Comparison of Dynamic and Static Performances of a Quaternary DistillationSequence

Gholamreza Baghmisheh, Mohammad Shahrokhi,* and Ramin Bozorgmehri

Department of Chemical & Petroleum Engineering, Sharif UniVersity of Technology, P.O. Box 11365-9465,Azadi AVe., Tehran, Iran

In this work, steady state and dynamic performances of quaternary distillation column sequences designedbased on steady state and dynamic cost functions have been investigated. To quantify the dynamic performance,product losses due to disturbances have been considered in the objective function. In addition, variations ofoperating costs such as utilities have been considered in the objective function. To separate a quaternarymixture into four products, 22 configurations have been used. It has been observed that the feed composition,disturbance frequency and magnitude affect the dynamic behavior strongly. To decrease the optimizationcomputational load, a scheme that provides a suboptimal result has been proposed. By performing simultaneousoptimization that requires much more computational time, it has been shown that the highest rankingconfigurations obtained by the proposed method are the same as those provided by simultaneous technique.The simulation results indicate that there is no clear pattern for configuration ranking based on column sequencespecifications.

1. Introduction

Design of a continuous chemical process is usually carriedout under steady state conditions for a given operating range,assuming that a control system can be designed to maintain theprocess at the desired operating level and within the designconstrains. However, favorable process static characteristicscould limit the effectiveness of a control system, leading to acondition that design specifications cannot meet. Usually,alternative designs are judged on the basis of economic aspectsalone, without taking controllability and dynamic behavior intoaccount. This may lead to elimination of easily controlled, butslightly less economical alternatives in favor of slightly moreeconomical designs that may be extremely difficult to control.1,2

Many papers have been proposed for finding the optimumdesign of a distillation column sequence using the superstructureapproach. Mixed-integer linear programming (MILP), mixed-integer nonlinear programming (MINLP), and genetic algorithmare the most popular methods that have been utilized foroptimization purposes. The MILP and MINLP techniquesrequire a process model and are time-consuming. Also usingthe rigorous model may lead to a large nonconvex problem.The genetic algorithm is the most recommended technique forthis purpose.3-7

Despite the interaction and conflict between design andcontrol, complex plants have been often operated reasonablywell. These plants usually have many surge tanks that rejectand minimize operation dynamic interactions. Nowadays buffersurge tanks have been utilized to isolate units of a moderncomplex plant and prevent total shutdown. Dynamic behaviorof a middle-vessel continuous distillation column (MVCC) hasbeen studied by Barolo and Papini,8 Phimister and Seider,9

Faanes and Skogestad,10 Bezzo and Barolo,11 and Loperena etal.12

As Luyben et al. have mentioned, process design impactsthe controllability far more than control algorithms do and designon the basis of steady-state economics is risky, because theresulting plants are often difficult to control (i.e., inflexible, with

poor disturbance-rejection properties), leading to off-specproducts, excessive use of fuel, and associated profitabilitylosses.13 Some heuristics and recommendations have beenreported in the literature regarding design and control effects,control philosophy, controller design, and tuning. Some of themhave been reported by Luyben et al.13 and have been used inprocess design.14 But these rules are case dependent; therefore,rigorous analysis should be carried out to select the bestalternative.

To analyze controllability and dynamic resiliency of adeveloped process, three vital steps must be considered. Thesesteps are selecting a control structure, tuning controller param-eters, and evaluating dynamic behavior. Evaluation of dynamicbehavior based on a suitable objective function and designinga test procedure are the most critical steps. Since static anddynamic behaviors of the column sequence can affect the totalcost, multiobjective optimization approach can be used. In thispaper, steady state and dynamic costs are incorporated in oneobjective function, and the best alternative has been found byminimizing this objective function. To quantify the dynamicperformance, products losses due to disturbances have beenconsidered in the objective function.

