MASS TRANSFER II Nandana Chakinala

CONTENT
Introduction to mass transfer
Distillation
Raoult’s law and Daltons law
VLE phase diagrams
Positive and negative deviations from Raoult’s law
Relative volatility
INTRODUCTION TO MASS TRANSFER
Categories of separations: Mechanical, Rate based, Equilibrium based
Mechanism of separations: Phase creation/Phase addition/Barrier/solid agent
For all the techniques, separations are achieved by enhancing the rate of diffusion of
certain species relative to mass transfer of all species by bulk movement within a
particular phase
The driving force and direction of mass transfer is governed by thermodynamics
The rate of separation is governed by mass transfer and extent of separation is
governed by thermodynamic equilibrium, in case of equilibrium based separations
DISTILLATION
Oldest MTO
Early use in the production of alcoholic bevarages
Difference between distillation (ethanol+water) and evaporation (Eg: Salt+water)
Distillation is an operation whereby a liquid mixture of miscible and volatile substances is
separated in to individual components or into group of components by partial vaporization
Eg: separation of a mixture of methanol and water into individual components, separation of
petroleum crude into gasoline, kerosene and fuel oil
Separation of mixture by distillation is based on the equilibrium distribution of components
between liq-vap phase. So VLE is important to understand
Methods of distillation
 Simple distillation: when B.P of components are quite different
 Fractional distillation: when B.P of components are similar
 VLE
• Separation based on equilibrium distribution of
components
• Under given set of conditions, equilibrium vapor
composition is related to liquid composition: VLE
• Given set of conditions????
• From Gibbs phase rule, degrees of freedom
=2
• Parameters available: T,P liquid composition and
vapor composition
CONST T OR CONST P BINARY EQUILIBRIUM
P vs. x diagram is used to determine to which
the feed mixture deviates from ideal solution.
For binary mixture

𝑃 = 𝑝𝐴 + 𝑝𝐵 = 𝑃𝐴∗ 𝑥𝐴 + 𝑃𝐵∗ 𝑥𝐵

𝑃 = 𝑃𝐵∗ + 𝑥𝐴 (𝑃𝐴∗ -𝑃𝐵∗ )

Greater the departure from straight line,

greater is the deviation from ideality

If the solution is non ideal, then activity

coefficients (γA and γB) enter equation 1 above

Seader
Starting from point A as feed (sub cooled
liquid)
Point B is the bubble point and the first
bubble of vapour appears, which is in
equilibrium with the liquid and is represented
by point C at the same T. BC is the tie line
As heating further proceeds, mole fraction of
hexane in liquid phase decreases.
At point E the relative amounts of vapour
and liquid

𝐿 𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝐸𝐹
=
𝑉 𝑆𝑒𝑔𝑚𝑒𝑛𝑡 𝐷𝐸

In this two phase region, vapour is at its dew

point and liquid at its bubble point
RAOULT’S LAW AND DALTON'S LAW
When two liquids that are completely soluble in one another are mixed together, the
partial pressure of a component equals the product of its vapour pressure when pure at
this T and its mole fraction in liquid state
𝑝𝐴 = 𝑃𝐴∗ 𝑥𝐴

Daltons law: In a mixture of non-reacting gases, the total pressure exerted is equal to
the sum of partial pressure of the individual gas components
𝑃 = σ𝑎𝑙𝑙 𝑖 𝑝𝑖
VLE PHASE DIAGRAMS :T-X-Y DIAGRAM AT CONSTANT P

Experimental data usually

are presented as P as a
function of composition at a
constant T, or T as a function
of composition at constant P

Cyclo pentane- Benzene system

P-X-Y DIAGRAM AT CONSTANT T

Dichloromethane-DCE system
 VOLATILITY
Tendency of a substance to vaporize
Related to substance vapour pressure
Relative volatility: volatility of one to other
component in a binary liquid mixture
If R.V is constant over entire composition range, we
can easily obtain y vs. x diagram from the V.P
knowledge of two components at a given T
(between B.P of two components)
𝑃𝐴∗
y mostly greater than x and so R.V greater than or For ideal solutions, 𝛼𝐴𝐵 = 𝑃𝐵∗
equal to 1
DEVIATION FROM IDEALITY
Maximum Boiling Positive deviation: Activity coefficient >1
Minimum Boiling
Azeotrope Azeotrope
Negative deviation: Activity coefficient < 1

