Computers and Chemical Engineering 31 (2007) 867874

Short communication

Control properties of thermally cosequences for different operat

Ab-Ma s/n,ugust2006

Abstract

The under onsidmost widely d dissavings with tion cstreams, tha n toTCDS unde asicproperties m wo Tthe one with minimum energy consumption. The control analysis properties are analyzed with the application of the singular value decompositiontechnique at zero frequency and closed-loop dynamic responses using standard PI controllers. The results show that the controllability propertiesof distillation sequences may change significantly depending on the selected operation point. 2006 Elsevier Ltd. All rights reserved.

Keywords: T

1. Introdu

Certainltion technothe foreseeindustriallygenerally rcessing tecwhen overcmake it movantage ofimprove thon distillatthem callsmal couplidistillationtion and ca

Corresponfax: +52 473

E-mail ad

0098-1354/$doi:10.1016/jhermally coupled distillation schemes; Control properties; Energy consumption

ction

y, the distillation is the most widely applied separa-logy and will continue as an important process forable future because there seems not to be anotherviable alternative around. Although distillation is

ecognized as one of the best developed chemical pro-hnologies there are still many barriers that could,ome, secure the position of the distillation and evenre attractive for use in the future. The main disad-the distillation is its high-energy requirements. Toe energy efficiency of separation processes basedion, several strategies have been proposed; one offor the use of complex sequences. For example, ther-ng has been used in the design of multicomponentsystems in order to reduce both energy consump-

pital costs when compared with conventional simple

ding author. Tel.: +52 473 73 20006x8142;73 20006x8139.dress: gsegovia@quijote.ugto.mx (J.G. Segovia-Hernandez).

column configurations. TCDS for ternary mixtures have partic-ularly been analyzed with special interest due to the remixingin the intermediate component (presented naturally in the con-ventional distillations sequences and associated with higherdemands of energy) is reduced and the use of the energyimproved (Hernandez, Pereira-Pech, Jimenez, & Rico-Ramrez,2003; Triantafyllou & Smith, 1992). There is a considerableamount of literature on the analysis of the relative advantagesof TCDS for ternary separations with equilibrium (Annakou& Mizsey, 1996; Dunnebier & Pantelides, 1999; Hernandez &Jimenez, 1996, 1999a; Hernandez, Segovia-Hernandez, & Rico-Ramrez, 2006; Tedder & Rudd, 1978; Yeomans & Grossmann,2000 among others) and nonequilibrium (Abad-Zarate, Segovia-Hernandez, Hernandez, & Uribe-Ramrez, 2006) models. Thesestudies have shown that those thermally coupled distillationschemes with side columns are capable of achieving typically30% of energy savings compared with the conventional schemes.Two of the schemes that have received special attention arethe systems with side columns: the thermally coupled systemwith a side rectifier (TCDS-SR, Fig. 1) and the thermally cou-pled system with a side stripper (TCDS-SS, Fig. 2). Also, the

see front matter 2006 Elsevier Ltd. All rights reserved..compchemeng.2006.08.004Juan Gabriel Segovia-Hernandez , EstebanJorge Alberto Marquez

Universidad de Guanajuato, Facultad de Qumica, Noria AltReceived 23 November 2005; received in revised form 1 A

Available online 20 October

standing of the dynamic behavior of distillation columns has received cused unit operations in chemical process industries. Thermally couplerespect to the operation of sequences based on conventional distilla

t appear to affect their controllability properties. One potential solutior conditions that do not provide minimum energy consumption. The bight change as well. In this work, we analyze the dynamic behavior of tupled distillationing conditionselardo Hernandez-Vargas,unozGuanajuato, Gto. 36050, Mexico2006; accepted 3 August 2006

erable attention due to the fact that distillation is one of thetillation sequences (TCDS) can provide significant energyolumns. TCDS exhibit a complex structure, with recyclethis problem has been suggested through the operation ofidea is that if one changes the operation point, the controlCDS structures under different operating points, including

868 J.G. Segovia-Hernandez et al. / Computers and Chemical Engineering 31 (2007) 867874

Nomenclature

FL interconnecting liquid flow (kmol/h)FV interconnecting vapor flow (kmol/h)F1 feed of composition 40/20/40 (%mol)F2 feed of composition 15/70/15 (%mol)G transfer function matrixIAE integral of the absolute error criterionKc proportional gainM1 mixture of n-pentane/n-hexane/n-heptanePI proportional integral controllerQ reboiler heat duty (kW)TCDS thermally coupled distillation sequencesTCDS-SR thermally coupled distillation sequence with

side rectifierTCDS-SS thermally coupled distillation sequence with

side stripper

Greek symbols* condition number* maximum singular value* minimum singular valueI

thermally cternary mixfeed compomodynamiurations (FHernandez& Rico-Ra

The unwith thermis an extrewith econo

Fig. 1. ThermSR).

