UNITOPERATIONS

OF CHEMICALEN GINEERIN G

Fourth Edition

WaueD L. McCabeLate R. J. Reynnlds Proje.fS(lr /n Cllemical Engineering

. North CarolinaState Uni,oers;t)'

Julian C. Smith

Profe.fSor of Chemical EngineeringC(lrnell. Uitil'er.dtJ'

Peter HarriottFredH. RhodesPra/essor of Chemical Enginl'ering

I . Comr:ffUniI1er.fit.!'

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UNIT OPERATIONS OF C\!IE1\ilCALENGiNEERING

Copyright@1985.1976.1961,1956byMcGraw-Hili,Inc.Allrightsreservf!d.Typeset in the United States 'OfAmerica. Except as permittedunder the United States Copyright Act 'Of1916,no part of thir!llpublication may be repr~duc~d or dlatl'.lbutedIn any forin orby any means. or stol'ed In Ii data base or retrieval system.without the prior written permission of the publisher.

8 9 0 DORIDOR. 9 9 8 '1 6 I) .. 8 2 1

ISBN 0-07-044828-0

., LIbrary of CoogleR"Cntalilginli In Publication Data

McCabe. Warren I., (Wsrren Lee); date.Unit 'Operations'Ofchemical engineering.

(McGraw:HiUchemical engineerhtg series).Includes index.1. Cl1emicalprocesses, 1. SmUh. Julian C, (Julian

Cleveland), date -Ii. Harriott. Pete1/'. III. Title-IV. Series,. .TPI55,7.MS 1985 660.2'842 84-10045

CHAPTER

EIGHTEEN

DISTILLATION

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In praCtice,distiJIa~ionmay be carried out by either of two principalmethods.Thefirst method is based on the production of a vapor by boiling the liquid mixture tobe separated and condensing the vapors without aUowiQgany liquid to return to thestill. There-is then no reflux. The second method is based on the return of part ofthe condensate to the still under such conditions that this returning liquid is brought

. into intimatecontactwith the vapors on their wayto the condenser.Either of thesemethodsmay be conductedas a continuous processor asit batch process.The firstsection of this chapter deals with continuous stea~y"state distillation processes,including single-stage partial vaporization without reflux (flash distillation) andcontinuous distillation' with reflux (rectification). Batch distillation is ~n unsteady- istate distillation process that is treated only briefly, since it is not as widely used ascontinuous distillation, and the computations are more complex. The last section isconcerned with the design and performance of tray-type distillation columns.

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Flash Distillation

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Flash distillation consists of vaporizing a definite fraction of the liquid in such a waythat the evolved vapor is in equilibrium with the residual liquid, separating the vaporfrom the liquid, and cond~nsing the vapor. Figure 18-1shows the elements of aflash-distillation plant. Feed ispumped by pump a through heater b, and the p~essureis reduced through valve c. An intimate mixture of vapor and liquid enters the vapor"l;-

115

110

1050'WIOOn:: 95F1C{ 901ffiIl. 85

~ 80

75170

650 0.2 0.4 0.6 0.8 . 1.0CONCENTRATION,MOLEFRACllON

.BENZENE

Table 18-1 Data for Example 18-1

Figure 111-3 Boiling-point diagram, system benrene~ .toluene at I atm. .

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

I-MOLES VAPORIZEDPER MOLEOF FEED

Fil!lIrt'IR-4 Rl'SIIIIsfor'ExAmple IR-I.

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DISTILLATION 475

SOLUTIONFor each of several values of f corresponding quantities - [(1/f) - I] arecalculated. Using these quantities ~s slopes, a series of straight lines each passing throughpoint (XF':x,,)is drawn on the equilibrium curve of Fig. 18-2.These lines intersect the equili-brium curve at corresponding values of x. and YD'The temperature of each vaporization isthen found from Fig. 18-3.The results are shown in Table 18-1and piQUedin Fig. 18-4.Thelimits for 0 and 100percent vaporization are the bllbbl~and dew points, respectively. '

ContimllousDistillation witli R.eftuux(Rectification)

Flash distillation is used most for separating components which boil at widely differenttemperatures. It is not effective in separating components of comparable volatility,since then both the condensed vapor and residual liquid are far from pure. By manysuccessive redistillations small amounts of some nearly pure components may finallybe obtained, but this method is too inefficient for industrial distillations when nearlypure components are wanted. Modern methods used in both laboratory and plantapply the principle of rectification, which is described in this section.

