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chemical engineering research and design x x x ( 2 0 1 3 ) xxx–xxx

Contents lists available at ScienceDirect

Chemical Engineering Research and Design

j ourna l h omepage: www.elsev ier .com/ locate /cherd

ptimal design of catalytic distillation columns: A casetudy on synthesis of TAEE

.A. González-Rugerioa,∗, R. Fuhrmeisterb, D. Sudhoffa, J. Pilarczykc, A. Góraka,d

TU Dortmund University, Department of Biochemical and Chemical Engineering, Laboratory of Fluid Separations, Emil-Figge Strasse 70,-44227 Dortmund, GermanyDanieli Froehling, Scherl Strasse 12, 58540 Meinerzhagen, GermanyResearch and Development Centre of Refinery Industry S.A., Chemikow 5, 09-411 Plock, PolandLodz Technical University, Faculty of Process and Environmental Engineering, Wólczanska 213, 90-924 Lodz, Poland

a b s t r a c t

The design of catalytic distillation (CD) columns is a challenging task because of the superposition of chemical

reaction and distillation in one apparatus. In this work, a method to design a cost-optimal CD column for chemical

systems with large number of components and chemical reactions is presented. The method is based on the following

steps: (1) estimation of the number of theoretical stages and catalyst volume by the decomposition of the CD column

into a sequence of chemical reactors and non-reactive distillation columns, (2) estimation of the column diameter

and operating conditions using an equilibrium stage model, and (3) design of the column applying an optimisation

algorithm and using a rigorous non-equilibrium stage model to represent the CD process. The method is applied to

determine the optimal column configuration and operating conditions for the synthesis of tert-amyl ethyl ether from

ethanol and isoamylenes. Eight components and four chemical reactions were selected to represent the chemical

system in the simulations.

© 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Octane enhancer; Tert-amyl ethyl ether; Heuristics; Evolutionary optimisation; Multiple reactions; Ether-

ification

In the last years, numerous studies regarding hetero-

. Introduction

eactive distillation (RD), in which chemical reaction and dis-illation are integrated into one single apparatus, is a wellnown example of process intensification. This integrationan offer several advantages when compared to sequen-ial reaction-distillation processes, such as reduction of theperating and investment costs, higher product yields and

ncreased catalyst lifetime (Sundmacher and Kienle, 2002;

Please cite this article in press as: González-Rugerio, C.A., et al., Optimal

TAEE. Chem. Eng. Res. Des. (2013), http://dx.doi.org/10.1016/j.cherd.2013.08

enig and Górak, 2007). However, the design of RD columns is

Abbreviations: 2M1B, 2-methyl-1-butene; 2M2B, 2-methyl-2-butene; 2istillation; ETBE, ethyl tert butyl ether; EQ, equilibrium stage; EtOH, eM2B; IUPAC, International Union of Pure and Applied Chemistry; MDErogramming; NEQ, nonequilibrium stage; PFR, plug flow reactor; RD, rAEE, tert amyl ethyl ether; TAME, tert amyl methyl ether; THEE, tert-heLE, vapour–liquid equilibrium.∗ Corresponding author. Tel.: +49 0231 755 6265; fax: +49 0231 755 3035.

E-mail addresses: [email protected] (C.A. Gonzá[email protected] (D. Sudhoff), Janusz.pilarczyk@obr

Received 4 March 2013; Received in revised form 24 July 2013; Accepte263-8762/$ – see front matter © 2013 The Institution of Chemical Engittp://dx.doi.org/10.1016/j.cherd.2013.08.030

challenging due to the interactions between multicomponentmass and heat transfer, phase equilibrium, hydrodynamicsand chemical reaction. Moreover, the complexity to designRD columns increases significantly for chemical systems withlarge number of components and chemical reactions. Thedesign of a RD column consists of the estimation of the columndimensions, feed locations and operating conditions whichsatisfy pre-defined design specifications (Ciric and Gu, 1994).

design of catalytic distillation columns: A case study on synthesis of.030

Mthp, 2-methylpentane; 2M2P, 2-methyl-2-pentene; CD, catalyticthanol; FCC, fluid catalytic cracking; IA, Isoamylenes, 2M1B and

, modified differential evolution; MINLP, Mixed Integer Non Lineareactive distillation; SRK, Soave–Redlich–Kwong equation of state;xyl ethyl ether; UNIFAC, UNIversal Functional Activity Coefficient;

ez-Rugerio), [email protected] (R. Fuhrmeister),.pl (J. Pilarczyk), [email protected] (A. Górak).d 29 August 2013

geneously catalysed RD processes, commonly referred as

neers. Published by Elsevier B.V. All rights reserved.

dx.doi.org/10.1016/j.cherd.2013.08.030

http://www.sciencedirect.com/science/journal/02638762

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dx.doi.org/10.1016/j.cherd.2013.08.030


2 chemical engineering research and design x x x ( 2 0 1 3 ) xxx–xxx

Nomenclature

ai activity of component i (mol mol−1)ann annualising factor (year−1)ai column diameter (m)D/F distillate to feed ratio (mol mol−1)DN nominal diameter (mm)Ei activation energy of reaction i (kJ mol−1)hcat catalytic section height (m)hsep separation section height (m)HETP height equivalent to a theoretical plate (m)KEtOH adsorption equilibrium constantKi chemical equilibrium constant for reaction ik0i pre-exponential factor for the Arrhenius equa-

tion (mol kg−1 s−1)ki reaction rate constant for reaction i

(mol kg−1 s−1)mTAEE mass flow rate of TAEE (tonne year−1)nexcess

alcohol,feed maximal alcohol excess in the feed to the CDcolumn (mol/s)

nstoichiometryalcohol,feed stoichiometric alcohol molar flow rate

(mol/s)ncomponents number of componentsni molar flow rate of species i (mol/s)ni,feed molar flow rate of unreacted and inert species

in the column feed (mol/s)nreactions number of reactionsri reaction rate (mol kg−1 s−1)toper annual operation time (8000 h year−1)T temperature (K)Tb boiling temperature (K)TIC total investment cost (euro)TOC total operating cost (euro year−1)V Vapour mass flow rate (kg s−1)xi molar fraction of component i in liquid phase

(mol mol−1)xaze

imolar fraction of component i at the azeotrope(mol mol−1)