2. Problem Statement

As mentioned before, traditionally, design of a process controlsystem is postponed until the process design is completed.Nowadays, it is broadly accepted that this is not a desirablesituation since this sequential design approach can lead toprocesses that are difficult to control. As a consequence, differentways to take controllability issues into account in the processdesign stage have been developed and described in the litera-ture.15 These methods can be classified into two groups: (i)methods which are able to screen alternative designs forcontrollability and (ii) methods which integrate process designand the control systems.16,17

In the first approach, controllability of alternative designs istested such that alternatives that might have acceptable steady-state economics but poor control performances are rejected inthe early stage of design. Controllability is quantified using

* To whom correspondence should be addressed. E-mail address:shahrokhi@sharif.edu.

Ind. Eng. Chem. Res. 2010, 49, 6135–6143 6135

10.1021/ie100169p 2010 American Chemical SocietyPublished on Web 06/03/2010

indices like the relative gain array (RGA) and singular valuedecomposition (SVD).16-19

In the second approach, static and dynamic characteristicsof a process are considered simultaneously in screening designalternatives. In this paper, 22 configurations have been consid-ered for separation of a quaternary mixture. If the first approachis used, the best selected steady-state sequence may have a poorcontrollability performance. Also if the simultaneous approachis used, screening different schemes may be very time-consuming. In the latter approach, the dynamic issues such ascontroller paring, controller tuning, and performance testevaluation (using load rejection criteria or set-point tracking)must be taken into account in addition to process design.

Despite the fact that this approach takes into account thedynamic performance of the process, the criterion used indynamic performance evaluation has been solely calculatedbased on the deviation of the controlled variables from theircorresponding set points (e.g., integral of square error, integralof absolute error, etc.). However, it should be noted that sucha criterion does not take into account the change in operationalcost of the whole process due to the changes in loads or setpoints of the controllers

To decrease limitations of existing methods, an approach isproposed that compares alternative designs based on an objectivefunction that includes steady state and dynamic costs. Toquantify the dynamic performance, integral of square deviationsof desired specifications such as products purities has been takenas an objective function.19-23 In this work to quantify thedynamic performance of different alternatives, an objectivefunction which includes costs due to off-spec products andutilities has been considered.

3. Distillation Column Sequences and AlternativeEvaluation under Steady State Conditions

In this paper, separation of a quaternary mixture using asimple distillation column without heat integration has beeninvestigated. According to the Douglas24 onion model meth-odology, the steady state distillation train is built and designedby means of shortcut or rigorous techniques. Having performedsteady-state analysis, alternative schemes are ranked accordingto their steady-state costs. To separate a quaternary mixture intofour products with at least 99.5 wt % purities, 22 configurationshave been used. These configurations have been developed togenerate the distinct thermally coupled distillation sequences.25,26

Typically, there are two ways to perform a separation for anonazeotropic multicomponent mixture: the sharp splits and thesloppy splits. A sharp split takes place when the two keycomponents are adjacent and each component in the feed appearsin a significant amount only in one of the two products. A sloppysplit occurs when the two key components are nonadjacent, andthere is at least one middle component distributed between thetop and bottom products.

In total, six first splits are identified that include three sharpsplits, two asymmetric sloppy splits, and one symmetric sloppysplit. Table 1 presents all of the 22 functionally distinctseparation sequences for quaternary mixtures. In this table, theunderline is used to indicate the distributed middle keycomponents; i.e., ABCD means that a sloppy split is performedfor the submixtures, with the two middle components B and Cdistributed in top (ABC) and bottom (BCD) products.

Among the 22 distinct separation sequences, there are 5sequences (1, 2, 4, 5, and 6) that contain a minimum numberof three individual splits; they formulate the subspace of thewell-known simple column sequences with only sharp splits.There are seven sequences (3, 7, 8, 9, 11, 14, and 15) with fourindividual splits; each of them includes only one sloppy split.There are seven sequences (10, 13, 14, 16, 17, 19, and 21) withfive individual splits. Sequences 10, 13, 14, and 17 include twosloppy splits, and the remaining sequences include only onesymmetric sloppy split. There are three sequences (18, 20, and22) containing the maximum number of six individual splits.The sequence 18 includes all sloppy splits for the submixtureswith three or more components.

