NPTEL - Gas Separation

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Earlier TopicsEarlier Topics

• Introduction to Cryogenic Engineering

• Properties of Cryogenic Fluids

• Properties of Materials at Cryogenic Temperature

• Gas Liquefaction and Refrigeration Systems

2Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay

Current TopicCurrent TopicTopic : Gas Separation

• Basics of Gas Separation• Ideal Gas Separation System• Properties of Mixtures and the Governing Laws• Principles of Gas Separation• Rectification and Plate Calculations

• The current topic will be covered in 7 to 10 lectures.

• Tutorials and assignments are included at the end of each lecture.


Topic : Gas Separation

• Basics of Gas Separation• Gas Separation methods

• Ideal Gas Separation System• Work requirement


Outline of the LectureOutline of the Lecture


• As mentioned earlier, cryogenic industry is huge owing to the various applications of the cryogens, both in liquid and gaseous states.

• For example, the use of inert gases like argon in chemical and welding industries has increased in the recent past.

• Liquid Nitrogen is used as precoolant in most of the cryogenic systems. Also, cryogens like LOX, LH2 are used in rocket propulsion.

IntroductionIntroduction


• In the recent past, LH2 is being considered as a fuel for an automobile.

• Production of Ammonia in RCF industry, requires separation of purge gases like Nitrogen, Argon and other inert gases at cryogenic temperatures.

• For most practical purposes, Air is considered as a mixture of 78% N2 + 21% O2 + 1% Ar.

• The other ingredients are Helium, Neon, Krypton etc. which occur in negligible quantities.



• Air is the raw material for the production of most of the gases and the process of separation of any gas mixture into its individual components is called as Gas Separation.

• In other words, this topic “Gas Separation” deals with separation of various gas mixtures and their purification.



• Different techniques of gas separation commonly used are

• Synthetic membranes

• Adsorption

• Absorption

• Cryogenic distillation

Gas SeparationGas Separation


Gas SeparationGas Separation• Synthetic membranes

are the porous media which allow only a certain gas molecules to pass through.

• The membrane in the figure allows only Gas Ato pass and hence the separation occurs.

• For example, a thin sheet of palladium allows H2 to pass through.

B

B

AB

AB

AB

BA

AB

A

B

BA

Piston

Membrane

B

B

AB

AA

AB A

B

BA

AA

AA

A

Gas Separation


Gas SeparationGas Separation• Adsorption is the physical

processes in which only a certain kind of gas molecules are adhered to the adsorbing surface.

• The adsorbate in the figure adheres only Gas A to the surface and hence the separation occurs.

• For example, finely divided Nickel adsorbs hydrogen on to its surface.

B

B

ABA

BAB

BAA

B AB

B

AB

B

A

BA

BAB

BAA

B ABB

A

Adsorbate

B

B

A

BA

BAB

BAA

B AB

B

ABA

B

A

BA

BA

A

B

AB

A

Adsorbate

A A A AAA

A


Gas SeparationGas Separation• Absorption is a chemical process in which a

substance in one physical state is taken into other substance at a different physical state.

• For example, liquids being absorbed by a solid or gases being absorbed by a liquid.

• When an incoming stream containing CO2 is passed through a solution of Sodium hydroxide, the later absorbs the gas and hence decreases the CO2 content in the outgoing stream.

• Hence, this chemical process helps in the separation of the mixture.


Gas SeparationGas Separation• Distillation is a process of separation

based on the differences in the volatilities (boiling points).

• If the process of distillation occurs at cryogenic temperatures, it is called as Cryogenic Distillation.

• The commercial production of gases like O2, N2, Argon, Neon, Krypton & Xenon is obtained by cryogenic distillation of Liquid Air.

A

B

Qin, 90 K

Qout, 77 K

A+B


• The separation of a mixture can be done at both room temperature and cryogenic temperature.

• For example in the case of Air, the following processes are possible.


Air(300K)

Liquefaction

LOX(90K) LN2(77K)

Cryogenic Separation

Separation

O2(300K) N2(300K)

Room Temp. Separation

LN2(77K)LOX(90K)


• Some of the advantages of Cryogenic separation over Room Temperature separation are

• The separation at lower temperatures is most economical (explained in further slides).