�v density of the vapour phase (kg m−3)

catalytic distillation (CD), have been published. In particular,different methods to design CD columns are available inthe open literature. Graphical, heuristic and optimisationbased approaches can be considered as the main designcategories (Almeida-Rivera et al., 2004). Graphical methodsare useful tools for feasibility analysis and screening of theprocess variants but these methods can only handle a limitednumber of degrees of freedom (ncomponents − nreactions ≤ 3). Twoconceptual developments that have contributed to extend theapplication of graphical methods are transformed compositionvariables (Barbosa and Doherty, 1988) and the element concept(Pérez-Cisneros et al., 1997). The main advantage of these twoapproaches is that the dimensionality of the chemical systemis reduced because the number of transformed variables orelements is lower than the number of actual components.To date, several graphical methods are available in literaturebased on either transformed variables (e.g. Carrera-Rodriguezet al., 2011) or elements (e.g. Jantharasuk et al., 2011). Recently,Avami et al. (2012) presented the feed angle method, which isbased on pinch point analysis rather than visual inspection,



and thus it seems to be promising to handle chemical systemswith multiple components and reactions. Nevertheless, all the

aforementioned methods yield only rough CD column designswhich must be improved with subsequent rigorous simula-tions because the geometric characteristics of the columninternals are not considered, which play a key role in actualmass and heat transfer across the vapour–liquid interface.Moreover, thermodynamic and chemical equilibrium are usu-ally assumed and economic issues are not directly addressed.

In addition to graphical methods, Subawalla and Fair(1999) presented an iterative method based on heuristic rules.This method overcomes some of the limitations of graphicalapproaches by considering the column internals and enablingthe CD column economics to be easily added to the procedure.Moreover, the method can be applied to chemical systemswith several components and multiple reactions. However,this method does not guarantee the optimal column becauseas pointed out by Li et al. (2012), no effective heuristics rulesare available that can ensure optimal integration betweenchemical reaction and distillation.

Algorithmic optimisation methods overcome the draw-backs of graphical and heuristic methods. A suitable objectivefunction for the optimisation algorithms is the annual operat-ing and the annualised investment costs. The constraints aregiven by the mass and energy conservation laws and productqualities (Ciric and Gu, 1994). Mixed Integer Non Linear Pro-gramming (MINLP)-based methods have been widely used dueto the nonlinearity of the CD model equations and the discreteand continuous variables that have to be optimised (Ciric andGu, 1994; Stichlmair and Frey, 2001; Gangadwala and Kienle,2007; to mention a few). Recently, optimisation methods basedon random search (e.g. simulated annealing-based, differen-tial strategies and memetic algorithm) have been applied todesign CD columns (Cardoso et al., 2000; Lima et al., 2006; Babuand Khan, 2007; Urselmann et al., 2011; among others). Thesemethods have several advantages, such as their easy imple-mentation and their ability to escape of local optimums, butthey may require a large number of iterations, leading to highcomputational effort. To apply the optimisation algorithm, thesearch space of the optimisation variables must be previouslyspecified. However, the selection of the search space is nottrivial (Urselmann et al., 2011; Avami et al., 2012).

Most of the optimisation algorithms published for thedesign of CD columns are based on several assumptions (e.g.,constant enthalpy of vapourisation, constant molar overflow)that may not realistically represent the phenomena occur-ring in a CD column (Damartzis and Seferlis, 2010). Althoughthe limitations of equilibrium stage (EQ) models have beenidentified (Baur and Krishna, 2002), only a few publicationspresented the design of CD columns using rigorous non-equilibrium stage (NEQ) models (see, e.g., Gómez et al., 2006;Dalaouti and Seferlis, 2006; Damartzis and Seferlis, 2010). Thefundamentals of both EQ and NEQ models are discussed inSection 4.3.1.

In this work, a method to design a cost-optimal CD columnis presented. In the first two steps of the method, heuris-tic rules and simple mathematical models, e.g., short cutmethods for non-reactive distillation columns, are applied todetermine the CD column configuration and operating con-ditions. Results obtained in these steps are used as startingvalues for the optimisation algorithm using a steady state NEQmodel. The method can be applied to design CD columns forchemical systems involving a large number of componentsand reactions for any kind of the modelling approach used for

design of catalytic distillation columns: A case study on synthesis of8.030

CD processes. Moreover, because a NEQ model is used in thefinal step of the design method, the geometric characteristics

dx.doi.org/10.1016/j.cherd.2013.08.030


chemical engineering research and design x x x ( 2 0 1 3 ) xxx–xxx 3

oaeToh

2

Tmab(2(

2

2

famrCri2srpCIEif

2

TAmm(Bs

Table 1 – Reaction rate equations for the synthesis ofTAEE and THEE (Linnekoski et al., 1997; Zhang andDatta, 1995).

Reaction Reaction rate equation (mol kg−1 s−1)

1 r1 = k1(a2M1BaEtOH−aTAEE/K1)

(1+KEtOHaEtOH)2

2 r2 = k2(a2M2BaEtOH−aTAEE/K2)

(1+KEtOHaEtOH)2

3 r3 = k3(a2M1B−a2M2B/K3)1+KEtOHaEtOH

4 r4 = k4(a2M2PaEtOH−aTHEE/K4)

(1+K′EtOH

aEtOH)2

Table 2 – Normal boiling points (Aspen PropertiesPlusTM).

Abbreviation IUPAC name Tb (K)

Isopentane 2-Methylbutane 300.62M1B 2-Methyl but-1-ene 303.92M2B 2-Methyl but-2-ene 311.22Mthp 2-Methylpentane 333.42M2P 2-Methyl pent-2-ene 340.1EtOH Ethanol 351.1TAEE 2-Ethoxy-2-methylbutane 374.2

in the distillate, while TAEE is the bottom product of the CDcolumn. Unreacted EtOH is recovered in the distillate stream

Table 3 – Azeotropes predicted by the UNIFAC model at4 bar (Aspen Properties PlusTM).

Component 1 Component 2 x1 (mol mol−1) Tb (K)

EtOH Isopentane 0.1320 344.3EtOH 2M1B 0.1293 348.3EtOH 2M2B 0.1859 354.5EtOH 2Mthp 0.3687 368.1

f the column internals are taken into account. The method ispplied to design a CD column for the synthesis of tert-amylthyl ether (TAEE) from ethanol (EtOH) and isoamylenes (IA).he synthesis of TAEE has not been extensively analysed in thepen literature and to our knowledge, no CD column designas been published for this reaction system yet.

. Chemical system

AEE is produced by the heterogeneously catalysed, exother-ic and chemical equilibrium limited reactions between EtOH

nd the two IA, 2-methyl-1-butene (2M1B) and 2-methyl-2-utene (2M2B), according to the chemical Eqs. (1) and (2)

Linnekoski et al., 1997). The isomerisation between 2M1B andM2B is an additional chemical equilibrium limited reactionEq. (3)).

