Chemical Engineering and Processing 41 (2002) 445–462

Hardware selection and design aspects for reactive distillationcolumns. A case study on synthesis of TAME

R. Baur, R. Krishna *Department of Chemical Engineering, Uni�ersity of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands

Received 15 May 2001; received in revised form 21 June 2001; accepted 2 August 2001

Abstract

We have carried out a step-by-step design study of a reactive distillation (RD) column for synthesis of tertiary-amyl ether(TAME) in order to investigate the influence of the choice of hardware on column design. Two different types of internals arecompared: active Raschig rings and catalytic bales. Firstly, an equilibrium (EQ) stage model is used to obtain conceptual columndesign parameters. Detailed mass transfer and pressure drop calculations are then carried out to determine the column diameterand heights of the reactive and non-reactive sections of the RD column. Active Raschig rings have superior mass transfercharacteristics but poorer pressure drop characteristics as compared to catalytic bales and therefore yield shorter and fattercolumn configurations. The detailed hardware configuration is finally checked with a rigorous nonequilibrium (NEQ) stage modelto ensure that the designs are adequate and to investigate scope for further improvement. Our study underlines the importanceof using NEQ models for column design and optimization. EQ stage models provide only initial estimates of column designs. Thechosen column configurations must be carefully checked with rigorous NEQ models. Furthermore, our study reveals that theamount of catalyst used in the reactive section needs to be carefully chosen; excess of catalyst could lead to promotion of thereverse reaction of TAME to the reactants. © 2002 Elsevier Science B.V. All rights reserved.

Keywords: Reactive distillation; Equilibrium stage model; Nonequilibrium stage model; Multiple steady states; Tert-amyl ether synthesis; Columnhardware; Hydrodynamics; Mass transfer; Flooding

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1. Introduction

Reactive distillation (RD) is an old idea that hasreceived renewed attention in recent years; witness therecent reviews of Doherty and Malone [1,2] and Taylorand Krishna [3]. In the area of RD column design,research has mainly been focussed on aspects such asconceptual design with the aid of residue curve maps[1,2,4], steady-state multiplicity and bifurcations [5–8],development of equilibrium (EQ) stage and rigorousnonequilibrium (NEQ) steady-state and dynamic mod-els [9–27]. Only more recently has attention been paidto hardware design aspects and the hydrodynamics andmass transfer in tray and packed columns [28–40].

For heterogeneously catalysed RD processes, hard-ware design poses many challenges [3]. The catalyst

particle sizes used in such operations are usually in the1–3 mm range. Larger particle sizes lead to intra-parti-cle diffusion limitations. To overcome the limitations offlooding during counter-current vapour–liquid contact-ing, the catalyst particles have to be enveloped withinwire gauze structures. Two commonly used structuresin industry are:1. Catalyst particles sandwiched between corrugated

sheets of wire gauze [29–34]. Such structures arebeing licensed by Sulzer, called KATAPAK-S, andKoch-Glitsch, called KATAMAX. They consist oftwo pieces of rectangular crimped wire gauze sealedaround the edge, thereby forming a pocket of theorder of 1–5 cm wide between the two screens.These catalyst ‘sandwiches’ or ‘wafers’ are thenbound together.

2. Catalyst particles enclosed in cloth wrapped in theform of bales [35–37].

The pressure drop and mass transfer characteristicsof these two structures are similar [41] and the major

* Corresponding author. Tel.: +31-20-525-7007; fax: +31-20-525-5604.

E-mail address: krishna@its.chem.uva.nl (R. Krishna).

0255-2701/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.PII: S 0 2 5 5 -2701 (01 )00166 -0

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462446

difference between the above two structures is withrespect to the radial dispersion characteristics. TheKATAPAK and KATAMAX structures have very highradial dispersion coefficients [30,34] because of the cris-crossing construction.

Another alternative hardware choice for heteroge-neous RD processes is to use standard packed columninternals such as Raschig rings and makes these catalyt-ically active; this is the strategy adopted by Flato andHoffmann [42] and Sundmacher and Hoffmann [43].Correlations for pressure drop and mass transfer forsuch packings are available in the literature [44–48].

The major objective of the present paper is to con-sider the various factors governing the choice of hard-ware for heterogeneously catalysed RD processes andto provide guidelines for making the proper choice. Toillustrate the various considerations we undertake thespecific design study of an RD column for synthesis oftertiary-amyl ether (TAME) using two specific hard-ware choices: catalytic bales and active Raschig rings.A further objective is to examine the need for rigorousNEQ models in RD column design.

2. Synthesis of TAME: reaction kinetics,thermodynamics and design specifications

TAME is formed by reversible, acid-catalysed,exothermic reaction of iso-amylenes (IA), consisting of

the isomers 2-methyl-1-butene (2M1B) and 2-methyl-2-butene (2M2B), with methanol

methanol+2M1B�TAME (1a)

methanol+2M2B�TAME (1b)

The reaction kinetics has been studied by two differ-ent groups in Clausthal [4,49–51] and in Helsinki [52–54]. In our design study we use the forward reactionrate constants as presented by the Clausthal group; thereaction kinetics is described by a Langmuir–Hinshel-wood rate expression in terms of the liquid phaseactivities [4,49–51]. The reaction equilibrium constanthas been calculated according to Rihko and Krause[52]. In addition to the above two reactions, the twoiso-amylenes undergo isomerization according to:

2M1B�2M2B (2)

In our simulations we implemented the kinetics ofisomerization as presented by Oost, Sundmacher, Hoff-mann and others [4,49–51]. The catalyst activity hasbeen specified by 900 eq[H+] m−3; the overall catalystvolume depends on the type of packing and voidage inthe column.

