Transcript When y intercept: operating line of rectifying section

Chapter 9 Distillation
1
[1. FLASH DISTILLATION(闪蒸)]
2.CONTINUOUS DISTILLATION
WITH REFLUX回流(蒸馏)
[Action on an ideal plate]
[Combination rectification and stripping (Fig.9.4-3)]
[Trap: 疏水器; accumulator: 集液器; condensate:
冷凝液; fractionating: 精馏; reboiler: 再沸器]
2
a
xFF
x
x
F
Condenser
a
F
L
n
L
n
ya a
Va n
VLa x
q
V
x
c
a
F
n
n
nL
n
x
LaHeata out
yna n
n
Control
y
Vn 1Accumulator
D
x
y
V
a
L
x
n
a
L
n
a
n
surface 1
x a qc
Ln
LVLanVnn y
xnn Lxann 1n 1 n 1 y La
xD
a
Overhead
Reflux
D
xnn x xnyLn nm
q
1
c
VnL1n xVyannn11
product
V
b
x
L
a m
a
a
VnL1n
x
V
xD
n
n 1 Lm
D
y nxn1 qm
F
yb Vb
yc nLL
Vb
1mn
q
Feed
q
x
cy Vn 1
y nxn1
c
a
x
n

1
L
mVn 1 Dmmxxmn m L y
x
D
F xm
y
b
FV
y
b
b
D
n

1
V
D
m
q
n 1
b
[Fig.9.4-4(p.104)]
V
c
xmVVm 1 m 1
Lmy n 1 xL
Lb
xF VaLmyn 1 xDLmymVn 1 y xb Lb
xD
xmm VxDmmmyL1mnyb11m b1 VD
b
xb
Va yxa mm yxmmymmb1LVb1q ry xb Reboiler
VmLm1 Vmmm
b x
1
bD
Control
x1m
B
V
L
Heat in q r
qr
V
m

1
m
L
surface y
2 a ay x
m

1
L
x
m
1
y LV b by L
m m1
m m1
a m 1
b b
m 1
m 1m
B
my1
m 1
mb r b b
yx
x B Bottoms product
y
La x mV 1 m xx1 q L x
B
3
1)Material Balances in Plate Columns
(1) Overall and more volatile
material balances for twocomponent systems
F  DB
FF,,xxFF
DD
(21(9.4-1)
.3)
FxF  Dx D  Bx B (9.4-2)
Units
D, B: kmol/h,
F
、Dof
、F,
W单位：
kmol / h
kg/h, lb/h
xF、xD、xW：mol分率
F , xF
F , xD
F
D xD
xD , xF, xB: molar
fraction, or mass
x D W , xW
fraction, dimensionless W , xL
W
L L
xxDD
W,,xxWW
W
F ,LL
xF
D LL
xDVV
B,VV
x 
B
L 114
Eliminating B from eq.(9.4-1) and (9.4-2) gives
D xF  xB