• There is an increased difference in the boiling points of the ingredients (explained in further slides).

• A large quantities of the gas can be separated.

• A high purity of the gas can be obtained.



• Consider a closed chamber filled with Gas A and Gas B as shown in the figure.

• Initially, the gases are separated by an impervious wall.

• If the wall is removed, the gases would mix.

• However, the replacement of wall would not result in the separation of gases.

BA

AA

AA

BB

BBA A

AA

A

BBB

BB BA

AA B B

BB

AA

B

B

ABA

BAB

BA A

B AB

B

A

B

AB

AB

BAB B

BA

AA

AA

BB

BBA A

AA

A

BBB

BB BA

AA B B

BB

AA

Is Gas Mixing Reversible?Is Gas Mixing Reversible?


• It is clear that the mixing of two different gases is an irreversible process because unmixing or separation of the mixture requires work input.

• The system in which all the processes are reversible is called as an Ideal System.

• Although in reality such a system does not exist, a system can be conceived to serve the required purpose as explained in the next slide.



Ideal Separation SystemIdeal Separation System• Consider a closed

chamber filled with a mixture of Gas A and Gas B as shown.

• The temperature and mixture pressure are Tm and pmrespectively.

• The partial pressures of Gas A and Gas Bare given by p1a and p1b respectively.

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AAp1a, p1b

Tm, pm


Ideal Separation SystemIdeal Separation System• The chamber has two

frictionless opposing pistons made of semi –permeable membranes as shown in the figure.

• As seen earlier, a semi – permeable membrane is a film which allows only one kind of gas to pass through but not the other.

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA


Ideal Separation SystemIdeal Separation System• The left piston (red)

allows only the Gas Ato pass through, but not the Gas B.

• Similarly, the right piston (green) allows only the Gas B to pass through, but not the Gas A.

• When both pistons are moved inward, the mixture is separated.

B

AB

AB

ABAB

AB

AB

BAAA

AA

BB

BB

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA

BA

AA

AA

B

BBBA A

AA

A

B

BB

AA

AA

AA


B

AB

AB

ABAB

AB

AB

BAAA

AA

BB

BB

WA WB

QR

Ideal Separation SystemIdeal Separation System• Since the processes are

reversible, the system interacts with the surroundings to maintain a constant temperature.

• The work of separation is the work required to compress each gas from p1a or p1b pmat a constant temperature Tm.

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA


Ideal Separation SystemIdeal Separation System• Since the left piston is

permeable to Gas A, the Gas A exerts no pressure on the left piston.

• Similarly, the gas Bexerts no pressure on the right piston.

• When both the pistons are moved inward, the mixture is separated at constant Tm.

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA

B

AB

AB

ABAB

AB

AB

BAAA

AA

BB

BB

WA WB

QR

BA

AA

AA

B

BBBA A

AA

A

B

BB

AA

AA

AA


Ideal Separation SystemIdeal Separation System• The entire processes

are assumed to be reversible.

• The process is reversed due to the difference in the concentrations of Gas A and Gas B.

• Hence, the mixing of the gases would move the pistons away and produce work.

BA

AA

AA

B

BBBA A

AA

A

B

BB

AA

AA

AA

Tm, pm

B

AB

AB

ABAB

AB

AB

BAAA

AA

BB

BB


Ideal Separation SystemIdeal Separation System• The Work produced in

this mixing process is same as the Work done to separate at constant Tm.

• The final condition is a system with a mixture of Gas A and B at pmand Tm.

• Also, the partial pressures of Gas Aand B are p1a and p1b.

BA

AA

AA

B

BBBA A

AA

A

B

BB

AA

AA

AA

Tm, pm

B

AB

AB

ABAB

AB

AB

BAAA

AA

BB

BB

WA WB

QR

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA


Ideal Separation SystemIdeal Separation System

• In other words, thermodynamically each gas is compressed reversibly and isothermally from its partial pressure to the mixture pressure.

Gas Const TA p1a pmB p1b pm

Initial Final

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA

BA

AA

AA

B

BBBA A

AA

A

B

BB

AA

AA

AA

Tm, pm



• In order to understand the process of compression, say for a Gas A, from p1a to pm, the following analysis is done.

