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Chapter 7: Distillation of Binary Mixtures 1
Chapter 7
Distillation of Binary Mixtures
Chapter 7: Distillation of Binary Mixtures 2
Graphical Methods for Analyzing Binary Distillation
In Chapter 5:
• We described a graphical method for analyzing multistage separation systems which involved drawing operating lines and equilibrium curves and stepping off stages. This approach is equivalent to the algebraic method and group methods. This approach was demonstrated using absorption and stripping.
Today’s lecture will focus on:
Extending these types of analysis to multisection cascades.
We begin by describing a typical binary distillation column.
We then describe the process generally and make important definitions.
We perform mass balances to get operating lines.
We plot equilibrium data to get an equilibrium curve.
We step of stages noting the cross-over between sections.
Chapter 7: Distillation of Binary Mixtures 3
McCabe-Thiele Method for Trayed Towers
Absorption and stripping cascades are common methods for separating vapor and liquid mixtures. A more complete separation can be achieved by combining these processes into a binary distillation column.
Total condenser
Feed
Overhead vapor
BoilupN
21
Distillation
f
Reflux drum
Rectifying section stages
Stripping section stages
Feed Stage
Bottoms
Partial reboiler
Reflux Distillate
L0 (absorbent)
VN+1 (vapor to be separated)
V1
LN
12
N–1N
Absorption
LN+1 (liquid to be separated)
V0 (stripper)
VN
L1
12
N–1N
Stripping
Chapter 7: Distillation of Binary Mixtures 4
Distillation Column
Feed
Rectifying section stages
Stripping section stages
Total condenser
Reflux drum
Reflux Distillate
Boilup
Feed Stage
Bottoms
Partial reboiler
Chapter 7: Distillation of Binary Mixtures 5
McCabe-Thiele Method for Trayed Towers
The general countercurrent-flow, multistage, binary distillation column shown below consists of
A column of N theoretical stages
A total condenser to produce a reflux liquid to act as an absorbent and a liquid distillate
A partial reboiler to produce boilup vapor to act as a stripping agent and a bottoms product
An intermediate feed stage.
This configuration allows one to achieve a sharp separation, except in cases where an azeotropeexists where one of the products will approach the azeotropic concentration.
The goal of distillationis to achieve a distillate rich in the light key and a bottoms rich in the heavy key.
Total condenser
Feed
Overhead vapor
BoilupN
21
Distillation
f
Reflux drum
Rectifying section stages
Stripping section stages
Feed Stage
Bottoms
Partial reboiler
Reflux Distillate
Chapter 7: Distillation of Binary Mixtures 6
McCabe-Thiele Method for Trayed Towers
The feed contains a more volatile component (the light key, LK) and a less volatile component (the heavy key, HK). At the feed temperature and pressure it may consist of a liquid, vapor or mixture of vapor and liquid. The feed composition is given by the light key mole fraction ZF. The bottoms composition is given by the LK mole fraction
XB, whereas the distillate composition is given by the LK mole fraction XD.
Total condenser
Feed (L/V)
Overhead vapor
BoilupN
21
Distillation
f
Reflux drum
Rectifying section stages
Stripping section stages
Feed Stage
Bottoms
Partial reboiler
RefluxDistillate
LK mole fraction zF
LK mole fraction xD
LK mole fraction xB
The difficulty in achieving the separation is determined by the relative volatility, αbetween the LK=1, and the HK=2.
α1,2 = K1 / K2
If the two components form anideal solution then Raoult’sLaw applies and:
Ki = Pis / P
The relative volatility is then just the ratio of the vapor pressures:
α1,2 = P1s / P2
sOnly a function of T
As T increases (pressure incresaes), α decreases until at some point it becomes equal to one and no separation is possible.
Chapter 7: Distillation of Binary Mixtures 7
McCabe-Thiele Method: Equilibrium Curve
We can rewrite the relative volatility in terms of the mole fractions of the light key in a binary mixtureas follows:
α1,2 = K1 / K2 =y1 / x1
y2 / x2=
y1 / x1
1 − y1( )/ 1 − x1( )=
y1 1 − x1( )x1 1 − y1( )
For close boiling point components the temperature, and thus α will be nearly constant in the column. Solving for the mole fraction of the LK in the vapor gives:
For components which do not have close boiling points α will vary depending on composition. The equilibrium curve will appear similar to that of fixed α, but won’t fit the equation above for constant α.
y1 =α1,2x1
1+ x1 α1,2 −1( )
y1
x1
Equilibriumcurve
45° line
y1
x1
45° line
Increasing relativevolatility
Chapter 7: Distillation of Binary Mixtures 8
Thermodynamic Considerations and Phase Equilibria: Binary Fluids
Lets consider a binary mixture AB, where
B is a heavy component (high boiling point)
and
A is a light component (low boiling point).
A T-x phase diagram of AB mixture, where
x is a mole fraction of component a might
look like this at some constant pressure P.