To select the best steady state alternative, total annual cost(TAC) with plant lifetime of 10 years has been calculated.

3.1. Steady-State Design Procedure. To design a steadystate scheme, two approaches have been used: a shortcut methodand a rigorous technique. In the shortcut method, first theminimum reflux ratio (Rmin) and minimum number of trays(Nmin) are estimated.27,28 The number of equilibrium stages (N)is obtained using the Erbar-Maddox29 graphic method. Theactual reflux ratio (R) is set to 1.2Rmin. Feed tray location hasbeen determined using the Kirkbride30 method. The pressuredrop for a single tray is obtained based on the heuristics rule(0.1 psi/tray).31 The feed thermal condition has been consideredas a decision variable and is optimized based on an objectivefunction.

The HYSYS process simulator has been applied for all casestudies. After “N” has been calculated, “R” has been recalcu-lated. In many cases the recalculated R was significantlydifferent from its initial value. To meet the desired productcompositions, two design variables of each column in thesequence have been specified. These variables can be chosenfrom bottom product rate, reflux ratio, boilup ratio, and top orbottom composition.

Our preliminary investigation results indicate that, if thecalculated R and N from the shortcut method are used, the resultscan have significant errors for some case studies.

In the rigorous design procedure, the parameters obtained viathe shortcut method are used as initial guesses for optimizingthe objective function. The objective function is the TAC,and the decision variables are

Table 1. Different Configurations of 22 Separation Sequences

no. of sequences separation sequence no. of sequences separation sequences

1 A/BCD f B/CD f C/D 14 ABCD f AB/C f A/B f C/D2 A/BCD f BC/D f B/C 13 ABCD f ABC f A/B f B/C f C/D3 A/BCD f BCD f B/C f C/D 14 ABCD f A/BC f BCD f B/C f C/D4 ABC/D f AB/C f A/B 15 ABCD f A/BC f BC/D f B/C5 ABC/D f A/BC f B/C 16 ABCD f AB/C f B/CD f A/B f C/D6 AB/CD f A/B f C/D 17 ABCD f ABC f BC/D f A/B f B/C7 ABC/D f ABC f A/B f B/C 18 ABCD f ABC f BCD f A/B f B/C f C/D8 ABCD f B/CD f A/B f C/D 19 ABCD f ABC f B/CD f A/B f C/D9 ABCD f BC/D f A/B f B/C 20 ABCD f ABC f B/CD f A/B f B/C f C/D10 ABCD f BCD f A/B f B/C f C/D 21 ABCD f AB/C f BCD f A/B f B/C11 ABCD f A/BC f B/C f C/D 22 ABCD f AB/C f BCD f A/B f B/C f C/D

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• number of theoretical trays• feed tray location• feed quality3.2. Synthesis Methodology. A superstructure configuration

has been built to generate 22 alternatives for the separation ofa four-component mixture with a simple column sequence. Thisstructure can be used for mixtures having more components.Generating a superstructure is straightforward using the statetask network (Figure 1) scheme proposed by Yeomans andGrossmann.32

Figure 2 shows the base unit of the superstructure. This unithas been built and saved as a template in the HYSYSenvironment. To have a realistic model, a condenser, heatexchanger, vessel, pump, and valve are used in HYSYS insteadof the shortcut method. To implement this design procedure,an application was developed by Visual Basic (VB). In VB,this application supports the ActiveX protocol to swap theinformation among HYSYS, Matlab, Excel, and the mainapplication which contains a cost estimation module, steady-state optimization engine, dynamic pressure-flow module, and

process identification unit (Figure 3). HYSYS and Matlabautomation have been used for model identification and control-ler tuning. The VB program contains all equipment costestimation modules and reports and saves the detailed calculationin the Excel files. Figure 3 shows such a configurationschematically.

