distillation - dl.chemgroup.irdl.chemgroup.ir/library/crystalization.purification.separation... ·...

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DISTILLATION

R. Smith and M. Jobson, Department of ProcessIntegration, UMIST, Manchester, UK

Copyright^ 2000 Academic Press

Introduction

Distillation is the most commonly used method forthe separation of homogeneous Suid mixtures. Separ-ation exploits differences in boiling point, orvolatility, between the components in the mixture.Repeated vaporization and condensation of the mix-ture allows virtually complete separation of mosthomogeneous Suid mixtures. The vaporization re-quires the input of energy. This is the principal disad-vantage of distillation: its high energy usage.However, distillation has three principle advantagesover alternative methods for the separation of homo-geneous Suid mixtures:

1. The ability to handle a wide range of feed Sowrates. Many of the alternative processes for theseparation of Suid mixtures can only handle lowSow rates, whereas distillation can be designed forthe separation of extremely high or extremely lowSow rates.

2. The ability to separate feeds with a wide range offeed concentrations. Many of the alternatives todistillation can only separate feeds that are alreadyrelatively pure.

3. The ability to produce high product purity. Many ofthe alternatives to distillation only carry out a par-tial separation and cannot produce pure products.

It is no accident that distillation is the most commonmethod for the separation of homogeneous mixtures.It is a versatile, robust and well-understood technique.We shall start explaining distillation by a single-stageseparation, before understanding how to set up a cas-cade of separation stages, which is distillation.

Single-Stage Separation

Consider the liquid mixture illustrated in Figure 1. Ifthis liquid mixture is partially vaporized then thevapour becomes richer in the more volatile compo-nents (i.e. those with the lower boiling points) thanthe liquid phase. The liquid becomes richer in the lessvolatile components (i.e. those with the higher boilingpoints). If we allow the system in Figure 1 to come toequilibrium conditions, then the distribution of thecomponents between the vapour and liquid phases is

84 I / DISTILLATION / Derivatization

Figure 1 Partial vaporization of a liquid mixture creates a separation.

dictated by thermodynamic vapour}liquid equilib-rium considerations. All components can appear inboth phases. However, involatile components willtend to stay in the liquid phase.

Rather than partially vaporize a liquid, as shown inFigure 1, we could have started with a mixture ofcomponents in the vapour phase and partially con-densed the vapour. We would still have had a separ-ation, as the liquid which was formed would be richerin the less volatile components, while the vapourwould have become depleted in the less volatile com-ponents. Again, the distribution of components be-tween the vapour and liquid is dictated by thermo-dynamic vapour}liquid equilibrium considerations ifwe allow the system to come to equilibrium. Anynoncondensable components present in the vapourwill tend to stay in the vapour phase.

For each component in the mixture, thermody-namic equilibrium is given by the condition when thevapour and liquid fugacities are equal:

f vi "f Li [1]

Fugacity is a thermodynamic pressure which, whensubstituted for pressure in thermodynamic expres-sions for ideal systems, allows them to be used fornonideal systems. It can be thought of as an escapingtendency. DeRning the vapour phase fugacity coef-Rcient �vi :

f vi "yi�vi P [2]

DeRning the liquid-phase fugacity coefRcient �Liand activity coefRcient �i:

f Li "xi�Li P [3]

or:

f Li "xi�i f 0i [4]

For moderate pressures f 0i is usually taken to be thesaturated vapour pressure PSATi :

f Li "xi�iPSATi [5]

These equations can be combined to give an expres-sion for the constant, K:

Ki"yixi

"�Li

�vi[6]

This expression provides the basis for vapour}liquidequilibrium calculations based on equations of state(e.g. Peng}Robinson equation). Alternatively:

Ki"yixi

"�iPSATi

�vi P[7]

This expression provides the basis for vapour}liquidequilibrium calculations based on liquid-phase activ-ity coefRcient models (e.g. Wilson equation). Atmoderate pressures:

Ki"yixi

"�iPSATi

P[8]

When the liquid phase behaves as an ideal solution,this expression simpliRes to:

Ki"yixi

"PSATi

P[9]

which is Raoult’s law. Correlations are available torelate component vapour pressure to temperature(e.g. the Antoine equation), activity coefRcientsto composition and temperature (e.g. the Wilsonequation) and fugacity coefRcient to mixture,pressure and temperature (e.g. from the Peng}Robin-son equation of state). Regression analysis of experi-mental data provides the adjustable parameters usedin the various models.

The ratio of equilibrium constants for two compo-nents measures their relative volatility:

�ij"KiKj

[10]

where �ij is the relative volatility between componentsi and j.

Figure 2 shows the vapour}liquid equilibrium be-haviour for a binary mixture of benzene and toluene.

Sepsci*41*TSK*Venkatachala=BGI / DISTILLATION 85

Figure 2 Vapour}liquid equilibrium for a binary mixture of benzene and toluene at a pressure of 1 atm.

Figure 3 Separation in a single equilibrium stage.

Figure 2A shows the behaviour of the temperature ofthe saturated liquid and saturated vapour as the moleraction of benzene is varied (the balance beingtoluene).

Figure 2A also shows a typical vapour}liquid equilibrium pair where the mole fraction ofbenzene in the liquid phase is 0.4 and that in thevapour phase is 0.62. Shown in Figure 2B is analternative way of representing the vapour}liquidequilibrium behaviour (x}y diagram). This plotsthe mole fraction of benzene in the vapour versusmole fraction of benzene in the liquid. A diagonalline across this diagram would represent a situationwhere the concentration in the vapour and the liquidare equal. The phase equilibrium behaviour, how-ever, shows a curve above the diagonal line. Thisindicates that the benzene has a higher concentrationin the vapour phase than the toluene, i.e. the benzeneis the more volatile component in this case. Figure 2Bshows the same vapour}liquid equilibrium pair asthat shown in Figure 2A with a mole fraction ofbenzene in the liquid phase of 0.4 versus a molefaction in the vapour phase of 0.62.

