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Chapter 9 DistillationChapter 9 Distillation

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[1. FLASH DISTILLATION([1. FLASH DISTILLATION( 闪蒸闪蒸 )])]

2.CONTINUOUS DISTILLATION WI2.CONTINUOUS DISTILLATION WITH TH REFLUXREFLUX 回流回流 (( 蒸馏蒸馏 ))

[Action on an ideal plate][Action on an ideal plate]

[Combination rectification and stripping (Fig.9.4-3)][Combination rectification and stripping (Fig.9.4-3)]

[Trap: [Trap: 疏水器疏水器 ; accumulator: ; accumulator: 集液器集液器 ; condensate: ; condensate: 冷凝液冷凝液 ; fractionating: ; fractionating: 精馏精馏 ; reboiler: ; reboiler: 再沸器再沸器 ]]

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Control surface 1

Control surface 2

Feed

Condenser

AccumulatorHeat out

Overhead product

Bottoms product

Reboiler

Reflux

Heat in

[Fig.9.4-4(p.10[Fig.9.4-4(p.104)]4)]

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1)Material Balances in Plate Columns1)Material Balances in Plate Columns(1) Overall and more volatile (1) Overall and more volatile material balances for two-material balances for two-component systemscomponent systems

(9.4-1)

(9.4-2)Units of F, D, B: kmol/h, Units of F, D, B: kmol/h,

kg/h, lb/hkg/h, lb/h

xxD D , x, xFF, x, xBB: molar fractio: molar fractio

n, or mass fraction, dimen, or mass fraction, dimensionlessnsionless

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Eliminating B from eq.(9.4-1) and (9.4-2) givesEliminating B from eq.(9.4-1) and (9.4-2) gives

Eliminating D givesEliminating D gives

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(2)Net flow rates(2)Net flow rates•Net flow rateNet flow rate in the in the upper section /rectifying sectionupper section /rectifying section

)8.21(

)7.21(

1 nn

aa

LVD

LVD

•Quantity D is the Quantity D is the net flow ratenet flow rate of material, of material, DxDxDD is the net flow rate of component A, all is the net flow rate of component A, all

upward in the upward in the upper/rectifying sectionupper/rectifying section of th of the column. Regardless of changes in V and L, e column. Regardless of changes in V and L, and x, y, the differences areand x, y, the differences are constant constant and eq and equal to D, and Dxual to D, and DxDD, respectively., respectively.

)9.21(11 nnnnaaaaD xLyVxLyVDx

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•Net flow rateNet flow rate in the in the lower/stripping sectionlower/stripping section

)10.21(1 mmbb VLVLB

•The The net flow ratesnet flow rates are also are also constantconstant but are i but are in a downward direction. The net flow rate of n a downward direction. The net flow rate of total material equals B; that of component A total material equals B; that of component A is Bxis BxBB. .

)11.21(11 mmmmbbbbB yVxLyVxLBx

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(3) Operating lines(3) Operating lines•Two sections two operating linesTwo sections two operating lines

•Operating line for rectifying section Operating line for rectifying section

111

n

aaaan

n

nn V

xLyVx

V

Ly (9.4-10(9.4-10))

111

n

Dn

n

nn V

Dxx

V

Ly (9.4-11(9.4-11))

DL

Dxx

DL

Ly

n

Dn

n

nn

1 (9.4-12(9.4-12))

Slope of operating line in rectifying section less than 1.0Slope of operating line in rectifying section less than 1.0

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•Operating line for stripping sectionOperating line for stripping section

Bmmmm BxxLyV 11 (9.4-13(9.4-13))

111

m

Bm

m

mm V

Bxx

V

Ly (9.4-14(9.4-14))

BL

Bxx

BL

Ly

m

Bm

m

mm

1 (9.4-15(9.4-15))

Slope of operating line in stripping section greater than 1.0Slope of operating line in stripping section greater than 1.0

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2)Number of Ideal Plates;McCabe-Thiele Method2)Number of Ideal Plates;McCabe-Thiele Method•McCabe-Thiele step-by-step construction foMcCabe-Thiele step-by-step construction for computing number of ideal platesr computing number of ideal plates （逐板计算法）（逐板计算法） : : Using equilibrium curve and operating lines.Using equilibrium curve and operating lines.

