Distillation
by Manuel De Guzman
J6 DISTILLATION
J6.1 Introduction
Distillation is defined as an equilibrium-staged separation process in which a liquid or vapor
mixture or both, containing two or more components, is separated into its component fractions
of desired purity by the application and removal of heat. This process is based on the
equilibrium stage concept, which means that vapor and liquid streams, after contacting each
other, leave a stage or unit saturated with the more volatile component (has lower boiling
point) and the less volatile component (has higher boiling point), respectively. The separating
agent for distillation is heat, and the mechanism of distillation is by the addition of heat.
The important variables that affect phase equilibrium (Fig. J6-1) in distillation are
temperature, pressure, and concentration.
vapor
A
B
A
B
liquid
Fig. J6-1: Phase equilibrium for binary system
Where A = more volatile component
B = less volatile component
Raoult’s law, an ideal law, can be defined for vapor-liquid phases in equilibrium.
PA = PA x A
where
(J6-1)
PA = partial pressure of component A
PA = vapor pressure of pure component A
xA = mole fraction of component A in liquid phase
Gibbs phase rule restricts equilibrium in vapor-liquid systems, as follows:
F=C–P+2
where
F
C
P
2
(J6-2)
= number of variants or degrees of freedom
= number of total components
= number of phases at equilibrium
= refers to temperature and pressure variables
The separation of one or more components from a mixture by distillation, a liquid-vapor
contacting system, involves both mass and heat transfer. As such, the calculation tools for
solving distillation problems are material and energy balances and vapor-liquid equilibrium
relationship. Sources of equilibrium data for distillation include the following:
J6-1
Distillation
by Manuel De Guzman
1.
2.
3.
4.
5.
6.
Vapor pressure data for pure components
Vapor pressure-temperature data using Antoine equation
Boiling point diagrams
Equilibrium curves
Relative volatilities
Distribution or partition coefficients using dePriestier charts
J6.1.1 Vapor Pressure Data for Pure Components
The compositions of vapor and liquid at equilibrium for a binary system can be expressed as
follows:
yA =
where
y
x
P
P
PA
xA
P
or
yB =
PB
xB
P
(J6-3)
= mole fraction of component A or B in vapor phase
= mole fraction of component A or B in liquid phase
= vapor pressure of pure component A or B at a given temperature
= total pressure
Equation (J6-3) is obtained by combining Raoult’s law (J6-1) and the relation (J6-4) that
states that the partial pressure of a component in an ideal gas or vapor is proportional to its
mole fraction.
PA = y A P
or
PB = y B P
(J6-4)
The relationship between xA and xB and between yA or yB is obtained from the sum of the mole
fractions of components A and B being equal to unity.
xA + xB = 1
and
yA + yB = 1
(J6-5)
J6.1.2 Vapor Pressure-Temperature Data using Antoine Equation
Antoine equation (J6-6) is useful in estimating the vapor pressure of a component at a given
temperature.
ln ( P  ) = A +
B
C +T
(J6-6)
where A, B, and C = constants
T = temperature
The vapor pressure ( P  ) calculated from equation (J6-6) can be substituted in equation (J6-3)
to get yA or yB.
J6-2
Distillation
by Manuel De Guzman
J6.1.3 Boiling-Point Diagrams
The vapor-liquid equilibrium relations for a binary mixture of components A and B are
usually given as boiling-point diagram at a given total pressure (Fig. J6-2). The upper curve is
the saturated vapor curve or the dew-point curve, and the lower curve is the saturated liquid
curve or the bubble-point curve. The area enclosed by these curves is the two-phase region.
The area above the upper curve is the vapor region, whereas the area below the lower curve is
the liquid region.
120
vapor region
saturated
vapor curve
Temperature, °C
110
vapor-liquid
mixture region
100
T
90
saturated
liquid curve
80
liquid region
70
xA
0
0.2
yA
0.4
0.6
0.8
1
Mole fraction A in liquid or vapor, xA or yA
Fig. J6-2: Boiling-point diagram
From the above boiling-point diagram, the equilibrium values of xA and yA at a given
temperature (T) can be read with the lower and upper curves, respectively, as indicated by
broken lines.
J6.1.4 Equilibrium Curves
A common method of plotting vapor-liquid equilibrium data is the so-called xy plot (Fig. J63). The equilibrium values of x and y at different temperatures, read from the boiling-point
diagram (Fig. J6-2), will result in a plot of equilibrium curve, as shown in Fig. J6-3.
J6-3
Distillation
by Manuel De Guzman
Mole fraction A in vapor, yA
1
0.8
equilibrium
curve
0.6
diagonal
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
Mole fraction A in liquid, xA
Fig. J6-3: Equilibrium diagram
J6.1.5 Relative Volatilities
By definition, the volatility of a component is the ratio of its partial pressure to its mole
fraction in the liquid.
volatility =
P
x
(J6-7)
Relative volatility, as a source of equilibrium data, is particularly useful in distillation
calculations. It is the ratio of the volatility of the more volatile component to that of the less
volatile component. Therefore, the relative volatility of the more volatile component (A) with
respect to the less volatile component (B) is
α AB =
( P x)A
( P x)B
(J6-8)
For ideal systems, pressure fraction equals mole fraction, i.e.,
PA Ptotal
y
= A
PB Ptotal
yB
The relative volatiliy (α
(J6-9)
), since x B = 1 − x A and y B = 1 − y A , may then be expressed as
AB
J6-4
Distillation
by Manuel De Guzman
α AB =
( y x ) A = y A x B = y A (1 − x A )
( y x ) B x A y B x A (1 − y A )
(J6-10)
Dropping the subscripts A and B, we have
α=
y(1 − x )
x (1 − y )
(J6-11)
Separation by distillation is much easier if α > 1; the separation becomes difficult if the value