Fig. 2. ThermSS).

acteristics.ers, pointeoptions ma

tedmpletime

ctedic pel Muz, H

ndezSegoia-HSerrintegral time

oupled distillation sequences for the separation oftures, over a wide range of relative volatilities andsitions, have been reported to provide a better ther-

c efficiency than the conventional distillation config-lores, Cardenas, Hernandez, & Rico-Ramrez, 2003;-Gaona, Cardenas, Segovia-Hernandez, Hernandez,mrez, 2005).derstanding of the control properties of columns

integrabeen irecentcondudynam(AbduJimeneHerna2006;Segov2004;al couplings for the separation of ternary mixturesmely important issue because many times designsmic incentives conflict with their operational char-

ally coupled distillation sequences with a side rectifier (TCDS-

Espuna, &works havepropertiesof the condicted saviobtained atthis work,structureswith minimerties are adecomposiusing stand

2. Design

The destillation seq(Fig. 3) areTCDS-SRand Jimeneoptions areThe designmal link inally coupled distillation sequences with a side stripper (TCDS-

Fidkowski and Krolikowski (1990), among oth-d out that despite their energy savings, TCDSy show controllability problems because of theirnature. For that reason, TCDS options have notmented extensively in the process industries untils (Kaibel & Schoenmakers, 2002). There have beennumerous research works on TCDS aiming at therformance analysis, especially for ternary mixturestalib & Smith, 1998; Hernandez & Jimenez, 1999b;ernandez, Montoy, & Zavala-Garca, 2001; Segovia-, Hernandez, & Jimenez, 2002a, 2002b, 2005a,via-Hernandez, Hernandez, Jimenez, & Femat, 2005;ernandez, Hernandez, Rico-Ramrez, & Jimenez,a, Espuna, & Puigjaner, 1999, 2003; Serra, Perrier,Puigjaner, 2001; Wolff & Skogestad, 1995). Thosefound the rather unexpected result that the control

of the integrated sequences were better than thoseventional schemes in many cases, so that the pre-ngs in both energy and capital would probably not be

the expense of operational and control problems. In

we analyze the dynamic performance of two TCDSunder different operating points, including the oneum energy consumption. The control analysis prop-nalyzed with the application of the singular value

tion technique and closed-loop dynamic responsesard PI controllers.

of TCDS

ign and optimization strategies for conventional dis-uences involving the separation of ternary mixtures

well-known. The energy-efficient design methods forand TCDS-SS schemes are described in Hernandezz (1996). Basically, preliminary designs of the TCDSobtained from the conventional sequences (Fig. 3).of TCDS-SR column is obtained by using a ther-

the vapor phase in the conventional direct sequence,

J.G. Segovia-Hernandez et al. / Computers and Chemical Engineering 31 (2007) 867874 869

Fig. 3. Convetures: (a) dire

which elimventional sbottom of t3a). The vademand inThe energydirectly froremoving tscheme andthe tray secof conventiis varied uncolumn is o

3. Singula

The undcolumns hadistillationchemical pables undethe predictbears mucof the septhis work,around theTransfer fucase, andtion. For mexample.

That mainterest: thgular valuevalues, or c

=

Table 1Mixture analyzed and feed composition

con

unce

inimtem

systetativ

ernatuesst dyb, 19con

ropenalyl proy Hdez, Ma

ses o

ene

sepomped fo

then inliqussum

Thethentional distillation sequences for the separation of ternary mix-ct sequence and (b) indirect sequence.

inates the reboiler in the second column of the con-cheme, and the tray section (named 4) is moved to thehe first column of conventional scheme (Figs. 1 andpor flow (FV) is changed until the minimum energythe reboiler of the TCDS-SR sequence is obtained.-efficient design of TCDS-SS option is obtainedm the conventional indirect distillation sequence byhe condenser in the second column of conventional

introducing a thermal coupling in the liquid phase;tion named 3 is moved to the top of the first columnonal scheme (Figs. 2 and 3b). The liquid stream (FL)til the minimum energy requirement for TCDS-SSbtained.

