Transcript Distillation - Sepuluh Nopember Institute of Technology

Distillation
CONTENTS
Flash Distillation
Differential Distillation
Distillation
Continuous Distillation with Reflux
Simple Steam Distillation
Plate Efficiencies
9-1 Introduction
1
Distillation
• It is a unit operation of separation of liquid
mixtures into their several components by partial
vaporizing and partial condensing, and the most
widely used method of achieving this end one of
the major operations in chemical and petroleum
industries, and the key operation of the oil refinery.
The unit operation makes use of difference in
volatility of individual components in a mixture.
Throughout the chemical industry the demands for
pure products, coupled with a relentless pursuit of
greater efficiency, has necessitated continued
research into the techniques of distillation.
3
2
Partial Vaporisation and Partial Condensation
• Abscissa-x represents the
mole fraction of the
volatile component in the
liquid
• Ordinate-y represents the
temperature at which the
mixture boils; boiling
curve ABCJ; dew point
curve ADEJ
• If a mixture of initial
composition x2 is at a t3
below its boiling point t2 ,
as shown by point G
A
D
t1K
M N
t’ L
t2
B
t3
E
G
C
J
0 x
1
y1
x2
x3
x or y
benzene - toluene
4
x4
1.0
• On the diagram, then on heating at constant
pressure the following changes will occur：
• a) When T reaches T2 , the liquid will boil, as
shown by point B, and some vapor of
composition y2 , shown by point E, is formed.
• b) On further heating, the composition of the
liquid will change because of the loss of the
more volatile component to the vapor and the
boiling point will therefore rise to some t’. At
this temperature the liquid will have a
composition represented by L, and the vapor a
composition represented by N. The mass ratio
of liquid remained to the vapor formed is (lever
rule)
massof liquid MN

mass of vapor ML
5
• c) On further heating to t1, all liquid is fully
vapourised to give vapor D, of same composition
y1 as the original liquid.
• It is seen that partial vaporisation of the liquid
gives a vapor richer in the more volatile
composition than the liquid. If the vapor initially
formed, as for instance at point E, is at once
removed by conden- sation, then a liquid of x3 is
obtained, represented by C. The step BEC may
be regarded as representing an ideal stage, since
the liquid passes from x2 to x3, which represents
a greater enrichment in the more volatile
component than can be obtained by any other
single stage of vaporisation.
6
• Starting with superheated vapor represented by
H, on cooling to D condensation will commence,
and the first drop of liquid will have a
composition of K. Further cooling to
temperature t’ will give liquid L and vapor N.
Thus partial condensation brings about
enrichment of the vapor in the more volatile
component in the same manner as partial vaporisation. The industrial distillation column is.
in essence, a series of units in which these two
processes of partial vaporisation and
condensation are effected simultaneously.
7
3
Raoult’s and Henry’s Laws
• 1. By Dalton’s law of partial pressures, the total
pressure is equal to the summation of the partial
pressure, that is
Pp
(9.1)
• Then, since in an ideal gas or vapor the partial
pre –ssure is proportional to the mole fraction of
the constituent:
pA  y A P
(9.2)
• For an ideal mixture, the partial pressure is
related to the concentration in the liquid phase
by Raoult’s law which can be written
pA  pA0 xA
(9.2)
8
• where is the vapor pressure of pure A at the
same temperature. This relation is usually found
to be true only for high values of xA or
correspondingly low values of xB , but mixture of
organic isomers and some hydrocarbons follow
the law closely.
• For low values of xA, the relation between pA and
xA can be expressed by Henry’s law, that is
p A  HxA
(9.3)
where H is the Henry’s constant, and not the vapor
pressure p A0 of the pure material.
9
Vapor pressure
• If the mixture follows the
Raoult’s Law, then the vapor
pressure of a mixture can be
obtained graphically from a
knowledge of the vapor pressure
of the two components. Thus, in
fig. 9.1 OA represents the
partial pressure of pA of A in a
mixture, and CB the partial
pressure of B. BA the total
pressure. Thus, in a mixture of
composition D, the partial
pressure pA is given by DE, pB by
DF, and the total P pressure by
DG.
G
B
E
O0
A
F
D
C
Fig.9.1 Mole fraction
in liquid x
10
2. Boiling Equation
• If it is known that the mixture follows the
Raout’s Law, then the values of yA for various
values of xA may be calculated from a
knowledge of the vapor pressure of the two
components at various temperature. Thus
pB  pB0 xB
(9.3)
0
pA  pA
xA
p A pB p A0
p
y A  y B    x A  xB  1
P P P
P
• Giving
P  pB0
xA  0
p A  pBo
(9.4)
11
3
Relative Volatility
• We have known that the distillation unit
operation makes use of difference in volatility of
individual components in a mixture to separate
the liquid mixture into several components. How
is the volatility of a component measured?
1.volatility
• The volatility is defined as the ratio of the partial
pressure to the mol fraction in the liquid, that is
pA
vA 
xA
pB
vB 
xB
(9.5)
12
2. Relative Volatility
• In order to measure the difference in volatility, a
relative volatility usually be defined as the ratio
of these two volatility, that is
v
p x
 A  A B
(9.6)
vB
pB x A
• Substituting PyA for pA, and PyB for pB:
y A xB

