energy-efficient complex distillation sequences control properties

Energy-Efficient Complex Distillation

Sequences: Control Properties

Salvador Robles-Zapiain,1 Juan Gabriel Segovia-Hernandez,1*Adrian Bonilla-Petriciolet2 and Rafael Maya-Yescas3

1. Universidad de Guanajuato, Facultad de Quımica, Noria Alta s/n, Guanajuato, Guanajuato, 36050, Mexico

2. Instituto Tecnologico de Aguascalientes, Departamento de Ingenierıa Quımica, Av. Lopez Mateos 1801, Aguascalientes,Aguascalientes, 20256, Mexico

3. Universidad Michoacana de San Nicolas de Hidalgo, Facultad de Ingenierıa Quımica, Ciudad Universitaria, Edif. M, Col.Felıcitas del Rıo, 58060 Morelia, Michoacan, Mexico

Four thermally coupled distillation systems were designed for the separation of five-component mixtures (the light-ends separation section ofa crude distillation plant); their steady-state design was obtained by starting from a conventional distillation sequence and then optimizing forminimum energy consumption. The thermally coupled distillation systems were compared to sequence based on conventional columns design.Comparison was based on controllability properties under open and closed loop operation, following the dynamic behaviour after commonindustrial operating disturbances. Simulation results were analyzed by the singular value decomposition technique and with the performanceexamination of elimination of feed disturbances using PI controllers. It was found that thermally coupled distillation systems are controllableand, sometimes, they exhibit dynamic responses that are easier to manage than in the case of conventional distillation sequences; this result isinnovative in the study of this kind of systems.

Quatre systemes de distillation couples thermiquement ont ete concus pour la separation de melanges a cinq composantes (la section de separationde legers d’une installation de distillation de brut); leur conception en regime permanent a ete obtenue en debutant par une sequence de distillationconventionnelle qui a ensuite ete optimisee quant a la consommation d’energie minimale. Ces systemes de distillation couples thermiquementont ete compares a une sequence basee sur la conception de colonne conventionnelle. La comparaison s’appuie sur les proprietes de controlabilitepour un fonctionnement en boucle ouverte et fermee, en suivant le comportement dynamique a la suite de perturbations operatoires industriellescommunes. Les resultats de simulation sont analyses par la technique de decomposition des valeurs singulieres et l’examen des performancespour eliminer des perturbations sur l’alimentation a l’aide de controleurs PI. On a trouve que les systemes de distillation couples thermiquementsont controlables, et parfois, ceux-ci montrent des reponses dynamiques qui sont plus faciles a gerer que dans le cas des sequences de distillationconventionnelles; c’est un resultat novateur dans l’etude de ce type de systemes.

Keywords: thermally coupled distillation schemes, controllability, energy consumption, multi-component mixtures, open loop dynamics, closedloop dynamics

INTRODUCTION

Distillation column configurations used to separate mix-tures containing three or more components into pureproduct streams have been studied for a long. For example,

Seader and Henley (1998) discuss algorithms to draw all the pos-sible configurations looking for sharp splits between componentsof adjacent volatilities. Such schemes are generally referred ashaving direct or indirect splits. Some other known configurationsinclude schemes similar to the prefractionator configuration forternary feed mixtures. Additionally, thermally coupled configura-tions with reduced numbers of reboilers and condensers have been

proposed (Petlyuk et al., 1965; Tedder and Rudd, 1978; Agrawal,1996; Agrawal and Fidkowski, 1999). The thermally coupleddistillation schemes are considered to be one of the most promis-ing systems because of its savings on both energy and capitalcosts.

∗Author to whom correspondence may be addressed.E-mail address: [email protected]. J. Chem. Eng. 86:249–259, 2008© 2008 Canadian Society for Chemical EngineeringDOI 10.1002/cjce.20021

| VOLUME 86, APRIL 2008 | | THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING | 249 |

Figure 1. Distillation sequence for five-component mixtures: (a) conventional sequence, (b) complex distillation column (TCDS-1).

