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Computers and Chemical Engineering 34 (2010) 460–466

Contents lists available at ScienceDirect

Computers and Chemical Engineering

journa l homepage: www.e lsev ier .com/ locate /compchemeng

ultiple steady states detection in a packed-bed reactive distillation columnsing bifurcation analysis

aveed Ramzana,∗, Muhammad Faheema, Rafiqul Ganib, Werner Witt c

Department of Chemical Engineering, University of Engineering & Technology, Lahore 54890, PakistanComputer Aided Process – Product Engineering Center, Technical University of Denmark, DenmarkLehrstuhl Anlagen und Sicherheitstechnik, Brandenburgicshe Technische Universität, Burger Chaussee 2 Lehrgebäude 4/5, Cottbus 03044, Germany

r t i c l e i n f o

rticle history:eceived 8 April 2009eceived in revised form 7 August 2009ccepted 2 September 2009

a b s t r a c t

A packed reactive distillation column producing ethyl tert-butyl ether from tert-butyl alcohol and ethanolwas simulated for detection of multiple steady states using Aspen Plus®. A rate-based approach wasused to make the simulation model more realistic. A base-case was first developed and fine-tuned to fit

vailable online 17 September 2009

eywords:eactive distillationate-based simulation

experimental data. Sensitivity analyses were then performed for reboiler duty and distillate molar flowas continuation parameters to trace the respective bifurcation curves in the region of multiplicity. Theresults show output multiplicity at three distinct steady states at high reboiler duties. Input multiplicitieswere detected at high reflux ratios. Temperature and composition profiles of the solution branches wereanalyzed to identify the stable and desirable steady state. The optimum operating point was determined

0.38

A

ultiple steady statesTBE synthesis

to be at a reboiler duty ofresults.

. Introduction

Reactive separation processes such as reactive distillation,orption-enhanced reaction absorption, reactive extraction andeactive crystallization combine the essential tasks of reaction andeparation in a single vessel (Lei, Chen, & Ding, 2005). The mostmportant example of such processes is reactive distillation, whichs a combination of chemical reaction and distillation in a singleolumn, and is perhaps the most important industrial applicationf the concept of multifunctional reactors.

Mathematical models of chemical processes include non-linearquations. Such systems of equations may have multiple solutions,lso known as multiple steady states (MSS). Existence of MSS is aharacteristic of numerous physicochemical processes, especiallyeactive mass-transfer operations (like reactive distillation). MSSan occur at the levels of a single apparatus, a group of functioningpparatuses, or even an entire chemical process system (VadapalliSeader, 2001).

Pisarenko, Epifanova, and Serafimov (1987) were the first to

btain three steady state solutions for the same set of inputs andperating parameters by simulation in a single-product RD column.ince then, several studies have appeared in literature reportinghe presence of MSS in RD processes. A comprehensive review of

∗ Corresponding author. Tel.: +92 42 920 4172; fax: +92 42 920 4449.E-mail address: ramzan50@hotmail.com (N. Ramzan).

098-1354/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.oi:10.1016/j.compchemeng.2009.09.001

kW and a reflux ratio of 5–7. These results closely match the experimental

© 2009 Elsevier Ltd. All rights reserved.

respective literature has been presented in (Güttinger & Morari,1999a; Taylor & Krishna, 2000).

Multiple steady states in reactive distillation processes posesome serious problems in design and operation of RD columns.Bekiaris and Morari (1996) have identified the following issues inthis respect:

. Simulation issuesi. Higher convergence failure rate during simulation of the pro-

cess.ii. Process simulators use numerical solvers that are designed to

obtain one solution of the system. The computation of onlyone solution may lead to misleading column profiles.

iii. Computation of only one solution may also lead to mislead-ing conclusions and decisions regarding a particular scenariounder consideration because of the elimination of certaineligible, and possibly, more feasible design alternatives.

B. Operational and control issuesi. When multiple steady states exist for a system, it is possible

that, for a particular disturbance, the column profile may jumpfrom a desirable to an undesirable steady state.

ii. Existence of MSS can cause erratic behavior in columns.C. Distillation design and synthesis issues

i. Each possible alternate design may have different controlproperties. As a result, one particular design alternative maybe much more difficult to control than another.

ii. Existence of MSS can influence the selection of equipment andthe separation scheme.

hemical Engineering 34 (2010) 460–466 461

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Güttinger and Morari (1999b) have provided an overview of theifferent physical phenomena (source of non-linearity) that result

n output multiplicities in hybrid RD columns. Gani and Jørgensen1994) have identified three distinct types of multiplicities (namelyutput multiplicities, input multiplicities, and internal state mul-iplicities) in reactive distillation columns. MSS observed in RDolumns may be stable or unstable states. Only stable steady statesave practical significance, i.e., some of the stable states are desir-ble. All the other states are trivial for all practical purposes.

