theories of mass transfer

7/27/2019 Theories of Mass Transfer

http://slidepdf.com/reader/full/theories-of-mass-transfer 1/44

Mass transfer operations in packed towers

An alternative to stage wise equipment:

The idea is to fill a column with solid packing:

- The packing shaped to provide liquid-vapour mass transfer area

- There is no discrete and identifiable stages

- Liquid and vapour are continuously contacted

- Mass exchange tends to bring the two phases to equilibrium.




Liquid inlet

Liquid outlet Gas inlet

Gas outlet




Materials:

• metal

• plastic

• ceramic

Choice of materials depend on the corrosiveness of

the system and the cost of the material




Tray operations

Surface area for mass transfer:

Bubble/liquid interface

Equilibrium:

Vapour and liquid phases leaving a stage are assumed to be in equilibrium;

non-equilibrium is accounted for with stage efficiencies

Operating points are given by set of ( )1, nn y x

Packed operations

Surface area for mass transfer :Surface area for packing

Equilibrium:

Vapour and liquid are not at equilibrium; non-equilibrium provides

the force for mass transfer




Advantages of packed columns

• Lower pressure drop for the gas phase,

e.g. for vacuum distillation

• Lower capital cost if the diameter (function of vapour flow rate) is less

than 0.6 m.

• Can be made of corrosion resistant material,

e.g. ceramics.




Advantages of plate columns over packed columns:

• More economical at higher vapour flow rates (i.e.

diameter).

• More suitable for large numbers of theoretical stages

(because of redistribution issue).

• Better for large fluctuations of temperature (leading to

packing attrition).

• More suitable for highly exothermic/endothermic

operations (easier to fit heat transfer surface).

• Better for highly fouling conditions (if the column size

allows for man-way access for cleaning).




1. Absorption principles (in this lecture and in online notes)

2. Mass-transfer fundamentals

3. Mass-transfer coefficients

4. Absorption in packed towers design principles

5. Design of absorption in packed towers: complete cycle



Absorption

Gas absorption is a process in which a gas mixture is inplaced in contact with a liquid for the purpose of

preferential dissolving of one or more components of

the gas mixture

Examples:

- NH3 is removed from oven gas by water

- CO2, H2S are removed from natural gas using

water solutions of alkaline salts- Benzene, toluene are removed from natural gas

using hydrocarbon oil



Equilibrium relations for dilute solutions:

solubility

- The maximum amount of the gas that can be dissolved in

a solvent at specific conditions (T,P) is called solubility



Absorption: Thermodynamics of the process

Imagine a system where we have a binary mixtureof two components A and B, one (A) is volatile and

the second one (B) is a non-volatile solvent.

The mixture coexists with an equilibrium gas of

almost pure volatile component, which has pressure

P. So if we place a piston on the top of the system,

exerting pressure P, the system will be inequilibrium.

The concentration of the volatile component A in

solvent B is called solubility of A in B at P, T. This

characteristics can be measured for a range of

binary systems under different P,T conditions.

In general solubility decreases with temperature. it isnatural to guess that if we heat the system up, the

energy supplied in the system will be used to

evaporate more of the volatile component A.

P, T



Thermodynamics of the process:Multicomponent mixture

Now we deal with a jar where a number of components is dissolved in the solvent and also

forms and equilibrium gas mixture.

Each component can be characterized with it’s own

solubility under these conditions (composition, P, T).

In general these solubilities (and other properties of the systems) must be described using methods of

multicomponent phase equilibria (or measured

experimentally).

In many cases the system can be described with

simplified relations

If ideal gas is in equilibrium with ideal mixture we canapply the following expression to find partial

pressures of the components:

If ideal gas is in equilibrium with non-ideal mixture,

Henry’s law applies

ii Px p

ii xT H p )(

P, T




Henry’s law

A A xT H p )(Henry’s law is valid for dilute solutions,

where A does not ionize, dissociate or

react in the liquid phase

For water H [atm/mole fraction]




Henry’s law

A A A xT H Py p )(Henry’s law is valid for dilute solutions,

where A does not ionize, dissociate or

react in the liquid phase

For water H [atm/mole fraction]




Solubility data



Absorption: General design considerations

1. Entering gas composition flow rate, temperature and pressure

2. Desired degree of separation

3. Choice of solvent:

- High gas solubility

- Low volatility

- Low corrosiveness

- Low cost

- Low viscosity

- Non-toxic, non-explosive

4. Minimum solvent flow rate -> actual solvent flow rate

5. Number of equilibrium stages

6. Heat/cooling requirements

7. Type of absorber

8. Geometrical parameters of the system/economy

Design

objective

Thermophysical

characteristics

Basic design

elements

Technical

specifications

Basic design

elements



Absorption: Design considerations

y

x

(mole fraction of A in L)

(mole fraction of A in V)

xa xb

ya

yb

equilibrium line

x*b

Operating line

)(*

A A x f y

P xT H y A A /)(*

Equilibrium line




y

x



xa xb

ya

yb

equilibrium line

x*b

The driving force for mass transfer

xn




Limiting conditions: gas-liquid ratio

This condition is called the limiting (L/V)min ratio. This is

the lowest flow of solvent possible in the system to achieve

the desired separation, although in an infinite number of

stages.