Numerous research works on thermally coupled distillationschemes have been conducted to analyze steady-state anddynamic performance, especially for ternary mixtures (Tedderand Rudd, 1978; Triantafyllou and Smith, 1992; Wolff and Sko-gestad, 1995; Abdul Mutalib and Smith, 1998; Hernandez andJimenez, 1999; Kim, 2000; Jimenez et al., 2001; Kim et al., 2002,2003; Segovia-Hernandez et al., 2002, 2004, 2006, 2007a). Asconsequence, some interesting observations have been built: forexample, for ternary mixtures the energy savings in the fully ther-mally coupled configuration can be less than 30% compared tothose of traditional schemes. Among the three possible thermallycoupled systems (the side rectifier, the side stripper configura-tions, and the Petlyuk column) for ternary mixtures, over a widerange of relative volatilities and feed compositions, the Petlyukcolumn tends to provide the most efficient designs, thermodynam-ically, compared to traditional configurations (Flores et al., 2003).

There are few works on extensions towards design and controlproperties of integrated systems for mixtures of more than threecomponents (Chrsitiansen et al., 1997; Blancarte-Palacios et al.,2003; Esparza-Hermandez et al., 2005; Hernandez et al., 2005).The reduced number of works in this field is due to the combinato-rial problem of the possible configurations for multi-componentseparations and, mainly, the lack of experience and knowledgeon thermally coupled distillation schemes for four or more com-ponents (Rong et al., 2000, 2001, 2003). This lack of knowledgehas caused industry people to expect that dynamic properties ofthermally coupled systems may cause more operational problemsthan conventional sequences, which lead to the lack of industrialimplementation.

There are only few studies about dynamic properties ofthermally coupled configurations for the separation of multi-component mixtures. Recently, a design procedure has beenreported for the design and optimization of multi-componentthermally coupled distillation columns (Calzon-McConville et al.,2006), which also developed a methodology for the study of con-trol properties. Taking as starting point that methodology, in thiswork we developed a comparative study of control properties ofthe four thermally coupled distillation sequences for the sepa-rations of five-component mixtures and those of conventionalsequences (Figures 1 to 4); dynamic operating performance isevaluated by using the singular value decomposition techniqueand rigorous dynamic simulations.

ENERGY-EFFICIENT DESIGNThe design of the thermally coupled distillation arrangementscould be performed through a sequence of superstructures suit-able for optimization procedures. This task is complicated and,frequently, may fail to achieve convergence. There have been threeimportant papers that deal with the optimal design of complex dis-tillation columns, Dunnebier and Pantelides (1999), Yeomans andGrossmann (2000), and Caballero and Grossmann (2001). Never-theless, for five-component mixtures, the problem is clearly morecomplicated than those solved by the mentioned authors, as con-sequence of the combinatorial nature of the system that gives riseto a superstructure significantly more complex to solve.

To deal with this problem, Calzon-McConville et al. (2006)have proposed a method to overcome the complexity of the

| 250 | THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING | | VOLUME 86, APRIL 2008 |


simultaneous solution of the tray arrangement and energyconsumption within a formal optimization algorithm. Theydecoupled the design problem into two stages: tray configurationand optimal energy consumption. The first stage of their approachis the development of preliminary designs for complex systemsbased on conventional distillation columns (see Figures 1 to 4).For this case study, conventional sequences consist of eight differ-ent tray sections, which are used as a basis for the arrangement ofthe tray structure of the thermally coupled schemes through a sec-tion analogy procedure (see Calzon-McConville et al., 2006, fordetails). After the tray arrangement for the integrated designs havebeen obtained, an optimization procedure (second stage) is usedto minimize the heat duty supplied to reboilers of each coupledscheme, using as constrains the required purity of the five productstreams, which yields operating conditions for each set of designspecifications and tray arrangements. Then, remaining degrees offreedom are used to design integrated designs that provide min-imum energy consumption. More details about the optimizationprocedure are shown in Calzon-McConville et al. (2006).

SINGULAR VALUE DECOMPOSITIONOne of the basic and most important tools of modern numeri-cal analysis is the singular value decomposition (SVD). Thereare numerous important applications of the SVD when quanti-tative and qualitative information is desired about linear maps.One important use of the SVD is in the study of the theoreticalcontrol properties in chemical process. One definition of SVD is:

G = V �WH (1)

Here, G is the matrix target for SVD analysis, � is a diagonalmatrix which consists of the singular values of G, V is a matrix

which contains the left-singular vector of G and W is the matrixcomposed by the left-singular vectors of G (more details aboutmathematic fundaments are shown in Klema and Laub, 1980).

