Distillation

Distillation
Distillation may be defined as the separation of the
components of a liquid mixture by a process involving
partial vaporization. The vapor evolved is usually
recovered by condensation.
Volatility
The volatility of any substance in a liquid solution may
be defined as the equilibrium partial pressure of the
substance in the vapor phase devided by the mole
fraction of the substance in the liquid solution:
p
v a  volatility of component a in a liquid solution = a
xa
The volatility of a material in the pure state is equal to
the vapor pressure of the material in the pure state.
Similarly, the volatility of a component in a liquid
mixture which follows Raoult’s law must be equal to the
vapor pressure of that component in the pure state.
Relative volatility
In order to determine the possible extent of separation
between the components of a mixture by the use of
distillation, it is neccessary to know the relative ease of
vaporization of the individual components. Hence we
introduce a Relative volatility (), which is defined as
the volatility of one component of a liquid mixture
divided by the volatility of another component of the
liquid mixture.
Usually Relative volatilities are
expressed with the higher of the two volatilities in the
numerator.
v
p x
(1)
 ab  a  a b
vb xa pb
If
the
vapors
follow
Dalton’s
law,
pa  ya P & p b  y b P
where P is the total pressure of the vapors, then
y x
(2)
 ab  a b
yb xa
This is often given as the definition of relative volatility,
it can be calculated directly from vapor-liquid
equilibrium data.
For binary mixtures, y b  1  y a & x b  1  x a , hence
x a
(3)
ya 
1    1x a
xa 
49
ya
  1   y a
(4)
50
Ignoring the
rearranging,
Simple Batch (differential) Distillation
double
derivative
term
dxdL
and
7
1. Liquid is charged to a
heated kettle
2. The liquid charge is
boiled slowly
3. The vapors are
withdrawn as quickly as
they form to a
condenser
4. The condensed vapor
(distillate) is collected
Integrating,
ln
8
where L1 is the original moles charged, L2 the moles left
in the still, x1 the original composition, and x2 the final
composition of liquid. Equation (8) is known as the
Rayleigh equation.
The first portion of vapor condensed will be richest in
the more volatile component A. As vaporization
proceeds, the vaporized product becomes leaner in A.
i.e., the composition changes with time.
The total mole amount in the liquid is L with the molol
fraction of A being x. Assume a small amount of dL is
vaporized so that the composition of the liquid changes
from x to (x-dx) and the amount of liquid from L to (LdL). Let y be the composition of A in the vapor.
The material balance of A gives
xL = (x-dx)(L-dL) + ydL
Expanding the right side, we have
xL = xL – xdL – Ldx +dxdL +ydL
51
(5)
(6)
The equilibrium curve gives the relationship between y
and x. Then the integration of Rayleigh equation can be
done numerically or graphically between x1 and x2.
The average composition of total material distilled, yav,
can be obtained using the material balance:
L1x1 = L2x2 + V yav
(9)
(10)
V = L1 – L2 = moles distilled
Example D1: A mixture of 100 mol containing 50
mol % n-pentane and 50 mol % n-heptane is distilled
under differential conditions at 101.2 kPa until 40 mol is
distilled. What is the average composition of the total
vapor distilled and the composition of the liquid left?
The equilibrium data are as follows, where x and y are
mole fractions of n-pentane:
1 0.867 0.594 0.398 0.254 0.145 0.059 0
x
y
1 0.984 0.925 0.836 0.701 0.521 0.271 0
52
Solution: The given values for the Rayleigh equation are
L1 = 100 mol, x1 = 0.50, L2 = 60 mole, V = 40 mol.
.
100
ln
0.510
60
The unknown is x2. To solve this by numerical
integration, the equilibrium relationship is converted to
the function of 1/(y-x) vs x as the following figure.
1 0.867 0.594 0.398 0.254 0.145 0.059 0
x
1 0.984 0.925 0.836 0.701 0.521 0.271 0
y
8.547 3.021 2.283 2.237 2.660 4.717
1/(y-x)
Flash (single stage, continuous) Distillation
Flash distillation vaporizes a definite fraction of the
liquid, the evolved vapor is in equilibrium with the
residual liquid, the vapor is separated from the liquid and
condensed.
