Mass Transfer operation lecture by chemical engineer

07-02-2024 Side 1
Madan Mohan Malaviya Univ. of Technology, Gorakhpur
Mass Transfer Operation-I
BCT-27
Dr. Prateek Khare
Assistant Professor
Department of Chemical
Madan Mohan Malviya University of
Technology Gorakhpur (UP State Govt. University)
Email: pkch@mmmut.ac.in

07-02-2024 Side 2

07-02-2024 Side 3
Topics
No.
Unit/Topics
1 Unit-1 Introduction to Mass transfer operation, Diffusion: Fick’s
law of diffusion,
2 Steady state molecular diffusion in fluids under stagnant,
3 Steady state molecular diffusion in fluids under laminar flow
conditions
4 Diffusion through variable cross-sectional area
5 Numerical solving on diffusion
6 Diffusion coefficient: measurement and prediction
7 Multi component diffusion
8 Diffusivity in solids and its applications
9 Introduction to mass transfer coefficient
10 Numerical solving on diffusion, multicomponent diffusion.
11 Equimolar counter-diffusion
12 Unit-2 Correlation for convective mass transfer coefficient
13 Correlation of mass transfer coefficients for single cylinder

07-02-2024 Side 4
14 Theories of mass transfer
15 Penetration theory, Surface Renewal Theory, Boundary Layer
Theory,
16 Interphase mass transfer theory
17 Overall mass transfer coefficient.
18 Numerical solving on Mass transfer coefficient and constant
19 Humidification Dehumidification definitions
20 Vapour liquid equilibrium and enthalpy for a pure substance,
vapour pressure temperature curve
21 Definition and derivations of relationships related with humidity
22 Fundamental concept of humidification, Dehumidification and
water cooling
23 Wet bulb temperature, Adiabatic and non-adiabatic operations
24 Classification and design of cooling towers
25 Design of cooling towers based on overall Mass transfer
coefficient.

07-02-2024 Side 5
Books
• Principles of Mass Transfer and Separation
Processes by Dutta B.K
• Transport Processes and separation Processes
by Chistie John Geankoplis
• Mass Transfer Operations by Robert Treybal
• Numerical Practice
• Mass Transfer (English, Paperback, Asokan K)

07-02-2024 Side 6
Links for online resources
NPTEL
IIT Guwahati Prof. B Mondal (Unit 1)
https://nptel.ac.in/courses/103/103/103103145/
IIT Kanpur Prof. Nishith Verma
IIT Guwahati Prof. Chandan Das (Unit 2)

07-02-2024 Side 7
Introduction of Mass Transfer
• When a system contains two or more components
whose concentrations vary from point to point, there is
a natural tendency for mass to be transferred,
minimizing the concentration differences within a
system.
• The transport of one constituent from a region of higher
concentration to that of a lower concentration is called
mass transfer.
• The transfer of mass within a fluid mixture or across a
phase boundary is a process that plays a major role in
many industrial processes.

07-02-2024 Side 8
Examples of such processes
• Dispersion of gases from stacks
• Removal of pollutants from plant discharge streams
by absorption
• Stripping of gases from waste water
• Neutron diffusion within nuclear reactors
• Air conditioning
• A lump of sugar added to a cup of coffee eventually
dissolves and then eventually diffuses to make the
concentration uniform.

07-02-2024 Side 9
Some common examples from daily life
• Water evaporates from ponds to increase the humidity of
passing-air-stream
• Perfumes presents a pleasant fragrance which is
imparted throughout the surrounding atmosphere.
The mechanism of mass transfer involves both
molecular diffusion and convection.
Mass transfer always involves mixtures.
The conventional engineering approach to problems of
multicomponent system is to attempt to reduce them to
representative binary (i.e., two component) systems.
To understand diffusion in mixture, some definitions and
relations which are often used to explain the role of
components within a mixture.

