(9) Heating and cooling requirements
•Assume Heat loss is relatively small,
column itself is essentially adiabatic .
•Heat effects of the entire unit are confined
to the condenser and the reboiler.
•Average molal latentqheat
and total

r  Vchange
sensible heat change in liquid streams is
small.
(绝热)
•Heat added at reboiler (qr)
qr  V 
1
a
x FF
x
x
F
Condenser
a q
F
L
n
n
L
ywa  a c
Va n

T1
m
VLa xn
q(cT2  T
Va
x
F
n
n
n Ln
x
T2
L
a out
y
Heat
a
n
a
Control
n
y
xan xn Vn 1Accumulator
D
y
V
L
a
L
a
n
surface 1
Ln
xa qc
LVLanVnn y
xnn Lxann 1n 1 n 1 y La
xD
a
Overhead
Reflux
xnn x xnyLn nm
D
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1mn
Vb
q
Feed
q
x
y nxn1
cy Vn 1
c
a
x
n

1
L
mVn 1 Dmmxxmn m L
x
F xm
D
y
yb
b
FV
y
b
D
n

1
V
D
m
q
b1
[Fig.21.8(p.649)]
xmVVmV
c
m

Lmynn11 xL
1
Lb
x F VaLmy n 1 x DLmymVn 1 y xbV Lb
xD
xmm VxDmmmyLm1nyb11m b1 D
b
xb
Va y xaVmm yxmmymmb1LVb1qry xb Reboiler
1
b x
bD
Vmmm
mLm
1
Control
q
x1m
r
B
V
L
Heat in q r
q
V
r
m

1
surface y
2 a Laymxm1
L
x
m
1
y LV b by L
m m1
m m1
a m 1
m 1
b b
m 1m
B
my1
m 1
mb r b b
m S
yx
x B Bottoms product
y
La x mV 1 m xx1 q L x
V
B
2
qr
V
•Steam consumption m
S 
(21.32)

S S
（蒸汽消耗量）
kW
qqqrrr =heat added at reboiler
m
SSS=steam consumption
m
m
Vb
VVV =Vb, vapor rate from reboiler
yb Vb
Vb
SSS =latent
Lb yb heat of steam yb
Vb

xb Lb latent heat of mixture


Lb
Vb yb =molal
Vb
q r xb
xb
yb LV
b b yb
Reboilerq
r
B qr
Heat in q r
Lb xbyb Lb
m S
x B B Bottoms product
B
xb q rLb xb
V
kg / s
km ol/ s
kJ / kg
kJ / kgm ol
3
a
•If condensate is not subcooled,
•heat removed in condenser:
qc  V
(V=Va)
VxaF Condenserx
a
Va
w 
y a T1 m
ya
La
T2
La
qc (T
Heat out
D
xxa
a
xD
•Water consumption/Cooling water flow
qq rate
qc
V
w 
m

c pc (T2  T1 ) c pc (T2  T1 )
cc
D
D
xxDD
(21.33)
qqrc =heat removed in condenser kW
W ; Btu / h


m
m
kg / s
V wS =water consumption
kg / h; lb / h

) (T2 V
VT1 ) =temperature rise of cooling C

C
water
SS
cal / g
4
•*[For enthalpy balances in detail, see
pp.672-675](自学)
•EXAMPLE 21.2 [(c)(d)]
5
(10) Minimum number of plates最小理论板
数/Total reflux全回流
•Effect of reflux ratio on number of plates:
RD  N  (num ber of ideal plates)
RD max    N  N min Why ?
RD min ( ?)  N   Why ?
•When total reflux,
(1) D  0, B  0, F  0
 0 
(2) RD(1) LD
/ D0,LB/ 00,RFD max

 then
LN
/ Dboth
(num
L coincide重合
/ 0ber
  of ideal
(3)
lines
with theplates)
(3)Operating
yn1(2) R
xR
nD D
diagonal,
(3) RyDnmax
1 x
n  N  N min Why ?
6
Equilibrium line
Operating line
xB
xD
RD  N  (num ber of ideal plates)
xB
xD
RD flow
Total reflux
max    N  N min Why ?
7
RD  N  (num ber of ideal plates)
•MethodRfor
Computing
D max    N  N min Why ?
R
(

?)