Rectification on SInideal plate Consider a single plate in a column or cascade of idealplates. Assume that the plates are numbered serially from the top down and that the,plate under consideration is the nth plate from the top. It is shown diagrammaticallyin Fig. 18-5.Then the plate immediately above this plate is plate,. - 1, and thatimmediately below it is plate n + 1. Subscripts are used on aU quantities showing

. the point of origin of the quantity. .

Two fluid streams enter plate ft, and two leave it. A stream of liquid, L"- 1mol/h,fromplate n - 1,and a stream of vapor, v,,+i mol/h, from plate n + 1, are broughtinto intimate contact. A stream.ofVapor, v" mol/h, rises to plate 11- 1,and a stream

fiWUII'e)iJ.S Material-balanct::diagram for plate n.

Fraction 1- f Temperature,Slope- -vaporizedf f Liquidx. VaporYD °C

0 0:0 0.50 0.71 92.20.2 -4 0.455 0.67 93.70.4 -1.5 0.41 0.63 95.00.6 -0.67 0.365 Q.585 96.50.8 -0.25 0.325 0.54 97.71.0 0 0.29 0.50 99.0

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b

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Vaportoe . condenser

{moleYo

c d

a

----1I

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Figure 111-1 Plant for flash distillation.

separator d, in whichsufficienttime is al1owedfor the vapor and liquid portions toseparate. Because of the intimacy of contact of liquid and vapor before separation,the separated streams are in equilibrium. Vapor leaves through line e and liquidthrough line g.

Flash distillationt of binary mixtures Consider t mol of a two-component mixturefed to the equipment shown in Fig. 18-I. Let the concentration of the feed be XF,inmole fraction of the more volatile component. Letfbe the molal fraction of the feedthat is vaporized and withdrawn continuously as vapor. Then 1 - f is the molalfraction of the feed that leaves continuously as liquid. Let J'Dand XBbe the concentra-tions of the vapor and liquid, respectively. Bya material balance for the more volatilecomponent, based on I mol of feed, all of that component in the feed must leave in thetwo exit streams,or

XF=fYD + (I - f)xn (18-1)

There are Cwounknowns in Eg. (l8~1), XBand YD'To l!se the equation a second re-lationship between the unknowns must be available. Such a relationship is providedby the equilibrium curve, as YDand XB are coordinates of a point on this curve. IfXBand Ynare replaced by x and J', respectively, Eq. (18-1) can be written

J - f XFy= --x+-f f (18-2)

The fnlctionfis not fixed directly hut depends on the enthalpy of the hot incoming

t flash distillation is used on a large scale in pel roleum refining. in which petroleum fractin"s are heated

in pipe stills and the heated fluid flashed into overhead vapor and residual-Hquid streams. each containingmany components.

. 'DiSTILLATION473

liquid and the enthalpies of the vapor and liquid leaving the flash chamber. For agiven feed condition, the fractionfcan be increased by flashing to a lower pressure,

Equation (18-2) is the equation of a straight line with a slope of -(1 - J)/fandcan be plotted on the equilibrium diagram. The coordinates of the intersection of theline and the equilibrium curve are x = XB and y = Yo. The intersection of thismaterial-balance line and the diagonal x = y can be used conveniently a~ a point onthe line.Lettingx = Xf in Eg. (t 8-2)gives "

J - f XF

Y= -jXF +7

from which y = XF= x. The material-balanceline crosses the diagonal at x = xl'for all values off .

Example 18-1 A mixture of 50 mole percent benzene and 50 mole percent toluene is subjectedto flash distillation at a separator pressure of I atm. The vapor-liquid equilibrium cprve andboiling-point diagram are shown in Figs. 18-2and 18-3. Plot the following quantities,all as functions of J, thefractionai vaporization: (a) the temperature inlhe separator, (b) thecompositionofthe liquid leavingtheseparator,and (c)thecompositionof thevapor leavingthe separator.

1.0

0.9

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0.4

0.3

0.2

01

0a 0.1 0.2 0.3 0..4 0.5 0.6 07 0.8 09 1.0.

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Figure 111-:2'Equilibrium curve, system benzcl1c-tolllene. Graphical construction for Example 18-1.