In the case where the SVD is used for the study of the theoreticalcontrol properties, two parameters are of interest: the minimumsingular value (�∗) the maximum singular value (�*), and its ratioknown as condition number (�):

�= �∗

�∗(2)

The minimum singular value is a measure of the invertibil-ity of the system and represents a clue of potential problemsof the system under feedback control. The condition numberreflects the sensitivity of the system to uncertainties in processparameters and modelling errors. These parameters provide aqualitative assessment of theoretical control properties of thealternate designs. The systems with higher minimum singular val-ues and lower condition numbers are expected to show the bestdynamic performance under feedback control (Klema and Laub,1980; Papastathopoulou and Luyben, 1991). Also, it is importantto note that a full SVD analysis should cover a wide range offrequencies.

The SVD technique requires a transfer function matrix (G inEquation (1)) around the optimum design of the distillationsequences, and registering the dynamic responses of productscomposition. For the distillation sequences presented in this work,five controlled variables were considered, the products compo-sition A, B, C, D, E. Similarly, five manipulated variables weredefined, reflux ratios (Rj) and heat duties supplied to reboilers(Qj), depending on the structure. For example in the case of CS-1and TCDS-1, we use the reflux ratio, where A is obtained and heat


Table 1. Transfer function matrix for CS-1 (M1F1)

Table 2. Transfer function matrix for TCDS-1 (M1F1)

duty in the other components. Tables 1 and 2 show the transferfunction matrix (G) for CS-1 and TCDS-1. It can be noted that thedynamic responses can be adjusted to first- or second-order mod-els. Similar transfer function matrix can be obtained for TCDS-2,TCDS-3, and TCDS-4 and for the all cases of study.

CASE STUDYTo compare the dynamic behaviour of the integrated arrangementswith the conventional sequence, two five-component mixture ofn-butane, n-pentane, n-hexane, n-heptane, and n-octane (mix-ture 1) and n-butane, isopentane, n-pentane, n-hexane, andn-heptane (mixture 2) were considered (examples of the light endsseparation section of a crude distillation plant), with a feed flowrate of 45.5 kmol/h. We selected those mixtures to reflect differentseparation difficulties. It is important to establish that studying afive-component mixture of hydrocarbons is a suitable example,given the applications of the hydrocarbon mixtures in the petro-chemical industry (Harmsen, 2004). The specified molar productpurity for components A, B, C, D, and E were 98, 94, 94, 94,and 97%, respectively. Two different molar compositions (A, B,C, D, E) equal to (0.35, 0.10, 0.10, 0.10, 0.35; F1) and (0.125,0.25, 0.25, 0.25, 0.125; F2) to examine the effect of the contentof the intermediate components were studied (similar to the caseof ternary and quaternary mixtures). Since the feed involves ahydrocarbon mixture, the Chao-Seader correlation was used forthe prediction of thermodynamic properties. The tray arrange-ments and some important design variables for a representativesequence, after the optimization task, are given in Table 3. Asfar as energy consumption is concerned, the optimized steady-state design provides energy savings of ∼35% with respect tothe best energy-efficient sequence based on conventional dis-tillation columns (Table 4; more details in Calzon-McConvilleet al., 2006).

Table 3. Design variables for the TCDS-4, case M1F1

Column Variables

Main column Stages = 41Feed stage = 9Reflux ratio = 1.72FV1 = 15.5 kmol/hFV2 = 19.8 kmol/hFV3 = 22.75 kmol/hPressure = 4.52 atm

Side rectifier 1 Stages = 10(where component B is purified) Distillate flow rate = 4.47 kmol/hSide rectifier 2 Stages = 11(where component C is purified) Distillate flow rate = 4.41 kmol/hSide rectifier 3 Stages = 11(where component D is purified) Distillate flow rate = 4.39 kmol/h

Table 4. Optimum reboiler duty (kW) for complex distillationsequences (case M1)

Feed Sequence Total reboiler duty (kW)

F1 CS-1 1181TCDS-1 793CS-2 1062TCDS-2 931CS-3 1168TCDS–3 708

F2 CS-1 2039TCDS-1 1471CS-2 1213TCDS-2 1123CS-3 1332TCDS–3 960


RESULTSThe theoretical control properties of conventional and thermallycoupled distillation sequences were obtained. The SVD techniquerequires transfer function matrices, which are generated byimplementing step changes in the manipulated variables of theoptimum design of the distillation sequences. In the second partof the study, dynamic responses under the action of proportionalintegral controllers (PI) were obtained for changes in the feedcomposition.