If positive deviation is too large, the

total pressure curve passes through a
minimum at a certain liquid concentration
and x-T , y-T curves passes through a
minimum. This is constant boiling mixture,
which produces vapour and liquid of
same composition. Hence azeotrope is
minimum boiling.
GENERAL GUIDELINES
1. Mixtures of isomers usually form ideal solutions
2. Mixtures of close boiling aliphatic hydrocarbons are nearly ideal below 10 bar
3. Mixtures of compounds close in molar mass and structure frequently do not
deviate greatly from ideality (ring compounds, unsaturated compounds,
napthenes)
4. Noncondensable such as H2S, CO2, H2 and N2 that are present in mixtures
involving heavier components tend to behave non-ideally w.r.t other compounds
Idea Solutions - Raoult’s law
• Equilibrium vapour composition can
be computed at given temperature.
• The value of 𝑦 ∗ at point D equals the
ratio of distance FG to EG.
∗
∗
𝑝 ҧ
𝐴 𝑝𝐴 𝑥
𝑦 = =
𝑝∗𝑡 𝑝𝑡
∗
𝑝𝐵ҧ 𝑝𝐵 (1 − 𝑥)
1−𝑦 = =
𝑝𝑡 𝑝𝑡
𝑝𝐴
𝛼=
𝑝𝐵
Tutorial # 1
• Compute the V-L equilibria at constant pressure of 1 std atm for
mixtures of n-heptane with n-octane, which may be expected to form
ideal solutions. (𝑇𝐵𝑃ℎ𝑒𝑝𝑡𝑎𝑛𝑒 = 98.4°𝐶, 𝑇𝐵𝑃𝑜𝑐𝑡𝑎𝑛𝑒 = 125.6°𝐶)
𝐵
Antoine Equation: log10 𝑃(𝑚𝑚𝐻𝑔) = 𝐴 + + 𝐶 𝑙𝑜𝑔10 𝑇 + 𝐷 𝑇 + 𝐸 𝑇 2
𝑇 (𝐾)

n-Heptane n-Octane
A 65.0257 29.0948

B -3.8188E+03 -3.01E+03

C -2.1684E+01 -7.2653
D 1.0387E-02 -2.27E-11
E 1.0206E-14 1.47E-06
 Positive Deviation from Ideality
• Total pressure is greater than computed for ideality.
𝑝𝐴ҧ ∗ + 𝑝𝐵ҧ ∗ 𝑅𝑒𝑎𝑙 > 𝑝𝐴ҧ ∗ + 𝑝𝐵ҧ ∗ 𝐼𝑑𝑒𝑎𝑙

• Partial pressure approaches ideality as mole fraction

approaches 1. So, Raoult’s law is applicable at high
concentration.
Minimum boiling mixtures - Azeotropes
• When positive deviation from ideality is large and vapour
pressures of both the components are not too far apart.
• The total pressure curve at constant temperature passes through
a minimum at some concentration. Such mixtures are names as
azeotrope or constant boiling mixtures
• Point L is point of azeotropism at this pressure, representing
minimum boiling temperature.
• Solution like these cannot be completely separated by ordinary
distillation methods at this pressure since 𝑦 ∗ = 𝑥 and 𝛼 = 1.
• Axeotropic composition as well as boiling point changes with
pressure.
• Ethanol-water azeotrope at 1 atm occurs at 89.4 mole% of
ethanol and 78.2oC.
 Negative Deviation from Ideality
• Total pressure is greater than computed for ideality.
𝑝𝐴ҧ ∗ + 𝑝𝐵ҧ ∗ 𝑅𝑒𝑎𝑙 < 𝑝𝐴ҧ ∗ + 𝑝𝐵ҧ ∗ 𝐼𝑑𝑒𝑎𝑙

• Partial pressure approaches ideality as mole fraction

approaches 1. So, Raoult’s law is applicable at high
concentration.
Maximum boiling mixtures - Azeotropes
• When the vapour pressures of the components is not too
great and negative deviation is large, the curve for total
pressure vs composition may pass through a minimum.
• Maximum in the boiling temperature at L.
• The equilibrium vapour is leaner in the more volatile
substance for liquids whose x is < than azeotropism
composition or > if x is larger.
• Less common than minimum boiling azeotropes.
• 11.1% HCl- 88.9% Water at 1 atm.
VLE OF PARTIALLY MISCIBLE LIQUIDS
Cyclohexane addition to ethanol-water
mixture forms minimum boiling
heterogeneous ternary azeotrope.

