase 1

Phase 2

The separation processes are classified depending on the nature of Phases 1 and 2:

Gas/Liquid: absorption and stripping; Vapor/Liquid: distillation; Liquid/Liquid: liquid extraction; Liquid/Solid: leaching, crystallization, adsorption, ion exchange; Gas/Solid: adsorption

Other separation processes include:, membrane processes, filtration, settling and sedimentation, centrifugal processes


Introduction Processing Methods:

Batch vs. continuous

Concurrent vs. countercurrent

Multi-stage process

V2

L0

V1

L1

time V2

L1

V1

L0

V1

L1

V2

L0

Batch process

Continuous process

V2

L1

V1

L0

L and V are [kg or moles] in batch processes and [kg/s or moles/s] in continuous processes.

The two phases having the same subscript (e.g. L1, V1) are in equilibrium

Multi-stage processing is possible only in case of countercurrent operation. Why?

NB: Design of stage processes requires equilibrium relations between the phases in contact


Equilibrium Relations Between Phases Phase Rule and Equilibrium:

Phase rule – determination of the degrees of freedom:

F = C – P + 2

Example: CO2-air-water system has 2 phases and 3 components

F = C – P + 2 = 3 -2 + 2 = 3; therefore, 3 variables need to be specified (e.g.: T, P, yCO2)

Where: P = number of phases at equilibrium

C = number of total components in the two phases

F = number of variants or degrees of freedom of the system

Gas-liquid equilibrium

For a specific system, equilibrium data is determined experimentally, but some

generalizations are applicable.

For a system involving ideal gas and liquid phases, Raoult’s law applies:

A A A A A sy P p x p

For ideal liquid solutions the activity coefficient is equal to unity

Where: yA and xA are the mole fractions of A bulk gas and bulk liquid

phases, pA and pAs are the partial and vapor pressures of A,

respectively, and A is the activity coefficient of A in liquid solution


Equilibrium Relations Between Phases Phase Rule and Equilibrium:

Gas-liquid equilibrium

Henry’s law is applicable for dilute phases (xA < 0.1)

o r 'A A A A Ay P p H x y H x

For xA > 0.1, pA is no longer directly proportional to xA

Where: H and H’ are the Henry’s law constants in appropriate units

CHG 3111/B. Kruczek

Absorption and Stripping

7

Mass Transfer Considerations

1. Mass transfer between phases

2. Single point analysis – film and overall mass transfer

coefficients

3. Introduction to equipment

4. Equilibrium stage and Height of Transfer Unit

5. Operation and design of packed towers


Mass Transfer Between Phases Gas-Liquid Interface

Description of the system

V

V

L

L

Liquid (L) and gas (V) phases, both containing solute A, are brought in contact; we shell

first consider a single point anywhere within the system

Liquid is assumed to be non-volatile, while the bulk gas phase is assumed to be insoluble

in the liquid so that only solute A is being transported.

Bulk liquid and bulk gas phases are not in equilibrium, but equilibrium at the interface is

established instantaneously

Gas-phase

A in gas G Liquid-phase

A in liquid L

yAi

xAi

yAG

xAL

Interface

NA

Film

where: yAG and xAL are the

mole fractions of A bulk

gas and liquid phases,

and yAi and xAi are the

corresponding mole

fractions at the interface

a n d f o r d i l u t e s o l u t i o n s 'A i A i A Ay f x y H x


(A) (B)

NA

Diffusion equation in a single phase (Fick’s law):

NA = -cDAB (dyA/dz) + yA (NA + NB)

Equimolar counterdiffusion Diffusion of (A) through non-diffusing (B)

NA= -NB NB = 0

(A) diffusing from the gas to liquid and

(B) in equimolar counter diffusion from

liquid to gas

(A) diffusing through a stagnant gas and then through a stagnant liquid

Ammonia (B) – Water (A):

Both ammonia and water are soluble in

each other and diffusion occurs by both

A and B

Air (B) –Water (A):

water vaporizes to air, but air is insoluble in water.

Air (B) & Ammonia (A) – Water (C):

Ammonia diffuses through B in the gas phase (air is

insoluble in water) and then through a non-diffusing

liquid (water does not vaporizes)

NA = k'x (xAi – xAL) = k'y (yAG – yAi) NA = kx (xAi – xAL) = ky (yAG – yAi)

Film Mass-Transfer Coefficients

(A) (B)

NA NB

Mass Transfer Between Phases


Composition of Phases at the Interface

Bulk phase concentration

yAi xAi

yAG

xAL

NA


Taking samples from the liquid and gas phases allows

determination of xAL and yAG, but not xAi and yAi

Composition of bulk liquid and gas phases at a specific

location determine an operating point P, which has

coordinates (xAL,yAG)

Determination of xAi and yAi for a given operating point P requires mass transfer

coefficients in the liquid and gas phases

For equimolar counterdiffusion:

AG A ixA y AG A i x A i A L

y AL A i

y ykN k y y k x x

k x x

The composition of point M is determined by

the intersection of the equilibrium line with a

straight line of the slope determined by the

mass transfer coefficients that passes through

point P.