To rank different alternatives the following steps are taken:(a) Using the superstructure scheme, different alternatives

are generated(b) For each alternative, the corresponding HYSYS flowsheet

is built.(c) The optimum steady state design of various alternatives

is obtained via HYSYS and the optimization module.(d) Using the dynamic pressure-flow module, the dynamic

model for each alternative is built, and through theidentification unit, a process model is obtained.

(e) The initial controller settings of each column are obtainedby the HYSYS autotuner and are optimized by MATLABsoftware using the process model.

Figure 1. State task network superstructure for a 4-component mixture.

Figure 2. Base unit with the applied control structure.

Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010 6137

(f) Having the optimal controller settings, various alternativesare ranked based on the proposed objective function.

4. Dynamic Simulation and Alternative Resiliency

4.1. Dynamic Model Construction. Dynamic simulationsof alternatives are carried out using the HYSYS software. Toconsider the pressure-flow concept in dynamic simulation whentransferring to dynamic mode, extra valves and pumps (Figure2) between equipment have been utilized. Pressure drop in thevalves and pressure rise in the pumps have been set, based onthe pressure-flow concept. The expert class prepared in VBhas been used to implement the pressure flow setting in HYSYS.The prepared program contains valve, vessel, pump, tray, andheat exchanger sizing modules. Also the following assumptionshave been made in dynamic simulation modeling:

• For all pumps, a template centrifugal pump curve charac-teristic with a usual revolutions per minute has been used.

• Equal percentage valves with 60% opening at the normaloperating flow rate have been considered for control valves.

• Condenser holdup is neglected compared to reflux drumholdup; reboiler holdup is incorporated in column sump;pipe holdup is neglected.

• Liquid residence time of vessels is considered to be 15 min,and the normal operating level is set to 50%. Also, thecolumns sump liquid residence time has been set to 20 min.

• Tray spacing is 2 ft; the weir height is set to 2 in.; the traydowncomer area to total tray area is set to 10%. These rulesof thumb settings are based on Ludwig’s31 recommendations.

• Pressure drop in the control valves is set to 2 bar and inthe heat exchangers to 0.5 bar.

The following control philosophy has been used in this study:Control of column top pressure was carried out by manipulat-

ing the cooling water flow rate (Figure 2).The reflux drum level has been controlled by the distillate

flow rate, and the bottom flow rate has been used to control thecolumn bottom sump level (Figure 2).

The main controlled variables are top and bottom composi-tions. The corresponding manipulated variables are the liquidreflux flow rate and vapor boilup, respectively, the so-calledLV configuration (Figure 2). This configuration is insensitiveto level tuning, but for the other configurations the level controltuning is very important.33 It is assumed that product composi-tions are measured without time delay.

Feed temperature is controlled by the suitable utility stream.4.2. Dynamic Plus Steady State Performance Index. To

quantify the dynamic performance, product losses due to

disturbances have been considered in the objective function. Inaddition, operating costs, such as utility cost, have been alsoincluded in the dynamic part of the objective function. The totalobjective function used for ranking the alternatives is givenbelow.

The steady state total annual cost has been defined by thefollowing equation:

where the fi, gi, and hi are functions reflecting the capital costof columns, heat exchangers, and vessels, respectively, obtainedby the method proposed by Guthrie.34 Furthermore, Qcold andQhot imply the condenser and reboiler duties. Also, Ccold andChot are the cooling water and steam utility costs. The rest ofvariables are defined in the Nomenclature.

The main disturbance in practice is variation of the feedcomposition, and this is considered to be the main load in thisstudy. The log sheet and data historian of 3 y of three units,aromatic fractionation and natural gas fractionation of the BandarImam Petrochemical Company (BIPC) and natural gas liquidsfractionation of the South Pars Gas Company (SPGC) have beenstudied. As mentioned above, the dominant identified distur-bances were variations of feed composition.

In the present work, variation of the feed flow rate has beenalso studied for one case.