Note Ihat in this case there is almost no change in L and V in the stripping section. in conlrast

10 Ihe7 percent decrease in t in the rectifying section. The lower operating line can hedrawn as,'a straight line to the intersection of the upper operating line and the q line,

Counting steps, about 27 ideal stages are required for this separation, compared to 21based on the assumption of constanl' molal overflow. The difference would be smaller if ahigher reflux ratio were used. The calculations were based on 1.2 times the nominal value ofRonln'but this really corresponds to about 1.1 times the true minimum reflux, as can be seenfromFig. 18-25. "

In Example 18-5, the molar liquid rate decreased about 7 percent in going fromthe top plate to the feed plate, main}y because of the higher molar heat of vaporization.of toluene. The terms for the change in sensible heat of the liquid and vapor streams'nearly cancel, since the liquid has a higher heat capucity but a lower flowrate thanthevapor. In the stripping section of the column, there was almost no change in liquidrate, although the vapor composition changed even more than in the rectifyingsection.The iiquid flow rate in the stripping section is always greater than the vapor rate, andin Example 18-5,the product of flow rate and heat capacity for the liquid was 1.73times that for the vapor. Only part Qf the energy needed to heat the liquid from thefeed plate temperature to the reboiler'temrerature could be supplied by cooling thev,apor, and the rest came from condensation of vapor in the column. The differencebetween the heat of condensation of toluene and the heat of vaporization of benzenewas nearly used up in providing the extra energy needed to heat the liquid,so that,there was only a slight increase in vapor flow from the reboiler to the feed plate.

Similar changes in L and V are likely to be observed for other ideal mixtures.The more volatile component has a lower molal heat of vaporization, since the heat

of vaporization is roughlyproportional to the normal boiling point (Tronton's rule).The changein V will be greatest in the upper section of the column, where L is lessthan V,andmaybealmost zero in the lower section, where 1~/V> .1.0.The percentagechange in (LjV) will be smaller than the' change in L or V, but th~ slight upwardshift of the operating 1inesmay be important when operating close to the minimumreflux ratio, as was the case in Example 18-5. For operation at twice the minimum

reflux ratio or greater, the effect of operating-line cur'vature would be very small.

The slope of a straight operating line is L/V for that section of thecoluinn, butthe localslopeofa curvedoperatinglineisnotequal to the local value of L/JI. Startingwith the equation for the rectifying section, Eq. (18-46), the following equations canbeobtained by replacingfirstLnand then Vn+ I with ';n+ J - Da,ndL" + D:

J~+ ,.I"n+I = (Vn+ t - D)xn + OXD

or Vn+.I{J'n'FJ- x,,) = D(XD - x,,)

(Ln + D)Yn+1 = 1-nxn + OXIJ

(lR-51)

or 1-"C\'n4t - X,,) = O(XIJ - ,\""1) (lR-52)

Dividing El]. (IR-52) by Eq. (18-51),

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(18-53)

DISTILLATION 507

Tlms (L"/v,, + I) is the slope of the chord connecting points (XD' xl» and ()lilt I' XII)' Asimilar derivation for the stripp,ing section shows that

BATCH DISTILLATION

Lm - )'",+1 -,XU

Vmtl- x~;- Xu(18-54)

In some small plants, volatile products are recOJ!eredfrom liquid solution by batchdistil1ation. The mixture is charged to a still or reboiler, and heat is supplied througha coilor through the wall of the vessel to bring the liquid to the boiling point and thenvaporize part of the hatch. In the simplest method of operation, the vapors are takendirectly from the still to a condenser, as shown in Fig. 18-26.The vapor leaving thestill at any time is in equilibrium with the liquid in the sti11,but since the vapor isricher in the more volatile component, the compositions of liquid and vapor are not'constant. ,

To show how the compositions change with time, consider what happens if II!)

mol are charged to a batch still. Let /I be the moles of liquid left in the still at a giventime and )' and x be the vapor and liquid compositions. The total moles of com-ponent A left in the sti11I1Awill be,;~,

If A = xn (18-55)

Ifa smallamount,of liquid tin isvaporized,thechangein the molesof componentA is J' dll, or dn... Differentiating Eq. (18-55) gives

alIA = d(xll) = "aX + x dll

II dx + x dn = )I dnHence

1!l;' By rearrangement,

(18-56)

dn = ~ (18-57)II Y-X .

Equation (18-57) is integrated between the limits of Xoand X I' the initial andfinalconcentrations, '

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in'dll fX' dx "I-= -=In-"0 n Xo )I - X 110

(18-58)

, Pr\Jdllclreceiver

Figure 18-26 Simpte dl~liIIl!lion In a hatchsliII.