+ OH O

TAEE EtOH M1B (1)

OH+ O

TAEE EtOH 2M2B (2)

2M2BM1B (3)

To produce TAEE at a commercial scale, the light gasolineraction from fluid catalytic cracking (FCC gasoline) is useds the IA feedstock. The FCC gasoline consists of approxi-ately 20 mole% of IA, 5 mole % of C6 reactive olefins and the

emaining components are nonreactive hydrocarbons (mainly

5 and C6 fractions). In this work, inert hydrocarbons are rep-esented by the components with the highest concentrationn the FCC gasoline; C5 fraction by isopentane, C6 fraction by-methylpentane (2Mthp) and C6 reactive olefins are repre-ented by 2-methyl-2-pentene (2M2P). In addition to the maineactions given by Eqs. (1)–(3), several side reactions may takelace, e.g., the formation of tert-hexyl ethyl ether (THEE) from

6 reactive olefins and EtOH as well as the dimerisation of bothA. Nevertheless, dimerisation reactions are minimised if antOH/IA molar ratio greater than one in the catalytic sections ensured (González-Rugerio et al., 2012), and thus only theormation of THEE is considered (Eq. (4)).

+ OH O

THEE EtOH 2M2P (4)

.1. Reaction kinetics

he reaction kinetics of TAEE synthesis on the catalystmberlyst 16 W and based on the Langmuir–Hinshelwoododel obtained by Linnekoski et al. (1997) were used in the CDodel. The reaction kinetics published by Zhang and Datta

1995) of THEE synthesis on Amberlyst 15 W were applied.



ecause the physical properties of these catalysts are ratherimilar (Table A.1 in Appendix), the published reaction rate

THEE 2-Ethoxy-2-methylpentane 417.1

equation for Amberlyst 15 W was assumed to be valid forAmberlyst 16 W as well. Reaction rate equations are shownin Table 1 and kinetic parameters are given in the Appendix(Tables A.2 and A.3). The chemical equilibrium limits the IAconversion to 39% at 333 K and at stoichiometric quantities ofIA and EtOH. In practice, an EtOH excess is used to increasethe equilibrium conversion.

2.2. Thermodynamics

Activity coefficients in the liquid phase were calculated usingthe UNIFAC model while fugacity coefficients were estimatedby the Soave–Redlich–Kwong (SRK) equation of state. TheUNIFAC-SRK model predicts VLE experimental data, if avail-able in literature, (Everson and Jansen, 2001; Arce et al., 2005)with an accuracy of 1.3%. Table 2 shows the component namesand their normal boiling points. Six homogeneous azeotropesare predicted by the UNIFAC model at 4 bar (Table 3).

3. Chemical process description

The FCC gasoline is mixed with EtOH and fed to a prereactor,in which chemical equilibrium is reached (Fig. 1). The outletstream from the prereactor already containing TAEE and THEEis subsequently fed into the CD column. Isopentane and IAare low boiling point components (Table 2) and are obtained


EtOH 2M2P 0.4385 373.3EtOH TAEE 0.8252 389.5

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Fig. 1 – Process flow diagram for TAEE synthesis from EtOHand IA.

due to the minimal boiling point azeotrope between EtOH andisopentane (Table 3).

Upstream of the CD column, a prereactor was assumed,which is operated at high pressure (8 bar) to ensure that onlythe liquid phase is present and at 340 K. An EtOH excess of 20%with respect to the stoichiometric amount for the main reac-tions was used to increase the equilibrium conversion. Underthese conditions, the IA conversion in the prereactor is 47.2%(Eq. (5)) and the selectivity of EtOH towards TAEE is 89% (Eq.(6)). Table 4 shows the inlet and outlet molar flow rates of eachstream in the prereactor. This calculation fixes the composi-tion of the feed stream to the CD column. In this contribution,only the design of the optimal CD column is carried out.

conversion of componenti = ninleti

− noutleti

ninleti

(5)

selectivityEtOH TAEE = noutletTAEE − ninlet

TAEE

ninletEtOH − noutlet

EtOH

(6)

3.1. Design specifications

As design specifications, a production capacity of150 ktone year−1 (≈45 mol/s at 8000 h year−1) of TAEE inthe prereactor – CD column system is set as the target. A highTAEE purity is not required in this chemical process, but dueto environmental regulations, the maximum content of IA inthe bottom stream of the column has been restricted (Cruzet al., 2007). A minimum IA conversion of 90% (based on thefeed to the CD column), a maximum TAEE concentration of0.01 mole % in the distillate and a maximum concentrationof IA and EtOH in the bottom product of the column of 1mole % are defined as targets. The proper hydrodynamicconditions within the column are considered by ensuringthat the column is operated at the liquid load of 80% of theflooding point of catalytic packing and in the range 65–80%for the non-catalytic packing.

3.2. Problem definition

Once the chemical system was set and the design specifica-tions defined, the design problem can be stated as follows



(Ciric and Gu, 1994): determine the height of the separation(hsep) and catalytic (hcat) sections, column diameter (d), feed

locations and operating conditions (Fig. 1) that satisfy thedesign specifications.

4. Design method

The method proposed to design a cost-optimal CD columnconsists of the following steps (Fig. 2):

Step 1: Sequential initialisationThe aim of this step is to determine the number of theo-retical stages for the separation sections and the catalystvolume to be used in the CD column. For this purpose, chem-ical reaction and distillation are decoupled (Fig. 3), i.e., theCD column is decomposed by a sequence of reactors andnon-reactive distillation columns. As a consequence, alreadyavailable short cut approaches for non-reactive distillationcolumns and simple mathematical models for ideal chemicalreactors can be applied. The decomposition of the CD col-umn has been previously performed by Subawalla and Fair(1999) and Pilarczyk et al. (2005), among others. Subawallaand Fair (1999) simulated on the one hand a non-reactivedistillation column to determine the number of theoreticalstages while on the other hand they used a series of chemicalreactors to estimate the catalyst amount. Later, the catalyticsection of the CD column is placed by checking the concen-tration profiles of the reactants in the non-reactive column,i.e., the catalytic zone is located in the stages with the highestreactant concentration. Afterwards, by successive iterationsthe number of stages in each section of the column and theoperating conditions are corrected. In the method proposedhere, the catalytic zone is placed in the column as shownin Fig. 3 and no additional iterations are carried out becausean optimisation algorithm is applied in the final step of themethod.In addition to the number of stages and catalyst volume,the molar reactant ratio in the column feed is also calcu-lated as shown by Sneesby et al. (1997). Moreover, heuristicrules are used to identify the feed location. Note that thisstep does not consider the geometric characteristics of thecolumn internals.The decomposition of the CD column used in this step yieldsinformation about the column structure, but neither theoperating conditions nor the column diameter can be deter-mined.Step 2: Simultaneous initialisationIn this step, the column diameter, the height of the columnand the operating conditions are estimated. With this aim,chemical reaction and distillation are coupled, and a steadystate EQ model is used to describe the CD process. First, thenumber of theoretical stages determined in step 1 is usedto calculate the column diameter by applying a simple EQmodel in which the reactions are not taken into account.Once the diameter is estimated, the column height can becalculated. Later, the reaction rate equations are includedin the EQ model, and the search direction of the operatingconditions to be used during the optimisation is identified.Step 3: Detailed optimisationFinally, an optimisation algorithm is applied to design theCD column using an NEQ model and considering investmentand operating costs as the objective function. The columndimensions and operating conditions obtained in the previ-


ous step are used as starting values during the optimisation.The following sections describe each step of the method

dx.doi.org/10.1016/j.cherd.2013.08.030



Fig. 2 – Structure of the design method proposed in this work.