The process scheme used in our design study essen-tially follows that of Subawalla and Fair [36] and isshown in Fig. 1. The flow scheme consists of a pre-reac-tor followed by an RD column. The use of an isother-mal pre-reactor is advantageous because high overall

Fig. 1. Column configuration including a pre-reactor adapted from Subawalla and Fair [36].

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Table 1UNIQUAC binary interaction parameters adopted from Subawalla and Fair [36] and parameters for the extended Antoine equation based on theAspen Plus data bank

UNIQUAC binary interaction parametersbij/[K

−1]Component i bji/[K−1]Component j

54.4Methanol −788.852-methyl-1-butene28.82Methanol −757.372-methyl-2-butene75.15TAME −511.92Methanol

−9.34Methanol −670.42Isopentane−6.852-methyl-2-butene 3.82-methyl-1-butene

−41.652-methyl-1-butene 20.71TAME82.98Isopentane −98.812-methyl-1-butene

−16.61 1.0422-methyl-2-butene TAME63.71Isopentane −81.442-methyl-2-butene

107.92 −144.72TAME Isopentane

Parameters for the extended Antoine equation. The parameters are taken from theln(Psat)=a+

b

T+c ln(T)+dTe

Aspen plus data banka

b cComponent da e

−6904.5 −8.8622Methanol 7.47×10−682.718 22-methyl-1-butene 97.33 −5631.8 −12.589 1.5395×10−2 1

−5640.5 −9.64532-methyl-2-butene 1.11×10−583.927 2−5911.7 −5.846462.342 1.61×10−17TAME 6

72.35Isopentane −5010.9 −7.883 8.98××10−6 2

a Remark: Psat is given in Pa and T in K.

TAME production rates can be obtained when the IAconversion in the pre-reactor is in the range 55–65%. Inour study we assume a pre-reactor with an IA conver-sion of 62.7%, identical to that assumed by Subawallaand Fair [36]. Subawalla and Fair [36] considered a feedstream to the pre-reactor to consist of four inert com-ponents: isopentane, n-pentane, 1-pentene and 2-pen-tene. In order to reduce the complexity of the systemwe decided to consider only a single inert component,isopentane. Although the boiling points of the inertcomponents differ, by about 8 K at 4.5 bar pressure,the choice of a single inert component does not signifi-cantly alter the thermodynamic behaviour. The activitycoefficients for the inert C5 components are close tounity and show almost ideal behaviour. The binarymixture of methanol and isopentane reveals a singleminimum-boiling azeotrope (xMeOH=0.269 at P=4.5bar), just as found between methanol and the four C5

inert components used in the Subawalla–Fair study.The UNIQUAC model with the binary parameterspresented in Subawalla and Fair [36] are used to de-scribe the thermodynamic non-ideality of the mixture.The vapour pressure is calculated by the extendedAntoine equation. Table 1 lists the parameters used forsimulation and design.

The process design specifications have been summa-rized in Table 2. Essentially we aim for a minimum IAconversion of 94%, maximum TAME impurity in topproduct of 50 ppm and a minimum TAME purity of99.6% in the bottoms product from the RD column.Subawalla and Fair [36] determined the conceptual

design parameters, such as number of theoretical stagesin each section, reflux ratio and catalyst load by succes-sive iterations using an EQ stage model until the pro-

Table 2Process specifications and the conceptual column design used fordesigning the hardware of the column

Design specifications

94Minimum desired IA conversion %ppm50Maximum top TAME impurity

99.6Minimum TAME purity in product % mol mol−1

80 %Percent of flooding

Conceptual column design

Number of theoretical stages:4In the rectifying section

19In the reactive zone10In the stripping section

1.5Reflux ratio17.6Reboiler load MW

Operating pressure 4.5 bar

Feed location:Pure MeOH feed located on stage 24

29Pre to reacted feed located on stage

Catalyst specifications:Catalyst activity 900 eq[H+] m−3

36Catalyst volume m3

96.79 %IA conversionppm5.36TAME impurity in the distillate% mol mol−1TAME purity in the product flow 99.9

rate

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Fig. 2. Maximum values for (a) IA conversion, TAME purity in the product flow and (b) TAME impurity in the distillate for reboiler loads withina range of 17 and 19 MW. Note the values are local maximum belonging to different reboiler loads.

cess specifications are satisfied. Initial estimates forthese calculations, like the number of stages and refluxratio, are obtained from Fenske–Underwood short-cutcalculations [2,44]. These considerations lead to achoice of four equilibrium stages in rectifying section,19 reactive stages (each of which is in thermodynamicequilibrium) and ten equilibrium stages in the strippingsection. The reflux ratio is chosen to be 1.5. Themethanol feed was placed below the reactive section ofthe RD column, whereas the premixed feed, from thepre-reactor, which contains 157 kmol h−1 of TAME, islocated in the middle of the stripping section. Oneshould ensure that TAME in the pre-reacted feed isstripped off before it reaches the reactive section, other-wise it will revert back to IA and methanol at thebottom of the reactive section. Table 2 summarizes theconceptual column design, which will be used for thehardware design, and the process specifications.

With these specifications we proceed with a step-by-step column design procedure with the two differentinternals chosen; this step-by-step procedure is essen-tially the one suggested by Subawalla and Fair [36]. Inthe first step we use the EQ stage model to study theinfluence of operating pressure and reboiler load oncolumn specifications.