07-02-2024 Side 10
Properties of Mixtures
• Concentration of Species:
Concentration of species in multicomponent mixture
For species A, mass concentration denoted by A is
defined as the mass of A, mA per unit volume of the
mixture.
---- (1)
• The total mass concentration density  is the sum of
the total mass of the mixture in unit volume:
where  i is the concentration of species i in the mixture.
V
m A
A 

V
A
m
A




i
i



07-02-2024 Side 11
• Molar concentration of, A, CA is defined as the number
of moles of A present per unit volume of the mixture.
----------------------------- (2)
Therefore from (1) & (2)
•
A
of
weight
molecular
A
of
mass
moles
of
Number 
A
A
A
M
m
n 
A
A
A
A
M
V
n
C




07-02-2024 Side 12
For ideal gas mixtures,
• from Ideal gas law PV = nRT]
•
•
• where pA is the partial pressure of species A in the mixture. V is the
volume of gas, T is the absolute temperature, and R is the universal
gas constant.
•
• The total molar concentration or molar density of the mixture is
given by
•
T
R
V
p
n
A
A 
T
R
p
V
n
C A
A
A 



i
i
C
C

07-02-2024 Side 13
Velocities
• Multicomponent system
• Various species have velocities;
velocity of mixture requires the averaging of the velocities of each
species present.
•
If  I is the velocity of species i with respect to stationary fixed
coordinates,
• then mass-average velocity for a multicomponent mixture defined in
terms of mass concentration is,
• By similar way, molar-average velocity of the mixture  * is







i
i
i
i
i
i
i
i 




C
V
C
i
i
i


*


07-02-2024 Side 14
• The velocity of a particular species relative to the mass-average or
molar average velocity is termed as diffusion velocity
(i.e.) Diffusion velocity = ( i - )
•
• The mole fraction for liquid and solid mixture, x A ,and for gaseous
mixtures, y A, are the molar concentration of species A divided by
the molar density of the mixtures.
(liquids and solids) (gases)
• The sum of the mole fractions, by definition must equal 1;
• (i.e.)
• by similar way, mass fraction of A in mixture is;
C
C
x A
A 
C
C
y A
A 
 
i
i
x 1  
i
i
y 1

 A
A
w 

07-02-2024 Side 15
Problem1:
• The molar composition of a gas mixture at 273 K and 1.5 * 10 5 Pa is:
• O 2 7%; CO 10%; CO 2 15%; N 2 68%
• Determine
• the composition in weight percent
• average molecular weight of the gas mixture
• density of gas mixture
• partial pressure of O 2.
HINT:
• Average molecular weight of the gas mixture moles
of
Number
mixture
gas
of
Weight

M
mol
g
M 68
.
30
1
68
.
30



07-02-2024 Side 16
Calculations:
Let the gas mixture constitutes 1 mole. Then
O 2 = 0.07 mol
CO = 0.10 mol
CO 2 = 0.15 mol
N 2 = 0.68 mol
Molecular weight of the constituents are:
O 2 = 2 * 16 = 32 g/mol
CO = 12 + 16 = 28 g/mol
CO 2 = 12 + 2 * 16 = 44 g/mol
N 2 = 2 * 14 = 28 g/mol
Weight of the constituents are: (1 mol of gas mixture)
O 2 = 0.07 * 32 = 2.24 g
CO = 0.10 * 28 = 2.80 g
CO 2 = 0.15 * 44 = 6.60 g
N 2 = 0.68 * 28 = 19.04 g

07-02-2024 Side 17
Total weight of gas mixture = 2.24 + 2.80 + 6.60 + 19.04
= 30.68 g
Composition in weight percent:
%
13
.
9
100
*
68
.
30
80
.
2


CO
%
51
.
21
100
*
68
.
30
60
.
6
2 

CO
%
06
.
62
100
*
68
.
30
04
.
19
2 

N
%
30
.
7
100
*
68
.
30
24
.
2
2 

O

07-02-2024 Side 18
moles
of
Number
mixture
gas
of
Weight

M
mol
g
M 68
.
30
1
68
.
30


RT
P
V
n

m
V
n


 density
molar
Average molecular weight of the gas mixture
Assuming that the gas obeys ideal gas law, PV = nRT
3
5
273
*
8314
68
.
30
*
10
*
5
.
1
m
kg
RT
PM
M
Density m 

 
 
5
10
*
5
.
1
*
100
7

Therefore, density (or mass density) =  mM
Where M is the molecular weight of the gas.
= 2.03 kg/m 3
Partial pressure of O 2 = [mole fraction of O 2] * total pressure
= 0.07 * 1.5 * 10 5
= 0.105 * 10 5 Pa

07-02-2024 Side 19
Fick’s law
An empirical relation for the diffusional molar flux, first postulated by Fick and, accordingly,
often referred to as
Fick’s first law, defines the diffusion of component A in an isothermal, isobaric system. For
diffusion in only the Z direction,
the Fick’s rate equation is
Z
d
C
d
D
J A
B
A
A 

where D AB is diffusivity or diffusion coefficient for component A diffusing
through component B,
and dCA / dZ is the concentration gradient in the Z-direction

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