4

4Tttot

in detail and in Section 4.4, points which deserve specialattention to apply the method to other chemical systems arediscussed.

.1. Step 1: Sequential initialisation

.1.1. Feed locationhe feed location depends not only on the volatilities of reac-

ants and products but also on the purities of the reactants andhe formation of azeotropes. Based on the relative volatilitiesf the components, the following heuristics rules are availableo determine the feed location (Bessling et al., 1997):

Heuristic 1. If the reactants are the most volatile componentsin the chemical system, the feed location must be close tothe bottom of the reaction zone, otherwise the feed location



must be close to the top of the catalytic section (Cheng andYu, 2005).

Table 4 – Feed and product molar flow rates in the prereactor.

Component FCC stream

Molar flow rates (mol/s)Isopentane 100.8

2M1B 16.45

2M2B 31.55

2Mthp 79.20

2M2P 12.00

EtOH 0.00

TAEE 0.00

THEE 0.00

Total mole flow (mol/s) 240.00

Heuristic 2. If the relative volatility of the reactants differssignificantly (˛AB ≥ 4; Barnicki et al., 2006) then two feeds arenecessary, one close to the bottom and another close to thetop of the catalytic zone.While based on the reactants purity (Subawalla and Fair,1999):Heuristic 3. If a feed containing the product is used andthe concentration of the product in the feed is close to itsconcentration at chemical equilibrium with the reactants(within approximately 20%), then the feed should be locatedin the separation zones to remove the products that enterthe column before they reach the reaction section to preventproduct decomposition.Heuristic 4. In some chemical systems, the formation ofazeotropes will also influence the feed location. For example,although EtOH is an intermediate boiling point componentin the TAEE synthesis, the minimal boiling point azeotrope


formed between EtOH and isopentane leads EtOH to behavelike a minimal boiling point component. Therefore, if pure

EtOH feed to theprereactor

Prereactoroutlet stream

0.00 100.80.00 2.240.00 23.110.00 79.200.00 9.17

57.60 32.120.00 22.640.00 2.83

57.60 272.11

dx.doi.org/10.1016/j.cherd.2013.08.030



Fig. 3 – Decomposition of the CD column into a sequence ofchemical reactors and non-reactive distillation columns. (a)Case when a prereacted/impure feed is used, (b) case when

i

pure reactants are used.

EtOH is used, it should be fed at the bottom of the reactivesection.

4.1.2. Estimation of the number of theoretical stages forthe separation sections and catalyst volumeTo estimate the number of theoretical stages for the separationsections and the catalyst volume, the CD column is decom-posed by a sequence of chemical reactors and non-reactivedistillation columns as shown in Fig. 3. Two different situa-tions can occur depending on whether a prereacted/impurefeed or pure reactants are used.

Fig. 3a shows the process configuration for the case inwhich a prereacted/impure feed is used. In this case, as men-



tioned in Section 4.1.1, the feed should be located in theseparation zones. Stripping and rectifying sections of the CD

column are modelled as non-reactive distillation columns.The number of theoretical stages for the separation sectionsis calculated with the Fenske–Underwood equation (Fenske,1932; Underwood, 1948), in which light and heavy key compo-nents must be selected as well as their percentage of recovery.The selection of the key components depends on the desiredseparation (see details in Section 5.1).

To estimate the catalyst volume, the reactive zone is rep-resented by a system of ideal reactors and flash separatorsin series (Subawalla and Fair, 1999; Pilarczyk et al., 2005). Inthis step, the number of reactors is increased until the tar-get conversion is reached. The catalyst volume in the reactorsis varied such that chemical equilibrium is achieved in eachreactor. Afterwards, the total volume of catalyst in the reactorsis used as the actual catalyst volume in the CD column.

If pure reactants are used, the process configuration shouldbe started with the chemical reactors followed by a singlenon-reactive distillation column to represent the separationsections of the CD column as shown in Fig. 3b. In the dis-tillation column, the number of stages obtained with theFenske–Underwood equation between the top and the feedcan be used as equivalent to the number of stages in the recti-fying section of the CD column. Similarly, the number of stagesbetween the feed and the bottom of the distillation columncan be used as representative of the stripping section of theCD column.

Although this step considers three sections of the column(rectifying, reactive and stripping), it is possible that not all ofthese sections are necessary, e.g., the rectifying section maynot be needed. However, the three sections of the CD columnshould be considered here, and the third step of the methodwill determine whether they are indeed required.

4.1.3. Calculation of the molar reactant excess in thecolumn feedThe molar reactant ratio has to be estimated considering thereaction stoichiometry and the composition of the reactants inthe azeotropes (Sneesby et al., 1997). The stoichiometric reac-tant amount is calculated by taking into account the productyield, target conversion and reaction stoichiometry. However,an excess of alcohol is beneficial for the production of high-octane gasoline components, such as tert-amyl methyl ether(TAME) and TAEE, by CD because of the following reasons:(1) side reactions, such as IA dimerisation, are suppressedif alcohol is in excess (Rihko et al., 1994), (2) the IA conver-sion will increase if the alcohol/IA ratio increases (Sneesbyet al., 1997) and (3) Sundmacher and Hoffmann (1994) demon-strated that interfacial mass transfer rates can be higher thanreaction rates and therefore less reactant is available in theliquid phase for reaction. This behaviour results from the min-imal boiling point azeotropes formed by the alcohol and theinert components, which can take the reactant away fromthe liquid phase, decreasing the alcohol/IA ratio (Subawallaand Fair, 1999). However, if the excess of alcohol is too large,alcohol will also be obtained in the bottom stream of the CDcolumn, decreasing the product purity (Hickey and Adams,1994). Therefore, an optimal reactant excess exists and mustbe determined. A first approximation of the optimal alcoholmolar flow rate (nexcess

alcohol,feed) can be made using the molar flowrates of inert components and non-reacted species (ni,feed)in the column feed as well as the azeotropic compositionbetween these components (xaze) and the alcohol at differ-


ent pressures as shown in Eq. (7). This equation was obtainedby analysing several case studies on the production of tertiary

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F

e

n

mfi

4

TeBetavv

4TtigG

Table 5 – Properties of KATAPAK SP11® (*Brunazzi andViva, 2006; **Buchaly et al., 2007; Behrens, 2006).