Plant for flash distillation.
The integration is done graphically from x1 = 0.5 to x2
such that the integral (shaded area) = 0.510. Hence x2 =
0.277. Substituting into Eq. (5) to solve for the average
composition of the 40 mol distilled,
100(0.50) = 60(0.277) + 40 yav
yav = 0.835
Consider 1 mole of a binary mixture fed to the above
equipment. By a material balance for the more volatile
component, we have
x F  fy D  (1  f )x B
(11)
where
xF = concentration (mole fraction) of A in the feed
yD and xB = concentrations of A in the vapor and
liquid
53
54
f = V/F = the molal fraction of the feed to be
vaporized
V = moles per hour of vapor
F = moles per hour of feed
L = F – V = moles per hour of liquid
Example D2: A mixture of 50 mole percent benzene
and 50 mole percent toluene is subjest to flash
distillation at a separator pressure of 1 atm. The vaporliquid equilibrium curve and boiling-point diagram are
given below.
Both yD and xB are unknown, but they are on the
equilibrium curve.
In general we have the following operating equation for
flash distillation by rearranging eq. (11):
x
f 1
y
x F
(12)
f
f
which passes the point (xF, xF).
Boiling-point diagram (system of benzene-toluene at 1
atm).
Plot the following quantities, all as functions of f, the
fractional vaporization:
(a) the temperature in the separator
(b) the composition of the liquid leaving the separator
(c) the composition of the vapor leaving the separator
55
56
Solution:
For each value of f, the corresponding quantity of [(f1)/f] is calculated, which is the slope of the operating
line. By using this slope and the point (xF, xF), one
straight operating line can be drawn on the x-y diagram.
different values of f, the solutions can be found. The
results are given in the following figure and table.
Equilibrium curve, system of benzene-toluene.
The coordinate of the intersection of the equilibrium and
operating lines gives the compositions of the leaving
liquid and vapor as (x, y). From the value of x or y the
temperature in the separator can be obtained from the
boiling-point diagram. By doing this procedure for
57
58
Continuous Distillation with Reflux (Rectification)
Flash distillation is not effective in separating
components of comparable volatility, or in obtaining
nearly pure components.
Rectification on an ideal
plate.
Vapor leaving plate n = yn
Liquid leaving plate n = xn
Vapor enterrng plate n = yn+1
Liquid entering plate n = xn-1
yn+1 is in contact (same
position) with xn
For an ideal plate, yn is in
equilibrium with xn
Distillation Trays
Allows efficient
mixing of vapor and
liquid enabling
rapid equilibration
Combination of rectification and stripping.
If we want to obtain both near pure top and bottom
products, the feed plate has to be in the central portion of
the column. The bottom is called the reboiler.
Rectification in the section below the feed plate is called
stripping, the bottom product can be nearly pure B.
59
Rectifying (enriching) section: all plates above the feed.
Stripping section: all plates below the feed, including the
feed plate itself.
Liquid flows down by gravity to reboiler. The bottom
product is withdrawn from the pool of liquid on the
downstream side of the weir and flows through the
cooler G.
60
The vapors rising through the rectifying section are
completely condensed in condenser C, and the
condensate is collected in accumulator D.
Distillation in the Enriching Section of Tower
A portion of liquid from the accumulator is returned to
the top plate, which is called reflux. It provides the
downflowing liquid. Without the reflux, no rectification
would happen in the rectifying section and the
concentration of the overhead product would be the
same as that of the vapor rising from the feed plate.
Condensate not returned to the top plate is cooled in heat
exchange E, called the product cooler, and withdrawn as
the overhead product.
Overal material balance for binary systems
Total material balance:
F=D+B
Component A balance:
FxF = DxD + BxB
(13)
(14)
Eliminating B gives
Material balances
Vn 1  Ln  D
Vn 1 yn1  Ln xn  Dx D
(15)
(16)
By rearranging Eq. (16) we obtain the operating line
L
Ln
Dx
Dx D
y n 1  n xn  D 
xn 
(17)
Vn 1
Vn 1 Ln  D
Ln  D
This is the operating line in the rectifying section.
