Control of a Distillation Column For

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C .2 .4 .6 8 1.0M O L E FRA CTION OF A IN L IQUID

Figure 7 McCabe-Thiele plot for = 2, g = 18 stages indicated, feed above 5ih p l d e

possible range of g is much greater.units, g = 4 . 4 for the acetone-\vater system.

For instance, in mass

NomenclatureD = distillate produ ct rate, moles/hr. (lb./hr.)F = feed rate, moles/hr. (lb./hr.)

g = ratio of latent heats of vaporization. moles .4mole BK = total latent heat content of vapor stream in rectifyingL = liquid flow rate, moles/hr. (lb./hr.)q = mole fraction of feed which is vapor (weight fraction)R = overhead reflux ratioS = bottom boilup ratioV = vapo r flow rate, moles/hr. (lb./hr.)TV = bottoms product rate, moles/hr. (lb./hr.)x = mole fraction of compone nt A in liquid (weight fraction)y = mole fraction of compone nt A in vapor (weight fraction)y = relative volatility

X = heat of vaporization, B.t.u./mole (B.t.u. lb.)SUI~SCRIPTSA = low boiling componentB = high boiling componentD = distillateF = feedm = plate number in stripping sectionn = plate number in rectifying section,V = bottom plate in columnTV = b o t t o m

(lb. A/lb. B)section, B.t.u./hr.

literature Cited(1) Alleva, R. Q., Chem. Eng. 69,111 Aug. 6, 1962).(2) Hovarth, P. J., Schubert, R. F., Zbid., 64,129 (Feb. 10, 1958).(3) Lewis. W. K.. J . Znd. Ene. Chem. 14.492 (1922)./4\ Lowenstein. J G.. Znd. E m . Chem. 54. 61(1962).(5j McCabe, W, L., Smith, f C.. Unit Operations of Chemical(6) McCabe, W. L., Thiele, E. W., Znd. Ene. Chem. 17, 605 (1925).Engineering, McGraw-Hill, New York, 1956.(7) Peters, W. A . , J . Ind. Eng. Chem. 14, 476 (1922).(8) Robinson. C. S., Gilliland, E. R., Elements of Fractional

RECEIVEDor review January 14, 1963ACCEPTEDune 14, 1963Distillation p. 127, McGraw-Hill, New York, 1950.

CONTROL OF A DISTILLATION COLUMN FORPRODUCING HIGHIPURITY OVERHEADSAND B OTTOMS STREAMS

J . S . M O C Z E K , R O B E R T E . O T T O , A N D T H E O D O R E J . W I L L I A M SMonsanto Chemical Co., St Louis , Mo.

A digit al computer study was performed to investigate the control of a large column for producing very high-purity overheads and bottoms. The column simulated represents the first unit of a BTX (benzene, toluene,xylene) distilla tion train. The operat ion involves removal of low boi ling constituents by pasteurization,with benzene withdrawal as a side stream. Extremely close control of side-stream flow ra te i s necessary tosatisfy material balance requirements. Since small deviations from the correct ra te exhibited large effectson plate temperature, temperature-indexed control of side-stream rate appeared promising. However,trays having the greatest temperature sensitivity to side-stream rate showed an anomalous behavior-theirtemperature increased with both decreases and increases of boilup rate. A control system adapted to theeffects noted was developed. No results from actual operating columns are included.

HILE considerable information has appeared concerningthe dynamics and autom atic control of distillation

columns, much of this discussion has been confined to rela-tively small columns 7 , 6-8, 70, 72, 73, 75, 78, 79 . Thisis du e mainly to the very large am oun t of calculation necessaryto develop such data on digital computing machines for largecolumns (9, 7 7 , 72 and the difficulty of obtaining sufficientvalid experimental dat a on such columns 2-4).

This paper presents some of the results of an extensive digitalcomputer study of the dynamics and control of large columnsby the Monsanto Chemical Co. The operation of columnsdesigned for very close separation of overhead and bottomsproducts was chosen for study, since their control is especiallycritical. A typical illustration is provided by the first distilla-tion unit of a BTX (benzene, toluene, xylene) fractionationtrain.

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Figure 1 presents a dragram of a typical benzene distillationunit of a BTX separation train.

The feed. containing some 50 mole benzene and a smallamount of .light ends (mostly water), is separate d into anoverhead product having a specified benzene content in excessof 99.94 mole yoand a bottoms produc t containing less tha n 0.05mole benzene. Because of the we t feed, a pasteurizingsection at the top of the column provides light ends removal,and the benzene product is withdrawn as a liquid side streamdirectly belo\+ the pasteurizing section. The wet distillate,normally about 1% of the feed, is removed at conditionsapproaching total reflux, and recycled to process.