This phase diagram can be also transformed
in y-x diagram where composition of vapour
phase in terms of mole fraction of
component A is plotted as function of the
liquid phase composition.
x1 y1x2 y2x3 y3x4 y4
T
Tb(B)
Tb(A)
V
L
T1
T2
T3
T4
xA
xA
yA
T1
T2
T3
T4y4
y3
y1
Chapter 7: Distillation of Binary Mixtures 9
Specifications
F Total Feed Rate
zF Mole fraction composition of the feed
P Column operating pressure (assume uniform in column)
Phase condition of the feed @P
Vapor-liquid equilibrium curve for the binary @P
Type of overhead condenser (total or partial)
xD Mole fraction composition of the distillate
xB Mole fraction composition of the bottoms
R/Rmin Ratio of reflux to minimum reflux
Results
D Distillate flow rate
B Bottoms flow rate
Nmin Minimum number of equilibrium stages
Rmin Minimum reflux ratio, Lmin/D
R Reflux ratio, L/D
VB Boilup ratio, V/B
N Number of equilibrium stages
Optimal feed- stage location
Stage vapor and liquid compositions
Specifications for the McCabe-Thiele Method
Chapter 7: Distillation of Binary Mixtures 10
McCabe-Thiele Method: Column Mass Balance
FzF = xDD + xBB
Feed (L/V)
BoilupN
21
f
Bottoms
Reflux
F, zF
D, xD
B, xB
Distillate
A mass balance in the LK component around the column gives:
A total mass balance around the column gives:
F = D + B
So we know that the mole fraction of the light key of the feed is between that of the distillate and bottoms:
D = FzF − xB
xD − xB
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
If D, F, are zF, specified, then either xD or xB can be specified.
Chapter 7: Distillation of Binary Mixtures 11
McCabe-Thiele Method: Rectifying Section
Vn+1yn+1 = Lnxn + DxD
Which we can rearrange to find:
The rectifying section extends from stage 1 to the stage just above the feed stage.
yn+1 =Ln
Vn+1xn +
DVn+1
xD
Feed (L/V)
BoilupN
n
1
f
Bottoms
Reflux
ZF
L, xD= x0
xB
DistillatexD
n
1 RefluxL0, xD= x0
DistillatexD
Lxn
Vyn+1
If L and V are constant in the column from stage to stage, then this is a straight line.
If we perform a material balance in the light key around the n stages of the rectifying section including the condenser:
Chapter 7: Distillation of Binary Mixtures 12
McCabe-Thiele Method: Constant Molar Overflow
If L and V are constant, then this is a straight line. This requires that:
The two components have equal and constant enthalpies of vaporization
The heat capacity changes are negligible compared to the heat of vaporization
The column is well insulated so heat loss is negligible
The pressure in the column is uniform
These conditions lead to the condition of constant molar overflow.
For this condition the amount of vapor
transferred to the liquid stream in each stage is
equal to the amount of liquid transferred to the
vapor stream. Thus the liquid and vapor stream
flow rates are constant in the entire section.
Feed (L/V)
BoilupN
n
1
f
Bottoms
Reflux
ZF
L, xD= x0
xB
Distillate
xD
yn+1 =Ln
Vn+1xn +
D
Vn+1xD
Chapter 7: Distillation of Binary Mixtures 13
McCabe-Thiele Method: Rectifying Section Operating Line
y =L
Vx +
D
VxD
The liquid entering stage one is the reflux L and its ratio to the distillate L/D is the reflux ratio R. If we have constant molar overflow, then R is a constant and
L
V=
L
L + D=
L / D
L / D + D / D=
R
R +1
D
V=
D
L + D=
1R +1
and
We define this equation as the operating line of the rectifying section.
Feed (L/V)
BoilupN
n
1
f
Bottoms
Reflux
ZF
L, xD= x0
xB
Distillate
xD
In the case of constant molar overflow we can then drop the stage subscripts:
yn+1 =Ln
Vn+1xn +
D
Vn+1xD
Chapter 7: Distillation of Binary Mixtures 14
McCabe-Thiele Method: Operating Line
x
Equilibriumcurve
45° line
n
1
f
Reflux
xD= x0
Distillate
xD
L, xn V, yn+1
y =L
Vx +
D
VxD
We can then rewrite:
as y =R
R +1x +
1R +1
xD
x0=xDx1
y
y1
y2
y =1
R +1xD
Rectifying Section Operating lineSlope=L/V=R/(R+1)<1
If R and XD are specified then we can graph the line shown in the following plot.
Chapter 7: Distillation of Binary Mixtures 15
McCabe-Thiele Method: Stripping Section
Lxm = Vym+1 + BxB
Which we can rearrange and use the constant molar overflow assumption to find:
The stripping section extends from the stage just below the feed stage to the bottom stage N. If we perform a material balance in the light key around the bottom stages of the rectifying sectionincluding the condenser we have:
y =L
Vx −
B
VxB
Feed (L/V)
BoilupN
n
1
f
Bottoms
Reflux
zF
L, xD= x0
xB
DistillatexD
y =VB +1
VBx −
1VB
x Band
Lxm
Vym+1
Boilup
NBottoms
B, xB
m+1
L, xN
V, yB
Since:
L
V=
V + B
V=
VB +1VB
L = V + B
ThenVB is called the boilup ratio.