The actual solvent flow is usually calculated a multiple of

(L/V)min (1.1-1.5 times)

y

x



xa xb

ya

yb

equilibrium line

x*b




Limiting conditions: Gas-liquid ratio; straight operating line

Condition: L, V constant -> L/V constant

This is possible for very dilute (<5% mole fraction) mixtures

so change in total number of moles of each flow is

insignificant

A) Limiting (L/V)min value:

y

x



xa xb

ya

yb

equilibrium line

x*b

ab

ab

x x

y y

V

L

*

min



Operations in packed towers:

Mass transfer theories

Liquid

m o l e f r a c t i o n

x

Gas

y

Liquid


x

Gas

yi xi

y

Mass transfer of A

BA





Liquid


x

Gas

yi x

Mass transfer of A

Two film theory:

resistance to the overall mass transfer is viewed as a combined

resistance of liquid and gas films at the interface

i

y





Mass transfer rate (per unit area)

Liquid


x

Gas

yi x

i y

i

y y yk r

x xk r i

x

x(mole fraction of A in L)


y equilibrium line

i y

i

x

y

x






Liquid


x

Gas

yi x

i y

i

y y yk r

x xk r i

x



y equilibrium line

i y

i

x

y

x






x x K r x *

* y y K r y


y equilibrium line

i y

i

x

y

x

* y

*

x





Liquid


x

i x

Gas

y

BA

C

* y


x x K r x *

* y y K r y


y equilibrium line

i y

i x

y

x

* y

* x





Liquid


x

i x

Gas

yB

A

C

* y


x x K r x *

* y y K r y


y equilibrium line

i y

i

x

y

x

* y

*

x






y equilibrium line

i y

i x

y

x

* y

* x

y

i

x

i

y k x xk

y y

K

1

)(

1*

y x y k k

m

K

11

Resistance of gas film

Resistance of liquid film

Overall gas resistance m






y equilibrium line

i y

i x

y

x

* y

* x

y x x mk k K

111



Overall liquid

resistance





y x y k k

m

K

11



Overall gas resistance

- when coefficients ky and kx are of the same order of magnitude and m is much greater then 1 the liquid phase

resistance is cont ro l l ing

- in the opposite situation when solubility is very high, the

gas film resistance is controlling



Consider an absorption column;For diluted gases the change in flow rates is neglected

Consider a mass transfer process in a section of

the column dZ (cross-section of the column is S) La,xa

Va,ya

Vb,yb Lb,xb

Z

dZ

SdZ y ya K Vdy y *)(

Integration leads to:

b

a

y

y

y Z

y

y y

dy Z V

aS K

dZ V

aS K

*0

S

Absorption in packed towers



La,xa

Va,ya

Vb,yb Lb,xb

Z

S

b

a

y

y y y y

dy

a K

S V Z

*

/

b

a

y

yy y

dy

*

change in the concentration divided

by driving force. This property is

called the number of transfer uni ts

(NTU)

a K

S V

y

/This property has units of length, is

constant for constant L/V and is called

the height of transfer uni ts

(HTU)




La,xa

Va,ya

Vb,yb Lb,xb

Z

S

OyOy

b

a y

N H y y

dy

a K

S V Z

*

/




To understand the meaning of these

definitions consider a specific case when

both the equilibrium and operating lines are

stra ight and parallel

The driving force is then constant

throughout the process and can be

moved outside the integral, leading to:

* y y

y y N ab

Oy


y equilibrium line

b x

b y

a x

a y

operating line




To understand the meaning of these

definitions consider a specific case when

both the equilibrium and operating lines are

stra ight and parallel

The driving force is then constant

throughout the process and can be

moved outside the integral, leading to:

* y y

y y N ab

Oy


y equilibrium line

b x

b y

a x

a y

operating line

Similar to the number of stages in

the tray process




* y y

y y N ab

Oy


y equilibrium line

b x

b y

a x

a y

operating line

Similar to the number of stages in

the tray process

a K

S V

y

/ HTU (Hoy) is the height

of packing required to achieve

one separation step

OyOy

b

a y

N H y y

dy

a K

S V Z

*

/




OyOy

b

a y

N H y y

dy

a K

S V Z

*

/

y

y ydy

y

dy y y y y

dy y y

dy N

ab

y

y

y

y

y

y

y

y

Oy

b

a

b

a

b

a

b

a

1

*1

**

*

*

**

ln

][][

aa

bb

aabb

y y

y y

y y y y y

Simplification using

average driving force

notion

Average driving force

calculated as logarithmic

mean of driving forces at

the top and bottom of the

column




Example: A gas stream of 3.0% A is passed through a packed column to

remove 99% of A by absorption in water. The absorber operates at

25C and 1 atm, V/S=20mol/h/ft2, L/S=100mol/h/ft2

y*=3.1x

kxa=60mol/h/ft3

kya=15mol/h/ft3

Find Noy, Hoy ZT neglecting changes in the gas and liquid flow

Absorption in packed towers: Example



effect of pressure


y equilibrium line

Consider the effect of pressure on

the equilibrium distribution of the

volatile component:

P xT H y /)( Henry’s law

P=1bar

P=2bar

Absorption in packed towers:




y

b x

b y

a x

a y



volatile component:


P=1bar

P=2bar

*

b x

If the L/V ratio remains the same

- at higher pressure we need fewer

stages

effect of pressure





y

b x

b y

a x

a y



volatile component:


P=1bar

P=2bar

*

b x

If the L/V is changed

- lower L/V ratio

- less solvent required

- higher pressure leads to more

efficient absorption

- lower pressure leads to more

efficient desorption (stripping)

effect of pressure




Absorption processes

Multicomponent absorption

- separate equilibrium and operatinglines

- for dilute mixtures, L/V constant ->

the slope of the operating lines

for all components is the same



Absorption processes with chemical reactions

- Can be used to obtain a more complete removal of a component from the

mixture

• NH3 from air by using dilute acid solution

• CO2 from natural gas by using dilute basic solution

b

a

b

a

y

y a

b

y

y

Oy y

y

y

dy

y y

dy N ln

*

Irreversible reaction

theories of mass transfer

Documents