Overheads on condensation separates in

to two liquid layers. Cyclohexane rich
layer is refluxed and other layer sent to
column 2 for recovery and recycle of
alcohol and cyclohexane
CALCULATION OF VLE
Material Balance:

Eliminating L
K-VALUE (VAPOUR-LIQUID EQUILIBRIUM RATIO)
For non ideal/ideal mixtures, the ratio of mole fraction of a component in one phase
to other phase is expressed as distribution coefficient or equilibrium ratio K
Yi/xi = K
If ideal gas law applies pi = yi ptotal applies to gas phase and the ideal∗ raoults law
𝑦 𝑝 (𝑇)
pi = xi pi*(T) applies to liquid phase, then for ideal system 𝑘𝑖 = 𝑖 = 𝑖
𝑥𝑖 𝑝𝑡𝑜𝑡𝑎𝑙
Meaning the above eqn yields Ki values at low pressures for components well below
their critical temperatures
At high pressures, values of K too large for components above critical temperatures.
So Ki should be made a function of T,P and composition.
For non ideal solutions, Ki can be calculated either from empirical relations or
thermodynamic relations or charts
BUBBLE POINT CALCULATIONS
Calculate the bubble point temperature of a liquid mixture given the total
pressure and liquid composition
 Yi = Kixi
 Summation of yi = 1 in vapour phase. Thus for binary mixture, 1= K1x1 +K2x2 in which Ki is
function of T (increases with T)
 For ideal solutions ptotal = pi*x1 + p2*x2 and you might use Antoine eqn for pi*
 Once the bubble point temperature is determined, the vapour composition can be calculated from
𝑝𝑖∗ 𝑥𝑖
𝑦𝑖 =
𝑝𝑡𝑜𝑡𝑎𝑙
 DOF analysis: Total variables are x1,x2,y1,y2;total P, T
 Prespecified: x1,x2,total P
 Independent eqns: y1=K1x1; y2 = K2x2 and y1+y2 = 1
DEW POINT CALCULATIONS
Calculate the dew point temperature of a vapour mixture given total P and vapour
composition
𝑦1 𝑦2
 σ 𝑥𝑖 = 1 𝑖𝑚𝑝𝑙𝑖𝑒𝑠 1 = +
𝐾1 𝐾2
𝑦1 𝑦2
 K is function of T. For ideal solution, 1 = 𝑝𝑡𝑜𝑡𝑎𝑙 +
𝑝1∗ 𝑝2∗
EXERCISE
If an equimolar liquid mixture of methanol and water is flashed at atmospheric pressure, calculate
the vapour composition
a. Assuming ideal vapour and liquid phase behaviour
b. Using Wilson equation

Data for methanol(1) and water(2) for Wilson equation at 1

atm
EQUILIBRIUM IN A MULTI COMPONENT SYSTEM
Experimental VLE data for multicomponent systems might not be available and has to
be computed using correlations
If the multicomponent system is ideal solution then , for any ith component
𝑛

𝑦𝑗∗ 𝑃 = 𝑝𝑗∗ = 𝑥𝑗 𝑃𝑗𝑣 𝑎𝑛𝑑 𝑃 = ෍ 𝑝𝑖∗

𝑖=1
At a given T, Vapour pressures of the components can be calculated. From the known
liquid compositions, vapour compositions can be calculated. Once vapour phase
composition is known, total P and partial pressures can be calculated
Bubble and dew point calculations can be done if we have access to K values for
multicomponent systems using Depriester chart
EQUILIBRIUM IN NON IDEAL SYSTEM
The fugacities of the component I in vapour and liquid phase becomes equal

Activity coefficient Fugacity coefficient

a. Wilson a. Activity coefficient models such

b. Non-random two liquid (NRTL) as Peng-Robinson, SRK
c. Universal quasi-chemical (UNIQUAC)
 BUBBLE POINT/DEW POINT FOR MULTICOMPONENT MIXTURE

N-component mixture, r-reference component

The R.V of ith component w.r.t rth component
Bubble point Dew point

Given liquid composition and P Given vapour composition and P

Assume T, calculate V.P or k-values of all components Assume T, calculate V.P or k-values of all components

Then calculate Yi Then calculate Xi

Summation of Yi should be equal to 1 Summation of Xi should be equal to 1