N


Why
?
D
min
•(1) Constructing method: constructing steps on
an x-y diagram between compositions xD and xB,
using 45°line as the operating line for both
sections of the column.
•(2)Analytic method for ideal mixtures
(pp.665-666)
ln[xD (1  xB ) / xB (1  xD )]
N min 
1
ln  AB
(21.42)
•Nmin is the ideal plates needed, not including a
reboiler.
8
ln[xD (1  xB ) / xB (1  xD )]
N min 
1
ln  AB
(21.42)
•Equation (21.42)
ln[ x (1is the
x ) Fenske
/ x (1  equation
x )]
（芬斯克方程）
,
N min 
1
(21.4
ln[ xwhen
xB )AB/ is
xBconstant.
(1  xD )] If the
•Which applies
ln
D (1 
N min 
1
(21
change in the value ofln  ABfrom the bottom of
D
B
B
D
the column to the top is moderate, a
ln[ xD (1 ofxthe
xB (1  xDvalues
)]
B ) / extreme
geometricmean
N min 
 1 is (21.42)
recommended forln  AB .
9
B
(11)
x F Minimum reflux（最小回流比）/Infinite number of
plates（理论板无穷多）
xD
x
a
c g
RD  N 
y
d
•When the
intersection of the
e
two operating lines
falls on the
f xB
x B equilibrium line
xF
(point d),
x
xB xD
F
b
N


,
R

R
D
Dm
x
x F x
xB
D
Fig.21.19
Minimum
x  ratio最小回流比 10
x D y  reflux
xF
D
RD  N 
•When the intersection of the two operating
lines falls on the equilibrium line (point d),
N  , RD  RDm
 RDm =minimum reflux ratio
•All actual columns operates at a reflux ratio
between the minimum and infinity
.
（无穷大）
RDm
La
 La 
    RD 

D
 D  min
(21.43)
11
•For the
normal type of equilibrium curve,
xB
RDm
xD  y
xD  y 
x F
 RDm 
(21.44)
RDm  1 xD  x
y  x
xD
x
g
c
y
a
d
e
f xB
b
xB
xF
xB
xB xD
x F x
xF
xD
12
•Eq.(21.44) cannot be applied to all systems.
•For example, ethanol-water system,
abnormal equilibrium curve.
13
a
xD c
RDm  1 xD
xD
RDm  1
xD
RDm  1
xD
xF
xD
xD
RDm  1
xB
xF
xD
xF
x
xFcan be
B reflux ratio
•In such a situation the minimum
x
B the slope of the operating line ac that
computed from
xB
is tangent to the equilibrium curve.
14
•Question: Is it the only way that the minimum reflux
ratio must be found by drawing the operating line that
is tangent to the equilibrium curve for abnormal
equilibrium curve?
•Factors influencing RDm include: (1)Equilibrium
relation (curve); (2)xD, xF, xB; (3)q (Thermal condition
parameter of feed). Therefore, it is not the only way for
determining RDm by drawing the operating line that is
tangent to the equilibrium curve for abnormal
equilibrium curve.
•For example, …
15
(12)Invariant zone夹紧区/恒浓区
Pinch Point
a
Pinch point
d
f
b
•Invariant zone: At minimum reflux ratio, near pinch
point夹紧点, where there is no change in either liquid
or vapor concentrations from plate to plate,so
xn1  xn , yn1  yn
16
(13)Optimum reflux ratio适宜回流比

RDm  RD  
• Effect of Reflux ratio on distillation:
 Given
,WhenRDRD, ,
Given FF,,xxFF, ,xxDD, x, Bx,BWhen
, ((aa)) N 
esesononequipm
entent
Fixed
Fixed chcharg
arg
equipm
,,
V
n ndiam
eter

Fixed
ch a
equipm
((bb)) Lent
V ,,VV 
colum
colum
diam
eter

Fixed
 Given F , xF , xD , xB ,When RD ,
m eter
Fixed
es ononequipm
equipm
(a) 
N 
Fixed ch
charg
arg es
entent
 Given F , xF , xD , xB ,When RD ,
Fixed charges on reboiler and
((ca)) LN
, L Fixed
,V ,V ch

colum
n
diam
eter

Fixed
ch
ar
arg es on equipm ent
condenser
Steam nand
cooling-water
costs
(d ) L ,V   colum
diam
eter Fixed
ch arg es on
17
Minimum reflux ratio
Annual cost
Total
Steam
c
)
2
(
+
)
1
ost=(
,(1)
s
t
s
o
c
r
e
t
a
w
ing
l
o
o
c
and
Optimum reflux
ratio
Fixed charges on equipment,(2)
RDm RDopt Reflux ratio
Figure 21.21
18
•The total cost reaches a minimum at a
definite reflux ratio, that is , optimum reflux
ratio RDopt.
•The optimum reflux ratio depends on the
cost of energy; it will be closer to RDm when
energy costs are relatively high, and farther
from RDm when distillation equipment is
made of expensive alloys.
•RDopt=(1.1~2.0)RDm
•[EXAMPLE 21.3][p.670]
19
(14)Nearly pure products
•When either the bottom or overhead
product is nearly pure, a single diagram
covering the entire range of concentrations is
impractical as the steps near x=0 and x=1
become small.
•Method 1: Auxiliary diagrams on a large
scale
•[calculations are usually done by computer].
20
•Method 2: Using Eq.(20.27) or (20.28).
•[At each end of the equilibrium curve, both
the equilibrium and the operating lines are
straight， so Eq.(20.27) can be used, and no
graphical construction is required]
•[Basis: Raoult’s law applies to the major（主要
的） component and Henry’s law to the minor
（次要的）component at each end of the
equilibrium curve. ]?[p.671]
•[EXAMPLE 21.4.]
21
(15) Some special cases of distillation
• a side-stream draw off (自学):
a) 3 operating lines; 2 q-lines (feed lines);
b) Equations of operating lines: Equations of operating
lines of top and bottom sections are the same as that
of the rectifying and stripping sections discussed
before. The equation of operating line in the middle
section of the column has to be derived.
22
2 2
1
, xD , q 3
D
3
3 3
2
F
,
x
,
q
F, ,qxF B
, q, x B
F
F
,
x
3
F
F , xF , q
D, x D
D, xD Assuming
F , xF D
,Lq, xD V 
D, xD , q
D, x D
molal
D, x D D
V, xLD , q