(1)Constant molal overflow(1)Constant molal overflow 恒摩尔溢流恒摩尔溢流

Conditions: (1)nearly equal molar heats of vapConditions: (1)nearly equal molar heats of vaporization of every component, (2)Sensible heatorization of every component, (2)Sensible heatss （显热）（显热） and heat lossesand heat losses （热损失）（热损失） omitted.omitted.

the the molar flow ratesmolar flow rates of vapor and liquid are ne of vapor and liquid are nearly arly constant constant in each section of the column, anin each section of the column, and operating lines are almost d operating lines are almost straightstraight..

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Constant molal overflow of vaporConstant molal overflow of vapor （恒摩尔气流）（恒摩尔气流）

Constant molal overflow of liquid Constant molal overflow of liquid （恒摩尔液流）（恒摩尔液流）

Units of above parameters: kmol/hUnits of above parameters: kmol/h

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Operating lines becomesOperating lines becomes

DL

Dxx

DL

Ly D

nn

1Rectifying sectionRectifying section

BL

Bxx

BL

Ly B

mm

1Stripping sectionStripping section

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(2)Reflux ratio: R(2)Reflux ratio: RD D or Ror RVV

)18.21(DL

L

V

LRand

D

DV

D

LR VD

In this text only RIn this text only RD D will be usedwill be used..

DL

Dxx

DL

Ly D

nn

1

111

D

Dn

D

Dn R

xx

R

Ry (9.4-18)(9.4-18)

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111

D

Dn

D

Dn R

xx

R

Ry

Construction of operating line of rectifying secConstruction of operating line of rectifying section:tion:

When When

y intercepty intercept （截距）（截距） ::

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operating line of operating line of rectifying sectionrectifying section

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(3)Condenser and top plate(3)Condenser and top plate

Plate1

Total condenser

（（ aa））

（（ bb））

（（ cc））

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•When a When a total condensertotal condenser is used, triangle is used, triangle （三角形）（三角形） abc abc in Fig.9.4-6in Fig.9.4-6aa represents the represents the top platetop plate in the in the column.column.

(a)(a)（（ bb））

Total condenser

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•Question: Why is the partial condenser used? Question: Why is the partial condenser used?

•For a partial condenser,For a partial condenser,xxCC is in equilibrium with y’, is in equilibrium with y’,

or xor xDD.. The The partial condenserpartial condenser, represented by the dotte, represented by the dotte

d triangle d triangle a’ba’b’’cc’’ in Fig.9.4-6b, is in Fig.9.4-6b, is equivalent to a theoequivalent to a theoretical plate. [retical plate. [ 分凝器相当于一块理论板分凝器相当于一块理论板 ]]

(b)(b)

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D

LR

DxxLyV

R

xx

R

Ry

xy

CD

DCC

D

DC

D

D

C

11

1

1

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•(y(y11, x, xCC) is on operating lin) is on operating lin

e of rectifying section. e of rectifying section. (y(y11, x, x

CC)) 的交点在操作线上。的交点在操作线上。

((bb

))

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•When a partial condenser is used, triangle When a partial condenser is used, triangle a’a’b’c’ b’c’ in Fig.9.4-6in Fig.9.4-6bb represents the top plate in th represents the top plate in the column.e column.

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•When condensate is liquid at its When condensate is liquid at its bubble pointbubble point, L=L, L=LCC, ,

V=VV=V11. .

•If the reflux is cooled If the reflux is cooled below the bubble pointbelow the bubble point, a portion , a portion of the vapor coming to plate 1 must condense to heat of the vapor coming to plate 1 must condense to heat the reflux; so the reflux; so VV11<V and L>L<V and L>LCC..

Plate1

Total condenser

（（ aa））

（（ bb））

（（ cc））

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•the reflux is cooled the reflux is cooled below the bubble pointbelow the bubble point, so V, so V11<V and <V and

L>LL>LCC..