Packing characteristics DN 50 DN 450

Specific geometric area (m2/m3) 199* 300Catalyst volume fraction 0.23** 0.46HETP value (m) ≈0.5** ≈0.5Maximum vapour load (Pa0.5), F-factor – ≈1.2

ig. 4 – Representation of step 2 of the design method.

thers (Sneesby et al., 1997; Subawalla and Fair, 1999).

excessalcohol, feed ≈ n

stoichiometryalcohol, feed +

nunreacted∑i=1

ni,feed

(1

xazei

− 1

)i

= unreacted and inert species (7)

Finally, if nexcessalcohol,feed > nactual

alcohol,feed, where nactualalcohol,feed is the

olar flow rate entering the column, more alcohol should beed to the CD column. Otherwise, the molar flow rate of alcoholn the prereactor feed (Fig. 1) should be decreased.

.2. Step 2: Simultaneous initialisation

he objective of this step is to determine the column diam-ter, the height of the column and the operating conditions.efore the column diameter is calculated, the geometric prop-rties of the selected catalytic packing are discussed becausehe column diameter strongly depends on the packing char-cteristics. Fig. 4 presents a schematic representation of theariables estimated in step 1 and their relationships with theariables calculated in step 2.

.2.1. Column internalshe selection of proper column internals is one important fac-

or in the design of a CD column. In this study, the columnnternals used previously during the experimental investi-



ation of the TAEE synthesis in a CD column published byonzález-Rugerio et al. (2012) are applied for column design,

i.e., Katapak SP11® and Mellapak 750Y®. As catalyst, thesulfonic acid ion-exchange resin Amberlyst 16 W, which isthermal stable up to 400 K was chosen.

Because the void fractions of Katapak SP11® and Mella-pak 750Y® are significantly different, the suitability of thenon-catalytic packing must be verified in the final designbecause the CD column must operate close to the optimalhydrodynamics of each packing.

The lack of information in the open literature about thescale-up from lab/pilot to industrial scale columns is one of themajor problems in the design of CD columns. Hoffmann et al.(2004) showed that the geometric properties, such as the cat-alyst volume fraction, specific surface area and void fractionof the catalytic packing MULTIPAK®, change with the diameterof the column. However, these authors also showed that thesegeometric properties did not change significantly for columndiameters larger than 400 mm.

Information about the maximum capacity and the sepa-ration efficiency of KATAPAK-SP11® is available in the openliterature (Brunazzi and Viva, 2006; Behrens, 2006; Buchalyet al., 2007). Table 5 shows a comparison between the spe-cific geometric area and the catalyst volume fraction of thiscatalytic packing for two different column diameters (50 and450 mm nominal diameters, DN). The use of the geomet-ric properties of the catalytic packing obtained with a DN50 column will provide poor CD column designs. In thiswork, the experimental measurements (Table 5) determinedby Behrens (2006) are used. This author carried out experi-ments in a column with a diameter of 450 mm, and thereforehis experimental data can be considered as representativeof an industrial scale column. Correlations published byHoffmann (2005) and by Rocha et al. (1993, 1996) were appliedfor the description of the mass transfer and hydrodynamicsin Katapak SP11® and Mellapak 750Y®, respectively. More-over, based on the fact that the catalytic particles could notbe fully wetted particularly in industrial columns due to liq-uid mal-distribution problems (Beckmann et al., 2002; Baurand Krishna, 2002), it was assumed that only 80% of thepacking area is wetted (Brunazzi E., personal communication,September, 2010).

4.2.2. Estimation of the column diameterThe column diameter (d) is a function of the vapour flow rate(V) within the column and mixture properties (i.e., vapourdensity, �v), and thus V and �v must first be estimated. To deter-mine the flow rates and the mixture properties, a simulationwith the EQ model is performed. The number of theoreticalstages for the separation sections estimated in Section 4.1.2is used in this simulation and the operating conditions arecalculated based on the design specifications or arbitrarilyspecified. Specifically, an initial guess of the reflux ratio andoperating pressure is given but the maximal operating tem-perature of the catalyst is taking into account. Afterwards, the


column diameter is calculated using Eq. (8), in which V and �v

dx.doi.org/10.1016/j.cherd.2013.08.030



are estimated using the non-catalytic packing but the F-factorcorresponds to the catalytic packing.

d = 2(

V

�F-factor

)1/2(�v)−1/4. (8)

4.2.3. Calculation of the column heightOnce the column diameter is known, the height of the cat-alytic section (hcat) is obtained according to Eq. (9) (Baur andKrishna, 2002) using the previously obtained catalyst volume(see Section 4.1.2) and the catalyst volume fraction. The heightof the separation sections can be calculated with the numberof theoretical stages obtained in Section 4.1.2 and the HETPvalue of the noncatalytic packing. In this step, the HETP valueis assumed to be constant.

hcat = 4(catalyst volume)�d2(catalyst volume fraction)

. (9)

4.2.4. Estimation of the operating conditionsFinally, the entire CD column (including three sections) is usedto determine the search direction of the operating conditionsto be used during the optimisation. Here, reflux ratio and pres-sure are varied to determine the direction in which the IAconversion increases. As base for this calculation, an EQ modelis applied, in which the reaction kinetics are included. At thispoint, a column which does not necessarily meet the designspecifications is obtained (infeasible column design) but it istaken as starting point for the application of the third step ofthe proposed method.

4.3. Step 3: Detailed optimisation

The optimal CD column is designed using an optimisationalgorithm and an NEQ model. The objective function selectedin this study is the production cost per tonne of TAEE. Refluxratio, EtOH molar flow rate and the column dimensions arechosen as decision variables for the optimisation.