How do we determine point M analytically?


Composition of Phases at the Interface

yAi xAi

yAG

xAL

NA


For the case of diffusion of A through stagnant B:

AG A ixA y AG A i x A i A L

y AL A i

y ykN k y y k x x

k x x

NB: If one is provided with k’ mass transfer coefficients, the determination of the composition at the interface in the

case of diffusion of A through stagnant B requires a trial and error procedure. Alternatively, the coordinates of

point M in this case can be determined analytically by solving a system of non-linear equations.


x

y

k

k

1 1w h ere :

y xy x

A A iMiM

k kk k

y x

1 11

1 1

and:

ln ln

AL Ai BL BiA BiM iM

AL Ai BL Bi

x x x xx x

x x x x

1 11

1 1ln ln

A i AG Bi BG

A BiM iMA i AG Bi BG

y y y yy y

y y y y


Overall Mass Transfer Coefficients

Compositions of phases at the interface during a mass transfer process cannot be

measured experimentally, thus k'y and k'x ((ky and kx) are difficult to estimate.

Alternatively, the rate of transfer of solute A can be described in terms of the overall

mass-transfer coefficients K'y and K'x

Where: y*A = mole fraction of A in gas phase that would

be in equilibrium with xAL

x*A = mole fraction of A in liquid phase that

would be in equilibrium with yAG


* *' 'A y A G A x A A LN K y y K x x

y*A

x*A


NB: The above overall mass transfer coefficients are applicable for a single point stretching from the bulk liquid

to the bulk gas phase. They are not applicable to describe the mass transfer along the entire column!


Overall Mass Transfer Coefficients in terms of Film Coefficients

Driving force for the mass rate equation in terms of the overall mass transfer coefficient


x*A

y*A

Slope = m''

E

D

Slope = m'

Approximation of the equilibrium line by the slopes m’ and m”, and unless Henry’s

law is applicable, m’ ≠ m”

* *G a s p h a s e d r i v i n g f o r c e l e n g t h o f l i n e A G A A G A i A i AP E y y y y y y

* *L i q u i d p h a s e d r i v i n g f o r c e l e n g t h o f l i n e A A L A A i A i A LP D x x x x x x

*

slope o f A i A

A i AL

y yEM m

x x

*s lo p e o f AG A i

A A i

y yM D m

x x

Re-expression od driving forces in terms of m’ and m”

*G a s p h a s e d r i v i n g f o r c e ' A G A A G A i A i A Ly y y y m x x

*L iq u id p h a s e d r iv in g fo rc e "

A G A i

A A L A i A L

y yx x x x

m







The solute A is being absorbed from a gas mixture of A and B in a wetted-wall tower with the

liquid flowing as a film downward along the wall. At a certain point in the tower the bulk gas

concentration yAG = 0.25 mole fraction and the bulk liquid concentration is xAL = 0.05. the tower

is operating at 298 K and 1.01x105 Pa and the equilibrium data are as follow.

The solute A diffuses through stagnant B in the gas phase and then through a non-diffusing

liquid. Using correlations for dilute solutions in wetted-wall towers, the film mass-transfer

coefficient for A in the gas phase is predicted as k’y = 1.465x10-3 kg mol A/s.m2..mol frac and for

the liquid phase k’x = 1.967x10-3 kg mol A/s.m2. mol frac.

Calculate the interface concentrations yAi and xAi and the flux NA.

xA yA xA yA

0 0 0.25 0.187

0.05 0.022 0.30 0.265

0.10 0.052 0.35 0.385

0.15 0.087

0.20 0.131

Example 1: Interface composition


Equipment for Gas – Liquid Contact

Tray tower

General information

Classification of the contact equipment

Tray towers

Gas in

VN+1, yN

Liquid in

L0, x0

Liquid out

LN, xN

Gas out

V1, y1

Liquid out

L1, x1

Gas in

V1, y1

Liquid in

L2, x2

Gas out

V2, y2

Packed towers

Wetted wall towers, spray towers and chambers

Towers are typically run in a countercurrent mode (why?)

