NON-EQUILIBRIUM MODELLING OF DISTILLATION

J. A. WESSELINGH

Department of Chemical Engineering, University of Groningen, Groningen, The Netherlands

There are nasty conceptual problems in the classical way of describing distillationcolumns via equilibrium stages, and ef® ciencies or HETPs. We can nowadays avoidthese problems by simulating the behaviour of a complete column in one go using a

non-equilibrium model. Such a model has phase equilibria, multi-component mass transfer,heat transfer, and ¯ ow models built in.

Keywords: distillation; design; operation; non-equilibrium; multi-component

INTRODUCTION

This is a lecture on the way that we engineers modeldistillation. How we have done such modelling, how wewould like to do it, and how far we have come at thismoment. The ideas that I will be bringing forward are notmy own. I owe them mostly to R. Krishna, R. Taylor, H.Kooijman and A. GoÂrak. These are people who have spent afair bit of their lives developing modern multicomponentsimulation methods of distillation. I am just using theirresults.

EQUILIBRIUM STAGE

Chemical plants consist of separate pieces of equipment(Figure 1). Some of these will probably be distillationcolumns. Any description of distillation begins with theconcept of `stages’ : fairly large parts of the column thathave well de® ned boundaries. For a tray column, we canregard a single tray as a stage. There is no natural boundaryto the stages in packed columns (unless we consider packedsections as stages). Even so, we engineers try also tosubdivide packed columns into stages, sometimes withludicrous results.

There are well de® ned ¯ ows entering and leaving anystage. These can be the main vapour and liquid ¯ owsthrough the column, or feed or drawoff ¯ ows. They mayconsist of mass or heat. Conceptually, the simplest kind ofstage is the `equilibrium stage’ or `theoretical plate’ . Forsuch a stage (which does not exist in reality), the (vapourand liquid) streams leaving the stage are assumed to be inequilibrium (Figure 2). This implies that the chemicalpotential of any component has the same value in vapourand liquid, and also that vapour and liquid have the sametemperature.

With the equilibrium stage model we can simulate manyof the properties of real systems. To describe an equilibriumstage, we `only’ need phase equilibrium data (thermody-namics) and mass and energy balances. The model isbeautifully consistent, and has attracted the attention ofgenerations of engineers and thermodynamicists. However,it has one great weakness: it has no direct connection to realequipment.

EFFICIENCY AND HETP

Of course, we engineers have found ways of coupling ourtheoretical models to practical equipment. The two conceptsmostly used for this purpose are (Figure 3):

· the (Murphree vapour) `ef® ciency’ of a tray or plate and

· the `height equivalent to a theoretical plate’ (HETP) forpackings.

When using a Murphree ef® ciency, we assume that thechange in vapour composition on a real tray is a certainfraction of that obtained in an equilibrium stage. This allowsus to approximate the behaviour of real trays. The conceptworks quite well for binary separations; the two componentsthere have equal ef® ciencies. Also the ef® ciencies are oftenfairly constant along a column, and therefore an ef® ciency isa useful way of summarizing practical experience. It oftenhas a value of about 0.7.

For packings, we look at the compositionof the liquid at acertain height. We then assume that further up in thecolumn, we will be able to ® nd vapour with a compositionthat is in equilibrium with the liquid considered. Thedifference in height between these two points is the HETP.Also here, this works fairly well for binary mixtures. TheHETPs are the same for the two components and they areoften fairly constant along a column. Experience shows thatthe value of the HETP is usually a few tenths of a metre.

Although the ef® ciency and the HETP have been usefulfor summarizing experience on trays and packings, theseconcepts have two serious de® ciencies:

· they are not easily related to the construction andbehaviour of equipment, and

· in multicomponent mixtures, their behaviour is extremelyconfusing.

I even think that these two concepts may be retarding thedevelopment of distillation, and will argue that there aregood reasons to give them a less prominent position thanthey have today.