r value decomposition (SVD)

erstanding of the dynamic behavior of distillations received considerable attention due to the fact thatis one of the most widely used unit operations in

rocess industries. As the disturbance in process vari-

Mixture

M1

Feed

F1F2

TheunderThe mthe sysof thea qualithe altlar valthe be& Lauto theSVD pSuch acontrodone bHernanVargas

4. Ca

Theternarydiate cassum

tent ofis giveuratedwere a

tively.ensurer actual operation conditions are almost inevitable,ion of the transient response of a distillation columnh importance in the sense of the effective controlaration process (Berber & Karadurmus, 1989). Inopen loop dynamic responses to set point changesassumed operating point were obtained as first step.nction matrices (G) were then collected for each

they were subjected to singular value decomposi-ore details about SVD see Klema & Laub, 1980, for

thematical operation presents three parameters ofe minimum singular value (*) the maximum sin-(*) and the ratio maximum to minimum singular

ondition number (*):

(1)

feed involvlation was(Seader &ing a threeexample, gthe petrochments andafter optimTables 2 an

5. Results

Two setcontrol prowere obtainwas induceunder SISOComponents (A, B, C)n-Pentane/n-hexane/n-heptane

Composition (%mol)40/20/4015/70/15

dition number reflects the sensitivity of the systemrtainties in process parameters and modeling errors.um singular value is a measure of the invertibility ofand represents a measure of the potential problemsm under feedback control. These parameters providee assessment of the theoretical control properties ofe designs. The systems with higher minimum singu-and lower condition numbers are expected to shownamic performance under feedback control (Klema80). For this initial analysis of the coupled schemes

ventional configurations, we simply estimated therties for each separation system at zero frequency.sis should give some preliminary indication on theperties of each system (similar analysis has beenernandez & Jimenez, 1999b; Segovia-Hernandez,, & Jimenez, 2005; Segovia-Hernandez, Hernandez-rquez-Munoz, Hernandez, & Jimenez, 2005).

f study

rgy savings obtained in the TCDS structure, forarations, depend strongly on the amount of interme-onent. For that reason, two feed compositions werer the mixture M1 (Table 1), with a low or high con-intermediate component. The mixtures descriptionTable 1; the feed flowrate was 45.36 kmol/h as sat-id and the specified purities for the product streamsed as 98.7, 98 and 98.6% for A, B and C respec-design pressure for each separation was chosen touse of cooling water in the condensers. Since thees a hydrocarbon mixture, the ChaoSeader corre-used for the prediction of thermodynamic propertiesHenley, 1998). It is important to establish that study--component mixture of hydrocarbons is a suitableiven the applications of the hydrocarbon mixtures inemical industry (Harmsen, 2004). The tray arrange-some parameters for the TCDS-SR and TCDS-SSization task for the case of study M1F1 is given ind 3.s of analysis were carried out: (i) the theoreticalperties of thermally coupled distillation sequencesed using SVD technique and (ii) servo-control: stepd as set point changes for each product compositionfeedback control at each output flowrate. Both set of

870 J.G. Segovia-Hernandez et al. / Computers and Chemical Engineering 31 (2007) 867874

Table 2Design variables for the TCDS-SS (M1F1)

Main column Side stripper

Pressure (atm) 1.44 1.44Stages 29 8Feed stage 20Interconnection stage 10FL (kmol/h) 25.3

Table 3Design variables for the TCDS-SR (M1F1)

Main column Side rectifier

Pressure (atmStagesFeed stageInterconnectioFV (kmol/h)

simulations(optimal reobtained bin differentof the FL o

5.1. SVD a

The SVwhich aremanipulatetion sequethree produheat duty wal. (1999) hating condumn may icontrollabiconditions.