yB x A
or
yA
xA

yB
xB
(9.7)
• This gives a valuable relation between the ratio
of A and B in the vapor and that in the liquid.
13
• Since with a binary mixture,
yB  1  y A
and
xB  1  xA
• The equation (11.6)and (11.7) can be simplified as
respectively
 
or
y A 1  xA
1 yA
xA
yA 
and
 A xA
1  (  1) x A
(9.8)
(9.9)
yA
(9.10)
  (  1) y A
• This relation enables the composition of the
 x,
vapor to be calculated for any desired value of
if is
xA 
14
• known. For separation to be achieved, must not
equal 1 and considering the more volatile
component, as  increases above unity, y
increases and the separation becomes much
easer.
• From the definition of volatility and relative volati
-lity of a component, it is seen that for an ideal
system the volatility is numerically equal to vapor
pressure of the pure component, and relative
volatility to the ratio of vapor pressure of the pure
components of A and B, that is
p A0
 0
pB
(9.11)
15
4
Methods of two-Component Mixture Distillation
• For distillation purposes it is more convenient to
plot y against x at a constant pressure, since the
majority of industrial distillation take place at
substantially constant pressure. This is shown
as following
16
Mol fraction in
vapor y
• This is a square with a
abscissa of mol fraction
x in liquid, ordinate of
mol fraction y in vapor
and a reference line-diagonal line. It is seen
that, for a binary mixture
with a normal y-x curve,
the vapor is always richer
in the more volatile
component than the
liquid from which it is
formed.
Mol fraction in liquid
x
17
• There are three main methods used in
distillation practice which all rely on this basic
fact; they are:
• 1)differential distillation. (addition)
• 2)flash or equilibrium distillation
• 3)rectification
• Of these, rectification is much more important,
and differs from the other two methods in that
part of the vapor is condensed and return as
liquid to the still, whereas, in the other methods,
all the vapor is either removed as much, or is
condensed as product.
18
• (Batch) differential distillation
Cooling water
y
x
Heating
Fig.9.2 Flow chart of batch distillation
• Flash or equilibrium distillation
V,y
Expansion valve
F,xf
pump
Heating agents
Fig.9.3 Plant of equilibrium distillation
S,x
19
9-2 Flash or equilibrium distillation
• This method, frequently carried as a continuous
process, consist of vaporizing a definite fraction
of the liquid feed in such a way that the evolved
vapor is in equilibrium with the residual liquid.
• The feed is usually pumped through a fired
heater and enters the still through a valve where
the pressure is reduced. The still is essentially a
separator in which the liquid and vapor
produced by the reduction in pressure.
20
• Let the concentraction of the feed be xF ; in mole
fraction of the more volatile component. Let F
be the molal rate of the feed, V be the molal rate
of vapor withdrawn continuously, and L be the
mole rate of the liquid. Let yD and xB be the
concentraction of the vapor and liquid,
respectively.
• By a material balance for the more volatile
component gives:
FxF  Vy D  Lx B
9.12
• Let f=V/F be the mole fraction of the feed that is
vaporized and withdrawn continuously as vapor.
21
• Combining above two Eqs. gives :
xF 
V
F V
yD 
x B  fy D  1  f x B (9.13)
F
F
• or
x
y
1    1x
(9.14)
22
9-3 Differential Distillation
1. Feature of Differential Distillation
• In this process the liquid is boiled slowly and the
vapors are withdrawn as rapidly as they form to
a condenser, where the condensed vapor is
collected. Since the vapor is richer in the more
volatile component than the liquid, it follows
that the liquid remaining becomes steady
weaker in this component, with the result that
the component of product progressively alters.
Thus, whilst the vapor formed over a short
period is in equilibrium with the liquid, the total
vapor formed is not in equilibrium with the
residual liquid.
23
2. Analysis of Differential Distillation
• Let L be the number of mole of material in the
still and x be the mol fraction of component A.
After a short time, suppose an amountds,
containing a mol fraction y of A, be vaporised .
• The equation for material balance is
Lx  ( L  dL)(x  dx)  ydL
(9.15)
24
• Neglecting the term dxdL and rearranging
dL
dx