Eliminating D gives
Net flow rate in the rectifying section
This is the overhead product, D = Va - La = difference
between the flow rates of vapor and liquid anywhere in
the upper section above n+1.
61
The reflux ratio, R = Ln/D. If R is constant, the operating
line will be straight on the y-x plot.
x
R
y n 1 
xn  D
(18)
R 1
R 1
62
The slope is Ln/Vn+1 or R/(R+1). It intersects the y = x
line (45o diagonal line) at x = xD. The intercept of the
operating line at x = 0 is y = xD /(R+1).
Distillation in the Stripping Section of Tower
The theoretical stages are determined by starting at the
operating line at xD and moving horizontally to intersect
the equilibrium line at x1. Then y2 is the composition of
the vapor passing the liquid x1. Similarly, other
theoretical trays are stepped off down the tower in the
enriching section to the feed tray.
Material balances
(19)
Lm  Vm 1  B
(20)
Lm x m  Vm 1 ym 1  Bx B
so that the operating line is
L
Lm
Bx
Bx B
y m 1  m xm  B 
xm 
(21)
Vm 1
Vm 1 Lm  B
Lm  B
This is the operating line in the stripping section.
If equimolal flow is assumed, Lm = LN = constant and
Vm+1 = VN = constant, Eq. (21) is a straight line when
plotted as y vs x, with a slope of Lm/ Vm+1. It intersects
the y = x line at x = xB.
The intercept at x =0 is y=-B xB/ Vm+1.
Again the theoretical stages for the stripping section are
determined by starting at xB, going up to intersect the
equilibrium line at yB, and then across to the operating
line at xN, and so on.
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64
Condenser and top plate
The material balance diagram for the top plate and
condenser is shown in the figure.
At the top plate, the composition is (xC, y1). The simplest
case is a total condenser, which condense all the vapor
so that the liquid has the same composition as the vapor.
Hence, xC = xD = y1. The enriching line starts with (xD,
xD), which is in the diagonal line. Triangle abc in the
figure represents the top plate.
65
Bottom plate and reboiler
The material balance diagram for the top plate and
condenser is shown in the figure.
The lowest point on the operating line for the column is
the bottom plate (xb, yr), which are the liquid
concentration leaving the bottom plate and the vapor
concentration leaving the reboiler. However, as shown in
the stripping section, the operating line can be extended
to cross the diagonal at point (xB, xB).
In a common
reboiler, the vapor
leaving the reboiler is in
equilibrium with the
liquid leaving as bottom
product.Then xB and yr
are in equilibrium curve,
and the reboiler acts as
an ideal plate. Triangles
cde and abc are the
reboiler and bottom
plates.
66
Effect of feed conditions
The condition of the feed stream F entering the tower
determines the relation between the vapor Vm in the
stripping section and Vn in the enriching section as well
as between Lm and Ln. If the feed is part liquid and part
vapor, the vapor will add to Vm to give Vn, and the liqud
will add to Ln to give Lm.
We define
1
1
(22)
Where HV is the enthalpy of the feed at the dew point,
HL the enthalpy of the feed at the boiling point (bubble
point), and HF the enthalpy of the feed at its entrance
conditions.
Feed conditions:
(a) cold liquid, q>1
(b) at bubble point
(saturated liquid),
q=1
(c) partial vapor,
0<q<1
(d) at dew point, q=0
(saturated vapor)
(e) superheated
vapor, q<0
q can also be considered as
the number of moles of
saturated liquid produced on
the feed plate by each mole
of feed added to the tower.
Lm = Ln + qF
(23)
Vn = Vm + (1 - q)F (24)
The point of intersection of the enriching and stripping
operating line equations on the y-x plot can be derived as
follows. Eqs. (16) and (20) can be rewritten as follows
without the tray subscripts:
Vn y  Ln x  Dx D
(25)
Vm y  Lm x  Bx B
(26)
Where the y and x values are the point of intersection of
the two operating lines. (25) - (26) gives
Vm  Vn  y  Lm  Ln x  Dx D  Bx B  (27)
Replacing by Eqs. (14), (23, (24), we have
(q-1)Fy = qFx – FxF
(28)
This is the q-line equation
and it passes the intersection
of the two operating lines.