Figure 3 shows a single equilibrium stage. Liquid isfed with composition x0 and vapour is fed with com-

position y2. Contact between the vapour and theliquid streams makes the vapour richer in the morevolatile components and the liquid richer in the lessvolatile components. Once the feed conditions andcompositions, the system pressure and the relativeSow rates of the vapour and liquid have been Rxed,then the temperature and compositions of the exitstreams are unique. Let us also, initially, make a sim-plifying assumption that the molar Sow rates of theliquid L and molar Sow rates of the vapour V areconstant for the stage. This assumption is known asconstant molar overSow and is true if sensible heateffects are small, molar latent heats of vaporiza-tion of the components are equal, heat of mixing isnegligible and there are no heat losses or gains. Let usnow carry out a mass balance around the equilibriumstage shown in Figure 3. First we assume constantmolar overSow:

L0"L1"L [11]

V2"V1"V [12]

A component mass balance gives:

Lx0,A#Vy2,A"Lx1,A#Vy1,A [13]

which can be rearranged to give:

y1,A"!LV

x1,A#Lx0,A#Vy2,A

V[14]

This equation can be plotted on an x}y diagram, asshown in Figure 4. The mass balance line is a straightline which depends on the liquid and vapour Sowrates and the feed compositions of liquid and vapour.In Figure 4 the liquid and vapour feeds are not inequilibrium. Following the mass balance line until it


Figure 4 Single-stage separation for a binary mixture.

Figure 5 A cascade of separation stages.

crosses the equilibrium line allows us to predict thevapour and liquid composition at the exit of the stage.We can now see quantitatively the separation carriedout by the single equilibrium stage. However, theseparation which is achieved on a single equilibriumstage is limited. We now need to consider how we canextend the idea to carry out further separation.

Cascade of Separation Stages

We have seen that a single equilibrium stage can onlyachieve a limited amount of separation. To extend theamount of separation we can make a cascade ofstages, as shown in Figure 5. It is assumed in thecascade that streams leaving each stage are in equilib-rium. Using a cascade of stages in this way allows themore volatile components to be transferred to thevapour phase, the less volatile components to betransferred to the liquid phase and a greater degree ofseparation to be achieved than for a single stage.

Figure 6 shows the liquid and vapour Sows con-necting the stages in a countercurrent cascade. Asbefore, we assume constant molar overSow:

L0"Lm"2"LN; V1"Vm"2"VN#1 [15]

We can write an overall mass balance for componenti across the cascade:

L0x0,i#VN#1yN#1,i"LNxN,i#V1y1,i [16]

We can also write a mass balance around the envel-ope shown in Figure 6 over m stages:

L0x0�i#Vm#1ym#1,i"Lmxm,i#V1y1,i [17]

This equation can be rearranged to give:

ym#1"LV

) xm#Vy1!Lx0

V[18]

This operating line relates the composition streamsafter m stages.

Figure 7 shows the cascade in terms of a moreconventional representation in a distillation column.At the top of the column we need liquid to feed thecascade. This is produced by condensing and return-ing some of the vapour which leaves the top stage.We also need vapour to feed the cascade at the bot-tom of the column. This is produced by vaporizing


Figure 6 Mass balance on a countercurrent cascade.

Figure 7 Refluxing and reboiling.

and returning some of the liquid leaving the bottomstage. The feed to the process is introduced at anintermediate stage; products are removed from thecondenser and the reboiler (vaporizer).

The method by which the vapour and liquid arecontacted with each other in distillation columns fallsinto two broad categories. Figure 8 shows a plate ortray column. Liquid enters the Rrst tray at the top ofthe column and Sows across what is shown inFigure 8 as a perforated plate. Liquid is preventedfrom weeping through the holes in the plate by theupSowing vapour. In this way the vapour and liquidare contacted. The liquid from the Rrst tray Sows overa weir and down a downcomer, to the next stage and

so on. The design of stage used in Figure 8 involvinga plate with simple holes is known as a sieve tray.Many other designs of tray are available involving,for example, valve arrangements for the holes in thetrays. In practice, the column will need more traysthan the number of equilibrium stages as mass trans-fer limitations prevent equilibrium being achieved ona tray.

The other broad class of contacting arrangement isthat of packed columns. Here the column is Rlledwith a solid material which has a high voidage.Liquid trickles across the surfaces of the packing andvapour Sows upward through the voids in the pack-ing, contacting the liquid on its way up the column.Many different designs of packing are available.

The design of a distillation column like the oneshown in Figure 8 involves a number of steps:

1. Set the product speciRcations.2. Set the operating pressure.3. Determine the number of theoretical stages re-

quired and the energy requirements.4. Determine the actual number of trays or height of

packing needed and the column diameter.5. Design the column internals, which involves deter-

mining the speciRc dimensions of the trays, pack-ing, liquid and vapour distribution systems, etc.

6. Carry out the mechanical design to determine wallthicknesses, internal Rttings, etc.

Let us start by considering the simplest case of binarydistillation.

Binary Distillation

Consider the mass balance on a simple distillationcolumn. By simple column, we mean that thecolumn has one feed, two products, one reboiler andone condenser. Such a column is shown in Figure 9,together with the feed and product Sow ratesand compositions. We can write an overall massbalance as:

F"D#B [19]


Figure 8 The distillation column.

Figure 9 Mass balance on a simple distillation column.