3. Step 1: Use of EQ stage model to fix columnpressure and reboiler load

The choice of the operating pressure is a trade-offbetween conversion and separation requirements. In-creasing pressure causes increased reaction rates and ashift of chemical equilibrium due to higher boiling

point temperatures in the reactive zone. On the other,increasing column pressure reduces the relative volatil-ity. Increased pressure results in larger MeOH feedrequirements whereas lower pressure requires higherdemand of catalyst load in order to meet the desiredspecifications. Keeping both the catalyst load andMeOH feed flow constant we investigated the influenceof the operating pressure on conversion and separationrequirements. Using the EQ stage model (describedextensively in the literature [9–27]) along with thecolumn specifications in Table 2, we varied the operat-ing pressure and investigated its influence on theTAME conversion and TAME mole fraction in thebottom product; the results are shown in Fig. 2(a). Theactive catalyst volume was taken to be 36 m3. The plotsin Fig. 2 show the local maxima when the reboiler loadranges from 17 to 19 MW at constant operating pres-sure. In Fig. 2(b) we note that the TAME impurity inthe top product of the RD column increases sharplywhen the operating pressure increases beyond 4.5 bar.Low operating pressures result in lower boiling pointtemperatures in the reactive section and lower maximalattainable TAME purity in the bottoms flow rate. Onthe other hand, high operating pressure, say above 5bar, will also significantly increase the TAME impurityin the distillate due to lower relative volatility andhigher methanol requirements for the azeotropic mix-ture. Therefore, operating the column at a pressurebetween 4.3 and 5 bar provides a potential setup thatmight satisfy all process specification. Furthermore, it isworth mentioning that our EQ model simulations showthat the RD column exhibits multiple steady states atoperating pressures above 4.2 bar for the reboiler loadsunder consideration. It is beyond the scope of this

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462 449

paper to discuss steady state multiplicity. Interestedreaders are referred to the paper by Mohl et al. [25].

On the basis of the results shown in Fig. 2, we choosean operating pressure of 4.5 bar. The process designspecifications are all met when operating at a reboilerload of 17.6 MW; see Table 2. For 4.5 bar pressure and17.6 MW reboiler load, Fig. 3(a) shows the correspond-ing liquid mole fraction profiles along the columnheight. Fig. 3(b) shows the TAME production ratealong the reactive section. In the rectifying section theMeOH– isopentane azeotropic composition is nearlyreached with 4 theoretical stages. The 19 theoreticalstages in the reactive section appears to be sufficient toachieve a high IA-conversion (96.78%) and removeTAME in order to avoid TAME decomposition. Thestripping section consists out of ten theoretical stageand provides a good recovery of 2M2B. Furthermore,ten theoretical stages appear to be necessary to bringthe TAME purity in the bottom product to 99.9%.

Using the EQ model we also studied the bifurcationbehaviour using the reboiler load as a continuationparameter. The results are shown in Fig. 4 as a plot ofTAME purity versus IA conversion. This plot is helpfulto see how the product specifications are met. The grayshaded area denotes the region for which process spe-cifications in Table 2 are fulfilled. As can be seen fromthe figure increasing reboiler load results in higherTAME product purity in the bottoms product flowrate. Reasons for this are increased internal flow rates

which facilitates the separation between isopentane andTAME in the stripping section. On the other handhigher reboiler loads also cause undesired lower bottomproduct flow rates as well as a possible drop in conver-sion. To illustrate this we also included the TAMEproduction rates per catalyst volume along the reactivesection for three steady states; see the insets to Fig. 4.The production rates exhibit typical profiles. At a re-boiler load of 17.55 MW the production rates increasemonotonically from the center of the reactive sectiontowards its end, close to the stripping section. Increas-ing the reboiler load to 17.6 MW results in a maximumTAME production close to the bottom of the reactivesection. Further increase of the reboiler load to 17.8MW even causes TAME decomposition at the very endof the reactive section. For a reboiler load of 18 MW,the design specifications are no longer met and we notea sharp drop in IA conversion. This is triggered by acomplex mechanism. It is observed that the isopentanemole fractions along the column height decrease forincreasing reboiler loads. This also implies thatmethanol and TAME concentration are increased inthe lower part of the reactive section. High TAMEconcentrations inhibit TAME production and evenmight result in TAME decomposition, as it is observedfor reboiler load of 17.8 MW. Further, bearing in mindthat the reaction order of methanol is negative, anexcess of methanol in the reactive section is possiblyslowing down the forward reaction rates. As can be

Fig. 3. Steady state profiles of EQ-model simulations: (a) composition profiles and (b) TAME productions rate. The reboiler load is set at 17.6MW.

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462450

Fig. 4. Bifurcation diagram in the IA-conversion and TAME bottoms product purity sub-space when the reboiler load, Qreb, is varied. Thesymbols denote steady states at reboiler load and product mass flow rate specified. The gray area denotes the region for which the specificationsare satisfied.

seen in Fig. 3, the methanol concentration increasesslightly towards the bottom of the reactive section,since the methanol feed is located below the reactivesection. Hence, the core TAME production shifts to-wards the rectifying section where the main TAMEformation takes place when the reboiler load is in-creased. In the bottom section less reactants are con-sumed. In the event of TAME decomposition, reactantsmay actually be formed at the bottom of the reactivesection. This mechanism in turn causes a higher internalrecycle of reactants and, therefore, lowers isopentanecomposition. This is also indicated when consideringthe overall conservation of mass. The bottoms productflow rates are decreasing with increasing reboiler dutyand so the distillate mass flow has to increase. Consid-ering that methanol and isopentane mole fractions inthe condenser are close to their azeotropic compositonand that almost all isopentane is recovered in thedistillate, the increase in distillate mass flow has to berealized by unreacted iso-amylenes.

The plot shown in Fig. 4 is important when weproceed further with the detailed design and choice ofcolumn internals.