`EXACT’ MODELS

If we do not wish to use ef® ciencies or HETPs, what

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should we do? The dream of the modern engineer is tosubdivide each piece of equipment into zillions of littleelements dx dy dz, each of which will contain part of oneof the phases in the equipment (Figure 4). We should thenset up difference forms of the Navier-Stokes equations tode® ne the hydraulic ¯ ows, the Fick or Maxwell-Stefanequations to calculate diffusion ¯ ow, Fourier equations forenergy transfer and all required balances and boundaryconditions. These myriads of equations are then to be solvedby our brilliant parallel supercomputer algorithms, and theywill tell us everything we wish to know. Such a model canbe used for trays, for packings or for any piece ofequipment. It will deliver beautiful and impressive multi-dimensional colour plots. It will describe unsteady,turbulent, chaotic two phase ¯ ow, the breaking up andcoalescence of drops, their moving and deforming bound-aries, interfacial motion and mass transfer, incomplete andirregular wetting of packings, gas and liquid entrainment...

Unfortunately, there are still a few problems. For arealistic simulation of the important phenomena in acolumn, my guess is that we would need elements withdimensions of about one micrometer. That is one millionelements per metre, or 101 8 elements per m3 of column. Thisnumber is almost 109 times the number of bytes on the twoGigabyte hard disk of the multimedia computer that you arethinking of buying for educating the kids (and for usingyourself in the evening to hone your communication skills).So it looks as if we still have a long way to go before we can

simulate the details of multiphase ¯ ow. Of course this alsomeans that the subject is a challenging one, and possibly agood topic to let our students and young engineers sharpentheir teeth. However, with this approach, we should notexpect complete solutions to practical problems in the shortterm.

NON-EQUILIBRIUM MODEL

Current non-equilibrium models are less ambitious. Theycontain a smaller number of elements per m3 than the`exact’ models above. Say, ® ve, instead of the 101 8 that wewere considering. We choose these elements such that theyallow a simple simulation of what we think are theimportant characteristics of our mass transfer equipment:

· the equilibrium distribution of all components betweenthe two phases (thermodynamics),

· the effects of large scale ¯ ow and mixing patterns and

· the effects of diffusional heat and mass transfer resistancenear phase interfaces.

How few elements we choose, is a balancing act. With toofew elements our model will not be realistic, with manyelements it will be impossible to obtain the modelparameters (although..., with 101 8 elements, you do notneed any model parameters).

EQUILIBRIUM DISTRIBUTION

At the interface between the two phases, we assume (alsoin the non-equilibrium model) that equilibrium exists. (Inabsorption with a chemical reaction, this may not be true,but we do not consider that here). To describe theequilibrium, we need a thermodynamic model of the

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Figure 1. Plant, separation equipment and stages.

Figure 2. The equilibrium stage.

Figure 3. Tray ef® ciency and `Height Equivalent to a Theoretical Plate’(HETP) lead to real equipment.

Figure 4. Exact models: the dream of the modern engineer.

mixtures considered. In multicomponent distillation andabsorption two kinds of models are in common use:

· multicomponent equations of state such as the Soave-Redlich-Kwong and Peng-Robinson equations and

· Gibbs excess energy models, such as the Wilson, NRTLand UNIQUAC / UNIFAC models.

The former are primarily used for high pressure equilibria ofsimple mixtures, such as those which dominate the oilindustry. The latter are useful for strongly non-idealmixtures at not-too-high pressures, such as are often foundin the chemical industry.

These are the same equations that we use in equilibriumstage calculations. They yield both the distribution coef® -cients of all components and their enthalpies. In non-equilibrium calculations we use the same equations toobtain the driving forces for mass transfer (which are thechemical potential gradients, as we shall see a little furtheron).

LARGE SCALE MOTIONS

Motions of gas and liquid on the scale of a tray orpacking, have a large effect on equipment performance. Theideal ¯ ow pattern in separation equipment is usuallycountercurrent plug ¯ ow. Modern structured packings givepatterns that are fairly close to this ideal. However, evenhere, things like turbulence, differences between thechannels, and maldistribution of liquid or vapour at feedpoints do cause deviations from ideality (Figure 5).Entrainment of liquid by the vapour, and of vapour by theliquid, causes backmixing. In large, long column sections,irregularities of the ¯ ow have been found to develop,

especially near walls and due to the contacting planesbetween packing elements.

On trays, the vapour is often assumed to pass upwards inplug ¯ ow. (I do not know whether anybody has ever beenable to check how well or how poorly this holds.) The liquidhas a cross ¯ ow pattern; at the sides of columns there canmore or less stagnant zones. On short tray passes the overalleffect is often similar to that of complete mixing of theliquid. If we have a spray of drops on the tray, there will be arange of drop sizes and the behaviour of small and largedrops may differ considerably. We may expect small dropsto attain equilibrium more rapidly than large drops.Something similar applies to bubbles of different sizes ina froth.