We can also write a component balance as follows:

Fzi"xD,iD#xB,iB [20]

However, to understand the design of the columnmore fully, we must be able to follow the mass bal-ance throughout the column. Let us start by consider-ing the mass balance for the part of the column abovethe feed } the rectifying section. Figure 10 shows therectifying section of a column and the Sows andcompositions of the liquid and vapour in the rectify-ing section. First we write an overall balance for therectifying section:

Vn#1"Ln#D [21]

We can also write a component balance:

Vn#1yn#1,i"Lnxn,i#DxD,i [22]

We assume constant molar overSow (L and V areconstant) and deRne the reSux ratio, R, to be:

R"L/D [23]

Given the reSux ratio, we can express the vapour Sowin terms of R:

V"(R#1) D [24]


Figure 10 Mass balance on the rectifying section.

Figure 11 Mass balance on the stripping section.

These expressions can be combined to give an equa-tion which relates the vapour entering and liquidSows leaving stage n:

yn#1,i"R

R#1 xn,i#1

R#1 xD,i [25]

On an x}y diagram for component i, this is a straightline starting at the distillate composition with slopeR/(R#1) and which intersects the diagonal line atxD,i.

Starting at the distillate composition xD in Fig-ure 10, a horizontal line across to the equilibrium linetakes us to the composition of the vapour in equilib-rium with the distillate, y1. A vertical step down takesus to the liquid composition leaving stage 1, x1. An-other horizontal line across to the equilibrium linegives us the composition of the vapour leaving stage2, y2. A vertical line to the operating line gives us thecomposition of the liquid leaving stage 2, x

�, and so

on. Thus, as we step between the operating line andequilibrium line in Figure 10, we follow the change invapour and liquid composition through the rectifyingsection of the column.

Now consider the corresponding mass balance forthe column below the feed, the stripping section.Figure 11A shows the vapour and liquid Sows andcompositions through the stripping section of a col-umn. An overall mass balance for the stripping sec-tion around stage m gives:

Lm"Vm#1#B [26]

A component balance gives:

Lmxm,i"Vm#1ym#1,i#BxB,i [27]

Again, assuming constant molar overSow (L andV are constant), these expressions can be combined togive an equation relating the vapour entering and theliquid leaving stage m:

ym#1,i"LV

xm,i!BV

xB,i [28]

We can plot this line in our x}y plot, as shown inFigure 11B. It is a straight line with slope L/V whichintersects the diagonal line at xB. Starting from the


Figure 12 Mass balance for the feed stage.

bottom composition, xB, a vertical line to the equilib-rium line gives the composition of the vapour leavingthe reboiler, yB. A horizontal line across to the operat-ing line gives the composition of the liquid leavingstage N, xN. A vertical line to the equilibrium linethen gives the vapour leaving stage N, yN, and so on.

Let us now bring together the rectifying and strip-ping sections at the feed stage. Consider the point ofintersection of the operating lines for the rectifyingand stripping sections. From eqns [22] and [27]:

Vn#1yi"Lnxi#DxD,i [29]

Vm#1yi"Lmxi!BxB,i [30]

where yi and xi are the intersection of the operatinglines. Subtracting eqns [29] and [30] gives:

(Vn#1!Vm#1)yi"(Ln!Lm)xi#DxD,i#BxB,i [31]

Substituting the overall mass balance, eqn [20], gives:

(Vn#1!Vm#1)yi"(Ln!Lm)xi#Fzi [32]

Now we need to know how the vapour and liquidSow rates change at the feed stage.

What happens here depends on the condition of thefeed, whether it is sub-cooled, saturated liquid, par-tially vaporized, saturated vapour or superheatedvapour. To deRne the condition of the feed, we intro-duce the variable q, deRned as:

q" heat required to vaporize 1 mol of feedmolar latent heat of vaporization of feed

[33]

For a saturated liquid feed q"1 and for a saturatedvapour feed q"0. The Sow rate of feed entering thecolumn as liquid is q ) F. The Sow rate of feed enteringthe column as vapour is (1!q) ) F. Figure 12A showsa schematic representation of the feed stage. An over-all mass balance on the feed stage for the vapourgives:

Vn"Vm#(1!q)F [34]

An overall mass balance for the liquid on the feedstage gives:

Lm"Ln#qF [35]

Combining eqns [32], [34] and [35] gives a rela-tionship between the compositions of the feed and the

vapour and liquid leaving the feed tray:

yi"q

q!1 ) xi!1

q!1 ) zi [36]

This equation is known as the q-line. On the x}y plot,it is a straight line with slope q/(q!1) and intersectsthe diagonal line at zi. It is plotted in Figure 12B forvarious values of q.

We are now in a position to bring together the massbalance for the rectifying and stripping sections.Figure 13 shows the complete design. The construc-tion is started by plotting the operating lines for therectifying and stripping sections. The q-line intersectsthe operating lines at their intersection. The intersec-tion of the operating lines is the correct feed stage, i.e.the feed stage necessary to minimize the overall num-ber of theoretical stages. The construction stepsoff between the operating lines and the equilib-rium lines. The construction can be started eitherfrom the overhead composition working down orfrom the bottom composition working up. The


Figure 13 Combining the rectifying and stripping sections.

Figure 14 (A) Total and (B) minimum reflux in binary distillation.

stepping procedure changes from one operating lineto the other at the intersection with the q-line. Weshould also note that a partial reboiler representsa separation stage and a partial condenser (as op-posed to a total condenser) also represents a separ-ation stage.