The other disturbances such as failures of cooling water, thesteam and power supplier system, and instrument air have beenignored in this study. Type, magnitude, and frequency of theload can change the value of the performance index, andtherefore, they should be fixed. Two methods have been usedto account for product losses (off-spec products). In the firstapproach which is used for high purity products, productcompositions are measured online and product streams areswitched to off-spec tanks when composition falls below the

Figure 3. Application structure.

objective function ) steady state total annual cost +off-spec and operating costs due to disturbances (1)

steady state total annual cost )

[ ∑i)1

no._of_columns

fi(NC, DC, PC, GC,S&T, HC, ...) +

∑i)1

no._of_heat_exchangers

gi(AHX, PHX, GHX,S&T, ...)] +

∑i)1

no._of_vessels

hi(HV, DV, PV, GV, ...)]/lifetime + (CcoldQcold +

ChotQhot) (2)

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desired value. In the second approach, switching to off-spectanks is based on offline measurements which are performedtwo or three times per day. This strategy can be used for lowpurity products. In this paper, for the high purity product case,an online analyzing approach has been utilized. But for the lowpurity product case, the off-line approach has been used. In theoff-line approach, an intermediate tank with 8 h residence timefor each product has been considered. If the composition of themixture in the off-spec tank fulfills the quality requirement ofthe products after 8 h, the tank content is transferred to themonthly or weekly main product tanks; otherwise, their contentsare transferred to an off-spec tank or returned to the feed tanksfor reuse. For the low purity case, a purity of 97.5 wt % hasbeen considered.

In this study, feed composition is assumed to change stepwisearound its nominal value with magnitudes of (10%-(15% ofthe nominal value. Frequencies of composition variations havebeen assumed to be 2, 4, 8, 12, 18, and 24 times/y for lowfrequency loads and 82, 110, 165, and 330 times/y for highfrequency loads.

At the first step, the initial values of single loop controllertuning parameters have been obtained using an autotuningvariation (ATV) test.35 To consider the loop interaction, thecontroller detuning technique proposed by Tyreus and Luyben36

has been used. In this tuning method, the controller parametersare modified according to the following formulas:

where KCATV and τC

ATV are ATV controller settings, FT is thedetuning factor, and KC and τC are recommended controllersettings. In the second step, each single distillation column hasbeen modeled according to the following equation:

where the Qi j are the transfer functions (second-order modelplus lag) relating top and bottom compositions to reflux andreboiler steam flow rates. Distillation towers usually have well-behaved open-loop characteristics. The open-loop eigenvaluesare negative and real. This results in open-loop dynamics thatdecay exponentially without oscillation. Therefore the second-order plus lag models are suitable.

Composition controller settings have been optimized basedon the process model using the Matlab software environmentby object link embedding (OLE) automation. The integral ofthe absolute errors (IAE) has been selected as the objectivefunction for loop tuning in each column. A series of set-pointchanges have been applied to the model for optimizationpurposes. Using the initial controller settings obtained from theATV method decreased the optimization runtime considerably.According to the described procedure, controllers’ settings foreach column have been obtained.

The final controller tunings of trains, containing 3, 4, 5, or 6distillation columns, may be obtained by three different ap-proaches. In the first approach, all composition control loopsare tuned simultaneously using an initial setting obtained foreach single column. In the second approach, one detuning factoris used for all columns and its optimal value is found throughoptimizing the objective function. In the third approach, eachcolumn has its own detuning factor obtained through theoptimization. In all approaches, controller settings are obtainedbased on minimization of the performance index given by eq1. In this study, the third approach has been used. Dynamiclosses have been calculated through dynamic simulation runsfor a specified period of time considering an external disturbanceacting on the system. To make the results independent ofdisturbance direction, a combination of eight random distur-bances has been used.

5. Results and Discussion

5.1. Case Study. Two sets of four-component mixtures havebeen considered. One set is an aromatics mixture (benzene,toluene, o-xylene, and biphenyl), and the other one is ahydrocarbon mixture (n-pentane, n-hexane, n-heptane, andn-octane). To evaluate the effect of feed composition, differentmixtures have been tested (Table 2).