The simplest ¯ ow model is that where both phases areassumed to be ideally mixed (Figure 6). This model onlycontains two bulk phases with convective ¯ ows in and out.In addition it contains three other elements: the phaseinterface and two mass transfer resistances on either side ofthe interface. We discuss these elements in the next section.

In the examples that we discuss further on, we will also beusing ¯ ow models which are a bit more realistic (Figure 7):

· on a tray: liquid mixed, vapour mixed or in plug ¯ ow, andno entrainment or backmixing,

· in a packing: both phases in plug ¯ ow, no maldistribution.

Even these models are not always adequate.There are many different ways to describe more

complicated ¯ ow patterns (Figure 8). We can approximateplug ¯ ow by stacking a number of mixed elements. When aphase consists of coarse and ® ne parts (such as large and

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Figure 5. Even in a structured packing, ¯ ow is not ideal.

Figure 6. The simplest non-equilibrium model.

Figure 7. More realistic ¯ ow models.

Figure 8. Complicated ¯ ow patterns using simple elements.

small drops), we may split it in two pseudo phases. We mayexpect a convective exchange between these pseudo phases.Entrainment and backmixing can be simulated by allowingextra ¯ ows going in and out of each phase. Finally,maldistribution can be simulated using parallel stages withdifferent ¯ ow ratios. As already mentioned, the problemwith these more complicated models is that we do not knowtheir parameters well enough.

MASS TRANSFER

The second important mechanism in our models is thedescription of mass and heat transfer between the phases (andpseudo phases). In most equipment, ¯ ow of both phases ishighly turbulent. (This applies both to the continuousand thedispersed phase.) Turbulence provides a rapid levelling ofconcentration and temperature differences. So on not-too-large scales (say up to ten centimetres), the concentrationsand temperatures in the bulk of ¯ uids can be taken ashomogeneous. However, near phase interfaces, turbulencedies out (Figure 9). Eddies do not pass across interfaces. Nearthese interfaces, only three transport mechanisms remain, allof which are much slower than turbulence:

· `drift’ : convective transport of both heat and matter due toan overall displacement of matter across an interface,

· diffusion: the transport of matter due to compositiongradients and molecular motion within the ¯ uid and

· conduction: the transport of energy by a temperaturegradient and molecular motion.

The layers (or `® lms’ ) where turbulence does not dominatetransport, are very thin: roughly one tenth of a millimetre ingases and ten micrometres in liquids.

The traditional description of mass transfer begins withFick’ s law. This states that ¯ ux of a component (in a binarymixture) is proportional to the concentration gradient of thatcomponent and a diffusivity. In addition, the componentmay also be carried along by drift:

Ni = -ctotalDi

dxi

dz, ) ) ) ) ) ) ) & ( ) ) ) ) ) ) ) *

diffusion

+ Ntotalxi, ) ) & ( ) ) *

drift

(1)

For most engineering applications, a difference approxima-tion of this equation suf® ces:

Ni = -kbinaryi ctotal D xi + Ntotalxi kbinary

i = Di

d(2)

The parameter kbinaryi is a binary `® lm theory’ mass transfer

coef® cient. We could also have used a more realistic`surface renewal theory’ to obtain it.

Unfortunately, the description above does not transferwell to mixtures with more than two components. (Andmost mixtures do contain more than two components!) Thisis for two reasons:

· it does not take the interactions between the differentcomponents into account and

· it does not allow for the fact that the driving force formass transfer is not the concentration gradient, but thegradient of the chemical potential.

The ® rst effect is often important, especially for thebehaviour of trace components. The second effect can beimportant is systems where liquid resistance dominates.

If we do take all the trouble to make a non-equilibriummodel of a column, we can best use a fundamentalmulticomponent model of mass transfer through the inter-face. A good choice are the Maxwell-Stefan equations.These equations consider each component i in turn. Thedriving force on i will cause it to move with respect tothe mixture. This motion is counteracted by friction with theother species j.

The driving force is the chemical potential gradient:

(driving force on i) = -d l i

dz(3)

This is a real driving force, with units of Newton per mole. Ifwe have equilibrium, we have no gradients, no drivingforces and no motion. The chemical potential containscontributions due to mole the fraction and the activitycoef® cient of i:

l i = RT ln(c ixi)+ const (4)

The contribution of the mole fraction gradient is similar tothat of the concentration in the Fick equation. However, thatequation does not consider the effect of non-ideality via theactivity coef® cient.

