Dr Saad Al-ShahraniChE 334: Separation Processes Aseotropes The increased repulsion between...
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Transcript of Dr Saad Al-ShahraniChE 334: Separation Processes Aseotropes The increased repulsion between...
Dr Saad Al-ShahraniChE 334: Separation Processes
Aseotropes
The increased repulsion between molecules can result in the
formation of an azeotrope, which is a liquid mixture whose
equilibrium vapor has the same composition as the liquid ( i.e. xi =
yi for an azeotrope).
a) Minimum-Boiling Homogeneous Azeotropes:
This type of azeotropes occurs due to repulsion between the
molecules
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
Txy diagramP constant
subcooled
vaporsubcooled
vapor
Pxy diagram(T constant)
> 1.0
(+) deviation
from ideality
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
xy diagram,ether P or T= constant
X=y
45 o lin
e
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
b) Maximum-Boiling azeotropes
This type of azeotropes occurs due to attraction between the molecules.
< 1
(-) deviation
from ideality Pxy diagram
Txy diagram
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
xy diagram
x=y
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
Example:
Ethanol and n-hexane from a minimum boiling point azeotrope at
3.2 mole% ethanol at 58.68 oC and 760 mmHg pressure. The vapor
pressure of ethanol and n-hexane are 6 psia and 12 psia
respectively, at 58.68 oC, determine iL for ethanol and n-hexane at
the azeotropic condition
solution
At azeotrope x=y
For methanol
EthLEthsatEthEth xPPy
EthEth xy
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
23.112
7.14
satHex
HexL P
P
For methanol
HexLHexsatHexHex xPPy
HexHex xy
45.26
7.14
satEth
EthL P
P
Note: foe ethanol and n-hexane L> 1.0, indicating repulsion (positive deviation from ideality
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
DePriester Charts For Light Hydrocarbons
Figures (a,b) give K-value charts for some Iight hydrocarbons. These
arts do not assume ideal vapor-phase behavior. Some corrections for
pressure effects are included.
Figure (a) is used for low temperatures and Figure (b) high temperatures.
To find the appropriate K-values, a straight line is drown on the
diagram connecting the temperature and pressure of the system.
intersection of this line with the K-value curve for each hydrocarbons
its K-value at this temperature and pressure.
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
RELATIVE VOLATILITY
The relative volatility is the ratio of K-values
For two component j and k
kLsatk
jLsatj
kk
jj
k
jjk P
P
xy
xy
K
K
/
/ , jk
If the system is ideal (i,e. obeys Raoult’s law, i.e. no attraction or
repulsion between molecules or =1.0)
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
For component j
P
PxyxPPy
satj
jjjsatjj / , 0.1 , jL
P
PxyxPPy
satk
kkksatkk / , 0.1 , kL
For component k
satk
satj
satk
satj
kk
jjjk P
P
P
P
P
P
xy
xy
/
/
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
Relative volatility for binary system
For two components system under equilibrium conditions (j,k):
)1/()1(
/
/
/
jj
jj
kk
jjjk xy
xy
xy
xy
jjk
jjkj x
xy
)1(1
Solve for yj
This equation is very important in distillation operation
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
Relative volatilities (are essentially constant. In general, they are
functions of temperature and composition.
jk= f ( T and composition)
In most systems, () decreases as temperature increases, which
means that separation of components becomes more difficult.
Therefore, It is often desirable to keep temperatures as low as
possible (use low pressure) to reduce energy consumption.
The following figure shows some VLE curves on an xy diagram for
various values of .
The bigger the relative volatility, the fatter the VLE curve and the
easier the separation (low number of stages required).
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
As → 1.0, the VLE curve approaches the 45o line x = y.
It is impossible to separate components by distillation if the value of is too close to unity. Distillation is seldom used if < 1.0 5.
X
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
For a multi-component system, the relative volatilities are defined with respect to some component, typically the heaviest one.
Relative volatility For a multicomponents system.
If we have multi-components system containing components (1,2,3, H), H is the heaviest one and (1) is the lightest one.
HH
jj
HjH xy
xy
K
K
/
/1
(1) )(111H
HH x
yxy
THERMODYNAMICS OF SEPARATION OPERATIONS
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
By the same manner
HHHH xy
xy
K
K
/
/ 2222
(2) )(222H
HH x
yxy
HHHH xy
xy
K
K
/
/ 3333
(3) )(333H
HH x
yxy
.
.
.
.
.
.
.
.
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
HH
jj
H
jjH xy
xy
K
K
/
/
(4) )(H
HjjHj x
yxy
(5) 1)(1
H
HjjH
n
jj x
yxy
(6) 1
/
1
n
jjjH
HH
xxy
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
Substitute (6) in (4)
1
n
jjjH
jjHj
x
xy
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
Example:
A multi-component liquid mixture has the compositions and relative
volatilities given in the table below. Calculate the composition of the
vapor phase.
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
The lever ruleVap.
yi
V, mol/h
Liq.
xi
L, mol/h
F = L + V
zi F = xi L + yi V
liq.phase
vap.phase
yz
zx
L
V
ii
ii
F
zi
Dr Saad Al-ShahraniChE 334: Separation Processes
THERMODYNAMICS OF SEPARATION OPERATIONS
0 1.0
y
Temperature
zi
x
T
T1sat
T2sat
The ratio of the product flows
(L,V) is the inverse of the ratio of
the lengths of the lines
connecting the feed mole fraction
of each of the products. This is
known as ”Lever Rule”
Note: the two phases must be under equilibrium conditions
yixi