The q-line has a slope of
q/(q-1) and passes through the
45o line at y = x = xF. The
right figure is an example of a
feed of part liquid and part vapor (0<q<1). First draw the
q-line, then the enriching line, the intercept of these two
lines can be used to draw the stripping line.
67
68
Lacation of the feed tray in a tower and number of
ideal plates; McCabe-Thiele method
To determine the number of theoretical trays needed in a
tower, the stripping and enriching lines are drawn to
intersect on the q line as follows.
In the above figure, the feed is part liquid and part vapor,
since 0<q<1. Hence, in adding the feed to tray 2, the
vapor portion of the feed is separated and added to
below plate 2 and the liquid added to the liquid from
above entering tray 2.
If the feed is all liquid, it should be added to the liquid
flowing to tray 2 from the tray above.
If the feed is all vapor, it should be added below tray 2
and join in the vapor rising from the plate below.
Since a reboiler is considered as a theoretical step, when
the vapor yB is in equilibrium with xB, the number of
theoretical trays in a tower is equal to the number of
theoretical steps minus one.
The value of q for cold liquid feed is
1
T –T
c
The value of q for superheated vapor feed is
1. Starting from the top at xD, the trays are stepped off
along the enriching line.
2. It is important to switch to the stripping line when the
triangle first passes the q line (intersection of the 2
operating lines), which is tray 2 in this case.
3. The trays are continued to step off along the stripping
line.
4. The number of theoretical trays required is 3.7 with
the feed on tray 2.
69
0
T –T
c
where
cpL = specific heat capacity of feed liquid
cpV = specific heat capacity of feed vapor
TF = temperature of feed
TB = bubble point of feed
TD = dew point of feed
70
Example D3. Rectification of a benzene-toluene
mixture
A liquid mixture of benzene-toluene is to be distilled in a
fractionating tower at 101.3 kPa pressure. The feed of
100 kmol/h is liquid, containing 45 mol % benzene and
55 mol % toluene, and enters at 327.6 K. A distillate
containing 95 mol % benzene and 5 mol % toluene and a
bottoms containing 10 mol % benzene and 90 mol %
toluene are to be obtained. The reflux ratio is 4:1. The
average heat capacity of the feed is 159 kJ/(kmol K) and
the average latent heat is 32099 kJ/kmol. Equilibrium
data for this system are given in the table below.
Calculate the distillate and bottoms in kmol/h, and the
number of theoretical trays needed.
Vapor-Pressure and Equilibrium-Mole-Fraction Data for
Benzene-Toluene System
Vapor pressure (kPa)
Mole fraction of
T (K)
benzene at 101.325 kPa
Benzene Toluene
xA
yA
353.3
101.32
1.000
1.000
358.2
116.9
46.0
0.780
0.900
363.2
135.5
54.0
0.581
0.777
368.2
155.7
63.3
0.411
0.632
373.2
179.2
74.3
0.258
0.456
378.2
204.2
86.0
0.130
0.261
383.8
240.0
101.32
0
0
F = 100 kmol/h, xF = 0.45, xD = 0.95, xB = 0.1,
R = Ln/D = 4.
Overall material balance
F=D+B
100 = D + B
Benzene balance
FxF = DxD + BxB
100(0.45) = D(0.95) + (100-D)(0.10)
D = 41.2 kmol/h
B = 58.8 kmol/h
The enriching operating line is
x
R
4
0.95
y n 1 
xn  D 
xn 
 0.80 xn  0.19
R 1
R 1 4 1
4 1
The q line is
1
1
The value of HV – HL = latent heat = 32099 kJ/kmol.
HL – HF = cpL(TB – TF)
where the heat capacity of the liquid feed cpL = 159
kJ/(kmol K), TB = 366.7 K (boiling point of feed), and
TF = 327.6 K (inlet feed temperature).