The complexity and difficulty in determination of MSS in RDrocesses has resulted in a plethora of methods being used overhe years for this purpose. These methods include both experi-

ental and model-based approaches adopting different solutiontrategies. Among the analytical approaches, the most notable ishe ∞/∞ analysis method, initially developed for the homogeneouszeotropic distillation (Bekiaris, Meski, Radu, & Morari, 1993). Thispproach considers the limiting cases of infinite number of traysnd column operation at infinite reflux for detection of multiplici-ies. This analytical method was later extended for application onybrid and non-hybrid reactive distillation columns (Güttinger &orari, 1999a,b). By the use of reactive residue curve maps, MSS

an be predicted graphically. The ∞/∞ singularity analysis can besed to determine the influence of column configuration on theossible existence of MSS.

A numerical method to calculate column multiplicities based oningle-stage model by a singularity theory approach was presentedy Gehrke and Marquardt (1997). However, this is a computa-ionally intensive approach, especially if higher-order singularities

ust be found.More recently, researchers have focused using commercially

vailable process simulators for determination of MSS in distil-ation columns using the inherent advantages of these programssuch as availability of extensive component property data, rigor-us thermodynamic libraries, robust solvers, and above all, abilityo incorporate user-developed modules for implementing newlgorithms with little programming). Vadapalli and Seader (2001)mplemented the arc-length continuation algorithm in a FORTRANubroutine in Aspen Plus® for computing bifurcations diagrams.annan, Joshi, Reddy, and Shah (2005) used HYSYS® for the sameurpose using initial guesses from the ∞/∞ approach. Yang, Wu,hao, and Wang (2006) used the built-in sensitivity analysis toolf Aspen Plus® for multiplicity analysis in reactive distillationolumns.

Through comparison of simulation and experimental resultsor several case studies, these researchers have well-establishedhe usefulness of process simulators for determination of regionf multiplicity and multiple steady states in reactive distillationolumns. However, an equilibrium-stage approach has been con-idered in most of the relevant literature, and researchers havesed the stage efficiencies to fit the available experimental datand account for the non-ideality of stages. This leaves a room forhe use of rate-based modeling approach in order to incorporatehe real geometrical column configuration and make the developed

odel more realistic. The present work was carried out to evalu-te the potential use of rate-based modeling for determination ofSS in an RD column using a commercial process simulator Aspen

lus®.

. Procedure for multiplicity analysis in RD columns usingspen Plus®

The focus of the present work is to describe a methodology usinghe built-in sensitivity analysis tool of Aspen Plus® for output multi-licity analysis of a packed-bed reactive distillation column using aate-based simulation approach. This proposed methodology will

Fig. 1. Overview of proposed methodology.

then be used for a case study on a real-world lab-scale reactivedistillation column. An overview of the research methodology isshown in Fig. 1 and important steps are outlined below.

i. First the column is simulated in equilibrium mode using themodule RadFrac®. This simulation step requires the specifi-cation of components, thermodynamic property model, feedconditions (thermal state, flow rate, and composition), operat-ing pressure, column configuration (including number of stages,feed location, type of condenser and reboiler, subcooling tem-perature, reaction stages) and reaction kinetics along with twoadditional specifications of operational parameters (such asreflux ratio, distillate flow rate, reboiler duty, etc.). The sim-ulation is run and the column is converged using appropriatespecifications.

ii. Murphree stage efficiency is adjusted in order to match the sim-ulated column profile with the experimental data.

ii. The calculation mode is changed to perform rate-based calcula-tions. Physical dimensions of the column and details about thetype and characteristics of packing used in each section are pro-vided. The temperature and composition profiles generated instep (ii) are used as initial estimates for rate-based simulation.The simulation is again run to achieve the convergence.

iv. Sensitivity analysis is carried out with the selected continuationparameter(s) to study their effects on the performance of thecolumn and to trace the respective bifurcation diagram(s).