L
yx
9.16
• Integrating gives
x1 dx
L1
ln

(9.17)
x
2 y  x
L2
• The integral on the right side needs the
information on equilibrium relation between y
and x, and can be solved graphically or
numerically. The average composition of total
material distilled, yav , can be obtained by
material balance:
L1x1  L2 x2  L1  L2 yav
25
9.4 Simple Steam Distillation
1. The Concepts
• Where the material to be distilled has high
boiling point, and particularly where
decomposition might be occur if direct
distillation were employed, the process of steam
distillation can be used. This method is often
used to separate a high-boiling component from
small amounts of nonvolatile impurities.
• If a layer of liquid water(A) and an immiscible
high-boiling component (B) are boiled at 1atm,
then, by the phase rule, for three phases and two
components,
F=2-3-2=1degree of freedom
26
• When the sum of separate vapor pressures
equals the total pressure, the mixture boils and
pA  pB  p
(9.18)
• Then the vapor composition is
pB
yB 
p
(9.19)
• Note that by steam distillation, as long as liquid
water is present, the high-boiling component B
vaporizes at a temperature well below its normal
boiling point without using a vacuum. The vapor
of water (A) and high-boiling component (B) are
usually condensed in a condenser and the
resulting two immiscible liquid phase seperated.
27
• The ratio moles of B distilled to moles of A
distilled is:
n A mA M A p A y A
pA