The friction force between i and j (per mole of i) isproportional to the local mole fraction of j, a frictioncoef® cient f i , j and the difference in drift velocities betweenthe two components:

(friction)i,j = xj f i,j(ui - uj) (5)

When we equate the driving force with the sum of allfriction forces on i, we obtain the Maxwell-Stefanequations:

-d l i

dz = Sn

j=1

xj f i,j(ui - uj) (6)

These equations allow a consistent description of diffusionin mixtures with any number of components.

We are usually not interested in species velocities throughthe interface, but in their ¯ uxes:

Ni = ciui (7)

Also, we will also normally use multicomponent diffusioncoef® cients instead of friction coef® cients:

� ij = RT

f ij

(8)

Finally, we will use a difference form of the resulting

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Figure 9. Mass transfer resistances: the `® lm’ near interfaces.

equations, which contain the multicomponent mass transfercoef® cients:

kij =� i,j

d(9)

We will not write out these equations; they are notenlightening. The important thing to understand, is that themulticomponent diffusivities and mass transfer coef® cientscan be estimated fairly well from binary data.

In the actual numerical calculations it is handier to use theinverse of our equations. We can write these in a form whichreminds us of the Fick equations. In this formulation, themass transfer coef® cients have been corrected for the effectsof thermodynamic non-ideality:

(N)= -ctotal[k](D x)+ (x)Ntotal (10)

You should not be misled by the simple form of theseequations. Especially the matrix of mass transfer coef® -cients is a very complicated (and incomprehensible)function.

In addition to the mass transfer equations, we need heattransfer equations. These require estimates of the heattransfer coef® cients in both phases, and they mustincorporate heat transport through the interface due to drift.

I have restricted myself to a brief (and incomplete)summary of what is required for the description of heat andmass transfer. If you really want to understand the subject,the best reference is the book by Taylor and Krishna1 . Youmust reckon on spending quite some time however;multicomponent mass transfer is not a simple subject.However, using the results of others is not at all thatdif® cult. A simpler introduction is given in Wesselingh andKrishna2 .

MODEL REQUIREMENTS

For the equilibrium stage model, we only need two kindsof physical properties:

· vapour / liquid equilibria and

· enthalpies.

The non-equilibrium model gives a much more completedescription of the equipment. However, it does requiremuch more data. Here we need, in addition to the two setsabove, all properties that are required to describe the ¯ ow,

heat transfer and mass transfer in the equipment, such as:

· densities

· viscosities,

· friction coef® cients,

· surface tension,

· interfacial area,

· diffusivities,

· thermal conductivity,

· heat and mass transfer coef® cients,

and so on. We need these for the different mixtures in everyelement of the equipment, not only for the separatecomponents. This means that we need a substantialdatabase.

The second point in which equilibrium and non-equilibrium models differ greatly is in how detailed theequipment must be described. In the equilibrium model, weonly need to give the number of stages and the location ofthe different feed and withdrawal points. The non-equilibrium model, in contrast, needs to contain a complete`drawing’ of the column (Figure 10):

· the number of trays in the different sections,

· the diameters of the sections,

· the tray heights,

· the downcomer con® gurations,

· the hole diameters,

· the free areas,

· the weir heights,and so on and so on...

When we are designing a column, we can leave it to theprogram to determine all these parameters. However, whenwe are simulating an existing column, we must provide allthese data. This input can be quite a burden.

All examples have been worked out using ChemSepversion 3.03. This is a non-equilibrium modelling programwritten by Ross Taylorand Harry Kooijman3 . (It also contains¯ ash and equilibrium models). ChemSep is available foreducational institutions for a small fee and it runs on IBM-type personal computers. (ChemSep requires a 386 or better,and 4 Mbytes of memory. It is a DOS program, but it alsoruns under Windows 3.1 and Windows 95). ChemSep has afriendly menu based input, and extensive graphic and tabularoutput options.

A program that is similar, and available commercially, isRATEFRAC from Aspen Technologies. RATEFRAC can

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Figure 10. The NE-model contains a `drawing’ of the column.

be incorporated in the ¯ ow schemes of complete processes;the current version of ChemSep only allows this to a limitedextent. However, RATEFRAC does take more time to learn,and it is a little more expensive.