5.2. Steady-State Optimization. The steady-state results forcase 7 are shown in the Table 3. This case reflects the operatingcondition of aromatic plant in Bandar Imam PetrochemicalCompany (BIPC) when the hydrodealkylation (HDA) unit isnot in service and toluene is one of the final products. Table 3shows that if the rigorous optimization approach is used, thebest configuration will be sequence 8, but if the sequences arebuilt by the shortcut method the best case will be sequence 1.Differences of TAC of the shortcut and optimization methodshave also been presented. As can be seen, the differences arenoticeable. In most case studies, the best case of the shortcutand optimization method are the same, but this cannot be

Table 2. Feed Specifications of the Case Studies

feed mole fractions

feed condition case no. benzene (A) toluene (B) o-xylene (C) biphenyl (D)

aromatic feed flow rate ) 1900 kmol/h case 1 0.40 0.30 0.20 0.10inlet temperature ) 30 °C case 2 0.10 0.20 0.30 0.40inlet pressure ) 1 bar case 3 0.10 0.10 0.40 0.40product purity ) 99.5 wt % case 4 0.30 0.30 0.30 0.10

case 5 0.17 0.44 0.22 0.17case 6 0.25 0.25 0.25 0.25case 7 0.33 0.36 0.16 0.15case 8 0.39 0.24 0.23 0.14

feed mole fractions

case no. n-pentane (A) n-hexane (B) n-heptane (C) n-octane (D)

paraffinic feed flow rate ) 1900 kmol/h case 9 0.10 0.10 0.40 0.40inlet temperature ) 30 °C case 10 0.10 0.20 0.30 0.40inlet pressure ) 1 bar case 11 0.40 0.30 0.20 0.10product purity ) 98.5 wt % case 12 0.30 0.30 0.30 0.10

KC ) KCATV/FT (3)

τC ) τCATVFT (4)

[topcomp

bottomcomp ] ) [Q11 Q12

Q21 Q22 ][refluxsteam ] (5)

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considered as a rule for all cases. Table 4 shows the steadystate ranking of 22 configurations for 8 case studies, obtainedby rigorous optimization method. As can be seen, the highestranking sequence is changed by changing the feed composition.

From the sequence rankings obtained in these case studies,the following results can be concluded:

(1) None of the sequences containing more than fourdistillation columns is the best case, i.e., sequences thathave more than one sloppy distillation column are not inthe top ranks.

(2) Having more than one intermediate component, it isimpossible or very difficult to predict the ranking ofsequences heuristically.

(3) Despite the extra distillation column, the sequences withone sloppy distillation column can be the best ones.

5.3. Dynamic Evaluation. To evaluate dynamic perfor-mances of different column trains, dynamic simulations of thesesequences considering feed composition variations have beenperformed. As mentioned in section 3.2, square wave distur-bances with different frequencies have been used. To make thedynamical results independent of disturbance direction, theaverage result obtained from eight random disturbances has beenused instead of a single random disturbance. Figure 4 showssuch disturbances for case study 7.

Dynamic simulations have been done for 14 cases for 2 feedcomponent types. For eight cases with aromatic feed the on-line off-spec detection and for four cases with paraffinic feedthe off-line off-spec tank strategy have been utilized. The results(Table 5) indicate that, in general, the steady state of alternativesranking is different from the dynamic one, but there are somecases where the best alternatives are the same.

As can be seen from Table 5, for case 3, alternatives rankingis effectively dependent on the load frequency. For example,case 11 whose steady-state rank is 13, has been promoted tothe third rank for high frequency loads. Also it is observed thatconfiguration 21 which has the second rank for the loadfrequency of 2-8, has fallen to low rank sequences for higherfrequencies. In this case study, the best case for frequenciesbetween 2 and 12 times per year is the sequence 5 and forfrequencies above 18 is the sequence 1.