nB mB M B
pB y B P  p A
(9.20)
• Where the subscript A refers to the component
being recovered, and B to steam, and m-mass;
M-molecular weight; P-total pressure; pA,pBpartial pressure of A,and B.
28
9-5 Continuous distillation with reflux
• For large-scale production, continuous
distillation, is often used to separate components
of comparable volatility, which requires the use
of distillation with reflux.
29
1
The Continuously Fractionating Process
• The operation of a typical fractionating column
may be followed by reference to Fig.9.4. The
column consists of a cylindrical structure
divided into sections by a series of perforated
trays which permit the upward flow of vapor. The
liquid reflux flows across each tray, over weir,
down a downcomer to the tray below. The vapor
rising from the top tray pass to a condenser and
then via an accumulator or reflux drum and a
reflux divider where part is withdrawn as the
overhead product D, and the remainder is
returned to the top tray as reflux R .
30
vapor
y1
Liquid reflux L xD
condenser
Warm cooling water
accumulator
cooler
Cooling water
Overhead product D
Reflux pump xD
Feed plate
ys
Vapor
Re-boiler
liquid
Feed F,xf
steam
condensate
trap
Bottom cooler
Bottom product W, xw
Fig.9.4 Continuous fractionating column with rectifying and stripping sections
31
• The liquid in the base of the column is frequently
heated, either by condensing stream or by a hot
oil stream, and the vapor rise through the
perorations to the bottom tray.
• This operation of partial condensation of the
rising vapor and partial vaporisation of the reflux
liquid is repeated on each tray. Vapor of
composition of y1 from the top tray is condensed
to give the top product D and the reflux R, both
of the same the composition y1. The feed stream
is introduced on some intermediate tray where
the liquid has approximately the same
composition as the feed. The part of the column
above the feed point is known as the rectifying
section; the lower portion is known as the
stripping section.
32
• In the arrangement discussed above, the feed is
introduced continuously to the column and two
products streams are obtained, one at the top
much richer than the feed in the MVC, and the
second from the base of the column weaker in
the MVC. This is operation of Continuous
fractionating. For the separation of small
quantities of mixtures, a batch still may be used
(commonly in the fine organic chemical industry),
which will be discussed in more detail later.
33
2
Action on an ideal plate
• On an ideal tray, by definition, the liquid and the
vapor leaving the tray are brought into
equilibrium. Consider a single tray in an ideal
cascade, such as tray n in fig.9.5.
34
• Assume that the trays are
numbered serially from the
top down and that the tray
under consideration is
thenth tray from the top.
Then the tray immediately
above tray n is tray n-1,
and that immediately
below it is n+1. Subscripts
are used on all quantities
to show the point of origin
of quantity.
• Two fluid streams enter
the nth tray, and two leave
it.
Ln-2
xn-2
Vn-1
yn-1
Ln-1
xn-1
Vn
yn
Ln
xn
Vn+1
yn+1
Ln+1
xn+1
Vn+2
yn+2
Fig 9.5
35
Tray n-1
Tray n
Tray n+1
A stream of liquid Ln-1mol/h from tray n-1 and a
stream of vapor Vn+1 mol/h from tray (n+1) are
brought into intimate contact. A stream of vapor
Vn mol/h rises to tray n-1, and a stream of liquid
Ln mol/h descends to tray n+1, and the
concentrations entering and leaving the nth tray
are as follows:
• Vapor leaving tray yn; liquid leaving tray xn;
• Vapor entering tray yn-1; liquid entering tray xn-1.
• By the definition of ideal tray there is equilibrium
relationship between xn and yn. That is
xn
yn 
1  (  1) xn
(9.21)
36
• This shown in fig.9.6.The
Partial condensation
vapor is enriched in the more
volatile component A as it
Partial
vaporisat
rises through the column.
iong
• And the liquid,is depleted of
xnxn-1yn+!yn 1.0
0
Mol fraction of A x or y
A as it flows downward.
Fig.9.6
• Thus the concentration of A in both streams of
vapor and liquid increase with the height of the
column; that is xn1  xn ; yn  yn1 . Although the
streams leaving the tray are in equilibrium, those
entering it are not. This can be seen from fig.9.6
37
3
Material Balances in Plat Columns
1. Overall material balances for two-component system
• How many top and bottom
products can be obtained for a
given feeds and required quality?
• The material balance for a total
D, xD
column gives
F  DB
(9.22a)
F, xf
• The material balance on the
more volatile component A is
W, xw
FxF  DxD  BxB
(9.22b)
38
• Thus:
D xF  xB