For thetions are anoptimize thLogically,the optimaare indicatthe differen

Table 4Reboiler duty(M1F1)FV (kmol/h)24.928.131.735.437.2 (optimal40.8

Table 5Reboiler duty, minimum singular value and condition number for TCDS-SR(M1F2)FV (kmol/h) Q (kW) * *

61.2 2494.1 0.2 18645.366.2 1302.9 0.5 1228568.0 1174.6 3.1 1984.172.6 1059.1 1.8 3057.476.6 (optimal value) 1042.7 0.7 4020.680.7 1052.0 0.1 19736.2

Table 6Reboiler duty, minimum singular value and condition number for TCDS-SS(M1F1)

l/h)

timal

ed (mblesre armalion.t nontroll

-SR4);

t betion,mbe

st vally c

ion is better conditioned to the effect of disturbances thantimal arrangement. As has been explained, the opera-nonoptimal conditions has a higher energy consumption) 1.43 1.4336 10

9n stage 17

37.2

were analyzed in the optimal operation conditionsboiler duty) and nonoptimal operation conditions

y fixing FL or FV (depending of the arrangement)values (remembering that reboiler duty is function

r FV values).

nalysis

D technique requires transfer function matrices,generated by implementing step changes in the

d variables of the optimum design of the distilla-nces and registering the dynamic responses of thects. In this work, the reflux flowrate, and the reboilerere chosen as the manipulated variables. Serra et

ave explained that working out of the optimal oper-itions, the controllability of the dividing wall col-mprove. Thus, it will be interesting to compare thelity of the TCDS with side column at nonoptimal

TCDS-SR and TCDS-SS several operational condi-

FL (kmo18.119.420.422.625.3 (op29.5

analyzthe Ta

Theat opticonditated aits conTCDS(Tableexhibicondittion nuthe bethermaconditthe option inalyzed: the optimal operation (FL or FV are used toe reboiler duty) and five nonoptimal operation values.nonoptimal values have a higher reboiler duty thanl operation. The reboiler duty and FL or FV valuesed in Tables 47. To compare the controllability oft operation values, their controllability indexes are

, minimum singular value and condition number for TCDS-SR

Q (kW) * *

1506.6 25.8 67.31056.4 28.4 53.4

832.6 29.3 48.5756.2 27.4 79.2

value) 746.9 26.6 80.9762.7 25.6 81.3

than optimis increasedis lower thwhen the cscheme. SiTable 5.

Table 7Reboiler duty(M1F2)FL (kmol/h)49.953.756.762.664.2 (optimal72.5Q (kW) * *

1131.8 65.9 14.7912.9 80.4 12.2805.8 99.1 10.6668.8 55.2 16.7

value) 636.9 49.9 18.5656.2 42.2 22.3

inimum singular value and condition number). In47, the * and * for all cases of study are showed.e important differences between the column operatedoperation and the column operated at nonoptimalIn the case of TCDS-SR (M1F1), when it is oper-optimal conditions (FV = 31.7 kmol/h; see Table 4)ability improves. In those nonoptimal conditions,present highest value of the minimum singular valuetherefore, it can be expected that coupled systemter control properties than the sequence, in optimalunder feedback control. The results for the condi-r show that sequence in the nonoptimal value offerlue (Table 4). As a result, it can be expected thatoupled distillation system in a different operatingal conditions. Consequently when the reboiler duty, the controllability has improved. The reboiler duty

an the conventional sequence (Table 13) in the caseontrollability parameters are better than the optimalmilar results are showed for TCDS-SR (M1F2) in the

, minimum singular value and condition number for TCDS-SS

Q (kW) * *

2753.4 1.7 2483.01249.8 3.7 1983.2

988.7 4.4 558.8894.3 4.0 788.2

value) 893.4 3.5 1040.7925.9 2.1 2328.1

J.G. Segovia-Hernandez et al. / Computers and Chemical Engineering 31 (2007) 867874 871

Fig. 4. Closed loop dynamic response for component A (M1F1) in the optimal reboiler duty: (a) TCDS-SR and TCDS-SS.

In the Table 6, the energy consumption and the * and *for the TCDS-SS (M1F1) are showed. When the arrangementoperated at optimal conditions is compared, it can be seen thatthe TCDS-SS has the lower energy consumption. However, theoptimal arrangement has bad control properties. In the caseof nonoptimal conditions (FL = 20.4 kmol/h; see Table 6) thescheme has better control properties. The nonoptimal complexschemes show higher values of the minimum singular value andoffer the best values in the condition number. Therefore, it can beexpected that that these coupled systems exhibit better controlproperties than the optimal sequences under feedback controland it can be expected that system are better conditioned to theeffect of disturbances than the optimal arrangements. Those arevery important results that show how, taking advantage of thecomplexity(not necesssumption aare showedtime, the re(Table 13)better than