EXAMPLES

To give you an idea of how non-equilibrium modellingworks in practice, I will discuss three examples:

1. a depropanizer: a high pressure column from an oilre® nery with four components, equipped with sieve trays,2. the non-isothermal absorption of acetone from a nitrogen/acetone mixture into water in a conventional packed columnand3. the extractive distillation of methyl cyclohexane usingphenol as a solvent in an old column with bubble cap trays.

In the ® rst example, we have relatively ideal solutions andsmall heat effects. In the second example, heat effects areimportant. The last example considers a strongly non-idealmixture with varying ¯ ows. These are examples from acourse that myself, A. GoraÂk, H. Kooijman and T. Reithregularly give to graduate students in chemical engineering.All examples can be done by our students within an hour(experienced engineers only need a fraction of these times).

A DEPROPANIZER

Our ® rst example is a column from an oil re® nery(Figure 11). The feed contains four components. In order ofvolatility: pentane, butane, propane and ethane. (In a realcolumn there would be more, but this is enough to showmost of the behaviour of the column). The column is to splitthe feed between butane and propane.

We will use the Peng Robinson equation of state todescribe the phase equilibria and enthalpies. We choose thetop temperature at 40 8 C (to allow cooling with ambient air).With the `Flash’ unit of ChemSep, we ® nd that we need apressure of 22 bar. With a total condenser, 28 sieve trays, apartial reboiler and a boiling point feed on stage 16,combined with a re¯ ux ratio of 2, we obtain the desiredseparation. (This is not necessarily an optimal design, butwe may change it later.) It takes me about two minutes to get

the required data into the program. I use `design mode’ , sothat the program sizes the column for me, and I do not needto provide any other data than the type of internal used(sieve trays). The run converges without dif® culty on my486 DX 66 MHz machine in 21 seconds. Output graphsshow ¯ ow rates (Figure 12) which are almost constant in thetwo sections, except for a sharp increase of the liquid ¯ ow atthe feed tray.

The ¯ ows of the components vary strongly along thecolumn (Figure 13), with ethane and propane beingconcentrated in the top and the other components in thebottom. The two minor components (ethane and pentane)have constant ¯ ow rates in the greater part of the twosections, the rates only changing rapidly at the ends of thecolumn. The propane ¯ ow generally decreases as wepass down the column, while butane increases. There arehowever several irregularities. These are mainly becausepropane is displaced by the minor components in certainparts of the column. Similar remarks can be made onbutane. We see that the trays above the feed stage do notprovide much separation between butane and propane;this is an indication that we should put the feed on a highertray.

The transfer rates of the components on the different traysdiffer wildly (Figure 14), showing how complicated such asystem is. In the greater part of the column the transfer ratesof ethane and propane are negative, which means that they

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Figure 11. A depropanizer.

Figure 12. Flow rates in the depropanizer.

Figure 13. Component ¯ ow rates in the depropanizer.

are moving into the vapour. The opposite holds for butaneand pentane.

We can get out any amount of detailed information on thecolumn. I restrict myself to the preliminary tray layoutprovided (as geometrical parameters) by the program(Figure 15). You can immediately ® nd out what the effectsare of modifying the design (for example the tray height, orthe free areas) by running the program again. Or you cancheck whether all trays are operating within their hydrauliclimits, and how this changes if you modify the design. Thisis one of the beautiful things of non-equilibrium models.

The non-equilibrium model does not use ef® ciencies.However, from its results, it can calculate the ef® ciencies ofeach component on each tray. These are shown in Figure 16and I advise you to look at these carefully. The ® rst thing tobe noted is that all four ef® ciencies are different. The secondis, that they vary wildly along the column. The two minorcomponents have extreme values of -200% (yes, negative!)and +200% (far larger than the 100% maximum expectedfor a tray with a mixed liquid). Even the ef® ciency of butanevaries between 70% and 110%. Remember that these areresults for a simple, almost ideal mixture; they are typical ofany multicomponent separation.

My experience is, that many engineers have dif® culty in

believing these results. They know from experience thatbinary ef® ciencies are fairly constant and well behaved. So Ihave added one calculation for a similar column, but nowwith a binary feed of only propane and butane (Figure 17).Here, indeed, we see that the ef® ciencies of the twocomponents are equal, and that they have a more or lessconstant value of about 85%.