Simulation results for case 4 (not shown) indicate that thefirst three high ranking configurations are independent of load

Table 3. Comparison of Estimated Fixed Capital and Operating Costs for 22 Distillation Sequences under Steady-State Conditions for Case 7

no. ofsequences

fixed capitalinvestment ($)

operatingcost ($/y)

total annualcost ($/y) withoptimization

total annualcost ($/y) with

shortcut method

relative differencesof shortcut and

optimization methods

relative differencesof sequences from

the best case(optimization method)

relative differencesof sequences from

the best case(shortcut method)

1 4,966,616 3,276,779 3,773,440 4,307,398 -14 0.1 0.02 6,473,676 3,406,352 4,053,720 4,414,820 -9 7.5 2.53 5,660,030 3,887,889 4,453,892 4,991,579 -14 18.1 15.94 7,600,960 3,709,182 4,469,278 4,959,099 -11 18.5 15.15 7,314,533 3,392,679 4,143,932 4,554,623 -10 9.4 5.76 5,432,070 3,353,438 3,896,645 4,500,658 -16 3.3 4.57 7,581,844 3,660,032 4,418,217 5,092,232 -15 17.2 18.28 5,920,587 3,178,534 3,770,593 4,361,595 -16 0.0 1.39 6,660,272 3,223,111 3,889,139 4,463,428 -15 3.1 3.6

10 6,422,635 3,542,799 4,185,063 4,803,541 -15 11.0 11.511 6,579,764 4,204,992 4,862,969 5,335,922 -10 29.0 23.914 6,927,754 4,523,405 5,216,180 5,818,454 -14 38.3 35.113 7,075,383 4,304,089 5,011,627 5,615,314 -14 32.9 30.414 6,613,686 3,669,750 4,331,119 4,808,303 -11 14.9 11.615 6,769,152 3,371,352 4,048,267 4,453,262 -10 7.4 3.416 7,344,328 3,734,268 4,468,701 4,961,637 -11 18.5 15.217 7,579,209 3,559,185 4,317,106 4,722,199 -9 14.5 9.618 7,397,637 3,938,604 4,678,368 5,187,119 -11 24.1 20.419 6,769,527 3,360,721 4,037,673 4,394,483 -9 7.1 2.020 7,447,776 3,596,154 4,340,932 4,891,408 -13 15.1 13.621 7,905,770 3,704,530 4,495,108 5,092,267 -13 19.2 18.222 7,488,257 3,707,793 4,456,619 4,856,804 -9 18.2 14.8

Table 4. Steady-State Ranking of 22 Configurations for Eight CaseStudies

Figure 4. Feed composition disturbances (case 7).

6140 Ind. Eng. Chem. Res., Vol. 49, No. 13, 2010

frequency. For case 2 (not shown), sequence 5 is independentof load frequency and it is the best scheme for all loadfrequencies except the frequency 330 times/y, but in general,alternatives ranking is changed as load frequency changes.

For the offline composition measurement strategy, case 10has been considered. To investigate the load type, the feed flowrate has been chosen as the main disturbance. As mentionedbefore, the acceptable product purity for this case is 97.5%.

The questions which arise are how high above the desiredproduct purity should the composition set point be chosen andwhat is its optimum value. To find the optimum compositionset point, the total costs (steady state plus dynamic) arecalculated for different values of the composition set point.Having these data, the total cost is plotted versus compositionset point, and the set point corresponding to the minimum valueof the total cost is selected as the optimum composition set point.It should be noted that the optimum set point also depends onthe load frequency. For the system under consideration, for thelow frequency loads the optimum set point is 98.5% while it is99.0% for the high frequency loads.

Table 6 illustrates the results of case 10. As can be seen forthis case, sequence 11 is the best alternative for all frequencies.

In the Table 7 the highest ranking configurations of thearomatic component set have been shown for two disturbanceswith different amplitudes ((10% and ( 15%) at all frequencies.As shown in this table, configurations 1 (known as the directsequence) and 5 (known as the indirect sequence) are often thebest alternatives.

From the simulation studies, the following results can beobtained:

(1) The heuristic screening rules that can be used for steadystate design are not applicable for the dynamic case.

(2) Ranking of distillation configurations is effectivelychanged by changing the load frequency or magnitude.

(3) Configurations that contained more than five distillationcolumns are never the best alternative.