SVD AnalysisFor the case study of M1F1, we got the next results: TCDS-1 andCS-1 arrangements (Figures 5 and 6) present similar conditionnumber and values of the minimum singular value for the wholefrequency range (specially in higher frequencies); therefore, it canbe expected that the conventional and complex systems exhibitsimilar control properties under feedback control and they are bet-ter conditioned to the effect of disturbances. Similar results can beshowed in the case of M1F2 (Figures 7 and 8) and with the mixtureM2. The results indicate that a conventional scheme does not nec-essarily provide an improvement of its controllability propertiesin comparison with a complex scheme (thermally coupled).

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-161.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-041.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14 1.E+16 1.E+18 1.E+20 1.E+22 1.E+24

Frequency, ω [ rad/h ]

Min

imum

sin

gula

r val

ue,

σσ* TCDS-1,

CS-1,

Figure 5. Minimum singular value TCDS-1 and CS-1 (M1F1).

1.E+01

1.E+02

1.E+03

1.E+04

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000 10000000


Con

ditio

n nu

mbe

r, γγ

CS-1, F1

TCDS-1, F1

Figure 6. Condition number TCDS-1 and CS-1 (M1F1).

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14 1.E+16 1.E+18 1.E+20


Min

imum

sin

gula

r val

ue, σσ

*

CS-1,

TCDS-1,


1.E+00

1.E+04

1.E+08

1.E+12

1.E+16

1.E+20

1.E+24

1.E+28

1.E+32

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06


Con

ditio

n nu

mbe

r, γ

CS-1,

TCDS-1,


Figures 9 and 10 show the minimum singular value and condi-tion number for the case study of M1F1. The CS-2 presents highervalues of �∗ and lower values of condition number for the wholefrequency range. Therefore, the CS-2 is expected to require lesseffort control under feedback operation and it is better conditionedto the effect of disturbances than the TCDS-2 scheme. According to

1.E-30

1.E-29

1.E-28

1.E-27

1.E-26

1.E-25

1.E-24

1.E-23

1.E-22

1.E-21

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14 1.E+16 1.E+18 1.E+20


Min

imum

sin

gula

r val

ue, σσ

*

TCDS-2,

CS-2,


1.E+09

1.E+16

1.E+23

1.E+30

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000


Con

ditio

n nu

mbe

r, γγ

TCDS-2,

CS-2,


1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14 1.E+16 1.E+18 1.E+20


Min

imum

sin

gula

r val

ue, σσ

*

TCDS-2,

CS-2,



1.E+00

1.E+04

1.E+08

1.E+12

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12 1.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 1.E+20


Con

ditio

n nu

mbe

r, γγ

TCDS-2,

CS-2,


SVD (Figures 11 and 12) for the case of M1F2 and CS-2 shows thebetter control properties than the TCDS-2 because that schemepresents lower values of the condition number and higher val-ues of the minimum singular value in comparison with TCDS-2arrangement. Similar results can be obtained for the case studywith mixture M2.

1.E-20

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14 1.E+16 1.E+18 1.E+20


Min

imum

sin

gula

r val

ue, σσ

*

TCDS-3,

CS-3,


1.E-06

1.E+01

1.E+08

1.E+15

1.E+22

1.E+29

1.E+36

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000 10000000 100000000 1000000000 10000000000


Con

ditio

n nu

mbe

r, γγ

CS-3,

TCDS-3,


1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12 1.E+14 1.E+16 1.E+18 1.E+20


Min

imum

sin

gula

r val

ue, σσ

*

CS-3,

TCDS-3,


1.E+00

1.E+04

1.E+08

1.E+12

1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10 1.E+11 1.E+12 1.E+13 1.E+14 1.E+15 1.E+16 1.E+17 1.E+18 1.E+19 1.E+20

Frequency ω [ rad/h ]

Con

ditio

n nu

mbe

r, γγ

CS-3,

TCDS-3,


1.E-18

1.E-16

1.E-14

1.E-12

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

1.E+00

1.E-

04

1.E-

02

1.E+

00

1.E+

02

1.E+

04

1.E+

06

1.E +0

8

1.E+

10

1.E+

12

1.E +1

4

1.E+

16

Frequency, ω [rad/h]