D, x , qconstant
1
B, xB y S11
D, xDB ,,qxV
L BV 
V  yS 1
B
,
x
B
2
S L
L
V
V  y S 1 L
3
L VLxS
y S 1 V
F , xF ,Lq xLS V
D, x D xS V L
D, xD , q V
B, x B
Fig. for Ex.21.11
1D, x , qD overflow in this
D
1
B, xB column. By
L2 2
B, x B
material
xS3 3 2 V 
V
balance:
1F , xF, q3x y, qS 1
F
y S 1F V yS 1  LxS  DxD  Dx D
2D, x F ,LxF , q L
DxD  Dx D
D
D , xD
L yS 1  xS 
3D, x  ,Dq,xxD  V 
V 
DDx xD S, q
FB,, xxF , qSD, xD , q
B
B , xB
D
23
D  B, x B
V ,xV
Assuming constant molal overflow in this
column, equation for the operating line of
V yS 1  LxS  DxD  Dx D
middle section is
L
DxD  Dx D
yS 1 
xS 
V 
V 
The upper operating line is given by Eq.(21.13)
L
DxD
yn 1  xn 
(21.13)
V
V
L
Dx
yn 1  Lxn  BxD
(21.13)
The lower
operating line is given
by Eq.(21.16)
ym 1 V xm  V B
(21.16)
V
V
L
Bx
ym 1  xm  B
(21.16)
V
V
24
 L  L  D,  L  L The operating lines for the 3
sections are shown in the
x



V  VB  V
following diagram. Dashed
Lx F L
lines
are for RDm=(L/D)min.
 
q 1
V x D  V
q  1
xD
q 1
（虚线）
y

F
q  1
 DxD  Dx D
DxD  Dx D

V 
L
DxD
 xn 
V
V
L
BxB
xB
(21.13)
xB
xB
xF
xB
xF
xF
xD
xD xD
25
How to determine the number of ideal plates?
26
(b) Direct steam heating直接蒸汽加热
•Live steam is injected directly below the
bottom plate.
•Equation of operating line of the rectifying
section is the same as that discussed before.
•The equation of operating line in the
stripping section of the column has changed.
27
B
,
x
V0 , y0 F , xD
B
F , xD
D, x D
m
B, xBF , xVF 0 , y0
F
,
x
F
D, xLD
V0 , yB0 , xBm
D, x D
B
,
x
B
F , xF
m V0 , yL0
V
F , xF
V
,
y
B, xxB 0 0L m V
m
B, x B
m
V0 , yy0
L xm
m 1 V
V0 , y0
L
m
xD
xm V ym 1 D,m
L V
F , xF
ym 1xm
L
BSteam
, xB
V xmD, x y
D
m 1
V
y
m 1
V0 , y0
xm
F , xF
xm
m
ym 1 B, x
B
y
m 1
Assuming
constant molal
overflow in this
column. By
material
balance:
L  V0  V  B
Lxm  V0 y0  V ym1  BxB
[ y0  0, L  B,V  V0 ]
B
BxB
ym1  xm 
V0
V0
28
L  V0  V  B
Lxm section
V0 y0  Voperating
ym1  BxB line is given by
The stripping
the following
[ y equation
0, L  B,V  V ]
0
0
B
BxB
ym1  xm 
V0
V0
The rectifying section operating line is given
by Eq.(21.13)
L
DxD
yn 1  xn 
V
V
L
BxB
ym 1  xm 
V
V
(21.13)
(21.16)
29
Fig. Live steam is injected
directly below the bottom
plate.
How to determine the number
of ideal plates?
xB
xB
xB
xF
xF
xD
30
•which cases will live steam be used for in
distillation?
•Water soln（水溶液）. Bottom product nearly
pure water.
31