4.3.1. CD process modellingIn the literature several mathematical models to representthe phenomena occurring in a CD process have been pre-sented (Taylor and Krishna, 2000; Noeres et al., 2003; Klökeret al., 2005). These models can be primarily classified aseither EQ or NEQ models. In the EQ model, it is assumedthat both bulk phases are perfectly mixed and that thestreams leaving each stage are at thermodynamic equilib-rium. In contrast to the EQ model, in the NEQ model itis assumed that thermodynamic equilibrium occurs only atthe vapour–liquid interface and actual multicomponent massand heat transfer rates across the vapour–liquid interface areaccounted for. Within the scope of this work, a steady stateNEQ model is applied during the optimisation step. Masstransfer and hydrodynamics related model parameters areestimated by empirical packing-type specific correlations. Theheterogeneously catalysed reaction is described by a pseudo-homogeneous approach, in which mass transfer resistancebetween the liquid phase and the solid catalyst is neglected.More details about the applied NEQ model can be found in thesupplementary information of this paper.

4.3.2. Optimisation algorithmThe modified differential evolution (MDE) algorithm (Babu and



Angira, 2006) is used as the optimisation method in this work.This optimisation algorithm is easy to implement and has the

ability to escape from local minimums (Babu and Angira, 2006).When compared to gradient based optimisation methods, theMDE has the main advantage of not being influenced by thestarting points chosen for the optimisation because the objec-tive function is evaluated simultaneously in several startingpoints. However, it is due to this reason than the MDE is slowerthan gradient based methods (Leboreiro and Acevedo, 2004).

In essence, the MDE is based on natural evolution, adoptingsome biological processes, such as mutation, recombinationand selection. The objective function, the constraints and thesearch space of the optimisation variables must be speci-fied for the MDE algorithm, as well as additional parameters,such as the maximal number of iterations. Moreover, thenumber of vectors whose components are the optimisationvariables must be established. The magnitudes of these com-ponents are generated randomly by the MDE within the searchspace and the objective function is calculated for each vector.The algorithm continues with the combination of the vectorsthrough the execution of stochastic operators (recombinationand mutation). After a subsequent calculation of the objectivefunction, selection takes place and only the vectors with thebest values of the objective function are kept. This procedureis repeated until either no better option is found (tolerancesare satisfied) or the maximum number of iterations is reached.

4.3.2.1. Objective function. Costs are the most important crite-ria for the evaluation of a chemical process. In this study, thesum of the annualised investment and the annual operatingcosts per tonne of TAEE is used as the objective function f.

f = min

(TOC + ann TIC

topermTAEE

)(10)

Subject to:

g(x) = 0

h(x)≥0

˛≥x≥ˇ

(11)

Here, TIC is the total investment cost, TOC is the total oper-ating cost, ann is the annualising factor (Ciric and Gu, 1994),toper is the annual operation time and mTAEE is the TAEE pro-duction. To estimate the TIC of the column, the costs of theshell material and the packing are considered. For the con-denser and reboiler, the investment costs are based on theheat exchanger type and material as well as the operatingpressure. The TIC is estimated using correlations set up byDouglas (1988), in which the economic factors were updatedto the year 2008. Additional economic factors are used to takethe peripheries into account according to Hirschberg (1999).The TOC is determined considering the consumption of steamand cooling water in reboiler and condenser, respectively.

The constraints of the optimisation problem are given byEq. (11), in which g(x) represents the CD process model equa-tions, i.e. mass and energy balances, equilibrium relations andsummation conditions. The system of non-linear algebraicequations consists of 5ncomponents + 1 equations per segmentafter the discretisation of the column height in axial direction(Krishnamurty and Taylor, 1985). For the TAEE synthesis, 130segments were used and thus, 5330 equations were solved.h(x) are the design specifications, such as product impurity,


IA conversion, and maximal F-factor; and x is the vector ofoptimisation variables.

dx.doi.org/10.1016/j.cherd.2013.08.030



4

BsCwt

1

2

3

wl

1

2

3

4

Table 6 – Number of theoretical stages and catalystvolume estimated with the sequentialreaction-distillation process.

Section Number of theoreticalstages or volume

Rectifying section 12Catalyst volume (m3) 48Stripping section 37

Table 7 – Molar EtOH flow rates estimated using thereaction stoichiometry and azeotropic composition.

At 4 bar

EtOH for reaction in the CD column 23.57EtOH – IA azeotrope 1.78EtOH – isopentane azeotrope 15.36Total 40.71

.4. Scope of the design method

efore the method is applied to design a CD column for theynthesis of TAEE, some general remarks about the design ofD columns are firstly given in this section. Later on, pointshich deserve special attention to apply the design method

o other chemical systems are discussed.

) A fundamental requirement to design CD columns areaccurate vapour–liquid equilibrium data and reactionkinetics. The latter must be measured at the operating tem-perature expected in the column.

) The application of NEQ models is only recommended ifaccurate correlations to describe the mass transfer andhydrodynamic behaviour within the packing are available.Otherwise, the EQ model should be used during the opti-misation.

) One of the main problems during the design of the CD col-umn is the scale-up. While a large number of mass transferand hydrodynamic correlations are available, which weremeasured at lab scale, relatively few information has beenpublished for pilot scale columns. This is particularlyimportant when the geometrical properties of the pack-ing differ significantly with the column diameter. Moreresearch in this area will help to solve this problem.

The steps of the design method proposed in this paper,hich should be done with caution are discussed in the fol-

owing.

) Heuristic rules are a valuable approach to determine goodestimations of the feed location and column configuration.However, to apply the heuristic rules, a deep analysis of thephysical and chemical properties of the chemical systemis required. The volatilities between reactants and prod-ucts, formation of azeotropes and purity of the feed streamwill have a crucial influence in the column feed location,the proper column configuration and the reactant molarratio in the column feed. Each chemical system has its owncharacteristic and therefore, the application of the heuris-tic rules presented in this paper must be done with caution.Particularly, the heuristic rule number four can only beapplied for chemical systems in which a minimal boilingpoint azeotrope containing the reactant is formed. Specialattention should be paid to the azeotropes present in thechemical system.

) For chemical systems non-limited by the chemical equilib-rium, the molar reactant ratio in the column feed shouldnot be calculated using Eq. (7). The analysis of the physicaland chemical properties of the chemical system will helpto determine the excess of reactant, if needed.

) The MDE algorithm has shown the ability to escape fromlocal optimums, however, it requires a large number ofevaluations of the objective function. Gradient based opti-misation methods are faster but the final solution isinfluenced by the starting point.

) Finally, it should be pointed out that steps one and two ofthe method do not guarantee to reach an optimal column,even if a feasible design is obtained. To tackle this situation,



an optimisation algorithm is used in the third step of themethod.

5. Application example

In this section, the method is applied step by step to design acost-optimal CD column for the synthesis of TAEE from EtOHand IA.

5.1. Step 1: Sequential initialisation

5.1.1. Identification of the feed locationThe feed stream to the CD column contains the reactants (IA)and the product (TAEE), which are some of the lightest andthe heaviest component, respectively. Therefore, the feed waslocated in the stripping section not only to ensure a high IAconcentration but also to avoid TAEE decomposition in thecatalytic section.