5.2. Dynamic simulations

The closed loop analysis was based on proportional-integral(PI) controllers. Several alternatives exist for tuning up the con-troller parameters. We attempted a common ground for com-parison by optimizing the controller parameters, proportionalgains (Kc) and integral times (I), for each conventional andintegrated scheme following the integral of the absolute error(IAE) criterion. For the integrated arrangements, the procedureis particularly complicated because of the interactions of themultivariable control problem. For these cases, the tuning pro-cedure was conducted taking one control loop at a time. Thus, theparameters obtained were taken from the following control loopuntil the three loops were considered. Those tuning parameters

sentivident

6).andtivelas t

ptimaoffered by the TCDS, a convenient operation pointarily the optimal condition) with low energy con-

nd good controllability can be chosen. Similar resultsfor TCDS-SS (M1F2) in the Table 7. One more

boiler duty is lower than the conventional sequencein the case when the controllability parameters arethe optimal scheme.

are presis, indimplemFigs. 4A, Brespecchosen

Fig. 5. Closed loop dynamic response for component B (M1F1) in the oFig. 6. Closed loop dynamic response for component C (M1F1) in the optimaed in Table 8 (case M1F1). For the dynamic analy-ual set point changes for product composition wereed for each of the three product streams (as showed inThe liquid compositions for the main product streamsC were taken as the controlled variables whereas,y, the reflux flowrate and the reboiler heat duty werehe manipulated variables. For all cases (optimal and

l reboiler duty: (a) TCDS-SR and TCDS-SS.l reboiler duty: (a) TCDS-SR and TCDS-SS.

872 J.G. Segovia-Hernandez et al. / Computers and Chemical Engineering 31 (2007) 867874

Table 8Tuning parameters obtained for each control loop (case M1F1)Control loop TCDS-SR TCDS-SS

AGain 450 kmol/kmol 480 kmol/kmolIntegral time 0.2 h 0.3 h

BGain 12 kmol/kmol 550 kWIntegral time 160 h 1.1 h

CGain 500 kW 390 kWIntegral time 0.1 h 0.1 h

nonoptimal conditions), the three control loops were assumedto operate under closed loop fashion. The performance of thesequences under analysis was compared through the evaluationof IAE values for each test. This part of the study was conductedwith the use of Aspen Dynamics 11.1.

Table 9 shows the IAE values obtained for each composi-tion control loop of the six cases for mixture M1, when feedF1 was considered. The TCDS-SR offered the best dynamicbehavior, based on the lowest values of IAE, for the controlof the three product streams in the value of FV = 31.7 kmol/h.This resultvalues of mfor the samating in noof TCDS-SFV = 68 kmponent (A)not create apoint. Thistechnique.

Table 9IAE results fo

FV (kmol/h)24.9

28.1

31.7

35.4

37.2 (optimal

40.8

Table 10IAE results for TCDS-SR (M1F2)FV (kmol/h) Component IAE61.2 A 3.3813E05

B 9.0250E05C 4.7100E06

66.2 A 2.2994E05B 6.8100E05C 4.4700E06

68.0 A 1.5296E05B 1.5033E05C 4.0700E06

72.6 A 3.9300E05B 5.3380E04C 4.2887E06

76.6 (optimal value) A 4.1049E05B 1.0800E03C 4.3057E06

80.7 A 4.3600E05B 1.5870E03C 4.4041E06

The analysis was completed with the consideration of the-SS. In Table 11 are displayed the IAE results for the case. Theis eqontrthrether duse o

of FL

ults for TCDS-SS (M1F1)ol/h) Component IAE

A 2.7472E05B 3.4400E05C 5.9866E06A 1.0075E05B 3.2518E05C 3.0560E06is similar at the case analyzed by SVD. The bestinimum singular value and condition number wase FV value. This situation corroborates that oper-noptimal conditions is a good option. In the caseR (M1F2) the best values of IAE are obtained inol/h (see Table 10). The control of the lightest com-, intermediate (B) and heaviest component (C) doesny significant problems in that nonoptimal operationbest FV value get is equal to that obtained with SVD