4 hemical Engineering 34 (2010) 460–466

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62 N. Ramzan et al. / Computers and C

. Case study: multiplicity analysis for ETBE synthesis

.1. ETBE synthesis via reactive distillation: column configuration

In the present work, the packed-bed reactive distillation col-mn, described in Umar (2008) has been selected for multiplicitynalysis. This column produces ETBE from TBA and EtOH over anon-exchange resin catalyst. The experimental rig is shown in Fig. 2,

ith the detailed column configuration given in Table 1. The exper-mental rig has 12 sampling points (including reboiler, condenser,nd multiple locations in column). During experimentation, sam-ling was done from 5 points (including condenser, reboiler, topf reactive section, middle of reactive section, and bottom of reac-ive section) at 20 min intervals for test runs of around 12 h (theolumn profiles become steady in 6–8 h for different operatingonditions). All samples had then been analyzed using gas chro-atography. Distillate molar flow rate was controlled using results

rom these extensive composition measurements. Because exten-ive experimental data was available with distillate molar flow ashe controlled variable, so it was chosen as the bifurcation param-ter for simulation studies.

.2. Reaction kinetics

The reactions undergoing in this system and the correspondingate equations have been described in literature (Assabumrungratt al., 2004; Umar, 2008). The reactions are:

TBA(A) + EtOH(B) ↔ ETBE(C) + H2O(D)TBA ↔ IB + H2OIB + EtOH ↔ ETBE

All these reactions occur in the liquid phase. Under atmosphericressure and the actual experimental conditions of temperatureaintained in the study, iso-butylene (IB) does not exist in the liq-

id phase (even in minute quantities). Therefore, the 3rd reactionnd the backward 2nd reaction can be safely neglected.

Since the reaction mixture exhibits high non-ideality in the pres-nce of polar compounds like water and ethanol, therefore, in ordero account for the non-ideal nature of reactants and products, com-

onent activities are used instead of their concentrations. The ratexpressions for the first two reactions can then be written as:

r1 = k1(aAaB − aCaD/Keq)

1 + KwaD

able 1onfiguration of reactive distillation column for ETBE synthesis.

Section Simulation stage De

Condenser 1 To

Rectifying section 2–5SePr(Svo

Reactive section 6–7 SeWth

Stripping section 8–11 SaReboiler 12 Pa

Column feeds – EtTB

Operating configuration –PrReEt

Fig. 2. Schematic of the packed-bed reactive distillation column for ETBE synthesis.

−r2 = k2aA

1 + KwaD

The rate constants are given by the following expressions:

k1 = exp(

26.877 − 11281T

)

tailed configuration

tal condenser, with subcooling to 35 ◦C

ction height = 1′; Diameter = 2′′

otruded metal packingize = 0.24′′; HETP ≈ 3′′; 4 theoretical stages; Specific surface = 1233 m2/m3; Freelume = 96%)

ction height = 2′; Diameter = 2′′

ire-gauze structured packing with catalyst loaded in pockets (HETP ≈ 1′; 2eoretical stages; Specific surface = 1235 m2/m3, Free volume = 97%)

me as in rectifying sectionrtial reboiler, with variable power input (0–800 W)

OH feed (95% pure, at top of reactive section)A feed (99.5% pure, 0.50 mol/min, at bottom of reactive section)

essure = 1 atmflux ratio = 7OH/TBA molar feed ratio = 1.3

hemical Engineering 34 (2010) 460–466 463

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W

T

K

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ity, three distinct branches are observed. The intermediate branchexists over a very small range of reboiler duties and is not read-ily identified because of unstable simulation behavior. Therefore, itcan be concluded that this is an unstable branch of the bifurcationcurve and represents a solution that has no physical significance.

N. Ramzan et al. / Computers and C

2 = exp(

14.861 − 7275.4T

)

ater inhibition parameter = Kw = exp(

−30.82 + 11253T

)

he equilibrium constant for the system is expressed as:

eq =[

aCaD

aAaB

]eq

However, it needs to be mentioned here that not even traces ofB were found experimentally, which also rules out the possibilityf second reaction, i.e., TBA dehydration does not take place underhe experimental conditions of this study.