F
xD  xB
(9.22c)
• And
B xD  xF

(9.22d )
F xD  xB
• The quantities of top and bottom products D, W
depend the feed rate F and the concentration of xf,
and the required product qualities of xD, and xw.
• The following equations apply:
B  Lb  Vb  Lm  Vm1 (9.22e)
BxB  Lb xb  Vb yb  Lm xm  Vm1 ym1 (9.22 f )
• Subscript m is uesd in place of n to designate a
general palte in the stripping section.
39
2. Operating lines
• The relationship of concentrations of the vapor
and liquid leaving an ideal plate abides by the
equilibrium curve. What rule should the relation
between concentrations of the vapor leaving an
ideal plate and of the liquid entering it obey?
• Since a stream of feed is introduced at feed plate,
the continuity of material flow in the rectifying
section is different from that in the stripping
section.
• Thus the situations of rectifying section and
stripping section must be considered separately.
40
1) Material balance in Rectifying section
• A material balance above
V1
L
plate n in rectifying section
Gives:
Vn1  Ln  D
(9.23)
(9.24)
n
Vn+1, yn+1Ln,xn
F, xf
n+1
• Expressing this balance on the
more volatile component:
Vn1 yn1  Ln xn  DxD
m
Vm+1,ym+1 Lm,
xmm+1
W, xw
• Thus:
Ln
D
yn1 
xn 
xD
Vn1
Vn1
D, xD
(9.25)
Fig.9.8
41
• Eliminating Vn+1 by Eq.(9.23),giving:
Ln
D
yn 1 
xn 
xD
Ln  D
Ln  D
(9.26)
The Eq.(9.26) is called the equation of the
operating line in the rectifying section.
42
2) Material balance in stripping section
• Similarly, taking a material balance for the total
stream and for the more volatile component from
the top to above mth plate and
Vm  Vm1  Constant
Lm1  Lm  constant
• Thus:
Lm  Vm  B
Vm1 ym1  Lm xm  BxB
(9.27)
43
• In a different form of Eq.(9.27a):
ym1 
Lm
B
xm 
xB
Vm1
Vm1
(9.27b)
• The equation gives the relation between the
compositions of the vapor rising to a plate and
the liquid on the plate in the stripping section. It
is called the equation of operating line for the
stripping section of a column.
44
4
Number of plates
1 .constant molar overflow
• If the molar heats of vaporisation are
approximately constant, the flows of liquid and
vapor in each part of the column will not vary
from tray to tray unless material enters or is
withdrawn from the section
• This is the concept of constant molar overflow.
45
2. The method of McCabe and Thiele
• The simplifying assumptions of constant molar
heat of vaporisation, of no heat losses, and of no
heat of mixing, led to constant molar vapor flow
and constant molar liquid flow in any section of
the column. We have obtained the equations of
the operating lines:
• Rectifying section
Ln
D
yn 1 
xn 
xD (9.26)
Ln  D
Ln  D
• Stripping section
Lm
B
ym1 
xm 
xB
Vm1
Vm1
(9.27b)
46
• They are all straight lines. The operating line for
rectifying section is a straight line of a slope L V ,
and of a intercept Dx D Vn . If xn=xD in equation
(9.26), then
n
n
yn1 
Ln
L D
D
xD 
xD  n
xD  xD
Ln  D
Ln  D
Ln  D
(9.28)
• and it must pass through a definite point A(xD,xD)
on the equilibrium diagram x-y . Further, if xn+1=0,
then yn+1= Dx V , this represents the another
definite point B(0, Dx V ). The two definite points
make the the operating line easily drawn out AB,
as shown in fig.9.9
D
n
D
n
47
Mol fraction in vapor y
xD
A
G
y
(xF, xF)
B
C
x
xD
xF
Mol fraction in liquid x
Fig. 9.9 determination of number o plate
48
• Similarly, the equation of operating line for
stripping section is also a straight line of
slop Lm Vm , and if xm=xB , then
Lm
Lm  B
B
ym1  xB  xB 
xB  xB
Vm
Vm
Vm
• and this represents the straight line has to pass
th -rough the point C(xB,, xB). The operating line
for stripping section is easy to be drawn out CG
with use of the slop Lm Vm and the point C(xB,, xB)
as shown in fig.9.10.
49
• When the two operating lines have been drawn
out, the number of theoretical plates required can
be determined by drawing steps between the equ
-ilibrium curve and the operating line starting
from point A. The method is called McCabeThiele’s.
50
Mol fraction in vapor y
y1 = x D
A
G
y
x2
x3
(xF, xF)
x4
B
C
xB
x
xF
xD
Mol fraction in liquid x
Fig. 9. 10 Determination Of Number O Plate by McCabe
3. Operating Lines(Feed Line)
• The equation for this line of intersection can be
derived as following:
• If the two operating lines intersect at a point with
coordinates(xD, yD), then
Vn yq  Ln xn1  DxD
Vm yq  Lm xm1  BxB
(9.29)
(9.30)
52
• Combining above two equations gives
(Vm  Vn ) yq  ( Lm  Ln ) xq  ( DxD  BxB )
(9.31)
• The relations (between Ln and Lm, Vn and Vm )
depend on the thermal conditions of feed.
Vn
Ln
F
qF
Lm
(1-q)F
Feed plate
Vm
53
• Let the feed be partially vapor, and the moles of
liquid per unit feed be q, the feed rate be F mol/h.
• Thus: the moles of saturated liquid in the feed
are qF, the moles of saturated vapor are (1-q)F.
when the stream of (1-q)F moles of vapor of
feed comes into the column, it flows upward and
is made up the vapor stream Vn in rectifying
section with the Vm. That is
Vn=Vm+(1-q)F
(9.32)
54
• And the stream of qF of liquid of feed comes
into feed plate, it flow down and adds to the
liquid stream Ln making up the liquid stream Lm
in stripp- ing section, that is
Lm  Ln  qF
(9.33)
55
• The means of q is:
heatto vaporiseonem ole feed
q
m olarlatentheatof the feed
• Thus, q has the following numerical limits for the
various thermal conditions of the feed:
• 1) cold feed, q>1
• 2) saturated liquid, q=1
• 3) saturated vapor, q=0
• 4) feed partially vapor, 1>q>0
• 5) feed superheated vapor, q<0
56
• From Eq.(9.22b), the last two terms in Eq.(9.31)
can be replaced by FxF. Thus, substituting
Eq.(9.32) and (9.33) into Eq.(9.31) gives:
(q 1)Fyq  qFxq  FxF
• And arranging it gives:
q
1
yq 
xq 
xF
q 1
q 1
(9.34)
• The equation is commonly known as the
equation of the q-line which represents a
straight line, and on which all intersections of
the operating lines must fall.
57
Mol fraction in
vapor y
• If xq=xF, then yq=xF . Thus, the point of
intersection of the two operating lines lies on the
straight line of slop q/(q-1) passing through the
point (xF,xF).
0<q<1
q=1
q>1
A
y
• When yq=0, xq=xF/q .
q=0
The line can thus be
f(xF, xF)
q<0
drawn through two easily
B
determined points. The
different five q-lines corr
C
x x
xD
F
esponding to five thermal
Mol fraction in liquid x
conditions of feed are drawn Fig.9.11 Effect of Feed
out respectively as following. Condition on Feed Line
58
• Summarizing the steps of determination of ideal
plates required by McCabe-thiele method for a
given condition of feed, requirement of
separation and reflux L gives
• 1) plotting the equilibrium curve on x-y diagram
based on the data of equilibrium;
• 2)determining the four definite points of A(xD,xD),
f(xF, xF), C(xB,xB) and B(0,DxD/Vn )on the diagonal
line or ordinate of the x-y diagram;
• 3) drawing the operating line of rectifying section
through the points of A and B; drawing the q-line
through the two points of f(xF, xF) and slope q/(q1); drawing the operating lines of stripping
section;
59
Mol fraction in
vapor y
• 4) determining the number of ideal plates
required by step-by-step construction starting
either from A point or B point till the concentration
x on one plate being slight lower (or greater ) than
xB (xD);
xD
A
E
• 5) counting the number
y
of the steps, the ideal
Gx
q
plates required being
B
equal to that of the
xb
steps.
C
xB
xF
xD
Mol fraction in liquid x
Fig. 9.12 determination of location of
feed point
60
5
The Reflux Ratio
1. introduction
• The analysis of fractionating columns is
facilitated by the use of a quantity called the
reflux ratio.
• The equation:
R
L
D