σ*

Min

imum

Sin

gula

r Val

ue

CS-4

TCDS-4


1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E

-04

1 .E

-02

1.E+

0 0

1 .E+

02

1.E+

0 4

1.E+

06

1.E +

0 8

1.E+

10

1 .E+

1 2

1.E+

14

1 .E+

1 6

1.E+

18

Frequency,ω[rad/hr]

CS-4

TCDS-4

Con

ditio

n nu

mbe

r, γγ


1.E-17

1.E-15

1.E-13

1.E-11

1.E-09

1.E-07

1.E-05

1.E-03

1.E-01

1.E+01

1.E

-04

1.E

- 02

1.E

+00

1.E

+02

1.E

+04

1.E

+06

1.E

+08

1.E

+10

1.E

+12


σ*

Min

imum

Sin

gula

r Val

ue

CS-4

TCDS-4



1.E+03

1.E+04

1.E+05

1.E+06

1.E

- 04

1.E

-03

1.E

- 02

1.E

- 01

1.E

+00

1.E

+01

1.E

+02

1.E

+03

1.E

+04

1.E

+05

1.E

+06

1.E

+07

1.E

+08


Con

ditio

n nu

mbe

rγ*

CS-4

TCDS-4


Results for TCDS-3 and CS-3 are displayed in Figures 13 and14 (case M1F1). TCDS-3 exhibit similar values of �∗ than theconventional scheme (CS-3), and the complex arrangementpresents similar values of condition number in comparisonwith the CS-3 scheme. In the case of M1F2, the TCDS-3 showshigher values of �∗ and lower values of condition number forthe whole frequency range. Therefore, the coupled scheme isexpected to require less effort control under feedback operationand it is better conditioned to the effect of disturbances than CS-3sequence (Figures 15 and 16). One more time, we can say thatcomplex distillation sequence offers better conditioning proper-ties against model uncertainties and process disturbances thanthe conventional columns. Similar results can be showed for themixture M2.

In the case of TCDS-4 and CS-4, for the case M1F1, results areshown in Figures 17 and 18. CS-4 arrangement present highervalues of the minimum singular value and lower condition num-ber for the whole frequency range; therefore, it can be expectedthat CS-4 system exhibit better control properties than the othersequence under feedback control and it is better conditioned tothe effect of disturbances than the other distillation scheme. Forthe case M2F1, Figures 19 and 20 show that at low frequenciesTCDS-4 exhibit higher values of �∗ than the other scheme, but asthe frequency increases, the minimum singular value decreasesdrastically, and the CS-4 offer the best values of this parameter.In the case of the number condition, TCDS-4 shows the lowestvalues at low frequencies.

Based on the trends observed, a distinction is given betweenthe best control option for coupled scheme and conventionalsequence. In the case of complex schemes, they have better controlproperties in comparison with conventional sequence, when cou-pled arrangement preferentially has side strippers (case TCDS-1and TCDS-3). In this case, the arrangement with thermal cou-pling is expected to require less control efforts under feedbackoperation. However, if the complex scheme preferentially has siderectifiers, its control properties are worst in comparison with theconventional sequence (for example, TCDS-2 and TCDS-4). In gen-eral, the structure of the sequence affects the dynamic behaviourof the TCDS for the separation of multi-component mixtures. Thisresult is similar to that reported by Segovia-Hernandez et al.(2005) in the case of control properties of alternative sequencesto the Petlyuk column (the dynamic behaviour depends on thetopology of the scheme).

Closed-loop analysisAccording to previous studies in thermally coupled distillationsequences (Cardenas et al., 2005; Esparza-Hermandez et al., 2005;Segovia-Hernandez et al., 2007b, among others) TCDS options canhave good dynamic responses in comparison to those obtained inthe conventional distillation sequences considering heuristic pair-ings in the control loops, that is, distillation composition–refluxrate and bottoms composition–reboiler heat duty (Haggblom andWaller, 1992). The PI controllers were tuned by minimizing theintegral absolute of error (IAE) (Stephanopoulos, 1984). There-fore, for each loop, an initial value of the proportional gain wasset; a search over the values of the integral reset time was con-ducted until a local optimum value of the IAE was obtained. Theprocess was repeated for other values of the proportional gain.The selected set of controller parameters was the one that pro-vided a global minimum value of the IAE. Although the tuningprocedure is fairly elaborated, the control analysis is conductedbased on a common tuning method for the controller parameters.For the distillation sequences of Figure 2, the dynamic responsesare showed in Figures 16 to 20 for the case of feed disturbance(when a 5% change in the feed composition of component A wasimplemented).