4. Step 2: Determination of column diameter andheight

For the reactive section we consider two choices:catalytic bales and active Raschig rings. For the calcu-lation of the column diameter and height with catalyticbales we use the correlations presented by Subawalla etal. [35]. For calculating the mass transfer within thecatalytic bales, Subawalla et al. [35] consider threemechanisms for mass transfer: (1) mass transfer withinthe packing; (2) mass transfer due to wall effects; and(3) mass transfer to drops in the open channels. Adetailed study of the three mass transfer contributionsshows that the mass transfer within the packings is thecontrolling contribution. Therefore we neglect masstransfer from drops and due to wall effects. The cata-lyst particles within the bales are not fully wetted andwe use the Bornhutter and Mersmann correlation [55]to determine the wetted packing area. In case of thecatalytic active Raschig Rings we consider two cases,rings with a nominal size of 1/4 and 1 in. Pressure dropand mass transfer are calculated using the correlationspresented by Billet and Schultes [47,48].

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462 451

For the non-reactive rectifying and stripping sectionswe choose the highly efficient Sulzer BX packing. Thedesign correlations for Sulzer BX packing are takenfrom the literature [56,57]. A summary of the correla-tions used and the key parameters are listed in Table 3.

The column diameter depends predominantly on thepressure drop, on the maximum percentage of floodingand the liquid and vapour loads. The maximum per-centage of flooding was specified to be 80%. An esti-mate for the maximum liquid and vapour load in each

section is obtained from simulation of EQ model forthe conceptual design (with reboiler load of 17.6 MW).These loads are listed together with other physicalproperties in Table 4. Table 5 presents the correlationsthat have been used to calculate physical properties;further details are available in Kooijman and Taylor[58] and on the ChemSep website: www.chemsep.org. Ingeneral, pressure drop correlations are expressed interms of liquid and vapour superficial velocities and,therefore, the pressure drop depends implicitly on the

Table 3Correlations and specification used for the packings

Raschig rings 1/4 in. Raschig rings 1 in.

Specifications and correlations used for Raschig rings0.680.64Void fraction (–)

600Packing area 190(m2 m−3)

Pressure drop Billet and Schultes [48]correlation

Billet and Schultes [47]Mass transfermodel

Specifications and correlations used for Bales0.76Void fraction (–)169Packing area

(m2 m−3)Pressure drop Subawalla et al. [36]

correlationThe computation of the irrigated and dry pressure drop is based on the data given in Subawalla et al. [36]. MassMass transfertransfer due to drops and wall effects are neglected. Hence only mass transfer in the packing is considered. Themodel liquid

holdup correlation of Bornhutter and Mersmann [55] is used to compute the wetted packing area.

Specifications and correlations used for Sulzer BXVoid fraction (–) 0.9Packing area 492

(m2 m−3)60Channel flow angle

(°)8.9Channel side (mm)

Pressure drop Bravo et al. [56]correlation

Rocha et al. [57]Mass transfermodel

Table 4Properties and correlations used to estimate column diameter and HETP

Rectifying section Reactive section Stripping sectionDescription

0.0607 0.1245Max liquid load (m3 s−1) 0.0613Max vapour load (m3 s−1) 4481 47714540Internal vapour flow rate (kmol s−1) 0.62–0.730.75–0.78 0.73–0.76Internal liquid flow rate (kmol s−1) 0.46–0.49 0.4–0.770.41–0.49

11.8–1511.3–11.710.9–11.6Vapour density (kg m−3)571–604Liquid density (kg m−3) 569–593 588–633

MeOHKey component 1 IsopentaneIsopentaneIsopentaneKey component 2 TAME TAME

1.30×10−6Vap. diffusivity ÐV (m2 s−1) 2.1×10−6 1×10−7

Liq. diffusivity ÐL (m2 s−1) 8.1×10−9 1.2×10−81.33×10−8

0.26–0.290.07–1.9 0.3–3.1Slope of equilibrium line (m)

The estimates are based on EQ to model simulation at a reboiler load at 17.6 MW.

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Table 5Correlations for calculating physical properties

Description Correlation

Vapour component density Soave–Redlich–Kwong EOSHankinson–ThomsonLiquid component densityDIPPRVapour component viscosity

Liquid component viscosity Letsou–StielFuller–Schettler–GiddingsVapour diffusion coefficientsDIPPRSurface tensionDescribed in Taylor and KrishnaMaxwell–Stefan model[45]

A detailed description of the listed methods can be found in Kooij-man and Taylor [58].

maximum 80% flooding is fulfilled. This procedure isapplied to correlations of each type of packing in thereactive section and to the correlations for Sulzer BXpacking in the non-reactive sections. The results aresummarized in Table 6 and presented in Fig. 5. Fig. 5shows the pressure drop curves against the F-factor forthe optimized column diameter. The large filled circlesdenote the maximum allowed F-factor for each packingtype (from considerations of 80% of flooding). As canbe expected from comparison of the packing voidages,the Raschig ring with a nominal size of 1/4 in. requiresthe largest column diameter of 6 m. The column diame-ter is significantly reduced to 4.5 m when 1 in. Raschigrings are used. Further reduction of the diameter to 3.3m is obtained with catalytic bales. Furthermore, whendesigning the column one should keep in mind that theRaschig rings predict a much steeper increase of thepressure drop with the F-factor than catalytic bales; see

cross-sectional area, i.e. on the column diameter(squared). Using the liquid and vapour loads obtainedfrom the conceptual design we can iteratively obtain aminimum column diameter for which the constraint of

Table 6Estimated column diameter and section heights for Raschig rings and Bales

Stripping section (m)Rectifying section (m) Reactive section (m)

Column diameterRaschig rings 1/4 in. – –6Raschig rings 1 in. –4.5–

–Bales 3.3 ––Sulzer BX 3.22.8

From HETPSection height From catalyst volume

– 3.9Raschig rings 1/4 in. 3.5 ––7.14.3Raschig rings 1 in. –

– 17.8Bales 17.4 –2.2–Sulzer BX 1.0

Fig. 5. Pressure drop versus F-Factor at constant maximum liquid load. The reboiler load is set at 17.6 MW. The filled black circles denote thedesign at 80% flooding and maximum vapour load. The maximum liquid and vapour loads per section are listed in Table 4.

