design of energy-efficient petlyuk systems

Computers and Chemical Engineering 23 (1999) 1005–1010

Design of energy-efficient Petlyuk systems

Salvador Hernandez b, Arturo Jimenez a,*a Instituto Tecnologico de Celaya, Departamento de Ingenierıa Quımica, Celaya, Gto. 38010, Mexico

b Uni6ersidad de Guanajuato, Facultad de Quımica, Guanajuato, Gto. 36050, Mexico

Received 23 September 1997; accepted 18 March 1999

Abstract

A strategy for the energy-efficient design of the fully thermally coupled distillation column (Petlyuk system) is presented. Thestrategy is based on a dynamic model and uses two recycle streams as search variables. The optimization procedure with thedynamic model provides the conditions under which a given design minimizes the heat duty supplied to the reboiler. Several casestudies are presented, and some trends of the optimal values of the recycle streams are identified. © 1999 Elsevier Science Ltd. Allrights reserved.

Keywords: Distillation column; Energy efficient; Petlyuk systems

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1. Introduction

Integrated distillation schemes such as thermally cou-pled distillation sequences with side columns and thefully thermally coupled distillation column, or Petlyuksystem (Fig. 1), provide choices of special interest forthe separation of ternary mixtures because of theirpotential energy savings. Several studies have been con-ducted to show the economic potential of those inte-grated schemes (Tedder & Rudd, 1978; Cerda &Westerberg, 1981; Fidkowski & Krolikowski, 1986,1987; Glinos & Malone, 1988; Fidkowski & Kro-likowski, 1990; Triantafyllou & Smith, 1992; Wolff &Skogestad, 1995; Annakou & Mizsey, 1996). In severalof these studies it has been stressed that despite theeconomic incentives of integrated distillation systems,their industrial implementation has been restricted be-cause of the need for reliable design methods and aproper understanding of their control properties.

We focus in this paper on the use of a rigorousdynamic model as a convenient tool for the design ofthe Petlyuk system. The approach is an extension of amodel previously developed for the design of thermallycoupled distillation sequences with side columns (Her-nandez & Jimenez, 1996); the case for the Petlyuk

distillation sequence shows further complications be-cause of the additional degree of freedom provided bythe additional recycle stream between the columns. Themodel is used to detect the operating conditions underwhich a given design for the Petlyuk system can providethe minimum energy consumption.

2. Model development

The dynamic model is based on the total mass bal-ance, component mass balances, equilibrium relation-ship (ideal VLE), summation constraints, energybalance, and stage hydraulics (Francis Weir formula).One set of equations must be written for each columnof the Petlyuk system. The equations are coupled be-cause of the two recycle streams between the columns;therefore, the full set of equations must be solvedsimultaneously. An important aspect for the design ofthe system is the specification of the two recyclestreams, a liquid stream that leaves column C-2 fromstage NR and enters at the top of column C-1, and avapor stream that leaves column C-2 from stage NS2and constitutes the feed stream at the bottom ofcolumn C-1 (Fig. 2). We define the following dimen-sionless variables for these streams, which lie between 0and 1 and are used as search variables in the optimiza-tion procedure:* Corresponding author.

0098-1354/99/$ - see front matter © 1999 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 9 8 -1354 (99 )00257 -4

S. Hernandez, A. Jimenez / Computers and Chemical Engineering 23 (1999) 1005–10101006

hV=VB

VNS2

(1)

hL=LT

LNR

(2)

Equations for PI controllers complement the closed-loop dynamic model. The model can be solved using anumeric technique such as Euler’s method.

3. Optimization strategy

The dynamic model requires a basic structure of thePetlyuk system. Such a preliminary design can be ob-tained by the shortcut method of Triantafyllou andSmith (1992), or through the implementation of someexpected distribution of the intermediate component.The dynamic model serves two purposes. First, it willdetect whether the proposed design can effectivelyprovide the desired products compositions, and sec-ondly it will identify the operating conditions underwhich a minimum energy consumption will be achieved.The following steps are used for the optimizationprocedure.1. Specify products compositions for the Petlyuk sys-

tem. These values are taken as set points for thedynamic model.

2. Establish the control loops between each manipu-lated variable (R, LS and QR) and its correspondingoutput variable (XD, XS and XB).