of α is close to 1.
If Raoult’s law (J6-1) is valid, the volatility is numerically equal to the vapor pressure of the
pure component (or volatility = P x = P ) for ideal systems. Thus, the relative volatility
(α AB) takes the form
α AB =
( P x)A
( P x)B
=
PA
PB
(J6-12)
J6.1.6 Distribution Coefficients
Equilibrium data for distillation can be obtained from the so-called equilibrium distribution
coefficient (K), which is defined as follows:
K=
y
x
(J6-13)
In general, K values depend on temperature, pressure, and composition. For many systems,
however, K values are approximately independent of composition.
J6.2 Types of Distillation
There are a number of ways by which distillation can be classified. Depending on the specific
purpose for which the separation technique is designed, the types of distillation basically can
be grouped into four categories.
1.
2.
3.
4.
According to the method of separation:
According to the nature of the process feed:
According to the method of operation:
According to the type of column internals:
simple
binary
batch
plate-type
or
or
or
or
J6.2.1 Distillation Methods of Separation
In practice, there are two main distillation methods of separation:
J6-5
fractional distillation
multicomponent distillation
continuous distillation
packed-type distillation
Distillation
by Manuel De Guzman
1. Distillation without reflux (= simple distillation)distillation in which no condensate is
allowed to return to the single-stage still pot to contact the rising vapors
2. Distillation with reflux (= fractional distillation)distillation in which a portion of the
condensate is allowed to return to the distilling column to contact the rising vapors
J6.2.2 Number of Components in Distillation
The feed introduced to and processed in the distilling column may consist of two or more
components. We have a binary distillation if the number of components present in the feed
mixture is limited to two, and we have a multicomponent distillation if there are more than
two components in the feed mixture.
J6.2.3 Distillation Methods of Operation
Basically, there are two distillation methods of operation:
1. Batch distillation
In batch distillation, the process is carried out in separate runs; the more volatile
component is evaporated from the still pot, and distillation is continued as long as the
change in the concentration of the more volatile component in the distillate is still
significant. Batch distillation is advantageous if small quantities of mixtures or varying
product compositions are required, if smaller number of plates is used, and if high purity
of the product is not desired.
2. Continuous distillation
In continuous distillation, there is a steady input of feed to the distilling column and a
continuous withdrawal of streams of constant composition from the top and bottom of the
column. In terms of lowest operating costs, continuous distillation is advantageous if a
large number of plates are used and the reflux ratio approaches the minimum value.
J6.2.4 Distillation Calculation Methods
There are two types of distillation columnsstaged and packed columns. For staged
distillation columns, calculations are of the equilibrium-based method; for packed distillation
columns, calculations are of the rate-based method.
1. Staged columns in distillation
Distillation may be carried out in staged or plate columns in which each plate provides
intimate contact between vapor and liquid in continuous countercurrent flow. Each plate
constitutes a single stage where there is simultaneous partial condensation of vapor and
partial vaporization of liquid.
J6-6
Distillation
by Manuel De Guzman
2. Packed columns in distillation
Distilling columns dumped with packing material is an alternative arrangement to plate
columns. The packing material provides high interfacial area for the exchange of the
components between the vapor and liquid phases. A true countercurrent flow of vapor and
returning liquid (reflux) occurs in packed columns, in contrast to the stage-to-stage flow in
plate columns.
Packed columns are used for smaller diameter columns since it is expensive to build a
staged column that will operate properly in small diameters. Packed towers have the
advantage of a smaller pressure drop and are, therefore, useful in vacuum fractionation.
Another advantage of packed columns is that they can be used to process corrosive
materials.
J6.3 Simple Distillation
There are three important types of distillation that occur in a single-stage still pot and that do
not involve rectificationsimple batch or differential distillation, equilibrium or flash
distillation, and simple steam distillation.
J6.3.1 Differential or Simple Batch Distillation
In simple batch or differential distillation, the compositions of distillate and bottoms change
with time; the total amounts and average compositions of distillate and bottoms are, therefore,
of more importance than the flow rates.
Consider a liquid charge L1 in the still pot, with a composition x1 of the more volatile
component, A, as in the following diagram:
Vapor
V, y
condenser
Distillate
D, xD
L2, x2
still pot
Fig. J6-4: Differential or simple batch distillation
where L2
V
D
x2
y
xD
= liquid remaining in still pot at any time
= vapors produced at any time
= distillate collected at any time
= instantaneous concentration of A in liquid remaining in still pot
= instantaneous concentration of A in vapors produced
= average concentration of A in distillate
J6-7
Distillation
by Manuel De Guzman
If an amount dL, with a composition y of the more volatile component, is vaporized, then a
material balance on the more volatile component gives
ydL = d ( xL ) = Ldx + xdL
L2
⌠