From this example we see that experience with binarymixtures does not translate to multicomponent mixtures in astraightforward manner. For a binary, an ef® ciency may be auseful way of summarizing experience. However in multi-component mixtures, ef® ciencies are hardly predictable.They are different for all components and may vary fromminus in® nity, through zero, up to plus in® nity. In myexperience, ef® ciencies in multicomponent separations arethoroughly confusing. Chemical engineers should abandonthe use of ef® ciencies. Non-equilibrium models have madethem irrelevant.

There are many other aspects of binary distillation, thatdo not translate well into multicomponentmixtures. Figure 18shows the McCabe-Thiele diagram of the two key compo-nents (also provided by ChemSep). In the ® rst instance itlooks much like that of a binary mixture. A closer inspectionshows that the operating lines are strongly curved. In thisexample they even run through a small loop near the feedstage. There are other differences between this example and aproper binary. Here, although the feed is at its boiling point,

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Figure 14. The mass transfer rates on each stage of the components in thedepropanizer.

Figure 15. The tray layout of our depropanizer.

Figure 16. Murphree vapour ef® ciencies of the components in thedepropanizer.

Figure 17. With a binary mixture, ef® ciencies are equal and well behaved.

the feed line is not vertical. A close look at the diagram showsthat the `stairs’ do not extend up to the equilibrium line. Thisis understandable; we are dealing with a non-equilibriummodel. However, we have seen that the ef® ciencies of thepropane and butane are not equal, so the height of each stepcannot be a direct measure of the vapour ef® ciency as it is in abinary mixture.

A PACKED ABSORBER

Our next example (Figure 19) seems to be a simpleproblem, suitable for an introductory lecture in separationprocesses. We are to absorb a small amount of acetone froma large stream of nitrogen. The solvent is water, and thecolumn is ® lled with Raschig rings (as it should be in anygood, old fashioned exercise). You might think this problemcould be adequately described using the Kremser equationand theoretical plates with a constant height (HETP). Let ushave a look, again using ChemSep.

I did this exercise using the NRTL equations for the phaseequilibria of the ternary mixture acetone±nitrogen±water,and the Onda equations for mass transfer in the packing.Both phases were taken to be in plug ¯ ow and the columnconsisted of 30 elements of one third of a metre each. Thesolvent ¯ ow is close to the minimum value and under theseconditions ChemSep will not converge in one go. I had tobegin with a large solvent ¯ ow. Then I used the results asstarting values for a new run. In eight runs, I brought thesolvent ¯ ow back from 2000 to 500 mol s- 1 . This may sounda lot of work, but each run only took about ten seconds.

Figure 20 shows the mass transfer rates in the differentsections. We see that acetone absorbs throughout thecolumn, but in an irregular manner. Nitrogen (which ishardly soluble in water) absorbs so little that this is notvisible in the plot. The most spectacular component iswater. Water condenses at about the same rate as acetone inthe upper part of the column, but evaporates with high ratesin the bottom sections. This means that there is a largeinternal water recycle in the column, which carries asubstantial amount of heat. All this shows up in thetemperature pro® le (Figure 21). We see notable differencesin temperature between gas and liquid. (We have alsoplotted the interface temperature; this shows that the greaterpart of the temperature difference is in the gas phase). If youhave a good look, you will see that the interface temperatureis higher than the bulk liquid temperature in the top of thecolumn, but lower in the bottom. This means that thedirection of heat transfer changes (at just about the positionof the temperature bulge). The situation is obviously farmore complicated than the simple textbook problem that wehad in mind!

The non-equilibrium model does not use HETPs.However, from its results, it can calculate the HETPs ofeach component in each element. These are shown in Figure22 and I advise you to look at these carefully. The ® rst thingto be noted is that all three HETPs are different. The secondis that they vary wildly along the column. Nitrogen has an

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Figure 18. The pseudo-binaryMcCabe-Thiele diagram of the depropanizer.

Figure 19. The acetone absorber.

Figure 20. Mass transfer rates of the components in the absorber.

Figure 21. Temperature pro® les in the absorber.

extreme value of -2.6 m (yes, negative!) and water of

+67 m. (You may argue that you are not interested in theHETP of nitrogen, but the point is that an HETP can benegative). Even the HETP of acetone varies from 0.4 to 1 m.Remember that these are results for what you thought was asimple introductory example.