5.1.2. Estimation of the number of theoretical stages forthe separation sections and catalyst volumeOnce the feed location was identified, the number of theo-retical stages and catalyst volume were estimated using theprocess configuration shown in Fig. 3a. In the first non-reactivedistillation column (stripping section), the Fenske equationwas used and 2M2B and 2Mthp were selected as the lightand heavy key components, respectively. The selection of thekey components depends on the separation requirements. Forexample, as the stripping section must prevent the presenceof impurities in the bottom stream of the CD column, 2M2Bwas selected as the key light component and 2Mthp was cho-sen as the key heavy component to prevent this componentleaves the column in the distillate stream.

Subsequently, the distillate stream of the stripping sectioncontaining the reactants was fed to the first reactor (catalyticsection). Four isothermal PFRs operating at 340 K, with a totalcatalyst volume of 48 m3 were necessary to reach an IA con-version of 90%. Finally, the effluent stream of the last reactorwas fed to the second non-reactive distillation column, whichrepresents the rectifying section. Here, the Fenske equationwas applied again, choosing 2M2B and TAEE as light and heavykey components, respectively. In Table 6 the estimations of thenumber of theoretical stages and catalyst volume are shown.


EtOH in the outlet of the reactor 32.12Second feed (pure EtOH) 8.59

dx.doi.org/10.1016/j.cherd.2013.08.030



Fig. 5 – Operating and investment costs for the optimal column.

Table 8 – IA conversion for different pressures and refluxratios.

IA conversion (%) Reflux ratio

2 2.5 3

Pressure (bar)3.8 34.4 43.4 68.24.0 32.9 41.6 67.04.2 31.6 39.9 65.6

Table 10 – Comparison between the starting valuescalculated with the first two steps of the method and theoptimal column structure and operating conditions.

Starting values Optimal column

Operating conditionsReflux ratio 3 3.52EtOH mole flow (mol/s) 8.59 6.44Reboiler heat duty (MW) 11.7 13.3IA conversion 67.0% 90.4%

Column dimensions (m)Rectifying section height 2.4 0.9Reactive section height 10.8 7.2Stripping section height 7.4 5.6Diameter 3.5 3.7

5.1.3. Calculation of the molar reactant ratio in thecolumn feedThe EtOH molar flow rate to the CD column was estimatedusing Eq. (7). In Table 7 the flow rates calculated at 4 barare shown. The results presented in Table 7 enable the fol-lowing conclusions to be drawn: if the column operates at4 bar, then the required EtOH flow rate (40.71 mol/s) is higherthan the actual effluent EtOH flow rate from the prereactor(32.12 mol/s). Therefore, it is necessary to increase the EtOHflow rate to the CD column. The additional EtOH molar flowrate was added to the column by a second feed located justbelow the reactive section (Fig. 1) due to the minimal boilingpoint azeotrope formed between EtOH and isopentane.

5.2. Step 2: Simultaneous initialisation

5.2.1. Estimation of the column diameterThe column diameter was estimated using the number of the-oretical stages of the non-catalytic sections shown in Table 6.Here, the EQ model was applied to estimate the flow rateswithin the column. To apply the EQ model, the packing andthe operating conditions had to be specified. The distillate-to-feed ratio (0.42 kmol/kmol) was calculated based on the feedcomposition, the desired conversion and the maximal con-tent of impurities in the bottom stream of the column andit is fixed during the optimisation. Reflux ratio and pressurewere selected at 2 and 4 bar, respectively. This simulation gave



a column diameter of 3.1 m.

Table 9 – Comparison of the best three CD columns found by th

Optimisation variable Column 1 (bestsolution)

Reflux ratio 3.52

EtOH mole flow (mol/s) 6.44

Rectifying section height (m) 0.9

Reactive section height (m) 7.2

Stripping section height (m) 5.6

TAEE production cost (euro/tonne) 18.38

5.2.2. Calculation of the column height and the operatingconditionsThe height of the catalytic zone was calculated using Eq. (9),while the height of the non-catalytic sections with the equilib-rium stages shown in Table 6 and the HETP of Mellapak 750Y®.A sensitivity analysis was carried out for this column config-uration using the EQ model including the reaction kinetics.The simulations with this model gave the results shown inTable 8. Note that increasing the reflux ratio and decreasingthe pressure increase the IA conversion. However, decreasingthe pressure increases the impurities in the bottom streamand the diameter of the column (Baur and Krishna, 2002).Therefore, a pressure of 4 bar was chosen during the optimisa-tion, which might meet all design specifications. Although thepressure was fixed during the optimisation, the algorithm caninclude the pressure as an optimisation variable with the con-sequence of increasing the computing time and decreasing theconvergence rate of the CD model. Based on the results pre-sented in Table 8, a reflux ratio of 3 was used a starting valueduring the optimisation. Additionally, the column diameterand height of the catalytic zone were updated considering areflux ratio of 3.


e MDE algorithm.

Column 2 Column 3

3.52 3.56.38 6.421.2 2.27.4 7.06.0 5.7

18.61 18.75

dx.doi.org/10.1016/j.cherd.2013.08.030



Fig. 6 – Sketch of the optimal column for the TAEEs

5

FovTE

F

ynthesis.

.3. Step 3: Detailed optimisation

inally, the column structure and operating conditionsbtained in the last step of the method were taken as startingalues for the optimisation algorithm using an NEQ model.



he height of each column section, the reflux ratio and thetOH molar flow rate in the column feed were selected as

ig. 7 – Composition (top) and temperature (bottom) profiles of th

optimisation variables (Fig. 1). Table A.4 in Appendix providesthe limits of the optimisation variables used in the MDE algo-rithm.

Based on the optimisation results, the percentage of flood-ing of the non-catalytic sections (both filled with Mellapak750Y®) was verified. The second stripping section (betweenthe FCC feed and the bottom of the column) was operatingclose to 100% of the maximal vapour load while the rectifyingand the first stripping section in the range of 65–80% of theflooding point. Therefore, another structured non-catalyticpacking with a higher capacity than Mellapak 750Y® wasused for the second stripping section: Sulzer BXTM. After thismodification, the optimisation algorithm was applied again.Afterwards, the percentage of flooding of the noncatalytic sec-tions was calculated again and the separation sections wereoperating between the 65 and 80% of the maximal vapourload.