⌡L1
(J6-14)
x
2
dL
dx
⌠
=
L
y
−x
⌡x 1
(J6-15)
x
2
L
dx
⌠
ln 2 = 
L1 ⌡x 1 y − x
(Rayleigh equation)
(J6-16)
This resulting Rayleigh equation is integrated graphically using the equilibrium y vs x data.
There are, however, simplified forms of the Rayleigh equation:
1. If over the range concerned, the equilibrium relationship is a straight line ( y = mx + b )
1 ( m −1)
L2  y2 − x 2 

=
L1  y1 − x1 
or
 L2 
 
 L1 
m −1
=
y2 − x 2
y1 − x1
(J6-17)
where m = slope
2. If Henry’s law applies (for dilute solutions)
L 
x 
1
ln  2  =
ln  2 
 L1  H′ − 1  x1 
H′ = Henry’s law constant = H/P
where
3. If the relative volatility α =
(J6-18)
y(1 − x )
αx
, from which y =
, may be assumed
(
α
−
1) x + 1
x (1 − y )
constant over the range concerned
•
In terms of concentration
(1 − x 2 ) L 2
(1 − x1 ) L1
or
•
1α
x L 
=  2 2 
 x1L1 
Note: α = α1α2
(J6-19)
L 
 x (1 − x1 ) 
 1 − x1 
1