For the case of component A, Figure 21 shows that both theCS and the TCDS successfully rejected the disturbance to bringthe product composition back to its design value. However, theresponse of the TCDS was remarkably better. The integrated dis-

Figure 21. Dynamic responses of component A for feed disturbance (M1F1; Figure 2).

Table 5. IAE results for CS-2 and TCDS-2 (M1F1)

Sequence Component A Component B Component C Component D Component E

CS-2 7.13065 × 10−4 2.70389 × 10−4 2.92806 × 10−4 4.77071 × 10−4 2.16417 × 10−4

TCDS-2 2.16125 × 10−4 5.97292 × 10−5 2.0778 × 10−5 0.00269654 2.8497 × 10−5


Figure 22. Dynamic responses of component B for feed disturbance (M1F1; Figure 2).

Figure 23. Dynamic responses of component C for feed disturbance (M1F1; Figure 2).

Figure 24. Dynamic responses of component D for feed disturbance (M1F1; Figure 2).

Figure 25. Dynamic responses of component E for feed disturbance (M1F1; Figure 2).

tillation sequence gives an IAE value of 2.16125 × 10−4 whichis lower than that of the conventional distillation sequence(IAE = 7.13065 × 10−4) (see Table 5). As a result, the integrateddistillation sequence presents a better dynamic response. When afeed disturbance was implemented in both distillation sequences,the dynamic response of the component B in the conventionaldistillation sequence reaches the new steady-state faster, but itpresents more oscillations. TCDS present better IAE value anddynamic behaviour (Table 5 and Figure 22). Figure 23 shows theresponses of the component C in the TCDS and conventional con-

figuration. The TCDS provided smooth response, while CS yieldedhigh deviation. The IAE values showed TCDS = 2.0778 × 10−5

and CS = 2.92806 × 10−4 (see Table 5). For component D (Fig-ure 24), the dynamic response of the integrated distillationsequence presents more oscillations and a rather poor behaviourwith large settling times. The conventional sequence presentbetter control properties and better IAE value (Table 5). Fig-ure 25 presents a similar behaviour for composition E of theheat integrated distillation sequence and conventional arrange-ment. The new steady-state is obtained in a very short time.


However, IAE value is better in the case of complex column(Table 5).

In general, the dynamic responses of TCDS options can be betterin comparison to the conventional distillation sequences. Whenother cases of study were subjected to the same test, similar trendson the dynamic responses of TCDS were obtained.

CONCLUSIONSAn analysis on control properties of four-coupled distilla-tion sequences that arise from modifications to conventionalsequences for the distillation of five-component mixtures has beenpresented. Results from singular value decomposition indicate,in general, that thermally coupled distillation systems exhibitbetter control properties than conventional schemes. The resultsfrom the theoretical control properties indicate that the presenceof interconnections does not necessarily provide operational dis-advantages, as originally expected due to the resulting complexstructural design. Also, in general, the thermally coupled dis-tillation sequences outperformed the dynamic responses of theconventional distillation sequences under closed-loop fashion.The results also suggest that control properties are ruled by thenumber of side strippers; when the coupled scheme preferen-tially has side strippers, their control properties are better than theconventional arrangement. If the complex scheme preferentiallyhas side rectifiers, its control properties are worse in compari-son with the conventional sequence. In general, it is apparentthat the presence of recycle streams instead of deteriorating thedynamic behaviour of thermally coupled distillation sequencesmay contribute positively to their dynamic properties.

ACKNOWLEDGEMENTSThe authors acknowledge financial support received from Uni-versidad de Guanajuato, Universidad Michoacana, InstitutoTechnologico de Aguascalientes and CONCyTEG, Mexico.

NOMENCLATUREG transfer function matrixV matrix of left eigenvectorsW matrix of right eigenvectors

Greek Symbols� condition number�* maximum singular value�∗ minimum singular valueω frequency

REFERENCESAbdul Mutalib, M. I. and R. Smith, ‘‘Operation and Control of

Dividing Wall Distillation Columns. Part I: Degrees ofFreedom and Dynamic Simulation,’’ Trans. IchemE. 76, 308(1998).

