18
1
Earlier Topics
• Introduction to Cryogenic Engineering
• Properties of Cryogenic Fluids
• Properties of Materials at Cryogenic Temperature
• Gas Liquefaction and Refrigeration Systems
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
2
Current Topic
Topic : 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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
3
Outline of the Lecture
Topic : Gas Separation
• Basics of Gas Separation
• Gas Separation methods
• Ideal Gas Separation System
• Work requirement
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
4
Introduction
•
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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
5
Introduction
•
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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
6
Introduction
•
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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
7
Gas Separation
•
Different techniques of gas separation commonly
used are
•
Synthetic membranes
•
Adsorption
•
Absorption
•
Cryogenic distillation
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
8
Gas Separation
Membrane •
B B A BA
A A B B
B B BA
A
A B
Piston
A BA
ABB
BA
B B
A
A
A
A
A
A
A
Gas 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 A
to pass and hence the
separation occurs.
•
For example, a thin
sheet of palladium allows
H2 to pass through.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
9
Gas Separation
B B A B B B B
A A B AA A B
B
A B B B B
A
A B
B A A
A B B A B A
•
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.
Adsorbate
B B A B B A B
A B B AA A B
B
A B A B B
B
B A A B
A A A
A
A
A A AA A
A
Adsorbate
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
10
Gas 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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
11
Gas Separation
Qout,
•
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.
77 K
B
A+B
A
Qin,
90 K
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
12
Gas Separation
•
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)
Separation
Liquefaction
LOX(90K)
LN2(77K)
Cryogenic Separation
O2(300K)
N2(300K)
LOX(90K) LN2(77K)
Room Temp. Separation
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
13
Gas Separation
•
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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
14
Is Gas Mixing Reversible?
A A AA BB B
B
A AA A
BBBB
A AA A
BBB
A AA
B B BB
B B B A B BB
A A A B A A
B B B
B B B B B
A
A
A
A
A A AA BB B
B
A AA A
BBBB
A AA A
BBB
A AA
B B BB
•
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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
15
Gas Separation
•
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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
16
Ideal Separation System
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
•
Consider a closed
chamber filled with a
mixture of Gas A and
Gas B as shown.
•
The temperature and
mixture pressure are
Tm and pm
respectively.
•
The partial pressures
of Gas A and Gas B
are given by p1a and
p1b respectively.
p1a, p1b
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
17
Ideal Separation System
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
•
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.
p1a, p1b
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
18
Ideal Separation System
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
•
The left piston (red)
allows only the Gas A
to pass through, but
not the Gas B.
B AB
A B A
B
A B
B
A
A B A
•
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.
p1a, p1b
A
A
A
A
A A A A
A A A
A A AAA
A A A A
B
B
B
BB
B B
B B
BBB
B
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
19
Ideal Separation System
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
•
p1a, p1b
QR
WA
A
A
A
A
B AB
A B A
B
A B
AB
A B A
B
B
B
BB
WB
•
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  pm
at a constant
temperature Tm.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
20
Ideal Separation System
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
•
Since the left piston is
permeable to Gas A,
the Gas A exerts no
pressure on the left
piston.
WB •
Similarly, the gas B
exerts no pressure on
the right piston.
p1a, p1b
QR
WA
A
A
A
A
B AB
A B A
B
A B
AB
A B A
A A A A
A A A
A A AAA
A A A A
B
B
B
BB
B B
B B
BBB
B
•
When both the pistons
are moved inward, the
mixture is separated
at constant Tm.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
21
Ideal Separation System
Tm, pm
A A A A
A A A
A A AAA
A A A A
A
A
A
A
B AB
A B A
B
A B
B
A
A B A
B B
B B
BBB
B
•
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.
B
B
B
BB
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
22
Ideal Separation System
Tm, pm
A A A A
A A A
A A AAA
A A A A
•
B
B
B
BB
WB •
The final condition is a
system with a mixture
of Gas A and B at pm
and Tm.
•
Also, the partial
pressures of Gas A
and B are p1a and p1b.
QR
WA
A
A
Tm, pm
A
A
B AB
A B A
B
A B
AB
A B A
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
p1a, p1b
The Work produced in
this mixing process is
same as the Work
done to separate at
constant Tm.
B B
B B
BBB
B
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
23
Ideal Separation System
Initial
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
p1a, p1b
•
Final
A A A A
A A A
A A AAA
A A A A
Tm, pm
B B
B B
BBB
B
Gas Const T
p1a  pm
A
p1b  pm
B
In other words, thermodynamically each gas is
compressed reversibly and isothermally from
its partial pressure to the mixture pressure.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
24
Ideal Separation System
Initial
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
p1a, p1b
•
Final
A A A A
A A A
A A AAA
A A A A
Tm, pm
B B
B B
BBB
B
Gas Const T
p1a  pm
A
p1b  pm
B
In order to understand the process of
compression, say for a Gas A, from p1a to pm,
the following analysis is done.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
25
Ideal Separation System
•
Let the mol. wt. of Gas A and Gas B be molwa
and molwb respectively.
•
Number of moles of Gas A is given by na = ma / molwa
•
Similarly, number of moles of Gas B is nb = mb / molwb
•
Then total number of moles in the mixture nm is
nm= na + nb
•
ya = na / nm
yb = nb / nm
Then the ratios
and
are the
mole fractions of Gas A and Gas B respectively.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
26
Ideal Separation System
Initial
Tm, pm
B B A B B B
A
A A B A A
A B
B B B B
B A
A A A A
p1a, p1b
Vtot
p1aVtot= na ℜTm
p1bVtot= nbℜTm
( p1a + p1b )Vtot = ( na + nb ) ℜTm
p1a + p1b =
pm
•
Final
A A A A
A A A
A A AAA
A A A A
Tm, pm
Va
pmVa= na ℜTm
B B
B B
BBB
B
Vb
pmVb= nbℜTm
Va na
=
Vb nb
The volume occupied by the each of the gas is
directly proportional to its number of moles.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
27
Ideal Separation System
•
From the earlier lectures, the work requirement
for a unit mass of gas compressed isothermally is
given by
−Wi
= Tm ( s1 − s2 ) − ( h1 − h2 )
m
•
The net ideal work requirement of the separation
process is the sum of the ideal work requirement
by Gas A and Gas B.
•
Mathematically,
•
Dividing the above equation −W −W
−Wi ,b
i ,a
i
+
by the mass of the mixture =
mm
mm
mm
mm, we get
−Wi = ( −Wi ,a ) + ( −Wi ,b )
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
28
Ideal Separation System
−Wi −Wi ,a −Wi ,b
=
+
mm
mm
mm
•
The total mass of mixture mm is the sum of mass
of Gas A and Gas B.
•
ma + mb
Mathematically, we have m=
m
•
•
Rearranging the terms, we can write the above
equation as
−Wi  −Wi ,a   ma   −Wi ,b   mb 
= 