ln 2  =
ln  2
+ ln

(
)
L
α
−
1
x
1
−
x
1
−
x
2 
2
 1
 1

(J6-20)
In terms of components
A 
B 
ln 1  = α ln 1 
 A2 
 B2 
J6-8
Note: α = αAB αAB
1
2
(J6-21)
Distillation
by Manuel De Guzman
J6.3.2 Equilibrium or Flash distillation
In flash distillation, the feed stream passes through a valve to reduce its pressure before it is
introduced or “flashed” into a drum where part of the feed stream vaporizes, and the resulting
vapor and liquid in equilibrium with each other are separated. The system is called “flash”
distillation because the feed, after entering the drum, vaporizes very rapidly.
Consider the following flash drum:
Vapor
V, y
Feed
F, xF
Liquid
L, x
Fig. J6-5: Flash distillation
For a binary system subjected to flash distillation, an overall mass balance gives
F =V +L
where
(J6-22)
F = feed
V = vapor
L = liquid
and on the more volatile component
x F F = yV + xL
(J6-23)
where xF = fraction of more volatile component in feed
y = fraction of more volatile component in vapor
x = fraction of more volatile component in liquid
Therefore,
V xF − x
=
F
y −x
If we let f be the fraction of feed vaporized (=
y=−
V F ),
1−f
x
x+ F
f
f
(J6-24)
the above equation becomes
(equation of a straight line)
J6-9
(J6-25)
Distillation
by Manuel De Guzman
A graphical solution to flash distillation problems constitutes a plot of equation (J6-25) in an
xy equilibrium plot (Fig. J6-6) and its intersection with the equilibrium line, whose
coordinates are x and y (indicated by broken lines). Or we can have an analytical solution by
trial-and-error method, since there are four unknowns (V, L, y, and x), and only three
equations are availabletwo material balances, (J6-22) and (J6-23), and the equilibrium
relationship between y and x.
Mole fraction A in vapor, yA
1
equilibrium
curve
0.8
y
1 −f
slope = −
f
0.6
0.4
0.2
x
0
0
0.2
0.4
0.6
0.8
1
Mole fraction A in liquid, xA
Fig. J6-6: Plot of solution to flash distillation
J6.3.3 Simple Batch Open Steam Distillation
In simple batch open steam distillation, steam is injected directly into the still pot. The reasons
for adding steam directly to the still pot are that it keeps the temperature below the boiling
point of water, which is good for heat-sensitive components, and it does not anymore require
heat transfer surface area.
The general equation for simple batch open steam distillation is as follows:
 nA 

P − εPA 
n A + n C 
dnS

−
=
dn A
 nA 

εPA 
n
+
n
A
C


where
or
S = open steam
J6-10
−
 n P 1
dn S  P
=   − 1 + C 
(J6-26)
dn A  εPA
 εPA n A
Distillation
by Manuel De Guzman
A = volatile component
C = nonvolatile impurity
n = moles
ε = correction factor if vapor deviates from ideal behavior
PA = vapor pressure of volatile component
P = total pressure
Equation (J6-26) takes different forms depending on the following cases:
1. Dissolved nonvolatile impurity is present in large amounts
 P

n P  nA
n S =   − 1 n A1 − n A 2 + C  ln 1
εPA  n A 2
 εPA 
(
where
)




