Integrated Distillation System With Prefractio

8/10/2019 Integrated Distillation System With Prefractio

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INTERACTION BETWEEN DESIGN AND CONTROLOF A HEAT-INTEGRATED DISTILLATION SYSTEM

WITH PREFRACTIONATORC. S. BILDEA and A. C. DIMIAN

Department of Chemical Engineerin g, University of Amsterdam, The Netherlands

This paper analyses the relationship between the design and control of a heat-integrateddistillation set-up consisting of a prefractionator and a side stream main column. Theseparation of a pentane-hexane-heptane mixture with moderate purity requirements

is considered. Both forward and reverse heat-integration schemes are investigated. Differentdesigns are possible, depending on the light/heavy split in the prefractionator and the heat-integration scheme. They are similar with respect to energy consumption, but very differentwith respect to dynamic behaviour. The differences are studied using frequency-dependentcontrollability analysis, as well as carrying out closed-loop simulation, in the presence of large feed composition disturbances. Thus, it is found that the forward heat-integration ismuch easier to control, using only temperature measurements. The low-cost design with asmall prefractionator has the best closed-loop performance. The reverse heat-integration canbe controlled only if a composition analyser of the side stream is available; a sharp light/heavysplit in the prefractionator gives better disturbance rejection. The superior dynamic behaviourof the forward heat-integration scheme was con rmed by the study of a high purity separationof the benzene-toluene-xylene mixture.

Keywords: integrated design and control; ternary separation; heat-integration;controllability analysis

INTRODUCTION

The direct and indirect sequences are well-known conven-tional con gurations for separation of ternary mixtures bydistillation. Due to the higher cost of energy during the lastdecade, there is an increased interest in alternative methods.They include heat integration 12 2 , thermal coupling 32 6 , andcomplex con gurations 72 8 . These alternatives have, forsome ranges of feed composition, lower energy consump-tion than the conventional con gurations. As an example 8 ,for a 25/50/25 benzene-toluene-xylene mixture, the pre-

fractionator/side-stream column (Figure 1) with reverse heatintegration and low operating pressure consumed 45% lessenergy than the direct sequence 8 .

The dynamics and control of these systems is asimportant as energy saving 92 15 . Ding and Luyben 15 studiedthe controllability of the prefractionator/side stream columnwith reverse heat integration. The control structure usedconcentration measurements and single-input single-output(SISO) loops, including split-range control. For the lowpurity separation, the system was found controllable.For the high-purity case, the system could handle onlysmall disturbances. However, they did not study the

controllability of the forward heat-integration arrange-ment. Moreover, the relationships between the design andcontrollability properties were not analysed.

The fact that the design of a process determines itscontrollability is well recognized 16 . However, no applica-tions to complex distillation con gurations are reported.

In the previous studies 92 15 , heuristic rules (endorsed byindustrial experience) were applied to obtain an approxi-mate design, which was later re ned by rigorous methods.Afterwards, the controllability analysis was performed.

For conventional distillation columns, there are fewdesign decisions to be taken and the design is almost estab-lished once the product purity is speci ed. However, moredecisions (for which no guidelines are available) are invol-ved in the design of complex con gurations. They willaffect the controllability properties, besides the energyconsumption, total annual cost or other economic index.

This work investigates the interaction between designand control of the heat integrated prefractionator/side-stream column con guration for ternary separation. Forthis arrangement, an important design decision refers tothe split between the light and heavy components to beperformed in the prefractionator. According to this, severaldesigns are possible. They are presented and discussedfor both the forward and reverse heat-integration arrange-ments. Multi-input multi-output (MIMO) controllabilityanalysis is performed based on linear models. For the par-ticular mixture considered in this work and forward heat-integration, the design with a small prefractionator performs

better. It has excellent controllability properties and goodcomposition control can be obtained using only temperaturemeasurements. The reverse heat-integrated alternative ismore interactive. In this case, good control can be achievedonly if at least one composition analyser is available.Controllability is improved if a sharp split between the light

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02638762/99/$10.00+0.00 Institution of Chemical Engineers

Trans IChemE, Vol 77, Part A, October 1999


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and heavy components is performed in the prefractionator.Finally, the performance of the proposed control structuresis evaluated by dynamic simulation.

Throughout this work, A, B and C will denote the light,intermediate and heavy components, respectively. For theparticular separation investigated, they are pentane, hexaneand heptane, respectively.

DESIGN OF THE PREFRACTIONATOR/SIDESTREAM COLUMN CONFIGURATION

The prefractionator/side stream column con gurationis presented in Figure 1. Typically, the design speci cationsare expressed as the purity of the product streams. Designdecisions refer to the range of operating pressures andthe quality of the separation to be performed in theprefractionator.

