(16) Use of Murphree efficiency默弗里板效
率/Determining the number of actual plates
实际板 [pp.692-693]
•When the Murphree efficiency is known, it
can readily be used in the McCabe-Thiele
diagram.
•Fig.21.33[p.693]
1
Fig.21.33

True equilibrium
curve
Effective
equilibrium curve
y
y n n
c
yn
d
ye  yynn
e
yn
b
y n 1xFyn 1
a
yn1
x
x
B

xF ab xyB nx1xByn 1
yn
M 
 x y1xF
y


F  y
y
ac
yn
y
n y n
x1
n x F n 1
t1 x D

xD
z

y
n
yn 1
yn.70)
yn ( 21
yn y yn 1   Mx(2 xyDn  yn 1 )
n
yn
xB
yn 1
y.n70
y

1
ye 
y


(
y

y
)
(
21
)
2
M
e
t
xn 1 1
yn 1
t2
x
x
x
F
B
B
 M  Murphree plate efficiency
x2
xn
xB
xD
x F xn
yn 1
2
y
3
x
y
x x

•Triangle acd represents the ideal plate and
triangle abe the actual plate.
•The actual plate, instead of enriching the
vapor from yn+1 to y*n, accomplished a lesser
enrichment yn- yn+1.
3
ab yn  yn 1
M 
 
ac yn  yn 1
yn  yn 1   M ( y  yn 1 )
ye  y   M ( ye  y )

n
(21.70)
(21.70)
 M  Murphree plate efficiency
•To apply a known Murphree efficiency to an
entire column, it is necessary only to replace
the true equilibrium curve ye versus xe by an
effective equilibrium curve y’e versus xe,
whose ordinates are calculated from the
equation (21.70).
4
•How to plot the effective equilibrium curve?
•Giving xn, find y*n from equilibrium curve and yn+1
from operating
yn from equation
 yncalculate
ab ynline,
1



M
(21.70),
then plot
 point (xn, yn) …
ac yn  yn 1
yn  yn 1   M ( yn  yn 1 )
ye  y   M ( ye  y )
(21.70)
(21.70)
 M  Murphree plate efficiency
•How to determine the number of actual plates?
•The reboiler is not subject to a discount for plate
efficiency, and the true equilibrium curve is used for
the last step in the stripping section.
5
Effective
xD curve
equilibrium
True equilibrium
curve
xD
xF
xD
xB
xF
How many
xF
actual plates
xB
are needed in
the1left
N actual  6.7 
construction?
M
N  3 plus a reboiler
N actual  6.7 
xB
1
1
M
 5.2 plates plus a
N actual  6.7 
 5.2 plates plus a reboileer
xD
M
xF
xB
xD
xF
xD
6
Effective
equilibrium curve
True equilibrium
curve
xD
How many
actual plates
are needed in
the left
construction?
xF
xBxD
N actual
xF  5.3 plates plus a reboiler
N xBfractional
3 plus a actual
reboilerplate, then
No
N actual  6 plates plus a reboiler
N  3 plus a reboiler
7
•Murphree efficiency can be different from
individual plates, and this is more accurate to
calculate the number of actual plates than by
overall efficiency of a column全塔效率.
8
3. BATCH DISTILLATION
（间歇精馏 ）
[pp.700-703]
1)Simple Distillation简单蒸馏(自学)
• (1)Flow diagram (Refer to Fig.21.37)
Cooling water
Condenser
x0 ( xF ), n0 ( F )
L  L  dL
y
dn
Batch Feed
间歇进料
x
釜液
W
n  n xdn
2
y
dD
Still
L  L  dL
Product 冷凝器
yreceiver

冷却水
dD
馏出液
HeaterPrDoduct
Bottom
n1  B
xx1  xB
y  x Dm
9
•There are many cases where batch distillation间歇精
馏 is preferred, particularly in the food and
pharmaceutical industries. Batch distillation is used
when small amounts of product are made in a pilot
plant to provide samples for product sampling or
testing.
•Features: 1)Unsteady state; 2)Without reflux; 3)Onestage partial vaporization process. The vapor leaving
the still at any time is in equilibrium with the liquid in
the still. [y is in equilibrium with x.]
10
Cooling water
Condenser
x0 ( xF ), n0 ( F )
L  L  dL
y
dn
Batch Feed
x
釜液
W
n  n xdn
2
y
dD
LProduct
 L  dL
冷凝器
yreceiver

冷却水
dD
馏出液
HeaterPrDoduct
Bottom
n1  B y  xDm
xx21  xB
11
(2)Rayleigh equation
（瑞利方程）
L  L  dL
At a given time,
n A  nx
(21.80)
dn A  d ( xn)  ydn
ndx  xdn  ydn
y
dn
x
釜液
W
Heater
L加热
L
n  n xdn
2
dn
dx
n1