n A1
= initial moles of volatile component in still pot
nA2
= final moles of volatile component in still pot
(J6-27)
2. Dissolved nonvolatile impurity is negligible
nS
P − εPA
=
n A1 − n A 2
εPA
where
mS
MS
mA
MA
or
mS P − εPA M S
=
mA
εPA M A
(J6-28)
= mass of steam
= molar mass of steam
= mass of volatile component distilled
= molar mass of volatile component
J6.4 Fractional Distillation
The industrial distillation column is a series of units in which two processes of partial
vaporization and partial condensation occur simultaneously. The liquid from a stage flows
down to the next stage where it is contacted with the rising vapor. This contact of liquid and
vapor flowing countercurrently with each other is repeated within the entire distilling column.
In analyzing the distilling column for calculation purposes, it may be divided into three
sections, as indicated in Fig. J6-7.
condenser
L0
Ln, xn
Feed
F, xF
n
Vn+1, yn+1
J6-11
Distillate
D, xD
Distillation
by Manuel De Guzman
m
Vm+1, ym+1
Lm, xm
reboiler
Bottoms
B, xB
Fig. J6-7: Fractional distillation column
Material balances can be made about each of the above three sections of the distilling column,
resulting in operating-line equations that relate the concentrations of the vapor and liquid
streams passing each other in each stage. An overall material balances at the top section of the
column gives the rectifying operating line; balances at the bottom section gives the stripping
operating line; and balances at the feed stage gives the feed line equation.
With these operating lines, the calculation of the amounts of streams entering and leaving the
column can be made. Calculations can be graphical using the McCabe-Thiele method
(sections J6.5 and J6.6) or the Ponchon-Savarit method (section J6.7), or they can be
analytical using the stage-to-stage method.
J6.4.1 Rectifying Operating Line
An overall material balance at the top section of the distilling column gives
Vn +1 = L n + D
(J6-29)
A total material balance on the more volatile component is given by
y n +1Vn +1 = x n L n + x D D
(J6-30)
From these two material balances, the following rectifying operating line equation results:
y n +1 =
Ln
x D
xn + D
Ln + D
Ln + D
(J6-31)
Equation (J6-31) is commonly expressed in terms of the reflux ratio R ( = L 0 D ), as follows:
y n +1 =
R
x
xn + D
R +1
R +1
J6.4.2 Stripping Operating Line
J6-12
(J6-32)
Distillation
by Manuel De Guzman
An overall material balance at the bottom section of the distilling column gives
Vm +1 = L m − B
(J6-33)
A total material balance on the more volatile component is given by
y m +1Vm +1 = x m L m − x B B
(J6-34)
From these two material balances, the following stripping operating line equation results:
y m +1 =
Lm
x B
xm − B
Lm − B
Lm − B
(J6-35)
J6.4.3 Feed Line
An overall material balance at the feed section of the distilling column gives
F + Vm +1 + L n = Vn +1 + L m
(J6-36)
A total material balance on the more volatile component is given by
x F F + y m +1Vm +1 + x n L n = y n +1Vn +1 + x m L m
(J6-37)
From these two material balances, the following feed line equation results:
y m +1Vm +1 − y n +1Vn +1 = x m L m − x n L n − x F ( Vn +1 − Vm +1 + L m − L n ) (J6-38)
Another form of equation (J6-38), in terms of the liquid content of the feed, q, is given as
follows:
y=
x
q
x− F
q −1
q −1
(feed line or q-line)
(J6-39)
J6.5 McCabe-Thiele Method
The graphical solution for fractional distillation problems developed by McCabe and Thiele is
based on the following assumptions:
1. There are no heat losses in the distilling column or the column is adiabatic.
2. The specific heat changes are negligible compared to latent heat changes.
3. The heat of vaporization per mole is constant; that is, the effect of concentration on the
molal latent heat of vaporization is insignificant.
The last assumption is the statement of constant molal overflow (CMO) and is the most
important.
J6-13
Distillation
by Manuel De Guzman
It follows from the assumption of CMO for the McCabe-Thiele method that the V’s above the
feed or in the upper section of the distilling column are equal to each other, which means that
the L’s are also equal to each other; the same is true for the V’s and the L’s below the feed or
in the lower section.
The McCabe-Thiele method makes use of an xy diagram on which the following are plotted:
diagonal, equilibrium data, and operating linesthree straight lines that represent the entire
distilling column.
These three operating lines for the McCabe-Thiele y-x diagram have the following forms:
1. Rectifying operating line  this equation given in (J6-31) is commonly expressed in terms
of the reflux ratio R ( = L 0 D ), as follows:
y n +1 =
R
x
xn + D
R +1
R +1
(J6-32)
2. Stripping operating line  this equation given in (J6-6), with the assumption of CMO,
becomes
y m +1 =
L
x B
xm − B
L−B
L−B
(J6-40)
3. Feed  together with equations (J6-41) and (J6-42) from the definition of q (quality of
feed or its liquid content),
L m = L n + qF
Vn = Vm + (1 − q ) F
(J6-41)
(J6-42)
material balances made at the feed stage (final form is given in equation (J9-38)), noting
that the feed line will intersect the rectifying and stripping operating lines at common
values of y and x, will give the following form of the feed line equation:
y=
x
q
x− F
q −1
q −1
(feed line or q-line)
(J6-39)
The feed entering the distilling column may have different conditions, as follows:
Feed Condition
subcooled
liquid
saturated
liquid
q
q-line slope
>1
>1
slant upward to the right,
1st quadrant
=1
=∞
vertical
J6-14
Distillation
by Manuel De Guzman
wet
vapor
saturated
vapor
superheated
vapor
between 1
= negative
and 0
slant upward to the left,
2nd quadrant
=0
=0
horizontal
<0
between 1
and 0
slant downward to the left,
3rd quadrant
The above description of the McCabe-Thiele method can be visualized in Fig. J6-8.
1
Mole fraction A in vapor, yA
equilibrium
curve
0.8
3
5
rectifying
operating line
6
0.4
1
4
q-line
0.6
2
7
8
0.2
10
stripping
operating line
9
xB
0
0
xF
0.2
xD
0.4
0.6
0.8
1
Mole fraction A in liquid, xA