For each column, a pressure pro le is assumed, which isrelated to the heat-integration scheme. For forward heat-integration, heat transfer is possible when the distillate of

the prefractionator is hotter than the bottom of the secondcolumn. This can be achieved if the pressure in the pre-fractionator is high enough. If reverse heat-integration isof interest, the second column is the one to be operated athigh pressure. It is noted that the pressure pro le depends onthe design of the columns; hence, several design iterationsmay be necessary.

To design the prefractionator, the fractional recoveriesof the light and heavy components, F AB z AB, A / F ABC , A z ABC , A andF BC z BC ,C / F ABC z ABC ,C , respectively are speci ed (the rstand second subscripts denote the stream and component,respectively). A binary A/C separation is considered andthe Underwood-Fenske method used to nd the minimumre ux and minimum number of trays. Then the re ux ratioand the number of trays are chosen (for example 1 .23 Rminand 23 N min ). This gives an approximate design, due to thepresence of the intermediate component. Consequently, arigorous method is used to adjust the product and re uxow rates until the desired A/C separation is achieved. At

the same time, the top and bottom concentration of theintermediate component is obtained.

The main column may be treated as two pseudo-conventional sections. The mass balance equations givethe ow rates of the product streams. The controlling feed(the one requiring the largest re ux 17 ) is found and the re ux

ratio set accordingly. Then a short-cut method is used to ndan approximate design. Finally, a rigorous method is usedto re ne the number of trays, feed and side stream locations.

Depending on the speci ed recoveries for the light and

heavy components in the prefractionator, different designsare arrived at. Consider a 150 kmol/h equimolar ABC feed.Let the desired purity of the A, B and C products be 0.99,0.98 and 0.99, respectively. Assume that the B productshould contain equal amounts of A and C, i.e. 0.5 kmol/hr.I t i s noted that the entire A (or C) that leaves theprefractionator with the bottom (or top) stream will end inthe side stream of the main column. Consequently, themaximum am ount of A (or C) in the prefractionator bottom(top) is 0 .5 kmol h2 1 .

To design the prefractionator, several speci cationsare possible. Table 1 displays four design alternatives.In the rst one, a sharp A/C separation is performed inthe prefractionator. Alternatively (Design II), the quantitiesof light in bottoms and heavy in distillate are allowed tobe close to their maximum allowed values, and a sharpA/B and B/C split is required in the main column. Otheroptions investigated are: (III) high recovery of the heavycomponent, low recovery of the light component and (IV)low recovery of the heavy component, high recovery of the light component.

The alternatives have different operating parameters(re ux, condenser and reboiler duty, etc.) and columnssize (number of trays, diameter). In addition, differentcontrollability properties are expected.

HEAT INTEGRATION CONSIDERATIONS

The forward heat integration is now considered. Thesame considerations apply to the reverse heat-integration.

Usually, the heat-integration is attempted by combining

in one heat exchanger the condenser of the rst column andthe reboiler of the second column. In most of the cases, it isfound that the duties do not match. The rst solution is toinstall auxiliary equipment. If there is a heat surplus(Q c1 > Qw2), a condenser is added to the rst column. If thereis a heat de ciency (Q c1 < Qw2 ), a reboiler is added to thesecond column. In both cases, the capital cost increasesbecause of the additional equipment, but one variable (duty)is preserved to be manipulated in the control structure.

An alternative solution is to change the columns designto match the duties. For heat surplus, we may increase thesecond column re ux and decrease the number of trays. Thisrequires higher reboiler duty. Because the additional dutyis obtained by heat integration, there is no penalty in termsof energy consumption. Note that the option of decreasingQ c1 may not work due to the minimum-re ux constraint. If there is a heat de ciency, Qc1 may be modi ed by increas-ing the re ux in the rst column. The number of trays is

598 BILDEA and DIMIAN


Figure 1. Prefractionator/side stream column con guration for ternaryseparation.

Table 1. Possible speci cations for the A/C split in the prefractionator. Thefeed consists of 150 kmol h 2 1 equimolar ABC mixture. For product purityA: 99%; B: 98%; C : 99%, the maximum ow rate of C in distillate and A in

bottom is 0 .5 kmol h2 1 .

Design I Design I I Design I II Design IV

Distillate (kmol h 2 1) )A 49.975 49.525 49.525 49.975C 0.025 0.475 0.025 0.475

Bottom (kmol h 2 1 )A 0.025 0.475 0.475 0.025C 49.975 49.525 49.975 49.525


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decreased, but the reboiler duty ( Qw1) must be increased.Because this does not come by heat integration, there is apenalty in terms of energy consumption. As in the previouscase, it is noted that decreasing Q w2 may not always work.

The systems investigated in this work are based on theperfect-match alternative. In this way one manipulatedvariable (the duty of the additional condenser or reboiler) ismissing. The inclusion of the auxiliary heat exchangershould lead to better controllability. However, the improve-ment may be minimal because only a small duty changewill be available.