F xD  xB
D xF  xB
 x x
B
Eliminating
F  xDDDgives
xBF
F xD  xB
B xD  xF

F xD  xB
(21.5)
(21.5)
(21.6)
(21.6)
5
(2)Net flow rates
•Net flow rate in the upper section /rectifying section
D  Va  La
(21.7)
D  Vn 1  Ln
(21.8)
Dx D  Va ya  La xa  Vn1 yn1  Ln xn
(21.9)
•Quantity D is the net flow rate of material,
DxD is the net flow rate of component A, all
upward in the upper/rectifying section of the
column. Regardless of changes in V and L,
and x, y, the differences are constant and
equal to D, and DxD, respectively.
6
•Net flow rate in the lower/stripping section
B  Lb  Vb  Lm  Vm1
(21.10)
Bx B  Lb xb  Vb yb  Lm xm  Vm1 ym1
(21.11)
•The net flow rates are also constant but are
in a downward direction. The net flow rate of
total material equals B; that of component A
is BxB.
7
(3) Operating lines
•Two sections
two operating lines
•Operating line for rectifying section
Ln
Va ya  La xa
yn 1 
xn 
Vn 1
Vn 1
(9.4-10)
Ln
Dx D
yn 1 
xn 
Vn 1
Vn 1
(9.4-11)
Ln
Dx D
yn 1 
xn 
Ln  D
Ln  D
(9.4-12)
Slope of operating line in rectifying section less than 1.0
8
•Operating line for stripping section
Vm1 ym1  Lm xm  Bx B
(9.4-13)
Lm
Bx B
ym 1 
xm 
Vm 1
Vm 1
(9.4-14)
Lm
Bx B
ym 1 
xm 
Lm  B
Lm  B
(9.4-15)
Slope of operating line in stripping section greater than 1.0
9
2)Number of Ideal Plates;McCabe-Thiele Method
•McCabe-Thiele step-by-step construction
for computing number of ideal plates（逐板计算法）:
Using equilibrium curve and operating lines.
(1)Constant molal overflow恒摩尔溢流
Conditions: (1)nearly equal molar heats of
vaporization of every component, (2)Sensible
heats
and heat losses
omitted.
（显热）
（热损失）
the molar flow rates of vapor and liquid are
nearly constant in each section of the column,
and operating lines are almost straight.
10

L
LL
V
VL

V
V
V
F , xF
D
xD
W , xW
L
LL
VL
FF,,xxFF
DD

VVL
L
L
11VL
xxDD
1VL L 1
22V
W
,
x
W
,
x

L
WW

2
L
21VV 
V L
3

VL
L
L
L
3
3
31V2V  LV  1 L
L 11
L

L
L
1
F
,
x
1312V L1VV  22 V L F
223
VV
D
21L312 VL1V2  进料板
V
V


V
V
1
进料板
x
32  进料板 D
1
V
2

3
V
进料板
3

2
L
1 B,11x
12 132
B

1
V
1
3

1
进料板
11
Constant molal overflow of vapor（恒摩尔气流）
V1  V2      Vn  V  Const (rectifying )
V

V





V

V

Const
(
stripping
)
1
2
m
V1  V2      Vn  V  常数(精馏段)
L

L





L

L

常数（精馏段）
1
2
n




V1  V2  molal
    Voverflow
Constant
of liquid （恒摩尔液流）
n  V  常数（提馏段）




L

L





L

L
常数（提馏段）
1
2
n
L  L      L  L const
(rectifying )
1
2
n
L1  L2      Lm  L  const ( stripping )
Units of above parameters: kmol/h
12
Operating lines becomes
L
Dx D
xn 
Rectifying section yn 1 
LD
LD
L
Bx B
Stripping section ym1 
xm 
L B
L B
13
(2)Reflux ratio: RD or RV
L V D
RD  
D
D
and
L
L
RV  
V LD
(21.18)
In this text only RD will be used.
L
Dx D
yn 1 
xn 
LD
LD
RD
xD
yn 1 
xn 
RD  1
RD  1
(9.4-18)
14
RD
xD
yn 1 
xn 
RD  1
RD  1
Construction of operating line of rectifying
section:When When
xD()xD , xD )
When xn  xDx,n yn x1 D, xyDn 1
 (xxDD ,
xD /( RDx: D/(1)RD  1)
y intercept
（截距）
15
When
xn  xD , yn1  xD  ( xD , xD )
xD /( RD  1)
operating line of
rectifying section
When
xn  xD , yn1  xD  ( xD , xD )
xD /( RD  1)
When
xn  xD , yn1  xD  (
xD /( RD  1)
16
yy11
V1 y1
V1
(3)Condenser
and
top
plate
L
L
D
y1 L
y1
V1 xx1
Partial
xD
x
V1 1
LTotal condenserL 1 condenser
y1VVV
V
V
1
1x V
Vapor
x

x

1
Vapor
Vapor
V
V
1
C
D
y1
x
1
1
1
1
y
L yy 2
y1
y1 y
V1
1
y
2
y1 V
yV1 2
V1
L 1
L L
y1 x1 LLLCC DL
D
L Liquid
LyLiquid
y1
C
x1
y2
2
V xxxC
x
x
L
1
1
x
1
x
C
x
L
D
D
x
x
1
L
V
LC
D1
1 C C
y 2V
Final
V
V y D
x1
x