There are two important limits that we need toconsider for distillation. The Rrst is illustrated inFigure 14A. This is total reSux in which no productsare taken and there is no feed. All of the overhead

vapour is reSuxed and all of the bottom liquid re-boiled. Figure 14A also shows total reSux on an x}yplot. This corresponds with the smallest number ofstages required for the separation. The other limitingcase, shown in Figure 14B, is where the reSux ratio ischosen such that the operating lines intersect at theequilibrium line. As this stepping procedure ap-proaches the q-line from both ends, an inRnite num-ber of steps are required to approach the q-line. Thisis the minimum reSux condition, and we term thecondition at the feed stage to be a pinch.

This method of design for binary distillation isknown as the McCabe}Thiele method. It is restrictedin its application because it only applies to binarysystems and involves the simplifying assumption ofconstant molar overSow. However, it is an importantmethod to understand as it gives important concep-tual insights into distillation, which cannot be ob-tained in any other way.

Multicomponent Distillation

Before a multicomponent distillation column can bedesigned, a decision must be made as to the two keycomponents between which it is desired to make theseparation. The light key component will be the onewe wish to keep out of the bottom product. Theheavy key component will be the one we wish to keepout of the top product. The recovery of the light keyor the concentration of the light key in the overhead


Figure 15 The Hengstebeck}Geddes method.

product must be speciRed, as must the recovery of theheavy key or the concentration of the heavy key in thebottom product. Intermediate boiling componentswill distribute between the products.

A number of short-cut methods are available forthe design of multicomponent distillation columns.Each considers different aspects of the design ofmulticomponent columns. Each of the short-cutmethods involves some simplifying assumptions andthe designer must be fully aware of these assumptionswhen applying these methods. One simplifying as-sumption, which all the methods have in common, isthe assumption of constant relative volatility. Therelative volatility for the feed composition can becalculated, but this might not be characteristic of theoverall column. By making some assumption of theproduct compositions, the relative volatility at the topand bottom of the column can be calculated anda mean taken:

(�i,j)mean"�(�i,j)top ) (�ij)bottom [37]

Fenske Equation

The Fenske equation is used to estimate the minimumnumber of stages, Nmin. This is at total reSux and theSows of component i and a reference component, r,are related by:

didr

"�Nmini,r )bibr

orxD,ixD,r

"�Nmini,r )xB,ixB,r

[38]

When component i is the light key component L, andr is the heavy key component, H, we can write:

Nmin"log �

dLdH

)bHbL�

log �L�H[39]

Nmin"log �

xD,LxD,H

)xB,HxB,L�

log �L,H[40]

Nmin"log �

rD,L1!rD,L

)rB,H

1!rB,H�log �L,H

[41]

Hengstebeck^Geddes Equation

The Hengstebeck}Geddes equation is used to esti-mate the composition of the products. The Fenskeequation can be written in the form:

log�dibi�"A#C log �i,r [42]

The parameters A and C are obtained by applying therelationship to the light and heavy key components.This allows the compositions of the non-key compo-nents to be estimated. This is illustrated in Figure 15.Having speciRed the distribution of the light andheavy key components, knowing the relative volatil-ities for the other components allows their composi-tions to be estimated. The method is based on totalreSux conditions. It assumes that the component dis-tributions do not depend on reSux ratio.

The Underwood Equations

The Underwood equations are used to estimate min-imum reSux ratio. There are two equations. The Rrstis given by:

n

�i"1

�i xi,F�i!�

"1!q [43]

This equation must be solved for the root �. This rootwill have a value between the relative volatilities ofthe light and heavy key components. Having obtainedthe value �, this is then substituted into the secondequation to determine the minimum reSux ratio, Rmin:

Rmin#1"n

�i"1

�i xi,D�i!�

[44]

The Gilliland Correlation

The Gilliland correlation is an empirical relationshipused to determine the number of stages, given theminimum reSux ratio Rmin and minimum number ofstages Nmin. The original correlation was presented in


Figure 16 A general stage for rigorous methods in multicomponent distillation.

graphical form. Two parameters were used to corre-late the experimental data:

Y"N!NminN#1 , X"

R!RminR#1 [45]

Various attempts have been made to represent thecorrelation algebraically. For example:

Y"0.2788!1.3154X#0.4114X0.2910

#0.8268 ) lnX#0.9020 ln�X#1X� [46]

The Kirkbride Equation

The Kirkbride equation is used to estimate the mostappropriate feed point for the column. It is given inthe form:

logNrNs

"0.206 log�zHzL

)BD

)�xB,LxD,H�

2

� [47]Rigorous Methods

All of the above equations are approximate in someway. To develop a completely rigorous approach todistillation design, consider Figure 16. This showsa general stage in the distillation column. Vapour andliquid enter this stage. A liquid side-stream can betaken, as can a vapour side-stream. Feed can enter

and heat can be transferred to or from the stage. Thisis a general stage and allows for many design optionsother than simple columns with one feed and twoproducts. By using a general representation of a stage,as shown in Figure 16, designs with multiple feeds,multiple products and intermediate heat exchange arepossible. We can write rigorous equations to describethe material and energy balance.

1. Material balance (Ncomp equations for each stage):

Lj�1xi,j�1#Vj#1yi,j#1#Fjzi,j!(Lj#Uj)xi,j!(Vj#Wj)yi,j"0 [48]

2. Equilibrium relation for each component (Ncompequations for each stage):

yi,j!Ki,jxi,j"0 [49]

3. Summation equations (one for each stage):

Ncomp

�i"1

yi,j!1.0"0Ncomp

�i"1

xi,j!1.0"0 [50]

4. Energy balance (one for each stage):

Lj�1HLj�1

#Vj#1Hvj#1 #FjHF!(Lj#Uj)HLj!(Vj#Wj)Hvj !Qj"0 [51]


Figure 17 Simulation results for multicomponent distillation.