r TCDS-SR (M1F1)Component IAE

A 3.4780E05B 2.141E04C 6.3500E06A 2.1993E05B 1.8700E04C 5.0100E06

TCDSM1F1resultIf the cof theshowsreboileThe cavalue

Table 11IAE res

FL (lbm18.1

19.4A 1.3030E05B 1.1400E04C 4.2470E06A 4.6000E05B 7.5700E04C 5.3400E06

value) A 4.8736E05B 1.8192E03C 5.4422E06A 5.1600E05B 3.6840E03C 5.5810E06

20.4

22.6

25.3 (optimal

29.5best nonoptimal value of FL is 20.4 kmol/h. Thisual to that obtained with SVD analysis for this case.ol policy calls for the change of set point compositione components, the TCDS-SS, in nonoptimal value,best behavior, with the lowest value of IAE and thety is lower than the conventional sequence (Table 11).f TCDS-SS (M1F2) is analyzed in the Table 12. The

= 56.7 kmol/h is the best option. In this value theA 2.2230E06B 3.2165E05C 2.4552E06A 2.5182E05B 3.3300E05C 6.9370E06

value) A 3.0143E05B 5.3643E05C 7.3955E06A 3.1012E05B 2.6570E03C 7.5617E06

J.G. Segovia-Hernandez et al. / Computers and Chemical Engineering 31 (2007) 867874 873

Table 12IAE results for TCDS-SS (M1F2)FL (lbmol/h) Component IAE49.9

53.7

56.7

62.6

64.2 (optimal

72.5

Table 13Energy requirventional sequ

Feed

F1F2

coupled scthe loweststreams. Thsingular va

6. Conclu

Upon acontrollabiing conditiThrough acomplex arTCDS conttimal condTCDS opermuch bettesumption iIn the bestconventionilar to the rIn general,TCDS withing conditiconsumptio

Acknowledgment

The autEP a

nce

arate,. (200mn byEnginutali

distilsactiou, O.,ratedarch,R., &mn seicatioier, Gllation

ki, Zl dist. A.,

ynamEnginn, G.micalA 1.9640E05B 1.4632E05C 4.3206E06A 1.8967E05B 1.2935E05C 2.3270E06A 1.0878E05B 1.1878E05C 1.9460E06A 2.2354E05B 1.6969E05C 5.4350E06

value) A 2.2605E05B 2.8032E05C 5.4990E06A 2.3212E05B 6.4620E04C 5.8302E06

ements (kW) for the separation of the ternary mixtures using con-ences

Direct sequence Indirect sequence

PROM

Refere

Abad-ZA. Rcoluical

Abdul MwallTran

AnnakointegRese

Berber,columun

Dunnebdisti162.

Fidkowstiona

Flores, Omodand

HarmseChe956.5 1039.51228.0 1276.7

heme offered the best dynamic behavior, based onvalues of IAE, for the control of the three productis result is consistent with the values obtained using

lue decomposition (Table 13)

sions

nalysis of the SVD and dynamic simulations, thelity of TCDS-SR and TCDS-SS in different operat-ons are compared for a given separation problem.n optimization procedure, the reboiler duty of therangements is minimized. At optimal operation, therollability is worse than the controllability in nonop-itions (not minimized reboiler duty). However, theating at nonoptimal conditions, their controllability isr. In the case of nonoptimal condition the energy con-s higher that the arrangement in optimal conditions.nonoptimal case, the reboiler duty is lower that theal sequence. The results obtained using SVD are sim-esults obtained using rigorous dynamic simulations.the result is very important because it indicates thatside column operated at some nonoptimal operat-

ons have the best controllability and the lower energyn.

Hernandez, SdistillationChemical

Hernandez, Stems. Com

Hernandez, S.pled distil38, 3957.

Hernandez, S.efficiencyJournal o

Hernandez, Smodynamternary m

Hernandez-GS., & RicoconventioQuarterly

Jimenez, A., Hysis of cosequences

Kaibel, G., &trial practESCAPE-terdam, T

Klema, V. C.,putation a25(2), 164

Seader, J. D.,Wiley & S

Segovia-Hernbehaviourtution of C

Segovia-HerndinamicoTecnologihors acknowledge financial support received fromnd Universidad de Guanajuato, Mexico.

s

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Control properties of thermally coupled distillation sequences for different operating conditionsIntroductionDesign of TCDSSingular value decomposition (SVD)Cases of studyResultsSVD analysisDynamic simulations

ConclusionsAcknowledgmentReferences