1
c
T –T
1
1.195
So the q line is
71
1
72
159 366.7 327.6
32099
1.195
0.195
0.195
6.128
5.128
The enriching and q lines are plotted in the figure below.
Their intersection identifys one point in the stripping
line. Linking this point to the bottom point y = x = xB =
0.1, we obtain the stripping line. The number of
theoretical steps is 7.6, or 7.6 steps minus a reboiler,
which gives 6.6 theoretical trays. The feed is introduced
on tray 5 from the top.
Total reflux ratio
In distillation of a binary mixture A and B, the feed
conditions, distillate and bottoms compositions are
usually specified and the number of theoretical trays are
to be calculated. The number of theoretical trays depends
on the operating lines. To fix the operating lines, the
reflux ratio R = Ln/D at the top must be set.
One limiting case is total reflux, R = ∞, or D = 0. The
material balance becomes
Vn+1 = Ln
Vn+1yn+1 = Lnxn
Hence, the operating lines of both sections are on the 45o
line, yn+1 = xn.
Total reflux
is an extreme
case, the
number of
theoretical
trays
required is at
its minimum
to obtain the
given
separation of
xD and xB.
However, in
reality we
have no product at all, and the twoer diameter is infinite.
73
74
Minimum reflux ratio
Another limiting case is the minimum reflux ratio, Rm,
that will require infinite number of trays for the given
separation of xD and xB. This corresponds to the
minimum vapor flow in the tower, and hence the
minimum reboiler and condenser sizes.
If the reflux ratio R decreases, the slope of the enriching
line R/(R+1) decreases, the intersection of this line and
the stripping line with the q line moves farther from the
45o line and closer to the equilibrium line. The number
of steps required to give a fixed xD and xB increases. At
the extreme case, the two operating lines touch the
equilibrium line, a “pinch point” at y’ and x’ occurs,
where the number of steps required is infinite. The slope
of enriching line in this case is
′
1
′
75
In some cases, where the equilibrium line has an
inflection in it as shown below, the operating line at
minimum reflux will be tangent to the equilibrium line.
The minimum reflux ratio refers to the situation that we
can have the maximum products (D and B) but the
number of trays required is infinite. Both total reflux and
minimum reflux are impossible in actual operation.
76
Operating and optimum reflux ratio
The actual operating reflux ratio lies between the two
limits. To select the proper value of R requires a
complete economic balance on the fixed costs of the
tower and operating costs. By experience, the optimum
reflux ratio has been shown to be between 1.2Rm and
1.5Rm.
Solution:
(a) First draw the equilibrium line and the q line as we
did in Example D3. The operating line for minimum
reflux ratio is plotted as a dashed line and intersects the
equilibrium line at the same point the q line intersects.
Reading the values of x’ = 0.49 and y’ = 0.702, we have
′ 0.95 0.702
0.539
0.95 0.49
1
′
Hence, the minimum reflux ratio is Rm = 1.17.
Example D4: Minimum reflux ratio and total reflux
ratio
For the rectification in Exanple D3, where a benzenetoluene feed is being distilled to give a distillate
composition of xD = 0.95 and a bottom product of xB =
0.10, calculate the following:
(a) Minimum reflux ratio Rm
(b) Minimum number of theoretical plates at a total
reflux
(b) The theoretical steps are drawn as shown between the
equilibrium line and the 45o line. The minimum number
of theoretical steps is 5.8, which gives 4.8 theoretical
trays plus a reboiler.
77
78
Special case for rectification
1. Stripping-column distillation.
In some cases the feed is added at the top of the stripping
column because we would like to have bottoms product
only. The feed is usually a saturated liquid at the boiling
point, and the overhead product VD is the vapor rising
from the top plate, which goes to a condenser with no
relux returned to the tower.
This stripping line is the same as that for a complete
tower. It intersects the y = x line at x = xW, and the slope
is constant at Lm/Vm+1.
If the feed is saturated liquid, then Lm = F. This is shown
in the figure. Starting at xF, the steps are drawn down the
tower.
If the feed is cold liquid below the boiling point, the q
line should should be used and q > 1: Lm = qF.