=specific heat of condensate=specific heat of condensate=temperature of liquid on top plate =temperature of liquid on top plate

=temperature of returned condensate=temperature of returned condensate= heat of vaporization of condensate= heat of vaporization of condensate

•The The actual reflux ratioactual reflux ratio in the column is then in the column is then

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(4)Bottom plate and reboiler(4)Bottom plate and reboiler

•For constant molar overflowFor constant molar overflow

BL

Bxx

BL

Ly B

mm

1

(9.4-21(9.4-21))

•WhenWhen

V

L

BL

Lslope

xxxyxx BBBmBm

),(, 1

•Construction of operating line of stripping sectionConstruction of operating line of stripping section

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V

L

BL

Lslope

xxxyxx BBBmBm

),(, 1

•WhenWhen

•Construction of Construction of operating line of operating line of stripping sectionstripping section

提馏段操作线过点（提馏段操作线过点（ xxBB ，， xx

BB ））

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•The vapor leaving the reThe vapor leaving the reboilerboiler （（ yryr ） ） is in is in equilequilibrium withibrium with the liquid le the liquid leaving as bottom productaving as bottom product（ （ xxBB ）） . . The reboiler aThe reboiler acts as an ideal platects as an ideal plate 再沸再沸器相当于一块理论板器相当于一块理论板 ..

yb

塔底集液层

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•At the plate where the feed is admitted, the lAt the plate where the feed is admitted, the liquid rate or the vapor rate or both may chaiquid rate or the vapor rate or both may change, depending on the nge, depending on the thermal condition of tthermal condition of the feedhe feed （进料热状态）（进料热状态） ..

•Five different feed typesFive different feed types: (a) feed cold liquid: (a) feed cold liquid冷液进料冷液进料 ; (b) feed saturated liquid; (b) feed saturated liquid 饱和液体饱和液体进料进料 ; (c) feed partially vaporized; (c) feed partially vaporized 汽液混合汽液混合物进料物进料 ; (d) feed saturated vapor; (d) feed saturated vapor 饱和蒸汽进饱和蒸汽进料料 ; (e) feed superheated vapor; (e) feed superheated vapor 过热蒸汽进过热蒸汽进料料 ..

(5)Feed plate(5)Feed plate

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•Thermal condition of feedThermal condition of feed 进料热状况进料热状况 . .

•Material balance about feed plateMaterial balance about feed plate

•Enthalpy balance of feed Enthalpy balance of feed plateplate

HenceHence

DefineDefine

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q =q = parameter of thermal condition of feedparameter of thermal condition of feed 进料热进料热状况参数状况参数 , or , or moles of liquid to stripping section of moles of liquid to stripping section of column per mole of feedcolumn per mole of feed 进料液化率进料液化率

For cold-liquid feedFor cold-liquid feed

DefineDefine

(9.4-22)(9.4-22)

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= specific heats of liquid and vapor, respe= specific heats of liquid and vapor, respectivelyctively

= temperature of feed= temperature of feed

= bubble point= bubble point （泡点）（泡点） and dew pointand dew point （露点）（露点） of of feed, respectivelyfeed, respectively

= heat of vaporization= heat of vaporization•For partially vapor feed, 0<q<1For partially vapor feed, 0<q<1

For cold-liquid feedFor cold-liquid feed

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DefineDefine

For superheated vapor feedFor superheated vapor feed

(9.4-23)(9.4-23)

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•Material balance of feed plateMaterial balance of feed plate

= fraction of feed that is vaporized= fraction of feed that is vaporized 进进料汽化率料汽化率

(9.4-25)(9.4-25)

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q Values of five feed typesq Values of five feed types

Cold feedCold feed

FLLVV

qHH LF

,

1,

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q Values of five feed typesq Values of five feed types

Feed at bubble point (saturated liquidFeed at bubble point (saturated liquid 饱和液体饱和液体 ))

FLLVV

qHH LF

,

1,

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q Values of five feed typesq Values of five feed types

Feed partially vaporFeed partially vapor

FLLLVV

qHHH LFV

,

10,

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q Values of five feed typesq Values of five feed types

Feed at dew point (saturated Feed at dew point (saturated vapor)vapor)

LLFVV

qHH FV

,

0,

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q Values of five feed typesq Values of five feed types

Feed superheated vaporFeed superheated vapor

LLFVV

qHH FV

,

0,

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??,

??