Fig. J6-8: McCabe-Thiele diagram
The above McCabe-Thiele diagram is used in determining graphically the total number of
stages for a given distillation operation. This is done by stepping off alternating horizontal and
vertical lines, with the operating lines and the equilibrium curve as boundaries, from xD to xB.
Each step represents a stage, and as shown in Fig. J6-8, the total theoretical number of steps
or stages is 9.6.
J6.5.1 Total Reflux for McCabe-Thiele Method
At total reflux,
R=
L 0 L0
=
=∞
D ≈0
And the y-intercept of the rectifying operating line becomes 0.
J6-15
(J6-43)
Distillation
by Manuel De Guzman
xD
x
= D =0
R +1 ∞ +1
(J6-44)
Therefore, the overall operating line is the 45º diagonal line. This results in the number of
stages N being minimum.
at total reflux ( R = ∞ ), → the number of stages N = N min
1
(J6-45)
1
Mole fraction A in vapor, yA
2
0.8
3
0.6
4
45° line
0.4
5
6
0.2
7
8
0 xB
0
xF
0.2
xD
0.4
0.6
0.8
1
Mole fraction A in liquid, xA
Fig. J6-9: Minimum number of stages by McCabe-Thiele method
As indicated in Fig. J6-9, the minimum theoretical number of stages is 7.1. This number is
based on stepping off horizontal lines then vertical lines, with the diagonal and the
equilibrium curve as boundaries, from xD to xB.
J6.5.2 Minimum Reflux Ratio for McCabe-Thiele Method
The minimum reflux ratio is one of the limiting operating conditions for distillation. It is a
useful hypothetical concept, which refers to the smallest amount of returning liquid to the top
of the column, at which the desired separation could just be obtained with an infinite number
of stages.
at R = R min , → the number of stages N = ∞
(J6-46)
For an ideal equilibrium curve, the graphical representation on the McCabe-Thiele diagram of
an infinite number of stages, as shown in Fig. J6-10, is the intersection of the rectifying
J6-16
Distillation
by Manuel De Guzman
operating line and the feed line at the equilibrium curve. This point of intersection is called
the pinch point.
y-intercept for
Rmin
Mole fraction A in vapor, yA
1
0.8
0.6
pinch
point
0.4
0.2
0
xB
0
xD
xF
0.2
0.4
0.6
0.8
1
Mole fraction A in liquid, xA
Fig. J6-10 Minimum reflux ratio for ideal system by McCabe-Thiele method
To have an infinite number of stages for a nonideal equilibrium curve, the rectifying operating
line must touch the equilibrium curve at the point of tangency, as illustrated in Fig. J6-11.
This point is called the pinch point at which the compositions of vapor and liquid do not vary
from stage to stage.
J6-17
Distillation
by Manuel De Guzman
y-intercept for
Rmin
Mole fraction A in vapor, yA
1
pinch
point
0.8
0.6
0.4
0.2
0
xB
0
xD
xF
0.2
0.4
0.6
0.8
1
Mole fraction A in liquid, xA
Fig. J6-11 Minimum reflux ratio for nonideal system by McCabe-Thiele method
J6.5.3 Optimum Feed Plate for McCabe-Thiele Method
The optimum feed plate location results in the fewest number of plates in the distilling
column. On the McCabe-Thiele diagram given in Fig. J6-8, this location is the step with one
end at the rectifying operating line and the other end at the stripping operating line. From Fig.
J6-8, the optimum feed plate is the 6th plate from the top of the column.
J6.6 Variation of Conditions for Fractionation using McCabe-Thiele
Method
J6.6.1 Two-Feed Stream Distillation
In distillation with two feeds, the overall operating line includes a third operating line in
addition to top and bottom operating lines. This third line is the middle operating line, which
can be obtained by making material balances around the upper section of the distilling column
that includes the first feed stream (positioned above the second feed stream).
J6.6.2 Distillation with Side Stream
If a product of intermediate composition is required, a side stream may be withdrawn. Three
additional variables are necessary, such as flow rate, type of side draw (vapor or liquid), and
location or composition. The operating line for the middle section can be derived from
J6-18
Distillation
by Manuel De Guzman
material balances around the upper or lower section of the distilling column that includes the
side stream.
J6.6.3 Partial Condensers
A partial condenser converts only part of the overhead vapor stream to liquid and returns this
liquid as reflux. The remaining vapor is withdrawn as the distillate product. The partial
condenser acts as one equilibrium stage.
J6.6.4 Total Reboilers
A total reboiler converts all the liquid from the bottom of the distilling column to vapor,
which, in turn, is returned to the bottom of the column. The material balances and the bottom
operating line with a total reboiler are exactly the same as with a partial reboiler. The only
difference is that a total reboiler is not an equilibrium stage.
J6.7 Ponchon-Savarit Method
If the assumption of constant molal flow of McCabe-Thiele method is no longer valid, the
solution to distillation problems is to solve material and energy balances simultaneously on
each stage in the distilling column. This solution can be done graphically by Ponchon-Savarit
method (Fig. J6-12), in which enthalpy-compositions are used, enthalpy being the vertical
axis and composition the horizontal axis.
Enthalpy of mixture, H or h (kJ/kmol)
40000
H vs yA (saturated vapor)
30000
20000
tie line
10000
h vs yA (saturated liquid)
0
0
0.2
0.4
0.6
0.8
1
Mole fraction A in liquid or vapor, xA or yA
Fig. J6-12 Ponchon-Savarit enthalpy-concentration diagram
J6-19
Distillation
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Fig. J6-12 shows the enthalpy-concentration plot for a binary vapor-liquid mixture of A and B
at a given constant pressure. The plot is based on arbitrary reference states of liquid and
temperature, and it considers latent heats, heats of solution or mixing, and sensible heat of the
components of the mixture.
J6.8 Analytical Calculation Methods for Distillation
J6.8.1 Total Reflux Ratio
If the relative volatility, α , of a binary mixture is approximately constant, the following
Fenske equation can be used to calculate the minimum number of stages when a total
condenser is used:
 x 1 − xB 