Figure 18 Effect of pressure on the distillation of a mixture of benzene, toluene, ethylbenzene and styrene.

This set of equations must be solved iteratively andthe calculations are complex. Many methods areavailable and in practice designers use commericalsimulation packages.

Figure 17 shows a typical result for the rigoroussimulation of a distillation column with a feed mix-ture containing benzene, toluene, ethylbenzene andstyrene. Because such simulations are numericallycomplex and time-consuming, short-cut calculationsare used to explore the various design parametersbefore setting up a rigorous simulation.

Choice of Operating Parameters

The feed composition and Sow rate are usually Rxed.Also, the product speciRcations are usually given inthe statement of the design problem. These may be

expressed in terms of product purities or recoveries ofcertain components. The operating parameters to beselected by the designer include:

1. operating pressure2. reSux ratio3. feed condition4. feed stage location5. type of condenser

Pressure

Once the products have been speciRed, the pressuremust be speciRed before the design can proceed. Pres-sure has an important effect on all aspects of thedistillation column design. Figure 18 shows thetrends of various properties of the distillation as


Figure 19 Effect of temperature on utility costs.

Figure 20 Range of reflux ratios.

pressure increases. As pressure increases, the relativevolatility decreases, making separation more dif-Rcult. Minimum reSux ratio also increases with in-creasing pressure, as does the minimum number ofstages. All of these trends point to operating thedistillation columns at a pressure as low as possible.However, the latent heat decreases with increasingpressure; this would have the effect of decreasingthe reboiler duty as pressure increases. Finally, Fig-ure 18 also shows the trend of condenser and thereboiler temperature as pressure increases; both in-crease with increasing pressure.

The temperature of the condenser and reboiler, asshown in Figure 18, dictate the choice of utilities tosupply heating and cooling. Figure 19 shows thetrend for the variation in utility costs for heating andcooling at different temperatures. Figure 19shows that extreme temperatures for heating andcooling require more expensive utilities. Matchingthe distillation condenser and reboiler againstcheap utilities is usually the dominant issue whenchoosing the operating pressure of the distillationcolumn.

When starting a distillation design, we usuallychoose to operate at atmospheric pressure unless thisleads to thermal degradation of products in the re-boiler because of high temperatures, or requires re-frigeration in the condenser. If product degradation isa problem, then we would operate the column undervacuum conditions to decrease the temperatures ofthe distillation. If refrigeration is required in the con-denser, then we might choose to increase the columnpressure until cooling water can be used for the con-denser (which means the overhead condenser temper-ature must be 30}403C or higher), unless very highpressures are required for the distillation.

Choice of Re]ux Ratio

Figure 20 shows the variation of the number of stagesrequired versus the reSux ratio. Starting from min-imum reSux, we require an inRnite number of stages.As the reSux ratio is increased, the number of stagesbecomes Rnite and decreases towards the minimumnumber of stages at total reSux. Actual reSux ratioswill lie somewhere between the two extremes.

Figure 21 shows a plot of annual cost versus reSuxratio. At minimum reSux ratio there is the require-ment for an inRnite number of stages and the annualcapital cost is correspondingly inRnite. However, asthe reSux ratio is increased the capital cost dimin-ishes. On the other hand, as reSux ratio is increasedfrom the minimum, the utility costs increase steadily.Combining the annual capital costs with the annualutility costs gives a total annualized cost which showsa minimum at the optimum reSux ratio. This opti-mum is usually fairly Sat for a signiRcant range ofreSux ratios and an initial setting of 1.1 times theminimum reSux ratio is often assumed.

Choice of Feed Condition

The feed condition affects vapour and liquidSow rates in the column, and in turn:

1. reSux ratio, heating and cooling duties2. column diameter3. most appropriate location of the feed stage


Figure 21 Capital}energy trade-offs determine the optimumreflux ratio.

Figure 22 Distillation trays. (A) Conventional tray; (B) highcapacity tray.

The feed temperature usually lies between the ex-treme temperatures of the column (condenser andreboiler temperatures).

Cooling the feed:

1. decreases the number of stages in the rectifyingsection but increases the number of stages in thestripping section

2. requires more heat in the reboiler but decreases thecooling duty of the condenser

Heating the feed:

1. increases the number of stages in the rectifyingsection but decreases the number of stages in thestripping section

2. decreases the heat requirement of the reboiler butincreases the cooling duty of the condenser

Heating or cooling the feed can reduce energycosts. If heat is added to the feed and saves heating inthe reboiler, the heating of the feed can be carried outat a lower temperature than would be required in thereboiler. Cooling the feed can be carried out ata lower temperature than cooling in the condenser. Inboth cases heating or cooling the feed is done at moremoderate temperatures and, in principle, witha cheaper utility.

Choice of Feed Stage Location

When choosing the feed stage location, our objectiveis to Rnd a stage in the column for which the composi-tion matches as closely as possible that of the feed.For binary distillation it is, in theory, possible to Rndan exact match between the composition on a stageand the composition of the feed. In practice, becausethere is a Rnite change from stage to stage, even for

a binary system, an exact match may not be possible.In multicomponent systems it is highly unlikely thatthe composition of all of the components can bematched. Mismatches between the composition onthe feed stage and that of the feed create inefRcienciesin the distillation. These inefRciencies lead to an in-crease in the number of stages required for the sameseparation, or more reSux, which means increasedenergy requirements, or a combination of both.

Distillation Equipment

Let us now turn our attention to the equipment usedfor distillation operations. As pointed out previously,there are two broad classes of internals used fordistillation: trays and packing.