VB =V
B
We define this equation as the operating lineof the stripping section.
This is also the operating line of the stripping section .
Chapter 7: Distillation of Binary Mixtures 16
McCabe-Thiele Method: Stripping Section
x
Equilibriumcurve
45° line
xNxB
y
yB
yN
Stripping Section Operating LineSlope=L/V=(VB+1)/VB
If VB and XB are specified then we can graph this as the line shown in the following plot.
y =VB +1
VBx −
1VB
x B
Lxm
Vym+1
Boilup
NBottoms
B, xB
m+1
L, xN
V, yB
xm
Ym+1
y =VB +1
VBx −
1VB
x B
Chapter 7: Distillation of Binary Mixtures 17
Feed Stage Considerations
In determining the operating lines for the rectifying and stripping sections we needed the bottoms anddistillate compositions and reflux and reboil ratios. The compositions can be independently specified, but R and VB are related to the vapor to liquid ratio in the feed.
FF
FFF
L
L
L
L
L
V
V < V
V
VV
V
V = VV = VF + V
V = F + V V > F + V
L > F + L L = F + L L = L + LF
L = L L < L
Subcooled Liquid Bubble Point Liquid Partially Vaporized
Dew Point Vapor Superheated Vapor
Chapter 7: Distillation of Binary Mixtures 18
Feed Conditions
So except in the cases where the feed is a supercooled liquid or superheated vapor the boilup is related to the reflux by the material balance:
V = L + D − VF
VB ≡V B
=L + D − VF
B
Distillation operations can be specified by the reflux ratio or boilup ratio although the reflux ratio (or R/Rmin) is most often specified.
Dividing by B gives the boilup ratio:
L = B + V
V = D + L
VF + LF = D + B
V = V + VF
L = L + LF
VF + L − L = D + B
VF + L − L = D + L − V
V = L + D − VF
Consider the cases where the feed is not a supercooled liquid or a superheated vapor:
Mass balance around the reboiler:
Mass balance around the condenser:
Mass balance around the column:
Vapor entering the rectifying section:
Liquid entering the stripping section:
Substitute this into the column balance:
Substitute in the reboiler balance:
In other words, the vaporentering the rectifying sectionis the vapor entering the condenserminus the feed vapor flow rate.
Chapter 7: Distillation of Binary Mixtures 19
The q-line
First, we define the parameter q by: q =L − L
F
yV = Lx − BxByV = Lx + DxD
Subtracting the two operating lines:
Gives: y V − V( )= L − L( )x + DxD + BxB
Using a material balance in the LK: DxD + BxB = FzF
Using a material balance around the feed stage to elminate vapor flow rates:
F +V + L = V + L
Simplifying and using the definition of q results in the q-line:
y =q
q − 1
⎛
⎝ ⎜
⎞
⎠ ⎟ x −
zF
q −1
⎛
⎝ ⎜
⎞
⎠ ⎟ x = zF ⇒ y = zF
minus
y V − V( )= L − L( )x + FzF
V − V = F + L − Ly F + L − L( )= L − L( )x + FzF
The q-line has slope q/(q-1)and intercepts the 45 degreeline at y=zF
Chapter 7: Distillation of Binary Mixtures 20
Construction Lines for McCabe-Thiele Method
Equilibriumcurve
45° line
x=zFxB
y
yB
yN
Stripping Section: Operating lineSlope=L/V=(VB+1) /VB
xD
Rectifying Section: Operating lineSlope=L/V=R/(R+1)<1
q-liney =
LV
x +DV
xD
y =L
Vx −
BV
xB
y =q
q − 1
⎛
⎝ ⎜
⎞
⎠ ⎟ x −
zF
q −1
⎛
⎝ ⎜
⎞
⎠ ⎟
Chapter 7: Distillation of Binary Mixtures 21
Feed Stage Location Using McCabe-Thiele
Equilibriumcurve
x=zFxB
y
yB
yN
xD
Equilibriumcurve
x=zFxB
y
yB
yN
xD
1
2
3
4
1
2
3
4
5
Feed stage located one tray too low. Feed stage located one tray too high.
Chapter 7: Distillation of Binary Mixtures 22
Construction Lines for McCabe-Thiele Method
Equilibriumcurve
x=zFxB
y
yB
yN
xD
1
2
3
4
Chapter 7: Distillation of Binary Mixtures 23
Summary
This lecture:• We extended the analysis used for absorption and stripping to binary distillation. • We described a typical binary distillation configuration. • We made definitions such as reflux ratio, constant molar overflow, etc.• We described operating lines.• We plotted the equilibrium curve.• We stepped through stages to show the change in composition as you go throughthe column.
Next lecture we’ll continue our discussion of binary distillation and the McCabe Thiele method.