3. Set a value for hV.4. Set a value for hL.5. Initialize time to start the rigorous dynamic

simulation.6. Integrate the dynamic model (for details see Her-

nandez & Jimenez, 1996).7. Compare product compositions with set point val-

ues. If they do not agree, increase time by Dt and goback to step 6. If they agree, a search point is

Fig. 2. Relevant variables for the design of the Petlyuk system.

completed; the operating values for R, LS and QRare detected.

8. Increase hL and go back to step 5 until the localminimum of heat duty is detected.

9. Increase hV and go back to step 4 until the overallminimum of heat duty is found.

It is important to note that an adjustment of theinitial design might be needed if the final steady statecompositions do not agree with the established setpoints.

4. Case studies

The method was applied to optimize some givendesigns for energy consumption for the nine cases thatarise from the separation of three mixtures with threedifferent compositions. Different mixtures were ana-lyzed in an attempt to understand the influence of therelative difficulty of the separation A/B with respect toB/C on the energy consumption and design of thesystem. The ease of separation index (ESI), as definedby Tedder and Rudd (1978), can be used to characterizeeach mixture:

ESI=aAB

aBC

(3)

Mixtures with ESI values of 1 (F1), higher than 1(F2), and lower than 1 (F3) were considered, as shownin Table 1. Three feed compositions were assumed: anequimolar mixture (M1), a mixture with a high contentof the intermediate component (M2), and a mixturewith a low content of the intermediate component(M3); feed compositions are given in Table 2. A feed

Fig. 1. Fully thermally coupled distillation column, or Petlyuk sys-tem.

S. Hernandez, A. Jimenez / Computers and Chemical Engineering 23 (1999) 1005–1010 1007

Table 1Mixtures analyzed

ESIComponents (A, B, C)Mixture

F1 n-Butane, n-pentane, n-hexane 1.041.86F2 n-Butane, i-pentane, n-pentane0.18i-butane, n-butane, n-hexaneF3

Fig. 3. Search for the optimal values for the mixture F1 withcomposition M1.

flowrate of 45.4 kmol h−1 as saturated liquid wasconsidered. The set points for the dynamic model,provided by the design specifications, were XD=0.987for the distillate product, XS=0.98 for the liquid side-stream product and XB=0.986 for the bottomproduct; these compositions reflect 98% recoveries ofkey components. For each case study, the parametersfor the PI controllers were obtained with the applica-tion of the Cohen–Coon technique (Stephanopoulos,1984).

4.1. Optimization of mixture F1

The mixture under analysis (n-C5, n-C6, n-C7) hasan ESI of 1.04. The tested design has the followingtrays arrangement (see Fig. 2):� NS1=9� NT1=16� NR=10� NE=19� NS2=28� NT2=35

The proposed design of the Petlyuk system is thentested and optimized (for minimum energy consump-tion) with the rigorous dynamic model. The optimiza-tion procedure detects the values of hV and hL thatminimize the amount of heat supplied to the reboiler.Fig. 3 displays the search for the optimal values. Forthe mixture under consideration, a minimum energyrequirement of 488.35 kW is achieved when hV=0.5369and hL=0.256.

The inefficiency of the conventional direct and indi-rect sequences with respect to the Petlyuk system hasbeen explained in terms of the composition profile ofthe intermediate component. In the conventional sys-tems, the composition of the middle component reachesa maximum at some point in the first column and thendeclines before reaching the top (indirect sequence) orthe bottom part of the column (direct sequence); this

remixing of component B affects the energy require-ments of the separation system. A proper operation ofthe Petlyuk system should extract the intermediate com-ponent at the tray where its composition profile reachesa maximum. Fig. 4 shows the composition profile ofcomponent B in the main column for the optimumconditions provided by the dynamic model. The actionof the controllers provides the desired feature that theliquid sidestream product is taken from the stage withthe maximum concentration of component B.

For the mixture with a high concentration of theintermediate component, M2, the optimal values for the

Fig. 4. Composition profile of component B in column C-2 for thePetlyuk system. Sidestream taken from stage 19.

Table 2Feed composition for each mixture analyzed

CompositionFeed

M1 0.333/0.333/0.333M2 0.15/0.70/0.15M3 0.45/0.1/0.45




tion search carried out for mixture M1. The optimalvalues for the search parameters are hV=0.7 and hL=0.575. It can be observed that for this mixture the localoptimum values in the neighborhood of the globaloptimum point do not differ significantly; several localoptimum solutions differ from the global optimum byless than 3%. Another interesting observation is thatonce hV is specified, the energy consumption for theseparation of this mixture changes more significantlywith hL than for mixture F1.