Trays

Figure 22A shows a conventional tray arrangement.Liquid Sows down a downcomer across a tray inwhich the upSowing vapour contacts the liquid Sow-ing across the tray. The liquid Sows down the nextdowncomer to the following tray, and so on. Theperforated plate used in Figure 22A, known as a sievetray, is the most common arrangement used. It ischeap, simple, and well understood in terms of itsperformance. There are many other designs of traywhich are used. Many use simple valve arrangementsin the holes to improve the performance and theSexibility of operation to be able to cope with a widervariety of liquid and vapour Sow rates in the column.One particular disadvantage of the conventional trayin Figure 22A is that the downcomer arrangementmakes a signiRcant proportion of the area within thecolumn shell not available for contacting liquid andvapour. In an attempt to overcome this, high capacitytrays, with increased active area, have been de-veloped. Figure 22B illustrates the concept. Again,many different designs are available for highcapacity trays.

When designing a column to use trays, we needto know the tray efRciency to convert from


Figure 23 Sieve tray performance.

Figure 24 Distillation packing. (A) Random or dumped pack-ing; (B) structured packing.

theoretical stages to real trays. The differencebetween the performance of an ideal stage and a realtray results from the fact that equilibrium is notachieved on a real tray because of mass transferlimitations. We therefore deRne an efRciency toconvert from the theoretical stages to real trays.Three different efRciencies can be deRned:

1. Overall tray efRciency, Eo:

Eo"number of theoretical stages

number of real stages[52]

Eo depends on the design of the tray and themixture being distilled and typically varies be-tween 60% and 90% for distillation.

2. Murphree tray efRciency, EM. This character-izes the performance of individual trays ratherthan having an overall measure as deRned by Eo.This is because efRciencies can vary through-out the column. The Murphree tray efRciencyfor stage j is deRned as:

EM"yj!yj#iyHj !yj#1

[53]

The Murphree tray efRciency measures thechange in concentration of the vapour phase for anactual tray relative to that for an ideal stage.

3. Point efRciency, EMP. This measures the ef-Rciency not only of an individual tray but at a localpoint on a tray. It is deRned in the same way as theMurphree tray efRciency, but at a point on thetray. It is deRned as:

EMP"yj,local!yj#1,localyHjlocal!yj#1,local

[54]

EMP varies across the tray and must be integratedacross the tray to obtain EM. The result will dependon the mixing pattern on the tray. For example, if thetray is perfectly mixed then EM"EMP.

Correlations are available to predict Eo, EM andEMP.

Trays have a range within which they can operatesatisfactorily in terms of the hydraulic design. Forexample, Figure 23 shows the range of operation ofa sieve tray. Using a sieve tray, internal Sows in thedistillation column are limited by:

1. Sooding, in which liquid cannot Sow down thecolumn

2. entrainment, in which liquid drops are carried upthe column by the vapour Sow

3. downcomer backup, in which liquid backs up inthe downcomers

4. weeping, in which vapour Sow is too low to main-tain liquid on the tray

5. coning, in which poor vapour}liquid contact oc-curs due to the vapour forming jets

Packing

Figure 24A shows a traditional design of packing,which is random or dumped packing. The random ordumped packing is pieces of ceramic, metal or plasticwhich, when dumped in the column, produce a bodywith a high voidage. The liquid trickles down over thesurfaces of the packing and the vapour is in contactwith the liquid as it Sows up through the voids in thepacking.

Figure 24B shows structured packing. This ismanufactured by sheets of metal being preformed


Figure 25 Flood point correlation for packing.

with corrugations and holes and then joined togetherto produce a preformed packing with a high voidage.This is manufactured in slabs and built up in layerswithin the column.

Many types of both random and structured pack-ing are available. We need to be able to calculate theheight of packing required by relating to the theoret-ical stages to the height of packing. For this we needthe height equivalent of a theoretical plate, HETP.Thus, the packing height is simply the product of thenumber of theoretical stages and the HETP. Correla-tions are available for HETP.

As with the hydraulic design of trays, packing hasa limited range over which the hydraulic design isacceptable. At very low vapour velocities through thepacking, liquid Sows are not inSuenced by the vapourSow. As the vapour velocity increases, the vapourstarts to hinder the downward Sow of liquid. This isthe loading point. A limit is reached at a high vapourvelocity, characterized by heavy entrainment of liquidand a sharp rise in the pressure drop across the pack-ing. This is the Sood point. Correlations are used todetermine the Sood point and a typical correlation isshown in Figure 25. We usually design the packingfor a vapour velocity to be some proportion of theSooding velocity (e.g. 80%).

Complex Distillation Arrangements

All of the distillation arrangements which we haveconsidered so far have involved one feed, producedtwo products, have a reboiler and condenser, andoperation has been assumed to be continuous. Distil-lation designs have been adapted to suit differentpurposes, as discussed below.

Batch Distillation

In batch distillation, the feed is charged as a batch tothe base of the distillation column. Once the feed hasbeen charged, it is subjected to continuous vaporiza-tion. This vapour would then Sow upwards throughtrays or packing to the condenser and reSux would bereturned as with continuous distillation. However,unlike continuous distillation, the overhead productwill change with time. The Rrst material to be distilledwill be the more volatile components. As the vapor-ization proceeds and product is withdrawn overhead,the product will become gradually richer in the lessvolatile components. Thus, batch distillation allowsdifferent fractions to be taken from the samefeed. The batch distillation strategy depends on boththe feed mixture and the products required from thedistillation. By careful control of the reSux, it ispossible to hold the composition of the distillate con-stant for a time until the required reSux ratio becomesintolerably large, as illustrated in Figure 26.