Additional energy can be recovered if various hot streamsare used to preheat the prefractionator or main columnfeed streams. Because this article concentrates on the con-trollability analysis, the owsheet only includes heatintegration between the feed and product streams.

DESIGN RESULTS

The general design speci cations were:

(a) Feed: 150 kmol h 2 1 , equimolar pentane/hexane/heptanemixture, at 25 C and 1 bar.(b) Product speci cation: pentane, 99%; hexane, 98%,

impuri ed with equal amounts of pentane and heptane;heptane, 99%; 25 C and 1 bar.

The following assumptions were made during the design:ideal vapour-liquid equilibrium; 100% tray ef ciency;saturated liquid re ux; columns feed: saturated liquid,0.1 bar pressure difference between the feed and the feedtray; 10 C pinch temperature difference for feed pre-heating; 10 temperature difference in heat-integratedreboiler/condenser; pressure drops: 0.01 bar/tray, 0.05 barin condenser; residence times of 5 min in re ux drumsand 10 min in reboilers; heat transfer coef cients of 500 kcal m 2 2 h2 1 K 2 1 in the heat exchangers.

Steady state design was performed in ASPEN PLUS 19 ,using RADFRAC

Y

models for the distillation columns.When pinch analysis was applied, the feed preheating lay-out presented in Figures 2 and 3 was obtained. Table 2

summarizes the results of column sizing. Table 3 presentsthe ow rate and composition of intermediate streams.

CONTROLLABILITY ANALYSIS

The main control objective is to maintain the productsconcentration at their setpoints. The composition of the feed

599INTERACTION BETWEEN DESIGN & CONTROL OF A HEAT-INTEGRATED DISTILLATION SYSTEM


Figure 2. Prefractionator/side stream column w ith forward heat integration.Figure 3. Prefractionator/side stream column w ith reverse heat integration.

Table 2. Results of the design of prefractionator/side stream column. Numbers in bold represent heat supplied/removed by heat integration.

Design I Design II Design III Design IV

PF C PF C PF C PF C

Forward heat integrationre ux ratio 2.007 2.393 1.958 2.355 2.144 2.405 1.55 2.1668total stages 24 28 12 30 15 28 19 28feed tray (from top) 12 6, 20 6 6, 23 10 5, 20 8 6, 20side-stream tray 12 12 12 12top stage pressure (bar) 7.3 1 7.1 1 7.4 1 7.0 1reboiler duty, 10 6 kcal h 2 1 1.138 1.052 1.150 1.068 1.149 1.081 1.087 1.008condenser duty, 10 6 kcal h 2 1 1.052 1.052 1.068 1.046 1.081 1.061 1.008 0.988feed preheat duty, 10 6 kcal h 2 1 0.455 0.442 0.493 0.432total duty, 10 6 kcal h 2 1 1.593 1.592 1.642 1.440

Reverse heat integratio nre ux ratio 0.891 2.588 0.980 2.568 1.016 2.568 0.828 2.5total stages 20 34 10 35 15 35 15 35feed tray (from top) 10 7, 25 5 6, 26 9 6, 25 6 7, 26side-stream tray 15 15 15 15top stage pressure (bar) 1 5.95 1 5.4 1 5.6 1 5.75reboiler duty, 10 6 kcal h 2 1 0.911 1.558 0.922 1.542 0.916 1.543 0.895 1.539condenser duty, 10 6 kcal h 2 1 0.8578 0.911 0.8856 0.922 0.869 0.9160 0.853 0.895total duty, 10 6 kcal h 2 1 1.558 1.542 1.543 1.539


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stream is considered as a disturbance. Because distributedcontrol systems implementing PID controllers are wide-spread in the chemical industry, decentralised control isof interest. In addition, an attempt is made to develop thecontrol system using temperature measurements to inferthe concentrations because composition analysers areexpensive, require maintenance and have unfavourabledynamics. The temperature-control trays were selected to beclose enough to product withdrawal, but still sensitive.Typical temperature pro les in the side stream column arepresented in Figure 4.

It is noted that the performance of the control system canbe improved if concentration controllers are added. Theymay give, in a cascade manner, the setpoint of thetemperature control loops. Therefore, the analysis will tryto assess both disturbance rejection and set point trackingproperties of different system designs. To accomplishthis task, the Closed Loop Disturbance Gain (CLDG)and the Performance Relative Gain Array (PRGA), res-pectively are calculated. For an excellent presentationof the controllability analysis tools, see Skogestad andPostlethwaite 18 .

The controllability properties of Design I and III (and

Design II and IV) are similar, for both forward and reverseheat integration schemes. For this reason, the results forDesign I and II are presented comparatively.