log  D
1 − x D x B 

Nm =
log α
where
Note:
α = αtop αbottom
(J6-47)
Nm = minimum number of stages
α top = relative volatility at top temperature
α botto = relative volatility at bottoms temperature
m
J6.8.2 Minimum Reflux Ratio
For ideal mixtures, or if the relative volatility, α , of a binary mixture could be taken as
constant, Rm may be obtained analytically using the Underwood equation as follows:
Rm =
1  x D α (1 − x D ) 
−
α − 1  x F
1 − x F 
(J6-48)
where Rm = minimum reflux ratio
J6.9 Complex Distillation Methods
Complex mixtures constitute less ideal mixtures, and their equilibrium data deviate from ideal
behavior. The methods for separating complex mixtures are azeotropic and extractive
distillation.
J6.9.1 Azeotropic Distillation
Azeotropic distillation is based on the addition of a new substance to the mixture to increase
the relative volatility of the two key components, and thus make the separation relatively
easy.
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Distillation
by Manuel De Guzman
J6.9.2 Extractive Distillation
With extractive distillation, the substance added is relatively nonvolatile compared with the
components to be separated.
J6.10 Multicomponent Distillation
The process of multicomponent distillation involves the separation of more than two
components from a mixture. The general principles of design of multicomponent distillation
columns are similar in many respects as to those described for binary systems. There is one
material balance for each component in the multicomponent mixture. Enthalpy or energy
balances are made, which are similar to those for binary case. Equilibrium data are used to
determine boiling points and dew points.
J6.11 Packed Columns for Distillation
The process of distillation in packed columns is one of continuous countercurrent mass
transfer. As mentioned in section J6.2.4, the method of calculations for packed distillation
columns is rate-based, i.e., calculations are based on mass transfer rate equations.
Although packed towers have continuous contact of vapor and liquid, they can be analyzed
like staged towers in which contact between vapor and liquid is discontinuous. The
assumption is that the packed column could be divided into segments of equal height. Each
segment is taken as an equilibrium stage where leaving streams of vapor and liquid are in
equilibrium with each other. This staged model is only fictitious, but the model can be useful
for the purpose of designing packed columns.
The height of each imaginary stage is referred to as the height equivalent to a theoretical plate
(HETP).
HETP =
height of packing
number of theoretic al stages
(J6-49)
The number of theoretical stages is calculated using the McCabe-Thiele or Ponchon-Savarit
graphical method.
J6-21