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508 MASS TRA~SFER AND ITS APPLICATIONS

Equation (18-58) is known as the Rayleigh equation. The function dx/(y - x) can beintegrated graphically or numerically using tabulated equilibrium data or an equiJi-brium curve. ' , '

A simple alternative to the ~~yleigh equation. can be derived for an ideal mixturebased on the relative volatility. Allhough the temperature in the still increases duringa batch distillation, the relative volatility~which is the ratio of vapor pres~ures,doesnot change much and an average value can be used. From Eq. (18-32),

YA XA-:::: IXAD-Ya XB

U the mixture has IIAmol of A and liBmol of B, the ratio IIA/IIBis equal to XA/XD;.when tIll mol is vaporized. the change in A is YAdn or dllA, and the change in BisYBall or dnD'Substituting these terms into Eq. (18-59)gives' '

dnA/dll dnA IIA--=-=IXAD-dna/dll dnB Ita

anA dnB- = IXAa-"A n8

(18-59)

or (18-60)

After integration between limitsIIA I1D

In ._~ = etAB In-/lOA " /lOB

~ =(~

)I/"AB

IIOD IIOA '

Equation (18-62)can be plotted as a straight line on logarithmic coordinates tohelp follow the course of a batch distitlation, orit can be used directly if the recoveryof one of the components is specified.

(18-61)

or (18-62)

Example 18-6 A batch of crude pentane contains 15 mole percent II-butaneand 35 percent'"-pentane. If a simple batch distillation at atmospheric pressure is used to remove 90percentof the butane, how much pentane would be removed? What would be the composition of the

remaintng liquid?

SOLUTIONThe final liquid is nearly pure pentane, and its boiling point is 36°C.The vaporpressure of butane at this temperature is 3.4 atm, givinga relative volatility of 3.4.For theinitial conrlitions, the boiling point is about 27°C,and the relative volaiility is 3.6.Therefore,an average value of 3.5 is used for (l(A8- ' .Basis: I molfeed

/lOA:; 0.15 (butane)

Front Equation (18-62)

/lA= 0.015 /lOB== 0.85 (pentane)

~ :; 0.11/3.5 ==0.5180.85

/lB == 0.518(0.85) = 0.440

n = 0.44+ 0.015= 0.455I

0.015 = 0.033XA = 0.455

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DISTlLLAnON 5119

Batch distillation with reftu~ Batch distiUation with only a simple still does notgive a good separationunless the relativevolatility is very high. In many I:ases,arectifying column with reflux is used to improve the performance of the batch still.If the column is not too large, it may be mounted-on top of the still, as shown in Fig.17-1,or it may be supported independently, with connecting pipes for the vapor andliquid streams. '

, The operation of a batch still and cohlmn can be analyzed using a McCabe-Thiele diagram. with the same operating~line equation that was used for the rectifyingsection of a continuous distillation: ,

Rv Xv}'u+ 1 = -R XII + R + 1

.Q+l ' V

(18-19)

The system may be operated to keep the top composition constant by increasingthe reflux ratio as the composition of the liquid in the reboiler changes. The McCabe-Thiele diagram for this case would have operating lines of different slope positionedsuch that tl)esamenumberof idealstageswasused to go from XDto XBat any time; Atypicaldiagram isshown in Fig. 18-27for a stitt with fiveidealstages includingthereboiler.The upperoperatinglineisfor the initial conditions, when the concentrationof low boiler in the still is about the same as the charge composition. (The concentra-tion XI/is slightly lower than XFbecause of the holdup of liquid on the plates). Thelower operating line and the dashed line steps show conditions when about one-thirdthe charge has been removed as overhead product.

To determine the reflux ratio needed for a constant Xv and a given Xn requires atrial-and-error calculation. since the last step'on the assumed operating tine must endexactly at Xn. However, °l1cethe initial refluxratio ischosen by this method, the valueof XB for a later stage in the distillation can be obtained by assuming a value of RD,constructing the opet;ating line, and making the correct number of steps ending at

v

Figure 18-27 McCabe-Thiele diagrams for Ii

batch distillation, Upper operating line andsolid lines: initial conditions; lower operatingline and dashed lines: after one-third of the

charge has been removed.x

""" MI\"" I KI\N:>I"'K ANI) IT:; J\I'I'LICATIONS

XB' Bya materialbalance,Eqs.(18-5)and(18-6),theamountofproductand remainingchargecan be calculated. .