SPEEDUP 20 was used to simulate the dynamic beha-viour of the different con gurations. In all cases, levelswere controlled by the P-only algorithm. The maximumallowed control error ( e max ) and the maximum controlaction ( umax ) were chosen as 50% of the steady state valueof the controlled and manipulated variables, respectively.The gain of the controllers was set to K p = umax / e max . Forpressure controllers, the maximum allowed control errorwas set to 0.1 bar and integral action ( T I = 0.2 h) was used.

Small adjustments of one of the operating parameters(reboiler duty) were necessary to get the same stationarystate as the one obtained by steady state simulation inASPEN PLUS . (The differences may be due to the localthermodynamic model used by SPEEDUP ).

SPEEDUP allows two different types of dynamic

simulation. In pressure-driven simulations, the pressure-drop across the valves determines the ow rates. In the ow-driven case, the ow rates are speci ed. The latteralternative assumes fast ow controllers and was used inthis study.

The state space linear model of the process was obtainedusing the CDI (Control Design Interface) facility offered



Table 3. Flow rate and composition of the streams leaving the prefractionator.

Design I Design II Design III Design IV

Forward heat integrationDistillate (kmol h 2 1 ) 66.5 67.54 64.84 73.20Pentane (%) 75.16 73.27 75.72 68.28Hexane (%) 24.81 25.91 24.21 31.17Heptane (%) 0.03 0.82 0.07 0.55

Bottoms (kmol h 2 1 ) 83.5 82.46 85.16 76.80Pentane (%) 0.02 0.62 1.07 0.03Hexane (%) 40.11 39.41 40.28 35.39Heptane (%) 59.86 59.97 58.65 64.58

Reverse heat integrat ionDistillate (kmol h 2 1 ) 68 66.75 65 69.5Pentane (%) 73.50 73.95 76.31 71.88Hexane (%) 26.46 25.22 23.46 27.43Heptane (%) 0.04 0.83 0.05 0.69

Bottoms (kmol h 2 1 ) 82 83.25 85 80.5Pentane (%) 0.03 0.77 0.47 0.05Hexane (%) 39.03 39.84 40.74 38.43Heptane (%) 60.94 59.39 58.79 61.52

Figure 4. Side stream column temperature pro les. E , feed; e , side stream;F , temperature control.


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by SPEEDUP :

dx( t )

dt = A x(t ) + B u( t ) + Bd d ( t )

y( t ) = C x( t ) + D u ( t ) + Dd d ( t )

e( t ) = r ( t ) 2 y( t )

(1)

x, u, d , y, e and r are the vectors of the state variables,

manipulated inputs, disturbances, controlled outputs, con-trol errors and setpoints, respectively. A, B, Bd , C , D and D d are matrices of appropriate dimensions. In order to obtainmeaningful controllability results, the inputs, disturbancesand outputs were scaled. In terms of scaled variables, thecontrol objective is to keep | e( t ) | < 1, using |u( t ) | < 1, whendisturbances |d ( t ) | < 1 affect the process.

In terms of transfer functions, the linear model of theprocess is given by:

y(s) = G(s) u(s) + G d (s) d (s) (2)where:

G (s) = C (sI 2 A)2 1

B + D (3a )G d (s) = C (sI 2 A)

2 1 Bd + Dd (3b )Linear models were used only for controllability analy-

sis. The full nonlinear model was used to evaluate theperformance of the control system.

Prefractionator/Side Stream Column withForward Integration

It is necessary to control four concentrations in theproduct streams: B in top, A and C in side stream, and B in

bottom. If inferential control is used, it is necessary tocontrol four temperatures in the main column, correspond-ing to the four sections. Additionally, large amounts of light/heavy component going in the bottom/distillate of theprefractionator make the separation in main column very

dif cult. Consequently, it may be desirable to control thecomposition of the streams leaving the prefractionator,controlling two temperatures in the stripping and rectifyingsections.

However, after closing the inventory control loops, onlyfour m anipulated variables are left: prefractionator re uxow rate and reboiler duty, main column re ux and side

draw ow rate. Moreover, dynamic considerations discou-

rage the use of prefractionator manipulated variables tocontrol temperatures in main column.

It was found that acceptable control could be achievedwhen only one temperature is controlled in the prefrac-tionator. Because the vapour dynamics are faster than theliquid dynamics, the re ux ratio is kept constant and onetemperature in the prefractionator bottom is controlled bythe reboiler duty. This loop gets the setpoint from acontroller regulating the temperature in the bottom of themain column. The main column re ux and side draw owrates are used to control temperature in the top and betweenthe side stream and the second feed, respectively. The

proposed control structure is presented in Figure 5.Table 4 gives the nominal values and scaling factorsfor the manipulated inputs, controlled outputs and distur-bances. The maximum change of the set point in tempera-ture control loops was assumed to be 5 C.

When decentralized control is of interest, the input-outputpairing may be evaluated using the Relative Gain Array,de ned as:

L = G (G 2 1 ) T (4)For both designs analysed, the chosen pairing correspond

to positive diagonal elements in the RGA matrix.