.3. Multiplicity analysis

The multiplicity analysis of the RD column for ETBE synthesisas carried out by following the procedure outlined in Section 2.

irst a base-case model was developed by specifying the necessaryolumn configuration and stream properties. The polarity differ-nce among alcohols and ethers is very high and the ETBE reactionystem is highly non-ideal (Jansen & Datta, 1995; Sneesby, Tadé,atta, & Smith, 1997). Also the kinetics of ETBE production fromthanol and TBA have been developed using UNIFAC model (Umar,008). Therefore, thermodynamic model UNIFAC was selected toccount for the liquid phase non-idealities in the reaction mixturend to ensure a complete consistency in simulation data. Since theeaction kinetics for this system do not comply with the standardower-law kinetics in Aspen Plus®, separate FORTRAN user sub-outine was developed, compiled and linked with the simulationase in Aspen Plus®. The simulation was run and fit to the availablexperimental data by adjusting the Murphree stage efficiency.

The equilibrium-based case was converted to rate-based case.etailed geometrical configuration of column sections and charac-

eristics of respective packing was added to the simulation case.iquid holdups of the random protruded metal packing and theire-gauze structured packing were respectively calculated by

tichlmair, Bravo, and Fair (1989) correlation and Bravo, Rocha, andair (1992) correlation. The simulation was again run and conver-ence was achieved.

. Results and discussion

.1. Base-case model simulation

Following the approach outlined in Section 2, an equilibriumodel was fitted to the available experimental data (Umar, 2008).

t was then converted to a rate-based model. The results of this datat are presented in Fig. 3.

.2. Determination of output multiplicity

For determination of output multiplicity in the system, reboileruty was chosen as the bifurcation parameter, and mass fractionf desired product ETBE in distillate as the dependent parameterstate variable). The molar flow rate of the distillate stream wasept fixed at 0.50 mol/min.

.2.1. Region of multiplicityThe region of multiplicity was detected by the two turning

oints with increasing and decreasing reboiler duties. First, theeboiler duty was gradually increased from 0.25 kW to 7.0 kW torace the forward branch. The turning point on this branch occurst 4.56 kW. Then the reboiler duty was gradually decreased from.0 kW to 0.25 kW, thus detecting the turning point at 4.40 kW. The

Fig. 3. Validation of simulation results with experimental data (reflux ratio = 7,reboiler duty = 0.375 kW).

region of multiplicity was thus identified to exist between 4.40 kWand 4.56 kW, as shown in Fig. 4.

It is worth-mentioning that the detected region of output mul-tiplicity is well above the experimental optimum operating pointof 0.375 kW (Umar, 2008).

4.2.2. Bifurcation curveThe region of multiplicity identified by Fig. 4 is used to trace the

bifurcation curve. The reboiler duty is gradually increased in smallsteps from low values (to the left of region of multiplicity in Fig. 4)to the turning point on the lower branch (4.56 kW). When thereis sudden jump of column profile, the reboiler duty is graduallydecreased in small steps to trace the intermediate branch. Againwhen the column profile suddenly jumps to a new branch (turningpoint at 4.40 kW), the reboiler duty is again increased in small stepsto trace the upper branch. The resulting bifurcation curve is shownin Fig. 5.

It is clear that outside the region of multiplicity, lower or highersteady states distinctly persist. Within the region of multiplic-

Fig. 4. . Detecting the region of output multiplicity with reboiler duty as the contin-uation parameter. The turning point occurs at different values when reboiler dutyis gradually increased or decreased.

464 N. Ramzan et al. / Computers and Chemical Engineering 34 (2010) 460–466

Fig. 5. Bifurcation diagram for the mass fraction of ETBE in distillate with reboilerduty as the continuation parameter.

4

tF

ts

Fig. 8. Liquid phase mass fraction profiles for the lower steady state.

Fig. 6. Liquid phase temperature profiles for the three steady states.

.2.3. Analysis of column profilesThe temperature and liquid phase composition profiles for the

hree steady states at a reboiler duty of 4.50 kW are shown in

igs. 6–10.

The liquid phase composition profiles (Figs. 8–10) show thathe ETBE concentration in reaction zone is the lowest for lowerteady state (LSS) and the highest for the higher steady state (HSS).

Fig. 7. Vapor phase temperature profiles for the three steady states.

Fig. 9. Liquid phase mass fraction profiles for the intermediate steady state.

Referring to the kinetics of the reaction system, it is expected thata higher concentration of ETBE in the reaction zone will favor the

reverse reaction, and may lead to poor conversion. It should also benoted from these profiles that the water content in reboiler almostdoubles in HSS compared to LSS, and may lead to greater waterinhibition effect and slow down the reactions.

Fig. 10. Liquid phase mass fraction profiles for the higher steady state.