x
x
xCV  xxDC  y1C xcondenser
x1
y2
D DV C 1
Liquid
y2
y2
VPlate1LCy 2
xD D

y

y
y
y 2
xC  x2D  y1
V
LC 2
LC （b）
LC （c）
y 2 xCLC
x

x

y
（a）
x
C
D
1
LC
D
y2
y LC
xC C
xC
xC
LC
 x x y
y
x
C
x
x
C
LC
C
D
1
C
C
17
xC
y
x
x1x1
y  xD
•When a total
is used, triangle
xxDD condenser
x1
Vplate
1
abc in Fig.9.4-6a
represents
the
top
in the
xxCC
xD
y1
column.
（三角形）
aa
y1  x D
y  xD
x1
xD
xC
a
b
xC
bb
a
y1  x D
cc
b
aya1  xyDc x D
byb   xxD1 a 
cxc1 x Db
x D xC

c
(a)
xC a
a
b
L Total condenser
V1 Vapor
V
V1 x1
y1
y1 V
L
DL y 2 D
Liqu
x1Liquid x
xDx1 LC
D D
Final
V
x

x

y
xCV  xxDC  y1C xcondenser
D
1
D
y2
y xC  xD 
yy 2
LC （b）
LC
y
18
xC
x
  xD
y
y1  x D
D
xused?
1
•Question: Why is the partial condenser
xCx x1
y  xD
C
x
D
•For a partial condenser,xC is in equilibrium
with y’,
a
V1
xD
a
x1
or xD. The partial condenser, representedxCby the
b bis equivalent
y1
xC
dottedV1triangle
a’b’c’ in Fig.9.4-6b,
x D to a
a
theoretical
y1 cxcD a
y1 L plate.D[分凝器相当于一块理论板]
xC
b
Partial
xD
x
y  axaD byc1  x Da
L 1 condenser
V1 V
b  cy   x D
V1x1 Vapor xVapor
C  x D  y1 yx11  xb
D
b
a
y1 y

c
y
x
yV1 2

y D yx Dc xaxb1 
c
1
D
L L
LyLiquid
C
xx1C y   xbxcD
2

a
D
x1 x
x
xL
xaD x cCy1  xbD
1 C C
1
Final
V
D

y

x
a
x
V
D
b
C
xC x
Liquid
condenser
c
D
y2
xD D
(b)
19
x
b
y2
1
c
a
x Dx
y1y x Dx
1
D
y1  xC y y x Dx
y1D  x D
•(y1, xC)Vis on operating
RDx1x1 yy1 xxxDDD
1
y1 
x

line
of
rectifying
section.
x Dx Cy   x D
RD  1D x1 RD y1 1 x D (y , x )的交点在操作线上。
V1 y1
1
C
xCx x1
V1 y1  LC CxC xDDx Dy   x D
D
y1 L
a a xD
x1
xC
Partial
LC b x
xD
x
L
1
b aC
RD 
xD
condenser
V
c
yD

x
a
Vapor
xVapor
c
V
1
D
V11x1 Vapor
xC
b
C  x D  y1
y  axaD byc1  x Da
y1 y

y
V
y
2
1
yx11  bxbD cya  x Db
L L
LyLiquid
C
2
1 
yxD cyxDc xaxLiquid
c
bD
x
1
1
x
L
x
xx1C y   xbxcD
1 C C

a
D
Final
V
D
y

x

x
c
1
D
a
C
xD x
b
VxC
Liquid
condenser
1

y

x
a
y2
D
xD D
xbC x
c
y
D
2
x
b
(
b
)
1
c
a x
L
x  x  y 20
C
C
C
x
D
1
y  xD
x Dx y   x D
 xxDD
y
y
RD
y1 xD x D
y1 
D
x1
y1  xx xC 
x
x
Cx
1
1
1x
RD  1
R