L I (0) =1.483 2 0.492 0.0090.019 1 .090 2 0.109

2 0.502 0 .402 1.100&?$ ?%



Figure 5. Forward heat-integration. Control structure. Standard notation is used. YC denotes ratio controller.


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L II (0) =2.308 2 1.326 0 .0190.082 1 .155 2 0 .163

2 1.316 1 .171 1 .145&?$ ?%Close-to-one diagonal elements denote little interaction.Small values in the RGA matrix also indicate that modeluncertainty is not a problem.The RGA_number, de ned as: RGA2 number = i I 2 L ( J v )i sum (5)has a small value and drops to zero for high frequency(Figure 6), showing that good control performance is

possible.

Design I is (slightly) less interactive. However, becauseinteractions can help the disturbance rejection, it cannot beconcluded that it is also better.

To analyse the disturbance rejection properties, theClosed Loop Disturbance Gain (CLDG) is calculated,

G d = G G2 1 G d (6)

where G is a matrix consisting of diagonal elements of G.Its elements, gdik , give the apparent gain of the k th

disturbance on the ith output under decentralized control.The necessary condition to avoid inputs constraints is:

| g ii | > | gdik | , ; k (7)Although in both cases the inputs are powerful enough to

reject disturbances (Figure 7), the second design is clearlybetter.

The ability of the system to follow set point changes canbe analysed using the Performance Relative Gain Array:

C = G G 2 1 (8)Its elements, c ij , show how the ith m anipulated input

must change when the jth setpoint is changed. More pre-cisely, input saturation is not a problem if:

| gii| > | c

ik |3 | R

k | , ; k , (9)

where Rk is the scaling factor of the k th setpoint.Figure 8 shows the frequency dependent PRGA for the

second design (the results for the rst design are similar). Toallow comparison with the loop gain, they are multipliedby the scaling factors for setpoint changes. The followingconclusions can be drawn:

f Fast change of the prefractionator bottom temperature( y I ) can not be achieved with the available manipulatedinputs (at high frequency, condition (9) is not satis ed fork = 1).f Input saturation may occur in the third loop (at highfrequency, condition (9) is not satis ed for i = 3).

However, there are few negative implications on thecontrollability properties. If temperatures are used toinfer concentration, fast setpoint tracking is not a concern.When composition controllers provide the setpoint for the



Table 4. Control of prefractionator/side stream column with forward heat integration. N ominal values and scalingfactors of outputs, inputs and disturbances.

Variable Nominal value Scaling factor

Design I y1 (PF stage 22 temperature, C) 167.3 1 y2 (C stage 4 temperature, C) 40.3 0.5 y3 (C stage 17 temperature, C) 81.8 0.5u1 (PF reboiler duty, 10 6 kcal h

2 1 ) 1.15 0.58u2 (C re ux ow rate, kmol h

2 1 ) 119.6 60

u3 (C side draw ow rate, kmol h2 1

) 50 25Design II y1 (PF stage 10 temperature, C) 161.2 1

y2 (C stage 4 temperature, C) 40.7 0.5 y3 (C stage 17 temperature, C) 78.6 0.5u1 (PF reboiler duty, 10 6 kcal h

2 1 ) 1.15 0.58u2 (C re ux ow rate, kmol h

2 1 ) 117.7 60u3 (C side draw ow rate, kmol h

2 1 ) 50 25

Disturbances Light in feed 0.333 0.1Intermediate in feed 0.333 0.1Heavy in feed 0.333 0.1

Figure 6. Forward heat-integration. RGA2 number . The RGA2 number hassmall values and drops to zero at high frequencies. Design I is lessinteractive.


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temperature control loops, the system will be almost allthe time close to the desired operating point; hence, onlysmall adjustments of the temperature setpoints will be

necessary.It is concluded that the prefractionator/side stream

column with forward heat integration has very good con-trollability properties. The practice of a small prefrac-tionator (doing just the necessary separation) is justi ed(at least for the case analysed) by its better disturbancerejection properties.

Prefractionator/Side Stream Column withReverse Integration

After closing the inventory control loops, four manipu-

lated variables are left for temperature (composition)control: prefractionator re ux ow rate, main columnre ux and side stream ow rate, and reboiler duty. Thereare six temperatures i t may be necessary to control,corresponding to the two sections of the prefractionatorand the four sections of the main column.

A control structure, similar to the one developed for theforward integration scheme, can be imagined (Figure 9).The re ux ow rate controls one temperature in the top

of the prefractionator (no input is available to control thetemperature in the bottom). In the main column, the re uxratio is kept constant and reboiler duty is used to control thebottom temperature. One temperature located either aboveor below the side stream is controlled by the side streamow rate. However, strong interactions make it unfeasible.