Operation of this column is extremely critical because of thevery high purity requircbments placed on the benzene product.and on the subsequent products of the fractionation train-Le., toluene an d xylene. Thus , not only must the benzene beexceptionally pure in the column overhead, but the columnmust send as much as possible of this benzene to the overheadproduct to prevent its contaminating the heavier constituentsin the bottoms product stream.

Many designers tend to employ reflux ratio a djustment as astandard method of produ ct purity control. A control schemefor the present columr based on this principle is shown inFigure 1. Here, a temperature controller set for maintaininga specified tempera tur: at a given location in the columncontrols reflux flow. Th e side-stream ra te is regulated by alevel controller in rhe reflux accumulator. An analyzer forthe bottoms produc t guides the control of column boilup.\Vhile reflux ratio contrtol is normally satisfactory. its suitability

-F C - -3TX F e e d 4P I t y

IYS i d e s t r e a r P r o d u c tC o l u m n

I

?e:oiier

2--a >i/ VBettors

Figure 1. Diagram of distillation systemAC. Analyzer controllerAR. Analyzer recorderFC. Flow controller11C. liqu id level controllerRAC. Ratio controllerTC. Temperature controller

Figure 2. Alternativescheme for top productcomposition control

iS i d e s t r e am P r o d u c t

for the operation described was questioned because of theapparent need of maintaining exact material balance flow ofthe side stream to achieve the high degree of separation re-quired.An alternative control method for the top section of thecolumn (Figure 2) involves the adjustment of side-streamwithdrawal, rather t han reflux ratio per .re for maintenance ofproduct composition. This scheme employs temperaturecontrol of side-stream rate, with reset of the temperature orflow set point provided by a chromatogr aph-contr oller whichanalyzes the side-stream produc t. Ou r discussion here isconfined to comparing these methods of top product control.The related problem of bottoms composition control is coveredin earlier references (75, 77, 78).Dig i ta l Comp utat ions an d Pre l iminary Resu lt s Obta ined

4 eries of digital computer calculadons was made to in-vestigate the effect of operating changes on product quality andcolumn conditions existing a t steady-state conditions, toappraise the relative merits of the two control methods, andto establish a desirable location for the sensing element of thetemperature controller, which would be used with eithermethod of control. A program similar to tha t of Rose,Sweeney, and Schr odt 9 ) nd that of Rosenbrock 7 7 , 72).withadded provisions for a complete heat balance of each plate,was employed with the IBM 704 computer. In commonwith all other known multic omponent programs employing therelaxation method, computations a re made in terms of theoret-ical, rath er than actual, plates. Thus, 39 theoretical ratherthan 50 actual trays were simulated on the computer. This isa necessary and to all indications valid approximation to thereal case. Pertinent data on the column simulated and theoperating conditions selected for study are given in Table I.Calculated values of physical time constants of various partsof the column system, representative of the simulated condi-tions, are given in Tab le 11.

The results of the steady-state calculations made for estab-lishing the characterisrics of the column (Table 111) indicatethe effects of reboiler heat input, side-stream rate, and feedcomposition changes on the purity of the product streamsand on the temperature and composition at several theoreticalplates in the column. Th e conditions at theoretical plates21. 22. and 23 ar e of special interest , since they a re sufficientlyclose to the feed plate to provide large temperature sensitivity,but sufficiently removed from it to avoid apprecia ble tempera-

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Table 1 Phys ica l Data and Operat ing Spec i f i ca t ions forColumn S im u la tedDiameterTraysNumberEfficiency,Pressure drop, p.s.i.Feed locationSide-stream locationPasteurizing sectionCondenserOpera ting pressure, p.s.i.g.Calculated holdups, molesCondenser, accumulator, andreflux pipingTraysAbove feedBelow feedSump, reboiler, and piping

TotalRate, moles/min.Temperature, O F.

Feed

Composition, mole

Overhead rat e,mole/min.Side streamRate, moles/min.Required composition, moleRat?, moles/min.Required composition, mole

Bottoms

8 feet 6 inches50 plus reboiler780,14/theoretical trayPlate 23, actualPlate 46, actualPlates 47-50 inc., actualTotal3 . 0 (top of column)

18, theoretical36, theoretical37-39 inc. , theoretical

240

139174470102322.26200-50 benzene-50 toluene, xylene, andheavy ends, small amountsof light ends, water, etc.0.2233 (li ht ends plus somebenzene?11.204>99,94 benzene10.833< OO . 05 benzene

ture effects from the xylene present in the feed. Th e steady-state conditions at theoretical plate 28 illustrate the behavior a tthe more removed location.