Agrawal, R., ‘‘Synthesis of Distillation Columns Configurationsfor a Multi-Component Separation,’’ Ind. Eng. Chem. Res. 35,1059 (1996).

Agrawal, R. and Z. Fidkowski, ‘‘New Thermally CoupledSchemes for Ternary Distillation,’’ AIChE J. 45, 485 (1999).

Blancarte-Palacios, J. L., M. N. Bautista-Valdes, S. Hernandez, V.Rico-Ramırez and A. Jimenez, ‘‘Energy-Efficient Designs ofThermally Coupled Distillation Sequences for Four-Component Mixture,’’ Ind. Eng. Chem. Res. 42, 5157 (2003).

Caballero, J. A. and I. E. Grossmann, ‘‘Generalized DisjunctiveProgramming Models for the Optimal Synthesis of ThermallyLinked Distillation Columns,’’ Ind. Eng. Chem. Res. 40, 2260(2001).

Calzon-McConville, C. J., M. B. Rosales-Zamora, J. G.Segovia-Hernandez, S. Hernandez and V. Rico-Ramırez,‘‘Design and Optimization of Thermally Coupled DistillationSchemes for the Separations of Multi-Component Mixtures,’’Ind. Eng. Chem. Res. 45, 724 (2006).

Cardenas, J. C., S. Hernandez, I. R. Gudino-Mares, F.Esparza-Hernandez, C. Y. Irianda-Araujo and L. M.Domınguez-Lira, ‘‘Analysis of Control Properties ofThermally Coupled Distillation Sequences forFour-Component Mixtures,’’ Ind. Eng. Chem. Res. 44, 391(2005).

Chrsitiansen, A., S. Skogestad and K. Lien, ‘‘ComplexDistillation Arrangements: Extending the Petlyuk Ideas,’’Comput. Chem. Eng. 21, S237 (1997).

Dunnebier, G. and C. Pantelides, ‘‘Optimal Design of ThermallyCoupled Distillation Columns,’’ Ind. Eng. Chem. Res. 38, 162(1999).

Esparza-Hermandez, F., C. Y. Irianda-Araujo, L. M.Domınguez-Lira, S. Hernandez and A. Jimenez, ‘‘FeedbackControl Analysis of Thermally Coupled Distillation Sequencesfor Four-Component Mixtures,’’ Trans. IchemE. 83, 1145(2005).

Flores, O. A., J. C. Cardenas, S. Hernandez and V. Rico-Ramırez,‘‘Thermodynamic Analyisis of Thermally Coupled DistillationSequences,’’ Ind. Eng. Chem. Res. 42, 5940 (2003).

Haggblom, K. E. and K. V. Waller, ‘‘Control Structures,Consistency, and Transformations,’’ in ‘‘Practical DistillationControl,’’ W.L. Luyben, Ed., Van Nostrand Reinhold, NY(1992), p 192.

Harmsen, G. J., ‘‘Industrial Best Practices of Conceptual ProcessDesign,’’ Chem. Eng. Processes 43, 671 (2004).

Hernandez, S. and A. Jimenez, ‘‘Controllability Analysis ofThermally Coupled Systems,’’ Ind. Eng. Chem Res. 38, 3957(1999).

Hernandez, S., I. R. Gudino-Mares, J. C. Cardenas, J. G.Segovia-Hernandez and V. Rico-Ramırez, ‘‘A Short Note onControl Structures for Thermally Coupled DistillationSequences for Four-Component Mixtures,’’ Ind. Eng. Chem.Res. 44, 5857 (2005).

Jimenez, A., S. Hernandez, F. A. Montoy and M. Zavala-Garcıa,‘‘Analysis of Control Properties of Conventional andNonconventional Distillation Sequences,’’ Ind. Eng. Chem.Res. 40, 3757 (2001).

Kim, Y. H., ‘‘Design of Fully Thermally Coupled DistillationColumn Based on Dynamic Simulations,’’ Korean J. Chem.Eng. 17, 570 (2000).

Kim, Y. H., M. Nakaiwa and K. S. Hwang, ‘‘Approximate Designof Fully Thermally Coupled Distillation Column,’’ Korean J.Chem. Eng. 19, 383 (2002).

Kim, Y. H., D. Choi and K. S. Hwang, ‘‘Industrial Application ofan Extended Fully Thermally Coupled Distillation Column toBTX Separation in Naphtha Reforming Plant,’’ Korean J.Chem. Eng. 20, 755 (2003).