V D
D
9.35a 
• And
L
L
RV 

V L V
9.35b
61
• Thus, introducing R in equation(9.26):
Ln
D
R
xD
yn1 
xn 
xD 
xn 
Ln  D
Ln  D
R 1
R 1
(9.36)
• Any change in R will therefore modify the slope
of the operating line. If R is known, the operating
line of rectifying section is most easily drawn by
joining point A(xd,xd) to B(0,xd/(R+1)). This
method avoid the calculation of the actual flow
rates Ln,Vv, when only the number of plates to be
estimated.
62
Mol fraction in
vapor y
2.The minimum reflux ratio Rm
Further reduction in reflux
xd
A
G
R will eventually bring the
ye
H
E
operating line AE, which
k
(xf, xf)
cuts the equilibrium curve
at the intersection of q-line
B
and the equilibrium curve,
C
xe x
xd
f
and when an infinite number
Mol fraction in liquid x
of stages is needed to pass
Fig. 9. 13 influence of reflux on
from xf to xd..
the number of plates required for
a given separation
63
• This arises from the fact that under these
conditions the steps become very close
together at liquid composition near xf , and no
enrichment occurs from the feed plate to the
plate above. These conditions are known as
minimum reflux, and the reflux ratio is denoted
by Rm. Any small increase in R beyond Rm will
give a workable system, though a large number
of plates will be required. It is important to note
that any line such as AG, which is equivalent to
a smaller value of R than Rm, represents an
impossible condition, since it is impossible to
pass beyond point G towards xf.
64
3. Calculation of minimum ratio Rm
• Figure 9.13 shown the slop of the line AE at the
minimum reflux ratio is
Rm
AH xd  ye