(4) In some cases, the best steady configuration has a poordynamic performance.

(5) Configuration 1 and 5 are often the best alternatives.(6) Products prices change the sequences ranking effectively.

6. Simultaneous Optimization Approach

In the previous section, the steady state and dynamicperformance evaluations have been carried out separately. Forthe steady state case, the total annual cost is optimized versusfeed quality, feed tray location, and number of trays. Fordynamic case, using the optimized steady state model, a dynamicperformance index is optimized using controller settings asdecision variables. To check the accuracy of this strategy, asimultaneous approach that optimizes the dynamic performanceindex with respect to all aforementioned decision variables hasbeen applied to two cases. Using genetic algorithm, some topranking sequences obtained by the proposed scheme have beenoptimized based on this approach. Each column has sevendecision variables namely feed tray location, feed quality,number of trays, and two proportional-integral (PI) controllerssetting. For each decision variable reflecting a design variable,4 bits and, for controllers’ settings, 6 bits have been allocatedin the binary chromosome. Therefore chromosomes’ length for

Table 5. Alternatives Ranking for Loads with Different Frequenciesfor Case 3

Table 6. Alternatives Ranking for Loads with Different Frequenciesfor Case 10

Table 7. Alternatives Ranking of First Component Set with Different Species Composition for Disturbance Amplitudes of (10% and (15%

Steady State Plus Dynamic Ranking

load amplitude ) 10% load amplitude ) 15%

casenumber

steady stateranking

low frequencyload (times/y)

high frequencyload (times/y)

low frequencyload (times/y)

high frequencyload (times/y)

2 4 8 14 18 24 82 110 165 330 2 4 8 14 18 24 82 110 165 3301 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 22 4 5 5 5 5 5 5 5 5 5 11 5 5 5 5 5 5 5 5 5 113 4 5 5 5 5 1 1 1 1 1 1 5 5 5 5 1 1 1 1 1 14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 35 8 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 1 1 1 46 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 2 2 27 8 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 28 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2

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trains with 3, 4, 5, and 6 columns will be 108, 144, 188, and216 bits, respectively. The initial values of decision variableshave been set to those obtained by the proposed approach. Theresult of sequences ranking for case 6, using the simultaneousoptimization technique and the proposed method, is presentedin Table 8. As can be seen for the high frequency loads, all topsix sequences are the same for the two approaches, and for lowfrequency loads, the differences are minor.

7. Conclusions

In this work, optimization of a quaternary mixture separa-tion using simple distillation sequences has been considered.In the first step, the total cost has been minimized understeady-state conditiona. Since process loads such as feedcomposition variations can affect the system performance,the transient behavior should be also taken into account.Therefore in the second step, optimization is carried out basedon a dynamic performance index that also includes transientbehavior of the sequence. To decrease the optimizationcomputational load, a suboptimal strategy has been proposedthat uses steady state optimal results and only considers thecontrollers setting as decision variables. To check theaccuracy of proposed approach (onion optimization strategy),the results are compared with those obtained from simulta-neous optimization approach. It has been shown that the firstranking schemes are the same for both approaches for twocase studies, but the computational time required for thesimultaneous approach is approximately 15 times more thanthat of the proposed scheme. Therefore the proposed sub-optimal technique can be used with a relatively highconfidence, for choosing the best distillation column sequencewith much less computational load.

Nomenclature

A ) areabottomcomp ) column bottom compositionC ) columnD ) diameterFT ) detuning factorG ) genusH ) heightHX) heat exchangerKC

ATV ) autotuning variation controller gainKC ) controller gainN ) number of stages

P ) pressureQi j ) transfer functions relating top and bottom compositions to

reflux and reboiler steam flow ratestopcomp ) column top compositionV ) vesselτC ) controller integral timeτC

ATV) autotuning variation controller integral timeS&T ) shell and tube or tray

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ReceiVed for reView January 25, 2010ReVised manuscript receiVed April 11, 2010

Accepted May 20, 2010

IE100169P

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