N. Ramzan et al. / Computers and Chemical Engineering 34 (2010) 460–466 465

srsrosb

et(m

4

lmprlmr

rd

Fig. 13. Input multiplicity with decreasing distillate molar flow at constant refluxratios.

Table 2Comparison of simulated and experimental optimum conditions.

Operating parameter Optimum (simulation) Optimum (experimental)

Fig. 11. Relative volatility profiles for the lower steady state.

The relative volatility profiles of the lower and upper steadytates at a reboiler duty of 4.50 kW are shown in Figs. 11 and 12,espectively. A comparison of these profiles indicates that LSS is aeparation-controlled state (as indicated by greater ˛ values in theeaction zone) whereas HSS is a reaction-controlled state. Thesebservations lead to the conclusion that LSS is the desirable steadytate. The optimum operating point of the system will lie on LSSranch towards low reboiler duties.

It can be concluded that the experimental verification of thexistence of multiple steady states cannot be achieved in this par-icular experimental column, because the region of multiplicityFig. 4) exists at much higher reboiler duties than what the experi-

ental column can practically handle (Table 1).

.3. Determination of input multiplicity

For determination of input multiplicity in the system, distil-ate molar flow rate was chosen as the bifurcation parameter, and

ass fraction of desired product ETBE in distillate as the dependentarameter (state variable). Simulations were performed at constanteflux ratios with decreasing distillate molar flow rates. The simu-ation results show the presence of input multiplicity (same ETBE

ole fraction in distillate at different reflux ratios) at high refluxatios (Fig. 13).

Fig. 13 shows that input multiplicity is observed only at higheflux ratios. Also the locus of multiplicity moves towards loweristillate flows with increasing reflux ratios. At low reflux ratios,

Fig. 12. Relative volatility profiles for the higher steady state.

Reflux ratio 5–7(nearly same results) 7Reboiler duty 0.38 kW 0.375 kW

input multiplicity may not occur at all, or it may occur at somepractically limiting scenario (for example, at a reflux ratio of 7,input multiplicity occurs at a distillate flow of 1.10 mol/min froma combined total flow of 1.15 mol/min). These observations leadto the conclusion that the direction of optimum operating point istowards low reflux ratios with low distillate flows.

4.4. Optimum operating conditions

Following the directions for optimum search from observationsof input and output multiplicity, several simulation runs were car-ried out to determine the optimum operating conditions for thesystem. A comparison of the simulation results from present workand experimental results from Umar (2008) is given in Table 2. The

composition profile for the simulated optimum conditions is shownin Fig. 14.

Fig. 14. Composition profile at the simulated optimum conditions (reflux ratio = 7,reboiler duty = 0.38 kW).

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66 N. Ramzan et al. / Computers and C

. Conclusions

The conclusions drawn from the simulation results are summa-ized below:

. Multiple steady states can be detected for ETBE synthesis ina packed-bed RD column using the built-in sensitivity tool ofAspen Plus®. A systematic methodology adopting a rate-basedsimulation approach was proposed for this purpose and thenapplied to a real-world lab-scale RD column for detection ofinput and output multiplicities.

. The region of output multiplicity was detected at high values ofreboiler duties (4.40–4.56 kW) with fixed molar distillate flowrate (0.50 mol/min). Within this region, three distinct branchesof the bifurcation curve were observed.

. After analysis of temperature and composition profiles of thesesteady states, it was concluded that the ISS was the unstablebranch of the bifurcation curve and represented a trivial solu-tion of the system. LSS was found to be more favorable to theforward/desired reaction.

. Relative volatility profiles of the LSS and HSS indicate that LSSwas a separation-dominant state, and hence the most desirablestable steady state.

. Input multiplicity was observed at high reflux ratios withdecreasing distillate molar flow.

. The region of input multiplicity was found to be shifting towardslower distillate flows with higher reflux ratios.

. Optimum operating point for the system was determined to be ata reflux ratio of 5–7 and a reboiler duty of 0.38 kW. These resultsclosely match the available experimental results.

. The regions of input and output multiplicities are well above theoptimum operating point, and therefore, these multiplicities arenot expected to appear in the normal operation of the column.

cknowledgements

The first two authors want to acknowledge the support providedy Department of Chemical Engineering, University of EngineeringTechnology, Lahore, and in particular, Dr. A.R. Saleemi and Dr.uhammad Umar for carrying out this project.

al Engineering 34 (2010) 460–466

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