Rm  1 EH xd  xe
(9.37a)
65
• Arranging the equation obtain
Rm 
xd  ye
ye  xe
(9.37)
• This is an universal formula for calculating the
minimum reflux Rm.
• 1) For feed at boiling point, the q-line is vertical
xe=xf, ye=yf is in equilibrium with xe .
Rm 
xd  y f
yf  xf
(9.37b)
66
q
ye
E
A
H
xd
A
H
Mol fraction in
vapor y
Mol fraction in
vapor y
xd
ye q E
(xf, xf)
B
(xf, xf)
B
C
xe=xf
Mol fraction in liquid x
xd
Fig. 14. influence of reflux on
the number of plates required for
a given separation
Cx
xf
e
Mol fraction in liquid x
xd
Fig. 14. influence of reflux on
the number of plates required
for a given separation
• 2)For feed saturated vapor, the q-line is
horizontal, so ye=xf , xe is in equilibrium with yf,
and
Rm 
xd  x f
x f  xe
(9.37c)
68
4. The number of plates at total reflux--Finsk’e Eq.
• For conditions in which the relative volatile is
co-nstant, Finske derived an equation for
calculating the required number of plates for
total reflux operation. Since no product is
withdrawn from the still, the equation of the two
operating lines become:
yn1  xn
(9.38a)
69
• Consider two components A and B, the
concentra -tions of which in the still are xsA and
xsB . Then the composition on the first plate is
obtained by
 xA 
 yA 
 xA 









1
x 
 y 

x
 B d
 B 1
 B 1
• since x1A=y2A, x1B=y2B
 xA 
 yA 
 yA

x 
 
 y 
  1 
 y
 B d
 B 1
 B



2
• Where the subscript outside the bracket
indicates the plate from the top, and d the top.
For plate 2
70
• the relation between vapor composition and that
of liquid on which is
 yA 
 xa 
    2  
 yB 2
 xB  2
• Substituting it into above equation gives
 xA 
y 
x 

   A   1 2  A 
 xB  d  y B 1
 xB  2
• And for nth plate:
 xA   y A 
 xA 
      1 2 3     n 1 w  
 xB  d  y B 1
 xB  w
71
• If an average value of relative volatility is defined
as
 av  n 1 2 3    n1 w
• The above equation become:
 xA 
n  xA 