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Fig. 6. Influence of the pressure on the estimated column diameterwhen the design F-factor and the maximum molar load is assumed tobe constant for varying pressure. The molar vapour load is assumedto be 792 mol s−1 and the vapour density was computed for arepresentative concentration in the reactive section at dew pointtemperature (yMeOH=0.145, yIA=0.048, yTAME=0.01, yisopentane=0.797).

The operating pressure was fixed in the foregoingsection based on thermodynamic and reaction kineticconsiderations. The choice of the operating pressurealso affects the hardware design due to change in thevapour density. Higher pressure will result in higherdensity what reduces the column diameter. In order toillustrate this we estimated the change of the designcolumn diameter with regard to the base case. Fig. 6shows this change in column diameter when the pres-sure is varied and the design F-factor (corresponds to80% flooding at P=4.5 bar) and molar flow rate arekept constant. Increasing or decreasing pressure (aslong as the reaction kinetics and thermodynamic con-siderations do not restrict this) is a trade off betweenoperational and investment costs. On one hand, reduc-ing pressure will decrease the operational costs but alsowill decrease investments due lower construction costs.On the other hand the investment costs will increasebecause the column diameter increases also.

The next step is to determine the heights of the threeseparate sections in the RD column. For this purposewe need to estimate the height equivalent of theoreticalplate (HETP) for the various chosen packings. In orderto estimate HETP we chose for each section two keycomponents. In the rectifying section the key compo-nents are MeOH and isopentane. For the reactive sec-tion and the stripping section we chose the inertisopentane and the product TAME. The HETP for thebinary key components has been calculated form thebinary mass transfer coefficient as described in standardtextbooks; e.g. Stichlmair and Fair [44]. The transfercoefficients for catalytic bales were obtained from Sub-awalla and Fair [36]. The physical properties are takenfrom the EQ-model simulations of the conceptual de-sign (see Table 3); the diffusivity values are specificed inTable 4. In order to illustrate the difference in masstransfer behaviour between Raschig rings and bales, weplotted the number of theoretical stages per meterversus the F-factor at a liquid load of 0.050 m3 s−1.Raschig Rings with a nominal size of 1/4 in. are muchmore efficient than 1 in. Raschig rings or bales. Forboth 1/4 and 1 in. Raschig rings, increase in the superfi-cial vapour velocity causes an increase in the vapourmass transfer coefficients, which control the overallmass transfer. The number of theoretical plates permeter packing for Raschig rings increases sharply be-yond the flooding point. The situation with respect tocatalytic bales is quite different; here the liquid phaseresistance is quite important. With increasing superficialvapour velocity, i.e. F-factor, the stripping factor (mVl−1) increases. This causes a significant reduction in thecontact time between the vapour and the liquid con-tained inside the bales. The liquid phase mass transfercoefficient is significantly reduced. This reduction com-pensates for the increase in the vapour phase masstransfer coefficient with increasing vapour load. The

Fig. 5(a). Hence, Raschig Rings with a nominal size of1/4 in. are most sensitive to possible flooding when thedesign F-factor (vapour load and density) for instanceis exceeded due to disturbances or a change in theoperation point, a consideration that should be takeninto account when designing control systems for thecolumn.

Comparing the values for the column diameter ob-tained in the reactive section with the ones from non-re-active sections using the Sulzer BX packing (Dcol=2.8m for rectifying section and Dcol=3.0 m for strippingsection) shows that the bottleneck for choosing thecolumn diameter is in all cases the flooding in thereacti�e section. Flooding of the Sulzer BX packing inthe non-reactive section cannot be expected for thechosen design loads; see Fig. 5(b). Furthermore, whenthe choice is made for Raschig rings in the reactivesection then the expensive Sulzer BX packing in thenon-reactive sections will be operated well below flood-ing. There is clearly a mismatch in the choice of activeRaschig rings in the reactive section with use of SulzerBX packing in the non-reactive sections. One couldcontemplate using cheaper random packings in thenon-reactive sections in this case; this option was how-ever not worked out in detail in the present study.Swaging of the column, i.e. using different columndiameters in different sections, is not a viable optionbecause of the high costs especially for operation atelevated pressures.

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462454

Fig. 7. Number of theoretical stages per meter vs. F-factor. The liquidload is kept constant at a value of 0.05 m3 s−1.

vapour only comes into contact with the liquid at thecloth surface and some entrained liquid drops withinthe open channels. Consequently the pressure drop islow, but the vapour– liquid mass transfer is also low.Low pressure drop is not compatible with good masstransfer.

In the next step the heights of reactive and non-reac-tive sections are estimated applying the same HETPestimation procedure on each stage. The physical prop-erties, such as molar flow rates, densities have beentaken from the simulation of the conceptual design; seeFig. 8. It is noticeable that the HETP predictions forthe non-reactive sections vary in all cases within a quitelarge range (0.1 up to 0.4 m). This spread is notobserved for the reactive section where the variance ofthe HETP prediction is comparably small. The reasonfor this is the fact that stripping factors (the ratio of theslopes of the equilibrium line to that of the operatingline, mV l−1) is nearly constant in the reactive sectionbut this is not the case in the non-reactive sections.Summarizing, the HETPs in each section gives indica-tion of the section height. It turns out that the height ofthe Sulzer BX packing in the stripping and rectifyingsection are almost the same for each case. We find thatthe four theoretical stages in the rectifying sectioncorrespond to a height of about 1 m, whereas the tentheoretical stages in the stripping section correspond toa height of about 2.2 m. As expected the heights in thereactive section will differ depending on the chosenpacking type. Using 1/4 in. Raschig Rings results in asection height of about 3.9 m and Raschig Rings with anominal size of 1-in. demands a reactive section heightof 4.3 m. The difference in height is much more evidentwhen focussing on the bales packing. In order to matchthe 19 theoretical stages of the conceptual design asection height of 17.8 m is predicted in our calculations.A summary of the height requirements for the differentsections is given in Table 6.

number of theoretical plates per meter packing is there-fore almost independent of the F-factor for catalyticbales.