A typical steady state RGA matrix is:

L I (0) =1.144 0 .008 2 0.153

2 0.164 2 0.001 1.1650.019 0 .990 2 0.012

&?$ ?%The small values of the last two diagonal elements

show strong interaction. Moreover, their negative signmeans that the system is not decentralized integralcontrollable 18 , i.e. there exists no diagonal controller withintegral ac tion such that both of the following conditionsare true: (a) The c losed loop system is stable. (b) The gains



Figure 7. Forward heat-integration. Frequency dependent loop gain, gii (} ) and CLDG elements, gdik (f k = 1, k = 2,3 k = 3). Design II has betterdisturbance rejection properties.


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of any subset of loops can be arbitrarily reduced withoutcausing system instability.

Adding a fourth control loop, in which the main columnre ux ow rate controlled top temperature, did not help.Several other control structures were tried and it was found

that the control of the temperature in the middle of the maincolumn is responsible for the negative diagonal e lementsin the RGA matrix. Hence, if only temperatures are measured,the side stream ow cannot be the manipulated variable in acontrol loop. However, keeping the side stream constant isunacceptable, because any change of the feed ow rate of theintermediate component will result in impure products.

A successful control structure (Figure 10) can be devel-

oped if the ow rate of the side stream is used to controlits composition. The nominal and scaling values of thecontrolled outputs, manipulated inputs and disturbancesare presented in Table 5.

For both designs analysed, the chosen pairing correspondto positive diagonal RGA elements:

L I (0) =

1.824 0 .028 0 .001 2 0.853

2.758 11 .90 0.002 2 13 .66

0.036 1 .273 0 .445 2 0.755

2 3.618 2 12 .20 0.552 16 .27

&?????$

?????%

,

RGA2 number (0) = 63 .3.

L II (0)

1.265 2 1.625 2 0.05 1.364

2 0.283 23 .15 0.050 2 21 .92

2 0.052 2 18 .66 0.151 19 .56

0.068 2 1.868 0 .803 1.997&?????$

?????%

,

RGA2 number (0) = 90 .5For high frequencies, both RGA2 numbers drop to zero,

showing that control performance is possible.Figure 11 presents the closed loop disturbance gain.

The main difference between Design I and Design II is inthe disturbance rejection properties of the second controlloop (main column top temperaturere ux ow rate). Inthe rst case, all disturbances can be properly rejected.



Figure 8. Forward heat-integration, Design II. Frequency dependentloop gain gii (} ) and PRGA elements c ik Rk (f k = 1, k = 2, 3k = 3). Fast setpoint change may cause input saturation.

Figure 9. Reverse heat-integration. Unfeasible control structure using only temperature measurements. Standard notation is used. YC denotes ratio controller.


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In the second case, the maximum allowed change of there ux ow rate is not big enough to reject any of the threedisturbances. There are also some problems with the rstcontrol loop (Design II performs slightly better). However,this loop is not directly related to product purity.

The frequency-dependent PRGA is similar to the forwardheat-integration case. Input saturation may occur in somecontrol loops, if fast tracking is required for certain setpoints.However, as previously discussed, this will rarely be the case.

It is concluded that the controllability properties of theprefractionator/side stream con guration with reverseheat-integration are worse than for the forward integrationscheme. If only temperature m easurements are available, goodcontrol is impossible due to strong interactions. A feasiblecontrol structure, in which the composition of the side stream

is measured, was developed. The controllability properties arebetter if the prefractionator performs a sharp A/C split.

The authors acknowledge the anonymous reviewerwho suggested an option to ratio the side stream to there ux ow rate. The closed-loop performance of thisstrategy was investigated. It achieves good control of thetop and bottom purity. However, there is a rather large(about 2%) steady state error of the side stream composition.Hence, when tight control of the intermediate product purityis not required, this control scheme is also a good option.

CLOSED LOOP DYNAMIC SIMULATION

The performance of the proposed control con gura-tions was tested using the SPEEDUP nonlinear model. A



Figure 10. Reverse heat-integration. Feasible control structure using side stream composition analyzer.

Table 5. Control of prefractionator /side stream column w ith reverse heat integration. Nominal values and scalingfactors of outputs, inputs and disturbances.