Example D5: Number of trays in stripping tower
A liquid feed at the boiling point of 400 kmol/h
containing 70 mol % benzene (A) and 30 mol % toluene
(B) is fed to a stripping tower at 101.2 kPa pressure. The
bottoms product flow is 60 kmol/h containing only 10
mol % A and the rest B. Calculate the kmol/h overhead
vapor, its composition, and the number of theoretical
steps required.
The bottoms product W usually has a high concentration
of the less volatile component B. Hence, the column
operates as a stripping tower, with the vapor removing
the more volatile A from the liquid as it flows
downward. Assuming constant molar flow rates, a
material balance of the more volatile component A
around the dashed line gives,
L
Wx
y m 1  m xm  W
Vm 1
Vm 1
79
Solution
F = 400 kmol/h
xF = 0.70
W = 60 kmol/h
xW = 0.10
Plot the equilibrium
and diagonal lines.
Overall material
balance gives
F = W + VD
80
400 = 60 + VD
VD = 340 kmol/h
Plate Efficiency
Component A balance gives
FxF = WxW + VDyD
400(0.70) = 60(0.10) + 340yD
yD = 0.806
For a saturated liquid, q=1, the q line is vertical. The
operating line is plotted through the point y = yW = 0.10
and the intersection of yD = 0.806 with the q line.
Alternatively, the slope of Lm/Vm+1 = 400/340 = 1.176
can be used. Stepping off the trays from the top, 5.3
theoretical steps or 4.3 theoretical trays plus a reboiler
are needed.
2. Enriching-column distillation
Enriching towers are also used at times, where the feed
enters the bottom of the tower as a vapor. The overhead
distillate is produced in the same way as in a complete
fractionating tower and is usually quite rich in the more
volatile component A. The liquid bottoms is usually
comparable to the feed in composition, slightly leaner in
A. If the feed is saturated vapor, the vapor in the tower
Vn = F.


To translate ideal plates into actual plates
Applicable to both distillation & absorption
1
Types of plate efficiency
1.1 overall efficiency
0 


for the entire column
simple but the least fundamental
1.2
Murphree efficiency
y y
M  n* n1
yn  yn1
where
yn = actural concentration of vapor leaving plate n
yn+1 = actural concentration of vapor entering plate n
yn* = concentration of vapor in equilibrium with liquid
concentration xn leaving downpipe from plate n


81
number of ideal plates
number of actual plates
for a single plate
in reality samples are taken of the liquid
on the plates, and the vapor compositions are
determined from a McCabe-Thiele diagram.
82
1.3 Local or point efficiency
y'  y' n1
'  n
y' en  y' n1
where
y'n = concentration of vapor leaving a specific point in
plate n
y'n+1= concentration of vapor entering plate n at the
same location
y'en
= concentration of vapor in equilibrium with
liquid
at the same point (x'n)

2.
for a specific location in a plate
Relationship between efficiencies
2.1 Murphree & local efficiencies
In small columns, good mixing can be achieved so that
the concentration is uniform in the tray.
y'n = yn, y'n+1 =yn+1, and y'en = yn*. Therefore, '   M .
83
In large columns, incomplete mixing of the liquid occurs
in the tray.  M is the integration of ' over the entire
tray.
2.2 Murphree & overall efficiencies
ln1  M ( mV / L  1)
0 
ln mV / L 
where m is the slope of equilibrium line. When
mV/L=1.0 or M 1.0, M = 0.
This relationship depends on the relative slopes of
equilibrium and operating lines.
M < 0 (stripping section)
M > 0 (enriching section)
M  0 for the whole column if the feed plate is near
the middle
3.


Use of Murphree efficiency
Draw an effective equilibrium line.
Use McCable and Thiele method between the
effective equilibrium line and the operating line.
4.

Factors influencing plate efficiency
Adequate and intimate contact between liquid and
vapor can enhance the efficiency; any excessive
foaming or entrainment, poor distribution, or shortcircuiting, weeping, or dumping of liquid, lowers
the plate efficiency.
Rate of mass transfer between liquid and vapor.

84