1

y D x D
y 
C
D
a
x
x
xD
•When
a
partial
condenser
is
used,
triangle
a
D
D
V1 y1  LC xC  xDx
x1
D
xC
1
a’b’c’ in Fig.9.4-6b
represents
the
top
plate
in
b
x
x
x
LC CC
b aC
x
xD
D
R

the column.
D
cxcD a
y

Daa
1
xC
xC
b
axaD by1  x D

b
b
y

y1  x D
a
a
c

b
y  xD
y

x
c
c
c
x

y

x
b
1
D
1
1
D
b
b
a
y  xD

c
x1
aya1  xyDc x D
a
x


c
y

x
D
c
x1
y1D  xbD 
x

byb   xxD1 a 
b
x
D
x

a
1C y   x c 
xD
D
x


x
cc1
cCy1  xbD
x Db
a
x
D
xC
x1

y

x
x D xC
a
D
b
x

c
c
C
a
xD
21
xC a
bx1
c
y1  xC
1
•When condensate is liquid at its bubble point, L=LC,
V=V1.
•If the refluxVV
is11 cooled below the bubble point,
a portion
V1
of the vapor coming
to plate
1 must condense
to heat
yy11
V1 y1
V1
the reflux; soLL
V1<V and yL>LC.
D
y L
V1 xx1
V1 1
V
y1V
V
V
1
y1 1
L yyy 2
V1
V1
L 11 2
x1 LLLC
y1
y1
x1 C
V xxxC
L
L
V 11 C
y 2V
x1
x1
y2
VPlate1LCy 2
V
LC 2
xCL
y
2
（a）
y2
xC CC
L
xCC
LCC
xC
1
1
Partial
xD
x
L
LTotal condenser 1 condenser
V1 Vapor
V1 V
Vapor
V1 x1
V1x1 Vapor x
C  xD  y
y1
y1 y
y
y1 V
yV1
2
L L
D
DL
L Liquid
LyLiquid
C
y2
2
x
x1 x
x Dx11 LC x D D
xL
C
1 C
V
V y D
DxFinal
xCV  xxDC  yx1C x
D Vx C 1
Liquid
condenser
y2
y2
xD D

y

y
y
y 2
xC  x2D  y1
LC （b）
LC
xC x
Dx D  y1
（c）
LC
LC

y
xC
xC
y  xC  x D  y1
xC
xC
22
•the reflux is cooled below the bubble point, so V1<V and
L>LC.
L
cT
(TT
TC )
L
c
)
C(
pc
1C
L
c
(
T

T
)
C
pc
1
L
T
C
pc
11  T
CC )


L

(
21
.
21
)
Cc
pc (
L
L

L

(
21
.
21
)
L
c
(
T

T
)
C
LL
L
LLC 
L

L

(
21
.
21
)
C
pc
1
C
 L 
( 21.21)
CC C
L  LCCC  L 
( 21.21)
CC
c
LCheat
c pc (T
condensate
TC )
ccpc
1
c
=specific
of
pc
pc
L  cLpc
(21.21)
pc
C  L 
T
of
TT111 =temperature
C liquid on top plate
T1 T1
c pc TTCC
TCC =temperature
TC
of returned condensate
T1 CCC = heat of vaporization of condensate
C 
[1  c pc ((TT11 TTCC ))cc ]]
C
TC R C LL  LLCCC LL  LL
CC [1  cpc
pc (T1  TC )c ]
((21
..22
))
L
[
1

c
L


L
L
D
C
pc
1
C
c
R



21
22
C
DD
D
ccolumn
cthen
] (21.22)
D
RD actual
D
LC  ratio
L LinC [1the
pc (T1  TC )is
D L reflux
D
D
•The
C
RDD
D

(21.2
D
)c ]
L LCD L DLC [1  c pc (T1  TCD
RD 


D
D
D
(21.22)
23
(4)Bottom plate and reboiler
•For constant molar overflow
L
Bx B
ym1 
xm 
L B
L B
(9.4-21)
•Construction of operating line of stripping section
•When xm  xB , ym1  xB  ( xB , xB )
L
L
slope 

L B V
24
Eq
ui
cu libr
rv iu
e m
Op
era
lin ting
e
x=
y
yb
yyb
b
a
yb
r
yr d y c yr
x
b
y B
x
xbB yb y r x B
e
x
b
xb 1 y r x B xb
xb 1 x x xb 1
B
b
x
xb xb 1
x
提馏段操作线过点（xB，xB）
•Construction of
operating line of
stripping section
•When
xm  xB , ym1  xB  ( xB , xB )
L
L
slope 