Variable Nominal value Scaling factor

Design I y1 (PF stage 4 temperature, C) 56.7 1 y2 (C stage 4 temperature, C) 104.1 0.5 y3 (C side stream purity, C) 0.98 0.02 y4 (C stage 27 temperature, C) 168 0.5u1 (PF re ux ow rate, kmol h

2 1 ) 60.6 30.0u2 (C re ux ow rate, kmol kmol

2 1 ) 129.4 36u3 (C side draw ow rate, kmol h

2 1 ) 50 25u4 (C reboiler duty, 10 6 kcal h

2 1 ) 1.56 0.78

Design II y1 (PF stage 4 temperature, C) 61.2 1 y2 (C stage 3 temperature, C) 98.7 0.5 y3 (C side stream purity, C) 0.98 0.02 y4 (C stage 28 temperature, C) 165.6 0.5u1 (PF re ux ow rate, kmol h

2 1 ) 65.4 30u2 (C re ux ow rate, kmol h

2 1 ) 128.4 36

u3 (C side draw ow rate, kmol h2 1

) 50 25u4 (C reboiler duty, 10 6 kcal h2 1 ) 1.54 0.78

Disturbances Light in feed 0.333 0.1Intermediate in feed 0.333 0.1Heavy in feed 0.333 0.1


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typical run required about 80 seconds, on a Pentium II350 MHz computer.

Design I was analysed for the forward heat-integrationcon guration. For the reverse heat-integration arrangement,

Design II was investigated. A lag time of 1 min wasassumed for temperature sensors. A dead time of 3 minwas assumed for composition analysers. Control structurespresented in Figures 5 and 10 were used. The parametersof the PI controllers were found by trial-and-error. They arepresented in Table 6.

The control system performance, as deviation of theproducts concentration from the design values, is presentedin Figure 12. Disturbances D1 , D2 and D3 correspond toincreases of the feed concentration of pentane, hexane and

heptane, respectively. In each case, one concentration wasincreased from 33.3% to 43.3%, while the other two weredecreased to 28.3%.

If the magnitude of the disturbances is taken into account,the performance of the control system seems acceptable.The purity deviation is less than 0.5% for all streams. The



Figure 11. Reverse heat-integration. Frequency dependent loop gain, g ii (} ) and CLDG elements, g dik (f k = 1, k = 2,3 k = 3). In Design II, the secondmanipulated input is not strong enough to reject the disturbances.


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Table 6. Controller tuning.

K p T I

Forward heat integrationLoop 1 0.012 10 6 kcal C 2 1 0.2 hLoop 2 60 kmol h 2 1 C 2 1 0.2 hLoop 3 25 kmol h 2 1 C 2 1 0.2 hLoop 4 5 C C 2 1 0.2 h(Column tray 27 temperatureLoop 1 setpoint)

Reverse heat integrati onLoop 1 10 kmol h 2 1 C 2 1 Loop 2 13 kmol h 2 1 C 2 1 0.2 hLoop 3 5 kmol h2 1 % 2 1 0.2 hLoop 4 0.78 106 kcal h 2 1 C 2 1 0.2 h

Figure 12. Control system performance. } pentane, f hexane, heptane. Disturbances D1 , D 2 , D 3 , correspond to increase of the feed concentration of pentane, hexane and heptane, respectively, from 0.33 to 0.43. Control structures are presented i n Figures 5 and 10 (the composition-tem perature cascadeswere not used). Controller tuning is presented in Table 6.


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settling time is less than 0.5 hours for forward heat-integration and less than 2 hours for reverse heat-integration. Itis noted that the steady state error in concentration can beremoved if concentration controllers are used.

CONCLUSIONS

The relationship between the design and the control of aheat-integrated distillation set-up consisting of a prefrac-tionator and a main column with side stream is analysed.Both forward and reverse heat-integration schemes wereinvestigated. Detailed results are presented for the separa-tion of an equimolar pentane-hexane-heptane mixture, withmoderate purity requirements. These results were con rmedby the high purity separation of the benzene-toluene-xylenemixture.

1. Four different designs were investigated, both forforward and reverse heat-integration. Energy integrationtook into account a total match of the reboiler and condenser

of the rst/second and second/ rst columns, respectively,as well as feed preheating with products excess enthalpy.Design I considered a tall prefractionator for sharp light/ heavy split, while Design II considered a shorter prefrac-tionator for a moderate light/heavy split. In the other cases,the prefractionator was designed for high recovery of thelight, or of the heavy component, respectively. In all designsthe number of stages varied signi cantly for the prefractionator,but remained practically constant for the main column.2. In all cases, the total energy consumption varied onlyslightly. Consequently, energy recovery cannot be a selec-tion criterion between alternatives. However, the dynamicbehaviour showed signi cant differences.3. MIMO linear controllability analysis in the frequencydomain was performed to evaluate the dynamic propertiesof alternative designs. Large disturbances in feed concen-tration of the three components were considered. Amongcontrollability indices Closed Loop Disturbance Gain(CLDG) and Performance Relative Gain Array (PRGA)were calculated. The controllability analysis predicts, inall situations, better dynamic properties for the forwardheat-integration scheme compared with the reverse one.This behaviour was tested by closed loop simulation withthe full non-linear m odel.4. For the preferred forward integration scheme, anef cient control structure, using only temperature measure-ments, was developed. The design with a short prefraction-ator has, by far, the best performance.5. The control of the reverse heat-integration scheme does notwork with only temperature measurements. The system iscontrollable only if the concentration of the side stream can bemeasured. Moreover, better disturbance rejection is possiblewith a sharp light/heavy split in the prefractionator.6. The behaviour of a high purity separation of a benzene-toluene-xyl ene mixture was tested, similarly to the work of Ding and Luyben 15 , who developed a quite complex controlstructure for the reverse heat-integration scheme. For

forward heat-integration, the simple temperature-basedcontrol structure works well. This con rms the better con-trollability of the forward heat-integration arrangement.7. It may be concluded that in general the forward heat-integration scheme is easier to control. A possible explanation

may be the absence of a positive feedback of energy, which isvery likely in the reverse heat-integration scheme.