Packed tower

Rate equation

Unlike the analysis so far, which were

focused on a single point, we are now

interested in nA = NA As not just NA

Purpose of the equipment is to maximize nA by:

Maximization of the interfacial area (As) exposed

between the phases

Optimization of the nature and degree of

dispersion of one phase into another

Apart from Absorption and Stripping, packed and tray

towers are used Humidification, Dehumidification,

Adsorption and Distillation applications


Equipment for Gas – Liquid Contact Tray Towers - types of trays

Sieve tray

Gas bubbles through holes (3 – 12

mm) in the tray and then through the

liquid flowing over the tray; flowing gas

prevents liquid going into the holes.

Depth of the liquid on the tray.

maintained by overflow, outlet weir.

Overflow liquid flows into downspout

to the next tray below;

bubble-cap tray

sieve tray

Bubble-cap tray

Gas rises through opening through the

openings in tray into the bubble caps,

and then through slots in the periphery

of each cap

Valve tray

Modification of sieve try – opening in

the tray are covered by lift-valve cover;

prevents liquid going through the

openings


Equipment for Gas – Liquid Contact

Random packing, for example Raschig rings (a), Berl saddle (b),

Pall ring (c), Intalox metal (d), Jaeger tri-pack (e)

Packed Towers

(a) (b) (c) (d) ( e)

Random

packing

Liquid out

Gas in

Liquid in

Gas out

Liquid

distributor

Liquid

re-distributor

Packing

support

Shell

Packed tower is uniformly filled with a packing material – no distinct equilibrium stages

Types of packing

Structured packing – assembled into repeatable structural elements,

rather than randomly damped into the column


Equipment for Gas – Liquid Contact Summary of packing characteristics

NB1: Ceramic Rasching Rings of nominal size 1.5 inch serve as a reference for the determination of mass

transfer coefficient in packed beds

NB2: Packing Factor is a measure of the capacity of the tower, and Fp ≈ a/e3


Equilibrium Stage in Gas – Liquid Contact Tray Towers

The objective: the liquid (L1) and gas (V1) leaving a tray are in equilibrium

V1,y1

Tray efficiency – Murphree efficiency (EM)

Represents the average tray efficiency and can be

expressed in terms of liquid or gas phase compositions

What can be done to maximize try efficiency?

2 1 1 0

2 1 1 0

' ' or MG ML

y y x xE E

y y x x

NB: If tray efficiency is 100%, the spacing between the trays determines the length of the tower to achieve

one full equilibrium stage

V1,y1

V2,y2 V2,y2 L1,x1

L1,x1

L0,x0 L0,x0

M

N

M’N’P = Incomplete Equilibrium Stage

y1

y2

x1 x0

N’ M’ y‘1

x’1

MNP = Complete Equilibrium Stage


Equilibrium Stage in Gas – Liquid Contact Packed Towers

Liquid out

Gas in

Liquid in

Gas out

Height of transfer unit is equivalent to one full equilibrium stage in a packed tower

V1,y1

V2,y2 L2,x2

L1,x1

H M N

MNP = Equilibrium Stage

y2

y1

x1 x2

Parameters affecting the size of transfer unit include:

Mass transfer coefficients in the liquid and gas phases

The operating conditions, i.e., flow rates of gas and

liquid, and temperature

Properties of the packing material (Table 10.6-1)

Solubility of solute in the liquid and gas phases


Equilibrium Stage in Gas – Liquid Contact

Height of transfer unit can be expressed in different ways

NB: In packed beds the surface area for mass transfer is unknown, therefore, mass transfer coefficient is

combined with the specific surface of bed

Height Transfer Unit (H) in Packed Towers

1'G

y y iM

V VH

k aS k a y S

Height of transfer unit based on the gas film:

1'L

x x iM

L LH

k aS k a x S

Height of transfer unit based on the liquid film:

1'OG

y y iM

V VH

K aS K a y S

Overall height of a gas-phase transfer unit:

Overall height of a liquid-phase transfer unit: 1'

OL

x x iM

L LH

K aS K a x S

Where: V and L are the average molar flows of gas and liquid phases respectively, S is the

cross sectional area of the tower, and a is the specific surface of packing

Question: Are HG, HL, HOG, HOL the same?