L B V
25
b
x
Plate b by
b
V
B
L
b
xb
xb V
V yr
yr B
B a xB
y
x Bb
d
yb
y bc y r
yr xB
e
x
b
xb 1 y r x B
xb 1 x x
B
b
x
era
lin ting
x= e
y
b
r
yr
x
y B
xx B
L
ui
cu l ibr
rv iu
e m
xB
Op
yb
yy b
yr
Eq
V
L
L
yr
xb
xb
B
V
Column
V
xB
sump
yr
yr
B
塔底集液层
B
xB
xB
xb
xb 1
L
L
xb
xb
V
V
yr
yr
B
B
xB
xB
Steam
Condensate
•The vapor leaving the
reboiler（yr） is in
equilibrium with the
liquid leaving as bottom
product（ xB ）. The
reboiler acts as an ideal
plate再沸器相当于一块
理论板.
26
(5)Feed plate
•At the plate where the feed is admitted, the
liquid rate or the vapor rate or both may
change, depending on the thermal condition
of the feed（进料热状态）.
•Five different feed types: (a) feed cold liquid
冷液进料; (b) feed saturated liquid饱和液体
进料; (c) feed partially vaporized汽液混合物
进料; (d) feed saturated vapor饱和蒸汽进料;
(e) feed superheated vapor过热蒸汽进料.
27
•Thermal condition of feed进料热状况.
•Material balance about feed plate
F V  L  V  L
•Enthalpy
feed
FH Fbalance
 V H V ofLH
L  VH V  L H L
Fplate
 V  L FVVL L  V  L
H  H ,H  H
V
L
FH

V
H

LH
 LVHV  L H L
FH F  V H V  LH
F
LH
V
L  VH
V L
HV  H F L  L
, HL  HL
H V  H V , HHLV HHLV 
HV  H L
F
H V  H F HLV LH F L  L
Hence  H V  HF L  L
VF H L
F
HV  H L q H
HV  H L
F
H V  H F HLV LH F L  L
q 

qDefine

F
H V  H L H VF H L
V
L
28
HV  H L
F
HV  H F L  L

Define q 
HV  H L
F
q = parameter of thermal condition of feed进料热
状况参数, or moles of liquid to stripping section of
column per mole of feed进料液化率
For cold-liquid feed
H V  c pLTb  
H F  c pLTF
H L  c pLTb
  c pL (Tb  TF )
q 

(9.4-22)
29
H L  c pLTb
  c pL (Tb  TF )
For cold-liquid feed  q 

c pL , c pV = specific heats of liquid and vapor,
c
, c,respectively
T c pLc pL
pV pV
F
 V  L  V  L of feed
Tb ,TTFTdcF pL=, cFtemperature
pV
F V  L  V  L
,dT=d FH
 LH L  VHV and
L H L dew point
 TbT,TT
bF
F  V H V point
bubble
of
FH F  V HV  LH L  VHV  L H L
HV , H L  H L
TdHV  respectively
 Tb ,feed,
（泡点）
（露点）
HV  HV , H L  H L
HV  H Fof vaporization
L L
 = heat

H H
L L
HV  H L vapor
F
•For partially
feed, 0<q<1

HV  H L
F
L L
q
 L  L  qF L  L  qF
F
V
F
30
HV  H L
F
HV  H F L  L
HDefine
qd  

V  c pV T
HV  H L
F
H F  c pV TF  
For superheated vapor feed
H L  c pV Td
q  
c pV (TF  Td )

(9.4-23)
31
F V  L  V  L
FH F  V HV  LH L  VHV  L H L
HV  HV , H L  H L
•Material balance of feed plate
HV  H F L  L