Fig. 7 emphasises the superior mass transfer charac-teristics of Raschig rings compared to bales; this con-trasts with the much poorer pressure dropcharacteristics witnessed in Fig. 5.

Qualitatively the situation can be understood as fol-lows. The vapour– liquid contacting with Raschig ringsis very intense as the vapour is in direct contact withthe falling liquid films (and drops). This leads to intensemomentum exchange and high pressure drop. But theinterphase mass transfer with Raschig rings is excellent.With catalytic bales, the situation is totally different.The catalyst particles are located within rolled-up clothlayers and the liquid flowing over the catalyst particlesis not in direct contact with the vapour that flowsthrough the open regions between the cloth layers. The

Fig. 8. HETP estimates as a function of the F-factor. The vapour and liquid loads are as specified in Table 4.

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462 455

Table 7Column configurations used for NEQ simulations

Case 2 Case 3Description Case 4Case 1 Case 5

Column diameter (m) 4.56 3.3 3.3 3.3Section height

1Rectifying section (m) 11 1 1Reactive section (m) 3.9 7.1 17.8 12.8 12.8Stripping section (m) 2.22.2 2.2 2.2 4.5

10.3 21.0 16.07.1 18.3Total height (m)

Catalyst load (m3) 36 36 36 26.275 26.275900 900 900 900Catalyst efficiency (eq m−3) 900

Packing typea

SBXNon-reactive sections SBXSBX SBX SBXReactive section RR 1/4 in. RR 1 in. Bales Bales Bales

Reflux ratio 1.5 1.5 1.5 1.5 1.517.65 17.8817.74 17.88Reboiler load (MW) 17.88

a Remark: SBX, Sulzer BX; RR, Raschig rings.

The height of the reactive section is also determinedby another constraint: the catalyst load required fromactivity considerations. We specified the catalyst load asthe catalytic active volume, i.e. the overall ring orparticle volume of the catalyst. For a given catalyticactive volume, Vcat, the minimum section height, h, canbe obtained from the volumetric constraint

h=4Vcat

(1−�)�D col2 (3)

where � denotes the packing voidage. In the develop-ment of the conceptual design we have chosen 36 m3

catalytic active packing volume. Using this volumedetermines the height requirements listed in Table 7.For the bales packing and the 1/4 in. Raschig Rings theminimum height do not exceed the estimations from theHETP calculations. This, however, is not true forRaschig Rings with a nominal size of 1 in. Hence inorder to maintain the overall activity of the catalyst it isrequired to consider a more than 60% taller sectionthan expected from the HETP estimations. Put anotherway the catalyst volume requirement is of overridingconsideration in the determination of the reactive sec-tion height for the 1 in. Raschig Rings. For catalyticbales, the catalytic load requirements almost coincideswith that from HETP considerations. Table 6 sum-marises the height requirements for various internalschoices.

Clearly, for each case the more stringent requirementhas to be met; this determines the chosen height of eachsection. The final chosen configurations are summarizedin the first three columns in Table 7. In order to give avisual impression we draw the configurations for 1/4 in.Raschig Rings, 1 in. Raschig Rings and Bales packingin Fig. 9. Using 1/4 in. Raschig Rings results in a fatbut short column, while incorporating catalytic balespacking will lead to a slim and tall column. Although

the columns are designed for the same yield andproduct purity, the differences in column configurationare significant. A further remark to be made is thatwhile use of 1/4 in. Raschig rings is justified for smalldiameter laboratory columns in experimental investiga-tions, for industrial use we would prefer to use largerdiameter rings which yield lower pressure drop. Pres-sure drop and flooding are important issues for com-mercial operation. In general, we would prefer to buildtall slim columns to short and fat ones because theprimary column cost determinant for high pressuresystems, excluding column internals cost, is the columndiameter and not the column height.

5. Step 3: Check chosen hardware design usingrigorous NEQ model

Our column designs have been arrived at by use of anEQ stage model, along with HETP calculations for thedifferent sections. The ‘final’ designs need to be checkedby use of rigorous NEQ stage simulations to see ifindeed the specifications are met. We therefore set upNEQ simulations of the three cases listed in the firstthree columns of Table 7; the details of the NEQ modelare available in our earlier publications [11–17]. Eachof the three cases has the same overall catalyst activityand volume (36 m3). For 1/4 in. Raschig rings andcatalytic bales we need to use additional inert particles/rings in order to fill the reactive section (to meet theconstraint of separation stages) without increasing theoverall catalyst activity. In practice, one might considerincreasing the catalyst load or decreasing the sectionheight slightly. This, however, would require a checkwhether a modified conceptual design would still satisfythe specifications. Such an iterative procedure was pro-posed by Subawalla and Fair [36]. Using 1 in. Raschig

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462456

rings, the minimum reactive section height due to thecatalyst volume constraint exceeds the estimates fromthe HETPs. In this case the number of theoretical stagecorresponds to approximately 30 (instead of 19 pro-posed by the conceptual design).