,,,, 21

LV

LV

givenisLVFF

Question: Bubble Question: Bubble point feeds,point feeds,

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•Feed lineFeed line 进料线进料线 ----Line of intersections----Line of intersections(( 交交

点点 )) of the two operating lines. of the two operating lines.

(6)Feed line(6)Feed line

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•For constant molal overflowFor constant molal overflow （恒摩尔流）（恒摩尔流） , the o, the operating line equations for two sections areperating line equations for two sections are

DL

Dxx

DL

Ly D

nn

1Rectifying sectionRectifying section

BL

Bxx

BL

Ly B

mm

1Stripping sectionStripping section

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Dnn DxLxVy 1 (9.4-26)(9.4-26)

Bmm BxxLyV 1 (9.4-27)(9.4-27)

That isThat is

To locate the point where the operating lines iTo locate the point where the operating lines intersect, let ntersect, let yyn+1n+1=y=ym+1m+1=y, x=y, xnn=x=xmm=x=x and and subtract subtract

Eq.(9.4-27) from Eq.(9.4-26)Eq.(9.4-27) from Eq.(9.4-26)::

BD BxDxxLLVVy )()(

BDF BxDxFx

)31.21(11 q

xx

q

qy F

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)31.21(11 q

xx

q

qy F

•Eq.(21.31)represents a straight line, called thEq.(21.31)represents a straight line, called the e feed linefeed line, on which all intersections of the op, on which all intersections of the operating lines must fall.erating lines must fall.

•The position of the line depends only on xThe position of the line depends only on xFF an an

d q. d q.

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(7) Construction of operating lines(7) Construction of operating lines

•The simplest method of plotting the operating liThe simplest method of plotting the operating lines is tones is to

(1)locate the (1)locate the feed linefeed line: :

q

qslope

xxxyxx

When

FFFF

1

),(,

)31.21(11 q

xx

q

qy F

1q

1q10 q

0q

0q

Fx

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(2) Construction of operating line of (2) Construction of operating line of rectifying rectifying section:section:

When When

y intercept:y intercept:

operating operating line of line of

rectifying rectifying sectionsection

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(3) Draw the (3) Draw the stripping linestripping line through point through point (x(xBB,x,xBB) and the intersection of the rectifying ) and the intersection of the rectifying

line with the feed line.line with the feed line.

Fx

10 q

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(8) [Optimum] Feed plate location(8) [Optimum] Feed plate location （适宜的进料位（适宜的进料位置）置）

When should the steps transfer from the rectifWhen should the steps transfer from the rectifying line to the stripping line?ying line to the stripping line?

The change should be made in such a manner The change should be made in such a manner that the that the maximum enrichment maximum enrichment per plate is obtper plate is obtained, so that the number of plates is as small ained, so that the number of plates is as small as possible.as possible.

The transfer should be made immediately after The transfer should be made immediately after a value of x is reached that is less than the x coa value of x is reached that is less than the x coordinateordinate(( 坐标坐标 )) of the intersection of the two opera of the intersection of the two operating lines.ting lines.

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How many ideHow many ideal plates are nal plates are needed?eeded?

Reboiler?Reboiler?

Partial condenPartial condenser?ser?

Is the number Is the number of ideal plates of ideal plates related with ferelated with feed flow rate F?ed flow rate F?

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Feed plateFeed plate

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Optimum feed plate location?Optimum feed plate location?xxFF xxDD

xxBB

Optimum Optimum feed plate feed plate location: location: plate 3plate 3

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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%?

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Mol fraction of benzene in liquid:

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Mol fraction of benzene in vapour :

0.22 0.38 0.51 0.63 0.7 0.78 0.85 0.91 0.96

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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

Similarly, xd=0.974 and xw=0.024

fx

44.0)92/60()78/40(

)78/40(

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•[EXAMPLE 21.2(a)(b)] [EXAMPLE 21.2(a)(b)]

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•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/sAnd: D'=top product rate = 1.6 kg/s '

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(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

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