F  V  L HVV HL L F
FH F  V HLV L LH
qF L  VHV  L H L
HV  HV , H L  H L
V  V  (q  1) F
(9.4-25)
H

H
L

L
V
F H  LH  VH  L H
FH

V
V  FV  (1V q ) F L
V
L
HV  H L
F
LH
H
FH
HVVH, H

VHVisvaporized进料
LHL
L
(1  q )  H
f V =Ffraction
of
feed
LL that
V
HV  H F L  L
 H
HLH
LV L L H

FH F  VqH
HVVV汽化率
VH
F ,LHL
L
V
L
H V  H L
F
H, VH
H
H
32
H HH
 LH L F
L
V
V
V L
F L
V
L
V
L
F
L
F
F
L
L
L
V
V
L
V
(a)
V
F
L
V
(b)
V
L
V
L
L
V
(c)
V
F
L
L
V
V
(d)
L
V
L
V
(e)
33
HV  H L
q Values of five feed types
V
L
F
F
HV  H F L  L
q

HV  H L
F
V
L
F
L
F
L
V
L
(a)
V
Cold feed L
H F  H L ,F q  1
(b)
(c
L
V
V
F
V V,L  L  F
34
HV  H L
q Values of five feed types
V
L
F
HV  H F L  L
q

HV  H L
F
V
L
F
V
L
F
L
L
(a)
V
V
(b)
(c)
L
V point (saturated liquid
V
Feed at bubble
L
F
H F  H L , q F1
)
饱和液体
V V,L  L  F
35
HV  H L
q Values of five feed types
V
L
F
HV  H F L  L
q

HV  H L
F
V
L
F
L
L
(b)
V
V
(c)
L
F
Feed V
partially vapor
HV  H F  H L , 0  q  1
V V,L  L  L  F
36
HV  H L
(a) of five feed types
q Values
L
HV  H F L  L
q

(b)
HV  H L
F
L
V
F
F
V
F
L
L
V
V (d)
(e)
Feed at dew point (saturated vapor)
HV  H F , q  0
V  V  F, L  L
37
(
(d)
HV  H L
F
HV  H F L  L
q Values of five feed types q  H  H  F
(b)
(c)
V
L
L
V
V
F
L
L
V
(e)
V
Feed superheated vapor
HV  H F , q  0
V  V  F, L  L
38
Question: Bubble
point feeds,
given
F1F,1F, 2F,2V,V, L, L isisgiven
,,
F1 , F2 ,V , L is given,
,
q
,
V
,
L
is
given
,
F1 , F2q,V
,
L
is
given
,
L,F,?V,?,VL, Lis is
VV1 F
?2 ?LF
,
F
given
given
,
,

V

? L  ?
F
,
F
V
,
L
is
given
,
1
1
2
2
1??L
21  2?



V

V

?
L
q1,,VLqV2 ,
V?,
,given
L
is
given
,
F1 , F2 ,V
,
is




?,
L

?
L
?
V? ?L
L? ? ?
V

L
?


V   ?, L  ?
V










V

?,
L

?
V

?,
L

?
?
V  ?V
L?? L 
 ?,
 ?,
L? ? ?
V
L?,
L 
VV 
VL?,
L  ?
V F, ?,
?
1 F2 , V , L is given,
V   V   V
L  L  F1
L  L  F2  L  F1  F2
39
(6)Feed line
•Feed line进料线 ----Line of intersections(交点)
of the two operating lines.
Equilibrium line
d
Operating line of
rectifying section
Operating line of
stripping section
xB
xB
xD
40
•For constant molal overflow（恒摩尔流）, the
operating line equations for two sections are
L
Dx D
xn 
Rectifying section yn 1 
LD
LD
L
Bx B
Stripping section ym1 
xm 
L B
L B
41
That is
Vyn1  Lxn  Dx D
(9.4-26)
F xVm LBx
 V B L
V ym1  L
(9.4-27)
FH F  V HVthe
 LHoperating
L  VHV  L H L lines
To locate the point where
HV =y,
HV , HxnL =x
 HmL =x and
intersect, let yn+1=ym+1
subtract Eq.(9.4-27) from
:
HV  H Eq.(9.4-26)
L