Klema, V. C. and A. J. Laub, ‘‘The Singular ValueDecomposition: Its Computation and Some Applications,’’IEEE Trans. Automat. Contr. 25, 164 (1980).

Papastathopoulou, H. S. and W. L. Luyben, ‘‘Control of BinarySidestream Column,’’ Ind. Eng. Chem. Res. 30, 705(1991).


Petlyuk, F. B., V. M. Platonov and D. M. Slavinskii,‘‘Thermodinamically Optimal Method for SeparatingMulti-Component Mixtures,’’ Inter. Chem. Eng. 5, 555 (1965).

Rong, B. G., A. Kraslawski and L. Nystrom, ‘‘The Synthesis ofThermally Coupled Distillation Flowsheets for Separations ofFive-Component Mixtures,’’ Comput. Chem. Eng. 24, 247(2000).

Rong, B. G., A. Kraslawski and L. Nystrom, ‘‘Design andSynthesis of Multi-Component Thermally Coupled DistillationFlowsheets,’’ Comput. Chem. Eng. 25, 807 (2001).

Rong, B. G., A. Kraslawski and L. Nystrom, ‘‘Synthesis ofPartially Thermally Coupled Column Configurations ofMulti-Component Distillations,’’ In ‘‘Proceedings of EuropeanSymposium on Computer Aided Process Engineering-13(ESCAPE),’’ Andrzej Kraslawski and Ilkka Turunen, Eds.,Elsevier, Amsterdam, The Netherlands (2003) 521.

Seader, J. D. and E. J. Henley, ‘‘Separation Process Principles,’’John Wiley & Sons, U.S.A. (1998).

Segovia-Hernandez, J. G., S. Hernandez and A. Jimenez,‘‘Control Behaviour of Thermally Coupled DistillationSequences,’’ Trans. IchemE. 80, 783 (2002).

Segovia-Hernandez, J. G., S. Hernandez, V. Rico-Ramırez and A.Jimenez, ‘‘A Comparison of the Feedback Control Behaviourbetween Thermally Coupled and Conventional DistillationSchemes,’’ Comput. Chem. Eng. 28, 811 (2004).

Segovia-Hernandez, J. G., S. Hernandez and A. Jimenez,‘‘Analysis of Dynamic Properties of Alternative Sequences tothe Petlyuk Column,’’ Comput. Chem. Eng. 29, 1389 (2005).

Segovia-Hernandez, J. G., S. Hernandez and A. Jimenez, ‘‘AShort Note about Energy-efficiency Performance of ThermallyCoupled Distillation Sequences,’’ Can. J. Chem. Eng. 84, 139(2006).

Segovia-Hernandez, J. G., E. A. Hernandez-Vargas and J. A.Marquez-Munoz, ‘‘Control Properties of Thermally CoupledDistillation Sequences for Different Operating Conditions,’’Comput. Chem. Eng. 31, 867 (2007a).

Segovia-Hernandez, J. G., S. Hernandez, R. Femat and A.Jimenez, ‘‘Control of Thermally Coupled DistillationSequences with Dynamic Estimation of Load Disturbances,’’Ind. Eng. Chem. Res. 46, 546 (2007b).

Stephanopoulos, G., ‘‘Chemical Process Control: An Introductionto Theory and Practice,’’ Prentice Hall, Englewood Cliffs, NJ(1984).

Tedder, D. and D. Rudd, ‘‘Parametric Studies in IndustrialDistillation: Part I. Design Comparisons,’’ AIChE J. 24, 303(1978).

Triantafyllou, C. and R. Smith, ‘‘The Design and Optimization ofFully Thermally Coupled Distillation Columns,’’ Trans. Inst.Chem. Eng. 70, 118 (1992).

Wolff, E. A. and S. Skogestad, ‘‘Operation of IntegratedThree-Product (Petlyuk) Distillation Columns,’’ Ind. Eng.Chem. Res. 34, 2094, (1995).

Yeomans, H. and I. Grossmann, ‘‘Optimal Design of ComplexDistillation Columns using Rigorous Tray-by-Tray DisjunctiveProgramming Models,’’ Ind. Eng. Chem. Res. 39, 4326(2000).

Manuscript received July 6, 2007; revised manuscriptreceived September 26, 2007; accepted for publication October 2,2007


energy-efficient complex distillation sequences control properties

Documents