Gas Const TA p1a pmB p1b pm

Initial Final

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA

BA

AA

AA

B

BBBA A

AA

A

B

BB

AA

AA

AA

Tm, pm


• Let the mol. wt. of Gas A and Gas B be molwaand molwb respectively.

• Number of moles of Gas A is given by

• Similarly, number of moles of Gas B is

• Then total number of moles in the mixture nm is

• Then the ratios and are the mole fractions of Gas A and Gas B respectively.


/a a an m molw

/b b bn m molw

m a bn n n

/a a my n n /b b my n n



m a a mp V n T m b b mp V n T1 a tot a mp V n T

a a

b b

V nV n

1 1 a b mp p p• The volume occupied by the each of the gas is

directly proportional to its number of moles.

Initial Final

Tm, pm

p1a, p1b

B

B

ABA

BAB

BA A

B AB

B

A

B

A

BA A

B

AA

BA

AA

AA

B

BBBA A

AA

A

B

BB

AA

AA

AA

Tm, pm

Vtot Va Vb

1 b tot b mp V n T

1 1 a b tot a b mp p V n n T


• From the earlier lectures, the work requirement for a unit mass of gas compressed isothermally is given by

• The net ideal work requirement of the separation process is the sum of the ideal work requirement by Gas A and Gas B.

• Mathematically,


1 2 1 2

im

W T s s h hm

, , i i a i bW W W

, , i a i bi

m m m

W WWm m m

• Dividing the above equation by the mass of the mixture mm, we get


• The total mass of mixture mm is the sum of mass of Gas A and Gas B.

• Mathematically, we have

• Rearranging the terms, we can write the above equation as

• Here, ma and mb are the mass of the Gas A and Gas B respectively.


, ,

i a i bi a b

m a m b m

W WW m mm m m m m

, , i a i bi

m m m

W WWm m m

m a bm m m


• The work requirement for each of the individual gas is given by the following equations.

• Substituting and rearranging, we get

Ideal Separation SystemIdeal Separation System, ,

i a i bi a b

m a m b m

W WW m mm m m m m

,1 2 1 2

i a

m a a a aa

WT s s h h

m ,

1 2 1 2

i b

m b b b bb

WT s s h h

m

1 2 1 2

1 2 1 2

aa a a a

mim

m bb b b b

m

m s s h hmW T

m m s s h hm


• It is clear that the work requirement decreases with the decrease in the temperature.

• Hence, the separation of mixtures at the cryogenic temperatures is most economical.

• The subscripts 1 and 2 denote the initial and the final conditions respectively.


1 2 1 2

1 2 1 2

aa a a a

mim

m bb b b b

m

m s s h hmW T

m m s s h hm


• It means that for each gas, s1 and h1 are at the partial pressure before the separation. And s2and h2 are at mixture pressure after the separation of the mixture.

• For the sake of understanding, let us first evaluate only entropy and enthalpy terms for each of the gases.


1 2 1 2

1 2 1 2

aa a a a

mim

m bb b b b

m

m s s h hmW T

m m s s h hm


• For an ideal gas, the specific entropy s and specific enthalpy h can be expressed as

• where, sr and hr are some reference values.

• Hence, s and h for Gas A are given by


ln ln p rs c T R p s

p rh c T h

1 1ln ln a pa m a a ras c T R p s

2 1ln ln a pa m a a ras c T R p s

1 a pa m rah c T h

2 a pa m rah c T h


• The entropy and enthalpy term for Gas A is as given below.

• Substituting, we get

• Also, for Gas B


1 2 1 2 a a a as s h h

1ln ln ln ln

pa m a a ra pa m a m ra

pa m ra pa m ra

c T R p s c T R p s

c T h c T h

1 2 1 21

ln

ma a a a a

a

ps s h h Rp

1 2 1 21

ln

mb b b b b

b

ps s h h Rp


• Substituting, we get the ideal work requirement as


1 2 1 2

1 2 1 2

aa a a a

mim

m bb b b b

m

m s s h hmW T

m m s s h hm

1 2 1 21

ln

ma a a a a

a

ps s h h Rp

1 2 1 21

ln

mb b b b b

b

ps s h h Rp

1 1

ln ln

i a m b m

m a bm m a m b

W m p m pT R Rm m p m p


• Since the process occurs at constant volume Vm, using an ideal gas equation we can write