An alternate method of running a batch distillation is to fix the reflux ratio andlet the overhead product purity vary with time, stopping the distillation when theamount of product or the average concentration" in the total pr6duct reache~ a certainvalue. To calculate the perform<\nceof the still, operating Jinesof constant slope aredrawn starting at different values of Xn and the actual number of stages is stepped offto determine XB' The total nl,lmber of moles left in the still is then calculated byintegration of Eq. (18-58),where Xv is equal to }'and x is equal to XB'

DESIGN OF SIEVE~PLATE COLUMNS

To translate ideal plates into actual plates, a correction for the efficiencyof the platesmust be applied. There are other important decisions, some at least as important asfixing the number of plates, that must be made before a design is complete. A mistakein these decisions results in poor fractionation, lower-than-desired capacity, pooroperating flexibility, and, with extreme errors, an inoperative column. Correctingsuch errors after a plant has been built can be costly. Since many variables that in-fluence plate efficiencydepend on the design of the individual plates, the fundamentalsof plate designare discussedfirst. .

The extent and variety of rectifying columns and their applications are enormous"The largest units are usually in the petroleum industry, but large and very complicateddistillation plants are encountered in fractionating solvents, in treating liquefied air,and in general chemical processing. Tower diameters may range from I ft (0.3 m) tomore than 30 ft (9 m) and the number of plates from a few plates to scores. Platespacings may vary from 6 in. or less to several feet. Formerly bubble-cap plates weremost common; today most columns contain sieve trays or lift-valve plates. Manytypes of liquid distribution are specified. Columns may operate at high pressures orlow, from temperatur~s of liquid gases up to 1600°F reached in the rectification ofsodium and potassium vapors. The materials distilled can vary greatly in viscosity,diffusivitYi'corrosivenature, tendency to foam, and complexity of composition. Platetowers are as useful in absorption as in rectification, and the fundamentals of platedesign apply to both operations.

Designing fractionating columns, especially large units ~nd those for unusualapplications, is best done hy experts. Although the number br ideal plates and theheat requirements can be computed quite accurately without' much previous experi-ence, other design factors are not precisely calculable, and a number of equally sounddesigns can he found for the same problem. In common with most engineeringactivities, sound design of fractionating columns relies on a few principles, on a num-ber of empirical correlations (which are in a constant state of revision). and muchexperience and judgment. I

The following discussion is limit.edto the usual type of column, equipped withsieve plates. operating at pressures not far from atmospheric', and treat ing mixtureshilvinl! ordinary properties.

,.

DISTlLlA TION 51I .

Normal operatio~ of sieve plate A sieve plate is designed to bring a rising streamof vapor into intimate contact with a descending stream of liquid. The liquidflows across the. plate and passes over a weir to a downcomer leading to the platebelow. The flowpattern on each plate is therefore crossflow rather than countercurrentflow, but the column as a whole is still considered to have countercurrent flow ofliquid and vapor. The fact that there is crossflow of liquid on the plate is important inanalyzing the hydraulic behavior of thecolumn and in predicting plate efficiency.

Figure 18-28shows a plate in a sieve-traycolumnin normaloperation.Thedowncomers are the segment-shaped regions between the curved wall of the columnand the straight chord weir. Each downcomer usually occupies 10 to 15 percent ofthe column cross section, leaving 70 to 80 percent of the column area for bUbbling orcontacting. In small columns the downcomermay be a pipe welded to the plate andprojecting up above the plate to form a circular weir. For very large columns, addi-tional downcomers maybe provided at the middle of the plate to decrease the lengthof the liquid flow path. In some cases an underflow weir or tray inlet weir is installedas showninFig.18-28to improvethe liquiddistributionand to preventYapo\"bubblesfrom entering the downcol11er. .

The vapor passes through the perforated region of the plate, which occupies most

of the space between downcomers. The holes are usually 1\ to t in. in si2:eand arrangedin a triangular pattern. One or two rows of holes may be omitted near the overflowweir to permit some degassing of the liquid before it pas$es over the weir. Some holesmay also be omitted near the liquid inlet to keep vapor bubbles out of the downcomer.Undernormalconditions,the vapor velocity is high enough to create a frothy mixtureof liquid and vapor which has a large surface area for mass transfer. The averagedensity of the froth may be as low as 0.2 of the liquid density, and the froth heightis then several times the value corresponding .to the .amount of liquid actually on theplate.. .

r.. Pressure~ P"-1Downcomer

~ -......

r- ""-,;r---- .r--. Weir// r-~ ~~.';/

"" f\:'.'~-----------Pressure~ P"

~~~.:::: -..~- Froth ~-

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I!'Wf ~..u"""'~,,, ",=

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"i~lIre 111.28Normal "pcrati"l! "f siew pl:1tc.

Pla\en -.1. " <J

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0 0" f +. J.E'hw +h...1

Platen.