For setting up the NEQ-model we incorporated thepressure drop and mass transfer correlations per sectionand per packing type. Physical properties, which havebeen used, are listed in Table 5. The column has beendiscretized in slices. High concentration and tempera-ture gradients in the non-reactive section suggest apply-ing a finer grid there. We used 40 slices in the rectifyingsection, 50 slices in the stripping section and 38 slices inthe reactive section. It turned out that the increasingthe discretization did not alter the results. A coarsergrid size, however, results in significant deviations. Atotal condenser is employed at the top of the columnand a partial reboiler at the bottom. The reflux ratiowas kept constant at 1.5, as specified in the conceptualdesign.

Fig. 10(a) and (b) shows the bifurcation diagram forthe three configurations, along with the base case EQ-model of the conceptual design. The qualitative be-haviour of the NEQ-models resembles the conceptualdesign using the EQ. In all three cases the NEQ modelsimulations show that the desired specifications cannotbe met if the reboiler load is maintained at the concep-tual design level of 17.6 MW; in each case the reboilerload has to be increased. For 1/4 in. Raschig rings avalue of 17.74 MW is required, For 1 in. Raschig ringsthe value is 17.65 MW and for catalytic bales thereboiler load needs to be increased to 17.88 MW. Belowthese specified values the TAME purity in the bottoms

product stream drops sharply; see Fig. 10(b). TheHETP computation made use of EQ-model simulationat a design reboiler load of 17.6 MW. None of theNEQ models can recover such high purity and conver-sion at a reboiler load of 17.6 MW. Therefore, thereboiler loads have to be adjusted. Fig. 10(a) presentsIA conversion versus bottoms TAME purity diagramfor the three configurations (with adjusted reboilerloads) obtained from NEQ simulations. The bales and1/4 in. Raschig Rings have, according to the HETPestimations, the same number of theoretical stages ineach section. Nevertheless, model predictions in theregion of interest differ significantly. Surprisingly, theNEQ-model predictions for 1 in. Raschig rings appearsto be closer to predictions for 1/4 in. Raschig rings thanpredictions for bales packing, despite the fact that thenumber of theoretical stages in the reactive section is60% higher (according to the HETP estimations).

Fig. 11 shows the steady state composition profilesfor the three case studies; in this figure the verticaldistance has been normalized to exactly coincide for thethree cases. When focussing on the composition profilesone can see that there is hardly any difference betweenthe two Raschig ring configurations; see Fig. 11(a). Thesame applies to the temperature profiles. Slightly highermolar vapour flow rates can be observed for 1/4 in.Raschig Rings compared with 1 in. Raschig Rings; seeFig. 11(b). This results from the fact that a configura-tion with 1/4 in. Raschig Rings requires a higher re-boiler heat duty (17.74 compared to 17.65 MW) to meetthe design specifications.

Although these differences are hardly visible in thecomposition and temperature profiles the effect on the

Fig. 9. Schematic of column configurations for the five cases shown in Table 7.

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462 457

Fig. 10. Bifurcation diagrams for Cases 1, 2 and 3 in Table 7 obtained with varying reboiler loads. The results are presented in (a) IAconversion–TAME purity space and (b) TAME purity vs. reboiler load.

TAME production rates are more pronounced. As canbe seen in Fig. 11(d) the extrema are more distinct inthe case of 1 in. Raschig rings and so is the overallconversion higher. Fig. 12 shows the mass transfer ratesof the reactants (a) methanol and (b) 2M2B along thereactive section in each of the 39 slices. The height ofthe reactive section with 1 in. Raschig rings exceededwith about 60% the height determined by the HETPestimations. This resulted in slightly higher mass trans-fer rates and production rates at a lower reboiler loadthan predicted for the 1/4 in. Raschig Rings.

Fig. 11(c) shows the pressure drop along the columnheight. The pressure drop computed in the reactivesection for Raschig rings exceeds the one for bales. Thenon-reactive sections of the Raschig ring configurationsare operating well below their flooding capacities. Fur-thermore, one should notice that the 1/4 in. RaschigRings is operating very close to flooding. This is causedby the fact that the design load have been chosen for areboiler load of 17.6 MW and not for reboiler load of17.74 MW. Furthermore, 1/4 in. Raschig rings aremuch more susceptible to a rapid increase of pressuredrop when the volumetric flow rates increase slightly;see also Fig. 5(a).

In case of bales packing we had to choose a reboilerload of 17.88 MW in order to meet the requiredspecifications. The achieved conversion is lower thanthe conversion obtained for Raschig rings; see Fig.10(a). This is caused due to TAME decomposition inthe bottom part of the reactive zone; see Fig. 11(d).TAME decomposition in the bottom of the reactive

section, observed in the bales configuration, is an unde-sired phenomena which indicates that the columnconfiguration can be further optimized. The mechanismtriggering TAME decomposition has been observedand described previously with EQ-model. Excess ofmethanol in the top of the reactive section favour theTAME production there, whereas increased mole frac-tions of the reactant in the bottom causes TAME todecompose. This is also indicated in Fig. 12 by thenegative mass transfer rates for MeOH and 2M2B forthe bales.

In order to optimize the configuration of bales pack-ing we decreased the height of the reactive section and,therefore, the overall catalyst load until we obtained anevenly distributed TAME production rate in the reac-tive section at the same reboiler load. A reactive sectionheight of 12.8 m results in an almost 30% lower catalystload! The TAME production rates are shown as Case 4in Fig. 13 and the detailed configuration is given inTable 7. The non-reactive sections have been kept thesame as for Case 3. Evaluating the conversion andproduct purity for varying reboiler load, however,showed that the desired specifications have not beenobtained; see Fig. 14. In a next step we increased theheight of the stripping section in order to compensatethe loss of separation due to the shortening of thereactive section. Increasing the height of the strippingsection to 4.5 m meets the given specification as can beseen in the specification subspace in Fig. 14. Increasingthe stripping section also does not affect the TAMEproduction rates in the reactive section. As shown in

R. Baur, R. Krishna / Chemical Engineering and Processing 41 (2002) 445–462458

Fig. 11. Steady state profiles for the configuration case studies 1, 2 and 3 specified in Table 7. (a) Composition, (b) molar vapour flow rate, (c)pressure drop and (d) TAME production rate profiles for each case study.