• Dividing one over the other, we have

• Where ya and yb are the mole fractions of Gas Aand Gas B respectively.


m m m mp V n T 1 a m a mp V n T 1 b m b mp V n T

1

m m m m

a m a m

p V n Tp V n T 1

m m m m

b m b m

p V n Tp V n T

1

1 m m

a a a

p np n y 1

1 m m

b b b

p np n y


• The ideal gas equation can also be expressed in terms of the mass of the gas as shown below.

• In general, and

• Here and R are the Universal Gas Constantand Specific Gas Constant respectively.


m m m mp V n T 1 a m a mp V n T 1 b m b mp V n T

mm m m

m

mp V Tmolw 1 a

a m ma

mp V Tmolw 1 b

b m mb

mp V Tmolw

m m m m mp V m R T 1 a m a a mp V m R T 1 b m b b mp V m R T

a

a

Rmolw

8.314 / J mol K


• From the earlier slide, using the ideal gas equation in terms of the gas mass, we have

• Dividing one over the other, we have


m m m m mp V m R T 1 a m a a mp V m R T 1 b m b b mp V m R T

1

m m m m m

a m a a m

p V m R Tp V m R T 1

m m m m m

b m b b m

p V m R Tp V m R T

1

1 m m m

a a a a

p m Rp m R y 1

1 m m m

b b b b

p m Rp m R y

a am a

m

m R R ym

b bm b

m

m R R ym


• Substituting, we have


1

1m

a a

pp y 1

1m

b b

pp y

a am a

m

m R R ym

b bm b

m

m R R ym

1 1

ln ln

i a m b m

m a bm m a m b

W m p m pT R Rm m p m p

1 1ln ln

i

m m a bm a b

W R T y ym y y m m m m m m mp V m R T n T

1 1ln ln

i

m a bm a b

W T y yn y y


• The ideal work of separation per mole of mixture (Gas A and Gas B) is given by

• On the similar lines, if the mixture is composed of three different gases, say Gas A, Gas B and Gas C, the ideal work of separation per mole of mixture is given by


1 1ln ln

i

m a bm a b

W T y yn y y

1 1 1ln ln lnim a b c

m a b c

W T y y yn y y y


• Generalizing the above equation for a mixture of N constituents, we have

• where yj is the mole fraction of jth component.

• Similar to the Liquefaction systems, the Figure of Merit (FOM) is defined as given below.


1

1ln

Ni

m jjm j

W T yn y

i i

m m

m m

W Wn mFOM W W

n m

SummarySummary


• Different techniques employed are Synthetic membranes, Adsorption, Absorption and distillation.

• The separation can be done at both room temperature and cryogenic temperature.

• In an Ideal system all the processes are reversible and the work requirement in an ideal gas separation is called as an Ideal Work.


• Ideal work requirement per mole of mixture to separate a mixture with N constituents is given by

• where yj is the mole fraction of jth component.

1

1ln

Ni

m jjm j

W T yn y

SummarySummary


• A self assessment exercise is given after this slide.

• Kindly asses yourself for this lecture.

Self AssessmentSelf Assessment1. Air is considered as a mixture of ________.

2. Thin sheet of palladium allows only __ to pass

through.

3. ________ is the processes in which only a

certain kind of gas molecules are adhered.

4. ___ is a chemical process for gas separation.

5. ______ separation is most economical.


Self AssessmentSelf Assessment6. In an ideal system, each gas is compressed from

its ____ to the ______.

7. In an ideal system is ______.

8. The Specific Gas constant for a Gas A (Ra) is

______.


1 2 1 2 a a a as s h h

AnswersAnswers


1. 78% N2 + 21% O2 + 1% Ar

2. Hydrogen

3. Adsorption

4. Absorption

5. Cryogenic

6. partial pressure, mixture pressure

7. G

8. F

1 2 1 2 1ln / a a a a a m as s h h R p p

/ a aR mol


Thank You!Thank You!

NPTEL - Gas Separation

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