(21.82)
y
n
yx
x1
dD
n1 dn
x1 dx
n1
(21.83) 釜液
釜液
n0 n  x0 y  x  ln n0
W
W
Eq.(21.83) is known as the Rayleigh equation. dx/(y-x)
x2
can be integrated graphically or numerically using x2
equilibrium data (y~x equilibrium relationship).
12
(3) For an ideal mixture,
That is, yyyAAA  AB xxxAAA
yyyAB   AB
xAB
AB x
x
B
y B   AB xBB
 AB x A
yA 
1  ( AB  1) x A
21..84
84))
(((21
21
.84)
(21.84)
ynnBA xx A xB
dn  dn
dn A,, yy Bdn
dn  dn
dnB
Because n AA  x AA ,,, yyyAAdn
dn
nnnAB xxxAB A  dn AA , y BBdn  dnBB
nBB  xBB , y A dn  dn A , y B dn  dnB
ndn
dn
dn
dn A
nA
B A //x
B
dn
dn
n
dn AA / dn  dn AA y AAB A n A
AB
dnAB///dn
dn  dn
dnAB  AB nnn
dn
B
dn
dn
dn
A
B
dnBB / dn  dnBB  yAB
nB
B
dn
nB
dnBA/ dn dn
dnBB
dn
dn
dn AA  AB dnBB
(21
21..85
85))
(
  AB
( 21.85)
AB n
n
dn
dn
n AAAA  
nBBB
n
n
(21.85)
or
AB
n A nnn A
nB nnnB
A 
ln
ln
21...86
86)))
A
BB
AB
ln


ln
21
86
ln
  ln
(((21
AB
AB
13
dn A
dnB
  AB
(21.85)
Afternintegration
nBbetween limits
A
nA
nB
ln
  AB ln
n0 A
n0 B
(21.86)
1 /  AB
nB  n A 

 
n0 B  n0 A 
(21.87)
14
Number of moles of product: D
Average concentration of product:
y  xDM
 F  D  B or n0  D  n1
D  F  B
And  FxF  Dx Dm  Bx B，
x0  xF , x1  xB , y  xDm
n1
 y  x0 
( x0  x1 )
n0  n1
EXAMPLE 21.9.
15
Advantages. The advantages of batch
distillation are that several products can be
made from a single unit, and can effectively
handle sludges and solids.
Disadvantages. For a given product rate, the
equipment is larger. It requires more
operator attention, uses more energy, and
because it is a dynamic process, is harder to
control and model.
16
2)Batch Distillation with reflux间歇精馏/有回流
的间歇蒸馏 [pp.702-703]
• In many cases, a rectifying column with
reflux is used to improve the performance of
the batch still.
• Flow diagram.
• Features: Unsteady state; Only rectifying section in
the column. Product concentration differs from
different operations.
17
• Two basic operation methods:
• (a). Keep the top composition (xD) constant
by increasing the reflux ratio as the
composition of the liquid in the reboiler
changes.
• (b). Fix the reflux ratio and let the overhead
product purity vary with time, stopping the
distillation when the amount of product or
the average concentration in the total
product reaches a certain value.
(某个)
18
• Calculation and analysis for the operation of
a distillation column.
• The plate column has been established, and
the following data are given: Equilibrium
relationship; xF; q; N and M (Nactual).
• In order to obtain overhead and bottom
products with required mole fractions of xD
and xB, the reflux ratio RD and the feed plate
position must be determined.
• Calculation method: Trial and error（反复试验）.
19
• Attentions of Operation analysis of distillation
column:
(a) Suitable feed plate position;
(b) Keep material balance: If D and B changed, xD and
xB will be changed too.
(c) Reflux ratio is the key measure of controlling
product quality. [For example, if N is given,
RDxD, xB .]
(d) If xF changed, feed plate position should be
changed too.
20
4. AZEOTROPIC AND EXTRACTIVE
DISTILLATION [pp.131]（恒沸精馏和萃取精馏）
• When relative volatility
near or equal to unity,
the separation of components is difficult by
conventional distillation, or impossible because of
azeotrope恒沸混合物 formation.
• Basic principles of azeotropic and extractive
distillation: Adding a third component(solvent) to
increase the relative volatility of the original
components, so that the mixtures with relative
volatility near or equal to unity can be separated by
conventional distillation.
（相对挥发度）
21
(1) Azeotropic distillation恒沸精馏
• Materials called entrainers(夹带剂)(third
component) are added to the original mixture, and
usually a new azeotrope with lowest-boiling points
有最低恒沸点的恒沸物 is formed. The new
azeotrope will of course contain one or more of the
feed components, and leaving behind component(s)
which may be recovered in the pure state.
• Example: Recovery and purification of ethanol and
water. Flow diagram…
• Selection of entrainers.
22
(2) Extractive distillation萃取精馏
• A solvent is added to the distillation tower to
increase relative volatility of key components in the
feed mixture. The effective extractive solvent萃取剂
will selectively interact with one (or more) of the
components, thereby increasing relative volatilities.
• Example:Use of furfural糠醛 to permit the
separation of butadiene丁二烯 from a mixture
containing butane丁烷 and butenes丁烯. Flow
diagram…
• Selection of extractive solvents.
23