At the end of the optimisation different columns withslightly higher values of the objective function that the oneassociated with the optimal column were found. In Table 9 acomparison of the best three columns found by the MDE algo-rithm is presented. Note that the cost associated with columns2 and 3 is only 1.25% and 2% higher than the one of the optimalcolumn. From the technical point of view, the three columnsmeet the design specifications. However, this does not meanthat any feasible design (e.g., the column obtained with sim-ulation studies) has a low cost. In Fig. 5 the distribution of thetotal cost for the best solution obtained with the MDE are pre-sented. The best solution found by the MDE algorithm has atotal cost of 18.38 euro/tonne TAEE. With the optimal column,an IA conversion of 90.4% (based on the inlet to the column)and a TAEE purity of 32.9% can be achieved.


Table 10 shows the optimal column structure and oper-ating conditions and compares the optimal values with the

e liquid phase for the best solution obtained with the MDE.

dx.doi.org/10.1016/j.cherd.2013.08.030



Fig. 8 – Reaction rate for the TAEE synthesis (left) and liquid and

Table 11 – Molar flow rates in the optimal column.

Component Mixturefeed

EtOH Distillate Bottom

Molar flow rates (mol/s)Isopentane 100.80 0.0 100.34 0.452M1B 2.24 0.0 0.20 0.012M2B 23.11 0.0 0.95 1.272Mthp 79.20 0.0 0.0 79.202M2P 9.17 0.0 0.0 9.02EtOH 32.12 6.44 15.5 0.0TAEE 22.64 0.0 0.0 45.56THEE 2.83 0.0 0.0 2.98

Total mole flow (mol/s) 272.11 6.44 116.99 138.49

model for column simulation.

Table A1 – Physical properties of catalysts (Rohm &Haas).

Amberlyst 16W Amberlyst 15W

Concentration ofactive sites (eq/l)

≥1.7 ≥1.7

Surface area (m2/g) 30 53Average pore

diameter (nm)25 30

Shipping weight (g/l) 780 770Moisture holding

capacity (%)52–58 52–57

Table A2 – Pre-exponential factors and activationenergies for the Arrhenius equation (Linnekoski et al.,1997; Zhang and Datta, 1995).

Reaction k0i(mol kg−1 s−1) Ei(kJ mol−1)

1 7.82 E11 76.82 1.72 E14 95.93 4.66 E10 72.9

starting values obtained with the first two steps of the method.A sketch of this column is shown in Fig. 6. Note that the start-ing values are a reasonable starting point for the applicationof the optimisation algorithm. As expected, the final columndiameter is larger than the estimation based on the noncat-alytic packing, because Sulzer BXTM has a higher void fractionthan KATAPAK SP11®. The analysis of the optimal column ispresented in Section 6.

6. Optimisation results and discussion

In Table 11, the molar flow rates in each stream of the optimalCD column are shown. Figs. 7 and 8 show the compositionand temperature profiles, reaction rate and liquid and vapourmolar flow rates along the column height. Based on these fig-ures several conclusions can be drawn:

• EtOH and isopentane are withdrawn at the top of the col-umn, almost reaching the azeotropic composition (Fig. 7,top). A short rectifying section is sufficient to prevent TAEEloss in the distillate stream. The first stripping section sepa-rates the TAEE that enters the column while the secondstripping section is responsible for the separation betweenEtOH and IA from TAEE.

• The feed is located in the stripping section to prevent TAEEdecomposition in the reactive zone. As a result, the for-mation of THEE is negligible because 2M2P tends to movetowards the bottom of the column (Fig. 7, top).

• The average temperature in the reactive zone is 348.8 K, andan increase of 8.3 K occurs from the top to the bottom ofthis section (Fig. 7, bottom). This temperature avoids prob-



lems with the thermal stability of the catalyst. At the bottom

vapour molar flow rates (right) along the column height.

of the column, the temperature increases due to the highconcentration of heavy components.

• The reaction rate is shown in Fig. 8 (left). A maximum inthe reactive zone appeared, which is an indication that thecolumn is operating at the optimal conditions.

• In Fig. 8 (right) the liquid and vapour molar flow rates areshown. A high vapour flow occurs in the reactive sectiondue to the reduced void fraction of the catalytic packing.

7. Conclusions

In this work, a method to design a cost-optimal CD columnfor chemical systems with large number of components andchemical reactions is presented. The complexity of the math-ematical models involved in the method is increased stepby step. In the first step of the method, the decompositionof the CD column into a sequence of chemical reactors andnon-reactive distillation columns is performed to determinethe column structure and the catalyst volume. Later on, anequilibrium stage model is applied to estimate the columndiameter and operating conditions. These two steps providestarting values for the next step, in which an optimisationalgorithm is applied using a rigorous non-equilibrium stage


4 1.42 E15 108.7

dx.doi.org/10.1016/j.cherd.2013.08.030



Table A3 – Coefficients for the calculation of the chemical equilibrium constant (Kitchaiya and Datta, 1995).ln Ki = Ai + BiT−1 + Ci ln + DiT + EiT2 + FiT3, K3 = K1K2

−1.

Reaction Ai Bi Ci Di Ei Fi

1 22.809 3136.3 −5.8227 0.0179 −6.395 E−6 −1.672 E−82 26.779 2078.6 −6.5925 0.0231 −1.126 E−5 −1.414 E−84 −84.431 6870.67 13.032

Table A4 – Limits of the optimisation variables used inthe MDE algorithm.

Variable Lower limit Upper limit

Reflux ratio 2 4Rectifying section height 0.5 2.5Catalytic section height 6.0 12.0First stripping section height 0.5 3.0Second stripping section height 1.0 6.0EtOH molar flow rate fed to the

CD column5.0 10.0

trTosoi

S

Ea

A

Cfi

A

TgK(

A

Si

R

A

A

AFenske, M.R., 1932. Fractionation of straight-run Pennsylvania

The method was applied to design a CD column for the syn-hesis of TAEE from EtOH and IA. No column design for thiseaction system could be found in the open literature before.he results presented in this contribution show the feasibilityf producing TAEE applying a CD column with an IA conver-ion higher than 90%. However, due to the high concentrationf heavy inert components in the column feed, the TAEE purity

s approximately 33 mole%.

upplementary information

quations to represent the catalytic distillation process using non-equilibrium stage model.

cknowledgement

. A. González-Rugerio is thankful to CONACyT-DAAD for thenancial assistance during the course of this work.

ppendix A.

he adsorption equilibrium constant for EtOH isiven by K′

EtOH = 2.75 for the THEE synthesis and by

EtOH = 3.75E − 3 · exp(− 2369.5/T) for the TAEE synthesissee Tables A1–A4).

ppendix B. Supplementary data

upplementary material related to this article can be found,n the online version, at doi:10.1016/j.cherd.2013.08.030.

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