L
F

y(V  V )  ( L 
HVL )HxL  Dx
F D  Bx B
FxF  DxD  Bx B
L  L  qF
V  V  (1  q ) F
q
xFFH F  V H V  LH L  VHV  L H L
y
x
(21.31)
1 q
1 HqV  H V , H L  H L
42
q
xF
y
x
(21.31)
1 q
1 q
•Eq.(21.31)represents a straight line, called
the feed line, on which all intersections of the
operating lines must fall.
•The position of the line depends only on xF
and q.
43
(7) Construction of operating lines
•The simplest method of plotting the operating
lines is to
q 1
(1)locate the feed line:
q
xF
y
x
1 q
1 q
(21.31)
When
x  xF , y  xF  ( xF , xF )
0  q 1
q 1
q0
r
q0
q
slope  
1 q
xF
44
(2) Construction of operating line of rectifying
section:When When
xD()xD , xD )
When xn  xDx,n yn x1 D, xyDn 1
 (xxDD ,
xD /( RDxD/(1)RD  1)
y intercept:
When
xn  xD , yn 1  xD  ( xD , xD )
xD /( RD  1)
When
xn  xD , yn 1  xD  ( xD , xD
xD /( RD  1)
operating
line of
) rectifying
section
When
xn  xD , yn 1  xD  (
45
xD /( RD  1)
(3) Draw the stripping line through point
(xB,xB) and the intersection of the rectifying
line with the feed line.
0  q 1
xB
xF
r
xD
xB
xD
RD  1
xB
xB
xF
xF
xD
xF
46
(8) [Optimum] Feed plate location（适宜的进料位置）
When should the steps transfer from the
rectifying line to the stripping line?
The change should be made in such a manner
that the maximum enrichment per plate is
obtained, so that the number of plates is as
small as possible.
The transfer should be made immediately after
a value of x is reached that is less than the x
coordinate(坐标) of the intersection of the two
operating lines.
47
Optimum
feed plate
location:
plate 3
a
Feed plate
3
b
5
How many
ideal plates
are needed?
r
Reboiler?
Partial
condenser?
xB
xF
Optimum feed plate location?
xD
Is the number
of ideal plates
related with
feed flow rate
F?
48
Problem

A continuous rectifying column treats a mixture
consisting of 40% weight benzene and 60wt% toluene
at the rate of 4 kg/s, and separates it into a product 97
% benzene on the top of column and a liquid containing
98wt% toluene at the bottom of column. The feed is
liquid at boiling point.
 (a) Calculate the weights of distillate and waste
liquor per unit time.
 (b) If a reflux ratio of 3.5 is employed, how many
plates are required in the rectifying part of the column ?
 (c) What is the actual number of plates if the plate
efficiency is 60%?
49
Mol

0.1 0.2 0.3 0.4 0.5 0.6 0.7
Mol

fraction of benzene in liquid:
0.8 0.9
fraction of benzene in vapour :
0.22 0.38 0.51
0.63 0.7 0.78 0.85 0.91 0.96
50
Solution
The equilibrium, data are plotted on Fig. llh. As the
compositions are given as weight %, they must first be
converted to mol fractions before the McCabe-Thiele
method can be used.
Mol fraction benzene in feed
(40 / 78)

 0.44  x f
(40 / 78)  (60 / 92)
Similarly,
xd=0.974 and xw=0.024
51
•[EXAMPLE 21.2(a)(b)]
52
•As the feed is a liquid at its boiling-point, the q-line is
vertical and may be drawn at xf =0.44.
(a) A mass balance over the column and on the more
volatile component gives in terms of mass flow rates:
•
4.0 = W' + D'
4× 0-4= 0.02W' + 0.97D'
from which:
W' gives = bottoms flow rate = 2.4 kg/s
And:
D'=top product rate = 1.6 kg/s '
53
(b) If R= 3.5, the intercept of the top operating line on
the y-axis is given by
xd /(R+1) = 0.974/4.5 = 0.216,
and thus the operating lines may be drawn as shown in
Fig.11h.
The plates are stepped off as indicated and 10
theoretical plates are required.
(b) If the efficiency is 60%, the number of actual plates
= 10/0.6 = 16.7
17 actual plates
54
55
56
57
58
59
60
61
62
63