Azeotropic Distillation

Figure 27 shows an x}y diagram in which the equilib-rium curve crosses the diagonal line. At the pointwhere the equilibrium curve crosses the diagonal, thevapour and liquid have the same composition; this isan azeotrope. A mixture in which the vapour andliquid have the same composition cannot be separ-ated by conventional distillation. There are twomeans by which a mixture such as that shown inFigure 27 can be separated. The Rrst uses two col-umns operating at different pressures and takesadvantage of the fact that the composition of theazeotrope might change signiRcantly with a change in


Figure 26 Reflux ratio can be varied in batch distillation to maintain overhead product purity.

Figure 27 Azeotropic behaviour.

pressure. The second method is to add a mass separ-ation agent (known as an entrainer or a solvent). Themass separating agent must change the relative vola-tility of the original mixture in a way which allowsthe separation to be achieved.

Steam Stripping

Sometimes live steam is added at the base of thedistillation column. When steam is used in this way,for example for the separation of hydrocarbon mix-

tures, the steam acts as an inert carrier, the presenceof which decreases the partial pressure of the compo-nents in the vapour phase. This is like operating thedistillation column at a lower pressure as far as theseparation is concerned. However, the use of strip-ping steam is not quite the same as reducing theoperating pressure.

Intermediate Reboiling and Condensing

Rather than use a single reboiler at the bottom of thecolumn and a single condenser at the top of thecolumn, it is possible to add or reject heat at inter-mediate points within the column. Below the feed butabove the base of the column, liquid can be with-drawn from one of the stages into an intermediatereboiler to be vaporized and the vapour returned tothe column. This inter-reboiling substitutes part ofthe reboiling at the base of the column. The advant-age of inter-reboiling is that the heat can be suppliedat a lower temperature in the inter-reboiler, com-pared with the temperature required for the reboilerat the base of the column.

Similarly, vapour can be withdrawn from the col-umn above the feed but below the top of the column,condensed and the liquid returned to the column.Cooling in the intercondenser substitutes cooling inthe overhead condenser. Because the cooling in theintercondenser is carried out at a higher temperaturethan the overhead condenser, this can have advant-ages in terms of the utility costs. In practice, it isdifRcult to extract part of the vapour Sowing up


Figure 28 Sequencing simple distillation columns. (A) Direct sequence; (B) indirect sequence.

Figure 29 Thermally coupled columns. (A) Side-stripper, (B) side-rectifier; (C) fully thermally coupled (Petlyuk) column; (D) dividingwall column.

the column into an intercondenser. Because of this, itis more usual to take a liquid side-stream from thecolumn, sub-cool the liquid and return the sub-cooledliquid to the column. The sub-cooled liquid providescondensation directly. Such arrangements are knownas pump-arounds or pump-backs.

Multiple Feeds

Sometimes it is necessary to separate two or morestreams with the same components but with dif-ferent compositions. If this is the case, it is wrong tomix the streams with different compositions toproduce a single feed for the distillation column. Thisis because we would mix streams only to separatethem later and this is thermodynamically inef-Rcient. If we have several streams with the samecomponents but signiRcantly different composi-tions, then it is better to feed them to the distillationcolumn at different points, trying as much aspossible to match the composition of each feed withthat of one of the stages in the column.

Multiple Products

It is sometimes possible to withdraw more than twoproducts from the same column. Part of the liquidSowing down the column or part of the vapour Sow-

ing up the column can sometimes be taken as a side-stream to form a third product. Such side-streamcolumn designs are only possible under specialcircumstances.

Column Sequences

If a feed mixture needs to be separated into more thantwo products, then more than one distillation columnwill usually be required. Figure 28 illustrates the op-tions for the separation of a mixture of three prod-ucts. In the Rrst arrangement, the lightest componentis taken overhead Rrst and the two heavier productsare separated in the second column. In the secondarrangement, the heaviest product is separated Rrstand then the two lightest products are separated inthe second column. For a three-product separation,there are two possible sequences, as shown in Fig-ure 28. As the number of products in the mixtureincreases, the number of possible distillation se-quences increases signiRcantly. For example, if wehave six products, then there are 42 possible se-quences of columns.

Thermal Coupling

Figure 28 showed different arrangements ofsimple distillation columns for the separation ofa three-product mixture. Each column had one feed,


Table 1 Cases not suited to separation by distillation

Case Problem Possible solutions

Separate materials of low molecular mass Low condensation temperature Absorption, adsorption, membranesSeparate heat-sensitive materials of high

molecular massThermal degradation of products Vacuum distillation

Separate components present in lowconcentrations

High flow rates in columns Absorption, adsorption

Separate classes of components (e.g.aromatics from aliphatics)

Boiling temperatures/volatilities ofcomponents in a class are not adjacent

Liquid}liquid extraction

Separate components with similar relativevolatilities

Difficult separation: high operating andcapital costs

Add mass separating agent and employextractive or heterogeneous distillationor liquid}liquid extraction,crystallization

Separate components which form anazeotrope

Azeotrope limits product composition Add mass separating agent and employextractive or heterogeneous distillationor liquid}liquid extraction,crystallization

Separate volatile and involatile components Distillation requires that all componentsare mobile for countercurrent flow

Evaporation, drying, nanofiltration

Separate condensible and noncondensiblecomponents

Only partial condenser can be usedoverhead

Use single-stage separation (flash)

two products and had a reboiler and a condenser.Sometimes, it is desirable to exchange heat betweencolumns directly using thermal coupling connections.Figure 29 shows some thermally coupled distillationdesigns for the separation of a three product mixture.Figure 29A shows a side-stripper and Figure 29Ba side-rectiRer. Figure 29C shows a fully thermallycoupled arrangement, sometimes known as a Petlyukcolumn. Figure 29D shows what is known as a divid-ing wall column. This is the same arrangement as thePetlyuk column but the arrangement is built ina single shell with a dividing wall down the middle ofthe column. The arrangements in Figure 29C and 29Dare both equivalent thermodynamically, if there is noheat transfer across the dividing wall in Figure 29D.