   av 

 xB  d
 xB  w
• Thus the number of plates required at the
conditi- on of total reflux is
 x A   xB 
lg[    ]
 xB  d  x A  w
n
lg  av
9.44
72
• and n is the required number of theoretical
plates in the column. The equation is called
Finske’s Eq.
73
5. Multiple feeds and sidestream
• In general, a side-stream is defined as any
product stream other than the overhead
product and residue (Sl’in fig.9.15).
Likewise, F1and F2 constitute separate feed
stream to the column. Side-streams are most
often removed with muti-component
systems, but they can be used with binary
system.
74
• For the purpose of illustration,
a binary mixture will be
Vn
considered, with one sideVs
stream,as shown in fig.9.15.
F1,xf1
S’represents the rate of
removal of the sidestream
and xs is its composition.
V
m
D,xD
Ln
Ls
S’,xs1
Lm
W,xw
Fig.9.15. Column with side-stream
75
• Multiple feeds and side-streams will alter the con
-tinuity of fluid flowing, so the number of
sections of a column is not as the same as that
of a column which has only one feed stream,
one top product stream and one bottom product
stream. Usually, the number of the operating
lines is equal to the summation of the numbers
of feed streams and side-streams and top
product stream and bottom product stream
minus unity. For fig.9.15, the number of
operating lines=1+1+2-1=3 .
• For that part of the column above the sidestream the operating line is still given by
R
1
yn 1 
xn 
xD
R 1
R 1
(9.45)
76
• Material balance for the section between the
feed plate and the side-stream of the tower gives
Vs1  Ls  S1  D
(9.46)
• and Vs 1 ys 1  Ls xs  S1xs1  DxD
(9.47)
Ls
S x  DxD
xs  1 s1
(9.48)
Vs
Vs 1
• Since the side-stream is normally removed as a
liquid, Ls=Ln-S1, and Vs=Vn.
• The operating line of bottom section of the
column is given the same as before.
ys 1 
77
• that is:
Lm
Wx w
ym1 
xm 
Vm
Vm
(9.49)
• The effect of any additional side-stream or feed
is to introduce an additional operating line for
each the stream. In all other respects the method
of calculation is identical with that for the
straight separation of a binary mixture outlined
earlier.
78
9-6 Batch distillation
1. The Processes
• In many instances processes
are carried out in batches. In
these cases the whole of a
batch is run into the boiler of
the still and, on heating, the
vapor is passed into a
fractionation column, as
indicated in fig.9.16
steam
product
boiler
condensate
Fig.9.16. Column for batch distillation
79
2.The Futures
• When the still is operating, since the top product
will be relatively rich in the more volatile
component, the liquid remaining in the still will
become steadily weaker in this component. As a
result, the purity of the top product will steadily
fall. The processes are unsteady state.
80
• According to the purpose of operation, two methods of operation for batch distillation are used:
• One is constant composition of the top product,
the other is operating at constant reflux ratio
which allows the composition of the top product
to fall.
• One of the added merits of batch distillation lies
in the fact that more than one product may be
obtained. The method of operating is particularly
useful for handing small quantities of multicomp-onent organic mixture.
81
9-7 Azeotropic And Extractive Distillation
• When the relative volatility of a mixture is equal or
vary close to the unity, the enrichment of the volatile
component either does not take place or take place so
slowly so that the mixture can not be separated into
the several components by the common distillation.
• For instance, a mixture of
alcohol and water, the concentration of alcohol reaches
A
96% by mass. The concentration of the vapor equals
that of the liquid, and no
further enrichment occurs.
Mol fraction of alcohol in liquid x
82
• This mixture is called azeotrope, and cannot be
separated by straightforward distillation.
• The equilibrium curve crosses the diagonal at A.
• The second type of problem occurs where the
rel-ativity of a binary mixture is very low, in
which case continuous distillation of the mixture
to give nearly pure product will required high
reflux ratios with corresponding high heat
requirements, in addition, it will necessitate a
tower of larger crosssection containing many
trays.
83
• The principle of azeotropic distillation lies in the
addition of a new substance to the mixture so as
to form an azeotrope with one or more of the components in the mixture and as a result is
present on the most of the plates of the column
in appreciable concentration. The minimum
boiling point ternary azeotrope is taken
overhead, and such substance is called
entrainer.
84
• The principle of extraction distillation lies in the
addition of new material to the mixture so as to
increase the relativity of the two key
components, and thus make separation
relatively easy. Furfural, which is a highly polar
solvent, lowers the activity of butadiene more
than it does for butane or butanes and alters the
relativity of the key components. The thirdly
additional material is termed solvent.
85
9-8 Plate Efficiency
1.Overall efficiency of the column
• The number of ideal stages required for a
desired separation may be calculated by one of
the methods previously discussed but in
practice it will normally be found that more trays
are required than ideal stages. Then the ratio
n the numberof ideal stages
E
100%
n p the numberof actual trays
(9.50a)
• represents the overall efficiency E of the column,
which may vary from 30 to 100 per cent. The
main reason for loss in efficiency is that the
kinetics
86
• for the rate of approach to equilibrium, and the
flow pattern on the plate, may not permit equilib
-rium between the vapor and liquid to be
attained. Some empirical equations have been
developed from which values of efficiency may
be calculated, but it is a considerable value.
• Murpheree suggested that the proportion of
liquid and vapor, and the physical properties of
the mixtures on the trays will vary up the column,
so the efficiency of individual plate is different
each other, and conditions on individual trays
must be examined.
87
2.Murphree plate efficiency
• The ratio of the actual change (yn-yn+1) or (xn-1-xn)
in composition achieved to
ideal change in composition
yn-1
is known as the Murphree
Plate n-1
plate efficiency, denoted for
yn
xn-1
vapor
Plate n
yn  yn1
xn
EMv 
(9.50)
yn+1
yn,e  yn1
Plate n+1
• For liquid
xn1  xn
Eml 
xn1  xe,n
xn+1
(9.51)
88
• where ye,n is the composition of the vapor that
would be in equilibrium with the liquid of actual
composition xn leaving plate n.
3. Factors influencing plate efficiency
• (1) plate operate properly.
• (2) rate of mass transfer, depends on the flow
parameter F
89