Equilibrium Stage in Gas – Liquid Contact

Recall the analysis for the determination of the conditions at the gas liquid interface

NB: In the literature the terms Hy, Hx, HOy, HOx are used instead of HG, HL, HOG, HOL; they are identical to

each other

Correlations between height transfer units

Since in packed beds the exact area of contact

between the phases is not known, k [mol/m2 s]

is replaced by ka [mol/m3 s] and:

an d OL L G OG G LH H L mV H H H mV L H

x*A

y*A

Slope = m''

E

D

Slope = m'

slope ' 'x yk a k a

1 1

y y x

m

K a k a k a

1 1 1

"x x xK a k a m k a

NB: for dilute solutions:

m’ = m” = m

Using the definitions of heights of transfer units (HG, HL, HOG, HOL) it can be shown that:


Mass Transfer Coefficients in Packed Towers

Complexity of prediction of individual film coefficients – empirical approach

Correlations for Height of Transfer Unit

Since the transport of solute A in absorption/stripping processes involves two phases, the

experimentally determined mass transfer coefficients are the overall (K'ya and K'xa) rather

than the individual (k'ya and k'xa) film coefficients.

For K'ya ≃ k'ya the solute must be highly soluble in the liquid phase, e.g.: NH3 – Air – Water

system, the liquid phase resistance is roughly 10% of the total resistance.

For K‘xa ≃ k‘xa the solute must very insoluble in the liquid, e.g.: CO2 – Air – Water system,

the gas phase resistance is practically negligible.

For the design packed beds, it is more practical to use the correlations for height of transfer

unit rather than for mass transfer coefficient (why?)

0 350 5 0 50 226

0 660 6 782 0 878

.. ..

For the gas film coefficient: . . .

ySc xG y

p

GN GH H

f

0 30 5

3

0 357

372 6 782 0 8937 10

...

For the liquid film coefficient: . .

xScL x

p

GNH H

f

where: Gx and Gy are the mass fluxes [kg/m2 s] of liquid and gas, and fp is the relative mass transfer

coefficient (Table 10.6-1)


Operation of Packed Towers Flow Rates of Gas and Liquid

Flow rates of liquid and gas directly affect the Height of Transfer Unit, but also they

determine the pressure drop and the operation mode in the tower

Liquid out

Gas in

Liquid in

Gas out

Liquid holdup and loading point

Liquid holdup is the quantity of liquid contained in the packed bed.

For a given liquid velocity (L) the loading point is the upper limit of

the gas velocity (V) for a reasonably constant liquid holdup.

Below the loading point, gas phase is continuous and liquid phases

is dispersed.

Above the loading point (loading region), liquid pools form at the top

of the column – gas pressure drop sharply increases as G increases.

In the loading region liquid entrainment is observed, liquid holdup

sharply increases, mass transfer efficiency decreases, and column

operation is unstable.

Flooding point – continuous liquid layer at the top of the column;

pressure drop increases infinitely with increasing G.

Therefore: Although a packed column can operate in the loading region, most columns are designed

to operate below the loading point, in the preloading region


Operation of Packed Towers Prediction of Pressure Drop

Pressure drop in random and structured packing

Random Packing

3m

-1

superficial gas velocity [ft/s]

and densities of gas and liquid lb ft

packing factor ft can be found in Table 10.6-1

G

G L

pF

2m

3m

kinematic viscosity of liquid centstokes

and mass velocities of gas and liquid [lb /s ft ]

and densities of gas and liquid lb ft

G L

G L

G G

where:

Structured Packing

Regardless of packing the pressure at flooding:

1 0 7

1

60 0 115

60 2

. 2

2

for ft : in. H O/ft .

For ft : in. H O/ft

p flood p

p flood

F P F

F P


Operation of Packed Towers Design Factors

Preliminary design procedure – type of packing, GL/GG, and total gas flow are known

The ratio of tower diameter to the random packing size should be 10:1 or greater

For every 3 m height of packing, a liquid redistribution should used to prevent liquid

channeling.

For random packing tower diameter should be less than 1.0 m

Loading in packed towers starts at 65 – 70% of the flooding velocity

Adsorption should be run at 50 – 70% of flooding velocity (upper end at high flow

parameter)

Therefore: The first step in the design of a packed tower is to determine the limiting

flow rates and hence the tower diameter

1. Knowing GL/GG the flow parameter can be evaluated

2. Determination of flooding pressure drop, which along with the flow parameter are used to

estimate the capacity parameter

3. Using the capacity parameter, the maximum GG is established.

4. For the suitable % of the flooding, the actual GG, GL, and DP are calculated.

5. Knowing the total gas flow rate and GG the tower internal diameter is calculated


Mass Transfer in Design Calculations

Predict HG, HL, and HOG and the percent resistance in the liquid phase for absorption of ammonia

from air by water in a dilute solution in a packed tower with 1.5 in. metal Pall rings at 303 K and

101.32 kPa pressure. The flow rates are Gx = 4.069 kg/s m2 and Gy = 0.5424 kg/s m2.

Example 2: Height of Transfer Units

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4.1 Gas Liquid Separation - Mass Transfer

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