For feed composition M2, the optimum values werehV=0.7 and hL=0.62 (see Fig. 8). The same behavior

parameters are hV=0.5 and hL=0.175, as shown inFig. 5. In the case of the mixture with a low concentra-tion of the intermediate component, M3, the values forthe energy-efficient design are hV=0.7 and hL=0.4, asshown in Fig. 6.


Petlyuk designs for a mixture (n-C4, i-C5, n-C5) withan ESI value higher than one were optimized for energyconsumption. Fig. 7 shows the results of the optimiza-

Fig. 6. Search for the optimal values for mixture F1 with compositionM3.


S. Hernandez, A. Jimenez / Computers and Chemical Engineering 23 (1999) 1005–1010 1009

Fig. 9. Search for the optimal values for mixture F2 with compositionM3.


trends that can be used to minimize the search space forenergy-efficient designs. The following recommendationsare developed as a function of the mixture properties andits feed composition, and are independent of the use ofa dynamic model or a steady state model for designpurposes.For mixtures with ESI=1:� If the content of the intermediate component B is

high (\30%), use hV=0.5 and perform an opti-mization search over hL.

is observed as with mixture M1; the optimality regionclose to the global optimum energy is fairly flat, such thatseveral local optimum values are within 3% of the globaloptimum, and the energy consumption is again a strongfunction of hL once a value for hV has been specified.Given these results, it can be concluded that for thesetypes of mixtures a value of 0.7 for hV provides anexcellent choice, and a search over hL should be con-ducted to determine its optimum value.

When a mixture with a low content of the intermediatecomponent is considered, M3, the optimization proce-dure yields the results shown in Fig. 9. The optimal valuesfor the search parameters are hV=0.4 and hL=0.31.Given the similar trend of local optimum values and thedependence between the two search parameters, onecould use for mixtures of this type a fixed value of 0.4for hV and conduct a search procedure over hL to obtainan excellent solution.


The optimization for energy consumption of proposeddesigns of the Petlyuk system for mixture F3 (i-C4, n-C4,n-C6) provided results with similar trends as thoseobserved for mixture F2, as seen in Figs. 10 and 11 whichshow the results for two of the three feed compositionsanalyzed. A general observation from all of the studiesconducted is that the optimal value of hL is always lowerthan that of hV.

4.4. Trends of the 6alues of the recycle streams

The results from the optimization studies showed someFig. 11. Search for optimal values for the mixture F3 with composi-tion M2.


� If the content of the intermediate component B islow (B10%), use hV=0.7 and carry out an opti-mization search over hL.

For mixtures with ESI"1:� If the content of the intermediate component is high,

use hV=0.7 and optimize hL.� If the content of the intermediate component is low,

use hV=0.4 and carry out an optimization searchover hL.For all cases, the optimal value of hL is lower than

that of hV. These observed trends can provide the basisfor useful heuristic design rules. It should be empha-sized that these trends were obtained for separations ofideal mixtures.

5. Concluding remarks

The dynamic model provides a robust tool for thedesign of energy-efficient Petlyuk systems. No conver-gence problems were observed for any of the casestudies. Some trends were observed for the optimalvalues of the two recycle streams used as search vari-ables. The results show that hV values can be correlatedto an ESI, and that there is no significant deviation inthe optimal solution with small changes in hV. There is,however, a high dependency on the energy consump-tion with respect to hL once a value for hV has beenspecified. Therefore, the results suggest that a propervalue for hV can be set ahead of design, but a searchover hL is still required to obtain a design with mini-mum energy consumption. Furthermore, we found thatin all cases the optimum value of hL was lower thanthat of hV. These observations reduce significantly thesearch space for the design of the Petlyuk system withminimum energy consumption.

Acknowledgements

The authors wish to acknowledge financial supportfrom CONACyT, Mexico and from the ProgramPROSAA of the Universidad de Guanajuato, for thedevelopment of this project.

Appendix A. Nomenclature

B bottomsD distillateESI ease of separation index

liquid flowrateLside productLS

moles of liquid retained in the base of theMBcolumnmoles of liquid retained in the refluxMDaccumulator

QR reboiler heat dutyR reflux flowrate

vapor flowrateVXD mole fraction of A in top product

mole fraction of C in bottoms productXBXS mole fraction of B in sidestream product

Greek symbolsa relative volatility

liquid or vapor fractionh

Subscriptsvapor stream supplied to the bottom ofBcolumn C-1

L liquidvaporV

T liquid stream supplied to the top of columnC-2

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