+


mm  ma   mm   mb   mm 
Here, ma and mb are the mass of the Gas A and
Gas B respectively.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
29
Ideal Separation System
•
−Wi  −Wi ,a   ma   −Wi ,b   mb 
= 

+


mm  ma   mm   mb   mm 
The work requirement for each of the individual
gas is given by the following equations.
−Wi ,a
−Wi ,b
= Tm ( s1b − s2b ) − ( h1b − h2b )
= Tm ( s1a − s2 a ) − ( h1a − h2 a )
ma
mb
• Substituting and rearranging, we get
  ma 


 ( ( s1a − s2 a ) − ( h1a − h2 a ) ) 
−Wi
  mm 

= Tm 

mm


 +  mb  ( ( s1b − s2b ) − ( h1b − h2b ) ) 
 m

  m

Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
30
Ideal Separation System
•
  ma 


 ( ( s1a − s2 a ) − ( h1a − h2 a ) ) 
−Wi
  mm 

= Tm 

mm


m
 +  b  ( ( s1b − s2b ) − ( h1b − h2b ) ) 
 m

m




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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
31
Ideal Separation System
•
•
  ma 


 ( ( s1a − s2 a ) − ( h1a − h2 a ) ) 
−Wi
  mm 

= Tm 

mm


m
 +  b  ( ( s1b − s2b ) − ( h1b − h2b ) ) 
 m

m




It means that for each gas, s1 and h1 are at the
partial pressure before the separation. And s2
and 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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
32
Ideal Separation System
•
For an ideal gas, the specific entropy s and
specific enthalpy h can be expressed as
s = c p ln T − R ln p + sr
=
h c pT + hr
•
•
where, sr and hr are some reference values.
Hence, s and h for Gas A are given by
s1a = c pa ln Tm − Ra ln p1a + sra
=
h1a c paTm + hra
s2 a = c pa ln Tm − Ra ln p1a + sra
=
h2 a c paTm + hra
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
33
Ideal Separation System
•
The entropy and enthalpy term for Gas A is as
given below.
( ( s1a − s2a ) − ( h1a − h2a ) )
•
Substituting, we get
(c
pa
ln Tm − Ra ln p1a + sra − c pa ln Tm + Ra ln pm − sra )
− ( c paTm + hra − c paTm − hra )
 pm 
Ra ln 
( ( s1a − s2a ) − ( h1a − h2a ) ) =

 p1a 
•
Also, for Gas B
 pm 
Rb ln 
( ( s1b − s2b ) − ( h1b − h2b ) ) =

p
 1b 
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
34
Ideal Separation System
 pm  •
Ra ln 
( ( s1a − s2a ) − ( h1a − h2a ) ) =