From this example we see that experience with binarymixtures does not translate to multicomponent mixtures in astraightforward manner. For a binary, an HETP may be auseful way of summarizing experience. However in multi-component mixtures, HETPs are hardly predictable. Theyare different for all components and may vary from minusin® nity, through zero, up to plus in® nity. In my experience,HETPs in multicomponent separations are thoroughlyconfusing. Chemical engineers should abandon the use ofHETPs. Non-equilibrium models have made them irrelevant.

EXTRACTIVE DISTILLATION

We will not spend much time on our last example. It isonly there to show that the non-equilibrium model is alsoapplicable to (what you think are) complicated non-idealmixtures. Here we consider the extractive distillation ofmethyl-cyclohexane (MCH) and toluene (Figure 23). These

two components have close boiling points; they cannot beseparated by conventional distillation. However, they dodiffer in polarity, MCH being the least polar of the two. Weseparate them by adding a large excess of a polar, non-volatile solvent (here phenol) to the liquid. This happens afew trays below the top of the column. The activity of MCHin phenol is larger than that of toluene, so it becomes themost volatile and ends up in the top of the column.

I did this run using the UNIFAC model to describe the(strongly non-ideal) vapour liquid equilibria. I used bubblecap columns and the AIChE design method for bubble captrays. This to honour my predecessors of forty years back.Also here, I needed to start with an excess of solvent to getChemSep to converge. Then I reduced the amount of solventuntil I got the ¯ ow pro® les shown in Figure 24. This is notan optimal design, but it can easily be improved. I had itwithin half an hour. Large non-idealities do not pose anyexceptional problems to the non-equilibrium model.

You might ask how the tray ef® ciencies behave. Well,even worse than those of the depropanizer. They run all overthe place. However, that should be nothing new to you, so Ihave not even plotted them.

FINAL REMARKS

In this lecture, we have had a look at the background ofnon-equilibrium modelling.We have seen that it can give usquite a detailed understanding of what is going on in adistillation column. It also allows us to see the effects ofchanging any design parameter, including the effects ofequipment geometry. This is an important extension ofthe classical analysis using equilibrium stages. The non-equilibrium models are also applicable to multicomponentseparations; they do not need ef® ciencies or HETPs whichare not predictable in multicomponent mixtures. Finally,modern non-equilibrium computer models of distillationcolumns are quite easy to use. So I hope to have convincedyou that there is every reason to start using them.

Does this mean that there are no problems left to besolved in distillation? Fortunately, not! Some of the manykinds of problems we still have to live with are:

1. Big numerical models do not solve problems; they onlyimprove upon your solution. So you must have an idea ofwhat you are doing, so as to provide starting values.Otherwise convergence is not assured.

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Figure 22. HETPs of the components in the absorber.

Figure 23. Extractive distillation of MCH/toluene using phenol as solvent.

Figure 24. Flows of the components in the extractive distillation.

2. The results are only as good as the important parts of themodel are. During development of the non-equilibriummodel it has become clear that our knowledge of the detailsof what happens inside a column is still very incomplete.3. Even carefully written programs contain bugs.

There are several areas where we have found that currentmodels and correlations (at least those in open literature) areinadequate:

· correlations for interfacial areas

· correlations for gas phase transfer coef® cients

· minimum load correlations and

· descriptions of maldistribution in packed columns.

It is time that we engineers try to get these data in order.

REFERENCES

1. Taylor, Ross, and Krishna, R., 1993, Multicomponent Mass Transfer,(John Wiley & Sons, New York).

2. Wesselingh, J. A. and Krishna, R., 1990, Mass Transfer, (EllisHorwood, Chichester).

3. Taylor, Ross and Kooijman, Harry, ChemSep, (a program available foreducational institutes for a small fee from CACHE Corporation, P.O.Box 7939, Austin, TX 78713-7939,USA.) You will need version 3.0 orhigher. (The program is continually being revised.) More information iscan be found on the WWW page of Taylor and Kooijman at http://www.clarkson.edu/, chengweb/faculty/taylor/chemsep/chemsep.html.You can also try http://www.che.utexas.edu:80/cache/

ADDRESS

Correspondence concerning this paper should be addressed to ProfessorJ. A. Wesselingh, Department of Chemical Engineering, University ofGroningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands.

This paper is a plenary presentation from the Distillation and Absorption1997 conference, Maastricht, The Netherlands, 8± 10 September 1997. Thepapers from the conference are to be published in the IChemE SymposiumSeries, No 142.

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Trans IChemE, Vol 75, Part A, September 1997