SummaryDistillation is a versatile, robust and well-understoodtechnique and is the most commonly used method forthe separation of homogeneous Suid mixtures. Thereare cases for the separation of homogeneous Suidmixtures for which distillation is not well suited.Table 1 presents a summary of these cases, alongwith possible solutions. It should be noted, however,that even though distillation is not well suited to theseparation duties in Table 1, distillation is still used insome form for many of these problematic cases.

Symbols

bi bottoms Sow rate of component iB molar bottoms Sow ratedi distillate Sow rate of component iD molar distillate Sow rateEM Murphree tray efRciency

EMP point efRciencyEo overall tray efRciencyf Li fugacity of component i in the liquid phasef Vi standard-state fugacity of component at the

temperature of the systemf 0i fugacity of component i in the vapour phaseF molar feed Sow rateH molar enthalpyKi equilibrium constant for component iL molar Sow of liquidNmin minimum number of stagesN number of stagesNcomp number of componentsP system pressurePSATi saturated vapour pressure of component i at

the system temperatureq feed conditionQ heat dutyR reSux ratior recoveryRmin minimum reSux ratioT temperatureU vapour velocityV molar Sow of vapourxi mole fraction of i in the liquid phaseyi mole fraction of i in the vapour phaseyHj mole fraction of vapour that would be in equi-

librium with liquid leaving stage jyHj,local mole fraction of vapour that would be in eq-

uilibrium with the local concentration on stage jzi feed composition of component i

�ij relative volatility between components i and j� density�Li liquid-phase fugacity coefRcient for com-

ponent i


�Vi vapour-phase fugacity coefRcient for component i�i activity coefRcient for component i

See Colour Plate 5.

Further ReadingGeankoplis CJ (1993) Transport Processes and Unit Op-

erations. New Jersey: PTR Prentice Hall.

King CJ (1980) Separation Processes. New York: McGraw-Hill.

Kister HZ (1992) Distillation Design. New York:McGraw-Hill.

Seader JD and Henley EJ (1998) Separation Process Prin-ciples. New York: John Wiley.

Stichlmair JG and Fair JR (1998) Distillation Principles andPractice. New York: Wiley-VCH.

ELECTROPHORESIS

D. Perrett, St Bartholomew’s and the Royal LondonSchool of Medicine and Dentistry,St Bartholomew’s Hospital, London, UK

Copyright^ 2000 Academic Press

An Outline of the HistoricalBackground to ElectrophoreticSeparations

The movement of charged particles under the inSu-ence of an electric Reld was observed as long ago as1807 by Ferdinand Frederic Reuss. In 1909, the term,electrophoresis, was introduced by Michaelis as a de-scription of this phenomenon and is derived from theGreek word elektron meaning amber (i.e. electric)and phore meaning bearer. Yet it was not until the1930s that electrophoresis, as we know it today,developed from the work of Tiselius, who, in 1948,was awarded the Nobel Prize for this development.Table 1 charts the development of the technique overthe last century. By the 1950s electrophoresis wasa common laboratory technique equivalent in useful-ness to planar chromatography techniques such aspaper and thin layer. However, with the advent ofhigh-performance liquid chromatography (HPLC) inthe 1970s, analytical electrophoresis became some-thing of a ‘Cinderella’ technique. Only in biochemicaland clinical laboratories did electrophoresis continuein use as a qualitative separation technique for mac-romolecules, such as proteins and DNA.

It has been claimed that currently at least half of allseparations are performed by electrophoresis sinceseparations of blood proteins and DNA digests areroutinely performed by the technique. The techniqueis now so routine in biomedicine and related disci-plines that it is rarely referred to in the abstracts andtitles of papers where it is a core technology, forexample DNA sequencing. Even so, it is mentionedby name in almost as many papers as is chromatogra-phy (Table 2). However, with the development of

capillary electrophoresis after 1981 electrophoresishas returned as a substantial topic of interest to main-stream analytical chemistry.

Fundamentals of Electrophoresis

Unlike chromatography, there is no formal Interna-tional Union of Pure and Applied Chemistry (IUPAC)deRnition of electrophoresis, although one is beingdeveloped at the time of writing. However, throughteaching the subject over the past 10 years, I havedeveloped the following deRnition:

‘Electrophoresis is a mainly analytical method inwhich separations are based on the differingmobilities (i.e. speed plus direction of movement)of two or more charged analytes (ionic com-pounds) or particles held in a conducting mediumunder the inSuence of an applied direct currentelectric Reld’ (Figure 1).

Electrophoresis therefore contrasts to chromatog-raphy which is deRned as a method used primarily forthe separation of two or more components of a mix-ture, in which the components are distributed be-tween two phases, one of which is stationary whilethe other moves. Another difference is that inchromatography the modelling of the separationfrom Rrst principles is complex, difRcult and im-precise whereas a relatively simple theoretical back-ground to electrophoresis has been developed and isreproduced below. For a more complete discussion ofelectrophoretic theory see Mosher et al. (1992).

In electrophoresis the movement is towards theelectrode of opposite charge to that of the particle orion being separated. Cations are positively chargedions and move towards the negative electrode (thecathode). Anions are negatively charged ions andmove to the positive electrode (the anode). It is im-portant to note that neutral species do not moveunder the inSuence of the electric Reld, although they

Sepsci*41*TSK*Venkatachala=BGI / ELECTROPHORESIS 103

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