 p1a 
 pm 
Rb ln 
( ( s1b − s2b ) − ( h1b − h2b ) ) =

p
 1b 
Substituting, we
get the ideal
work
requirement as
  ma 


 ( ( s1a − s2 a ) − ( h1a − h2 a ) ) 
−Wi
  mm 

= Tm 

mm


 +  mb  ( ( s1b − s2b ) − ( h1b − h2b ) ) 
 m

  m

−Wi
mm
  ma 
 pm   mb 
 pm  
Tm  
 Ra ln 
+
 Rb ln 
 
 p1a   mm 
 p1b  
  mm 
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
35
Ideal Separation System
•
Since the process occurs at constant volume Vm,
using an ideal gas equation we can write
pmVm= nmℜTm
•
•
p1aVm= na ℜTm
p1bVm= nbℜTm
Dividing one over the other, we have
pmVm nmℜTm
=
p1aVm na ℜTm
pmVm nmℜTm
=
p1bVm nbℜTm
pm nm
1
= =
p1a na ya
pm nm 1
= =
p1b nb yb
Where ya and yb are the mole fractions of Gas A
and Gas B respectively.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
36
Ideal Separation System
•
The ideal gas equation can also be expressed in
terms of the mass of the gas as shown below.
pmVm= nmℜTm
pmVm
=
p1aVm= na ℜTm
p1bVm= nbℜTm
mm
ma
mb
p1aVm
ℜTm =
ℜTm =
ℜTm
p1bVm
molwa
molwm
molwb
pmVm = mm RmTm
p1aVm = ma RaTm
p1bVm = mb RbTm
•
ℜ
In general, Ra =
and ℜ 8.314 J / mol − K
=
molwa
•
Here ℜ and R are the Universal Gas Constant
and Specific Gas Constant respectively.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
37
Ideal Separation System
•
From the earlier slide, using the ideal gas
equation in terms of the gas mass, we have
pmVm = mm RmTm
•
p1aVm = ma RaTm
p1bVm = mb RbTm
Dividing one over the other, we have
pmVm mm RmTm
=
p1aVm ma RaTm
pmVm mm RmTm
=
p1bVm mb RbTm
pm mm Rm 1
pm mm Rm
1
=
=
=
=
yb
p1a ma Ra
ya p1b mb Rb
ma Ra
= Rm ya
mm
mb Rb
= Rm yb
mm
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
38
Ideal Separation System
pm
1
=
p1a ya
−Wi
mm
•
pm
1
=
p1b yb
ma Ra
= Rm ya
mm
mb Rb
= Rm yb
mm
  ma 
 pm   mb 
 pm  
Tm  
 Ra ln 
+
 Rb ln 
 
 p1a   mm 
 p1b  
  mm 
Substituting, we have
−Wi
mm

 1 
 1 
RmTm  ya ln   + yb ln    pmVm= mm RmTm= nmℜTm
 ya 
 yb  


 1 
 1 
−Wi
=
ℜTm  ya ln   + yb ln   
nm
 ya 
 yb  

Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
39
Ideal Separation System
•
The ideal work of separation per mole of mixture
(Gas A and Gas B) is given by

 1 
 1 
−Wi
=
ℜTm  ya ln   + yb ln   
nm
 ya 
 yb  

•
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 
 1 
 1 
−Wi
=
ℜTm  ya ln   + yb ln   + yc ln   
nm
 ya 
 yb 
 yc  

Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
40
Ideal Separation System
•
Generalizing the above equation for a mixture of
N constituents, we have
•
•
N
 1 
−Wi
= ℜTm ∑ y j ln  
y 
nm
j =1
 j
where yj is the mole fraction of jth component.
Similar to the Liquefaction systems, the Figure
of Merit (FOM) is defined as given below.
−Wi
nm
=
FOM =
−W
nm
−Wi
mm
−W
mm
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
41
Summary
•
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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
42
Summary
•
Ideal work requirement per mole of mixture to
separate a mixture with N constituents is given
by
N
 1 
−Wi
= ℜTm ∑ y j ln  
y 
nm
j =1
 j
•
where yj is the mole fraction of jth component.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
43
•
A self assessment exercise is given after
this slide.
•
Kindly asses yourself for this lecture.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
44
Self Assessment
1. 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.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
45
Self Assessment
6. In an ideal system, each gas is compressed from
its ____ to the ______.
7. In an ideal system
(( s
1a
− s2 a ) − ( h1a − h2 a ) ) is ______.
8. The Specific Gas constant for a Gas A (Ra) is
______.
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
46
Answers
1. 78% N2 + 21% O2 + 1% Ar
2. Hydrogen
3. Adsorption
4. Absorption
5. Cryogenic
6. partial pressure, mixture pressure
7. G( ( s1a − s2 a ) − ( h1a − h2 a ) ) =
Ra ln ( pm / p1a )
8. FRa = ℜ / mola
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
47
Thank You!
Prof. M D Atrey, Department of Mechanical Engineering, IIT Bombay
48