REFERENCES1. Rathore, R. N. S., Van Wormer, K. A. and Powers, G. J., 1974,

Synthesis strategies for multicomponent separation systems withenergy integration, AIChE J , 20: 491.

2. Morari, M. and Faith, D. C., 1980, The synthesis of distillation trainswith heat integration, AIChE J , 26: 916.

3. Petlyuk, F. B., Platonov, V. M. and Slavinskii, D. M., 1965,Thermodynamically optimal m ethod for separating multicomponentmixtures, Int Chem Eng , 5: 555.

4. Tedder, D. W. and Ruud, D . F., 1978, Parametric studies in industrialdistillation, AIChE J , 24: 303.

5. Alatiqi, I. M. and Luyben, W. L., 1985, Alternative distillationcon gurations for separating ternary mixtures with small concentrationof intermediate in the feed, Ind Eng Chem Process Des Dev , 24: 500.

6. Nikolaides, I. P. and Malone, M. F., 1988, Approximate design andoptimization of thermally coupled distillation with prefractionation, Ind Eng Chem Res , 26: 1839.

7. Doukas, N. and Luyben, W. L., 1978, Economics of alternativedistillation con gurations for the separation of ternary mixtures, Ind Eng Chem Proc Des Dev , 17: 272.

8. Cheng, H. C. and Luyben, W. L., 1985, Heat-integrated distilla-tion columns for ternary separation, Ind EngChemProc Des Dev , 24: 707.

9. Tyreus, B. D. and Luyben, W. L., 1976, Dynamics and control of heat-integrated distillation columns, Chem Eng Prog , 72: 59.

10. Frey, R. M., Doherty, M. F., Douglas, J. M. and Malone, M. F., 1984,Controlling thermally linked distillation columns, Ind Eng Chem Proc Des Dev , 23: 483.

11. Chiang, T. P. and Luyben, W. L., 1985, Incentives for dual compositioncontrol in single and heat-integrated distillation con gurations, Ind Eng Chem Proc Des Dev , 24: 352.

12. Mizsey, P., Hau, N. T., Benko, N., Kalmar, I. and Fonyo, Z., 1998,Process control for energy integrated distillation schemes, Comp Chem Eng , 22: S427.

13. Doukas, N. and Luyben, W. L., 1978, Control of an energy-conservingprefractionator side stream column distillation system, Ind Eng Chem

Proc Des Dev , 20: 147.14. Alatiqi, I . M. and Luyben, W. L., 1986, Control of a complex

sidestream column/stripper distillation con guration, Ind Eng ChemProc Des Dev , 25: 762.

15. Ding, S. and Luyben, W. L., 1990, Control of a heat-integratedcomplex distillation con guration, Ind Eng Chem Res , 29: 1240.

16. Luyben, W. L. and Luyben, M. L., 1997, Essentialsof Process Control ,(McGraw Hill, New York).

17. Nikolaides, I. P. and Malone, M. F., 1987, Approximate designof m ultiple-feed/side-stream distillation systems, Ind Eng Chem Res ,26: 1839.

18. Skogestad, S. and Postlethwaite, I., 1996, Multivariable Feedback ControlAnalysis and Design , (John Wiley & Sons, Chichester).

19. ASPEN Technology Inc., 1997, ASPEN PLUS User Manual 9.3-2 ,(Aspen Technology Inc., Cambridge, MA, U SA).

20. ASPEN Technology Inc., 1997, SPEEDUP User Manual5.5-6 , (AspenTechnology Inc., Cambridge, MA, USA).

ACKNOWLEDGEMENTWe would like to acknowledge the nancial support provided for

C. S. Bildea by The Graduate School for Process Technology (OSPT),The Netherlands.

ADDRESSCorrespondence concerning this paper should be addressed to

A. C. Dimian, Department of Chemical Engineering, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The

Netherlands. (E-mail: [email protected]). C. S. Bildea is nowat Department of Chemical Engineering, University PolitechnicaBucharest, Spl. Independentei 313, 77206 Bucharest, Romania.

The manuscript was received 11 January 1999 and accepted for publication after revision 1 July 1999.


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Integrated Distillation System With Prefractio