Fig. 12. Mass transfer rates of (a) methanol and (b) 2M2B in the reactive section. Comparison of Cases 1, 2 and 3.

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Fig. 13. TAME production rate in the reactive section for threecolumn configurations, Cases 3, 4 and 5 containing bales; see Table 7.The reboiler load is fixed at 17.88 MW for all three cases.

column design. We modified the previous EQ-model byproportionally decreasing the reactive section (using acatalyst load of 26.735 m3) and increasing the strippingsection. Hence, the rectifying section contains 4, thereactive section 14 and the stripping section 20 theoret-ical stages. The pure methanol feed is located below thereactive section and the feed from the pre-reactor in themiddle of the stripping section. Fig. 15 shows thepredictions of the modified EQ-model in the specifica-tion subspace when the reboiler load is varied. The twomarkers in Fig. 15 denote the steady states for 17.88MW. As noticed in the previous case for the conceptualdesign the high conversion predicted by the EQ-modeland the NEQ-model for the modified bales configura-tion Case 5 are qualitatively similar but not quantita-tively. For instance, the conversion at reboiler load of17.88 MW seems to differ only slightly but focussing onthe column profiles reveals larger differences. Fig. 16shows the comparison between prediction of the EQ-model and the NEQ model for Case 5. The separationof TAME in the stripping section is much more pro-nounced for the EQ model that that predicted by theNEQ-model; see Fig. 16(a). This also affects the TAMEproduction rates where the EQ-model predicts TAMEdecomposition in the lower part of the reactive section;see Fig. 16(b). However, a design with negative reactionrate would have been rejected. Hence, the design wouldfocus on higher reboiler load in order to avoid TAMEdecomposition. In turn, the NEQ-model predictsrapidly dropping purity for such reboiler loads. Thisexample shows that the valuable information obtainedfrom conceptual design requires careful further studieswith rigorous models reflecting column internals. Theimportance of using rigorous NEQ models is evidentfrom Fig. 16.

Fig. 14. Bifurcation diagram in the IA-conversion–TAME puritysubspace for the three column configurations Cases 3, 4 and 5containing bales in the reactive section; see Table 7.

Fig. 15. Comparison between Case 5 in Table 5 and an equivalent EQmodel (NRSec=4, NReSec=14, NStSec=21) in the IA-conversion–TAME purity subspace. The catalyst load is Vcat=26.275 m3 forboth cases.

Fig. 13 (Case 5) the TAME production rates slightlyincreases due to better removal of TAME in the bottomof the reactive section. The differences in various de-signs (Cases 3, 4 and 5) of column containing balespacking are substantial, as can be visualized in Fig. 9.Compared with the design obtained from the EQ-model, almost 30% of catalyst are saved and the overallcolumn height is reduced by 2.7 m. Case 4 does notmeet the specifications but Case 5 does.

The obvious advantages of the bales configurationwith reduced catalyst load poses the question whether amodified conceptual design could have predicted such a

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Fig. 16. TAME composition profile and TAME production rate along the dimensionless section heights for Case 5 in Table 5 and EQ-model(NRSec=4, NReSec=14, NStSec=21).

6. Concluding remarks

We have carried out a step-by-step design study forsynthesis of TAME in an RD column to investigate theinfluence of the choice of internals on column design.The following major conclusions can be drawn fromthis study.1. Active Raschig rings have superior mass transfer

characteristics but poorer pressure drop characteris-tics as compared to catalytic bales. This leads toshorter fatter column configurations; see Fig. 9. Adetailed cost comparison needs to be made for thecolumn configurations shown in Fig. 9 in order toarrive at the final choice. Such a cost comparison isnot within the scope of our study.

2. EQ stage models provide only conceptual estimatesof column designs. The chosen column configura-tions must be carefully checked with rigorous NEQmodels. We have noted in particular that the re-boiler load had to be increased beyond the concep-tual estimate of 17.6 MW in order to obtainconfigurations meeting with the design specifica-tions; see Fig. 10.

3. In the TAME case study we have demonstrated thatconceptual design with bales (Case 3) can be im-proved substantially by reducing the catalyst load inthe reactive section and increasing the separationcapability of the stripping section; compare Cases 3and 5 with bales in Table 7 and Fig. 13.

4. The limitations of the EQ model have been under-lined in the simulation results given in Fig. 16 for

Case 5. Both EQ and NEQ models predict nearlyequal IA conversion and TAME purity. However,as can be seen in Fig. 16, the EQ model overesti-mates the separation capability in the strippingsection and predicts TAME decomposition at thebottom of the reactive section.

Appendix A. Notation

column diameter (m)Dcol

Maxwell Stefan diffusivity (m2 s−1)Ði, j

height (m)hslope of the equilibrium line (dimensionless)mnumber of theoretical stages (dimensionless)N

Qreb reboiler heat duty (W)pressure (Pa)Psuperficial velocity (m s−1)Ucatalytic active volume (m3)Vcat

Greek symbols� voidage of the packing (dimensionless)

Subscriptsrefers to the liquid phaseLrectifying sectionRsecreactive sectionReSec

StSec stripping sectionrefers to the vapour phaseV

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