I n all cases, feed at essentially saturated conditions wasadmitted at theoretical plate 1 which had been establishedby previous calculations as the optimum feed location for thebase conditions selected. The calcuIaTed values corre-

sponding to these conditions are given in item 1 of Table 111.Th e effects of a 25% increase and a 25% reduct ion in heat

input on product composition are given in items 2 and 3>respectively. Th e effects of corresponding changes in theside-stream flow rate, shown in items 4 and 5: illustrate therelatively minor effect of vap or rate or reflux ratio. Th ecritical importance of maintaining correct material balanceflow conditions is indicated in items 6 and 7>which show thepronounced effect of minut e changes in side-stream rate on Theproduc t compositions. These results demonstr ate conclu-sively that t he purity of the side-stream a nd bottoms products isprimarily d epend ent on th e control of side-stream rate: rathe rthan on reflux ratio , thus establishing the basic superiority ofthe proposed control scheme shown in Figure 2.A comparison of items 1 >6, and 7 in Table I11 shows thatsmall changes in product composition resulting from incorrectmaterial balance are accompanied by significant temperaturechanges at theoretical plates 21 to 23. As would be antic-ipated, rhe temperature changes at locations further removedfrom the feed point, such as at theoretical tray 28, are con-siderably smaller. Thi s directs the choice of locations for thesensing element of the temperature controller, at least for thisparticular case, to the former plates.

Table II.Column trays

Calculated Physical Time Constants of SimulatedC o l u m nWeir f low time constant

weir flow area= 0.039 min. =700 sq. ft. /min. weir coefficientFT = A / K = 27.1 sq. ft.Liquid mixing time constant

11.80 cu. f t .94.4 cu. ft./min..WIT = V / F = = 0.125 min. = volume

liquid flow rateSump ? reboiler, and pipingHeat transfer time constant

W ,C ,UA

6,290 Ib. metal x 0.124 B.t. u.ilb.. O F.2.78 (B.t.u./'F.,min.,sq. f t . ) x 2090sq. ft.R =

heat capacityheat flow rate0.134 min. =

Liquid mixing time constant967 cu. ft.

97.6 cu. ft./min. = 9.91 min.M R = V / F =Condenser, accumulator, an d reflux piping

Liquid mixing time constant365 cu. ft.

52.3 cu. ft./min..WA = V / F = = 6.98 min

Effects o f Boi lup Rate on Tray TemperaturesHowever, upon comparing items 2 and 3 with item 1 ? a n

anomalous behavior is noted-the temperatures a t theoreticalplates 21 to 23 increase when th e column boilup is either re-duced or increased by 25% from the base value. A s shown initems 8, 9, and 11, a similar temperature increase of varyingmagnitude is obtained at these plates \vhen the reboiler heatinput is increased by 3 5 15: and 5 . Item 12 shows thatunder conditions where the boil up is reduced by 5 . platetemperature may be either reduced o r increased. depending onthe plate location. Theore tical plate 28 exhibits relativelynormal temperature and composition behavior with respect tothe boilup changes, an d the effect of boilup on product com-position also appears norma l.

Figures 3 and 4 illustrate the anomaly just mentioned byplotting the tray temperature offset caused by boilup changes.Tray 28 is the first tray whi ch does not show significant reversetem,perature behavior in the range of boilup rate considered.

Calculations were then made for several other types of upsetconditions Ivhich might affect the column, to determine if theanomalous behavior just exhibited occurred for these condi-tions as well. Reductions in feed rate and feed compositioncause termperatme changes of approximately the same magni-tude (items 1 4 and 16) and thus set up nearly equal controlcorrection errors whether the temperature sensor is on tray 21or 28.

On the other hand, as indicated by items 13 and 15 , in-creases in feed rate and feed composition cause decidedlydifferent responses at the t\vo plates in question. Th e responseon tr ay 21 is approximaeely one third the size and opposite insign to that for decreases in rate and composition, while theresponse of tray 28 amounts t o only a fraction of a degree changein temperature or about one fiftieth of that previously ob-tained. If one were to use temperature response alone from

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Table 111 Effects o f Boi lup, S ide-St ream Rate, an d Feed Changes on Product Compos i t ion and P la te Temperature

I tem12

3456789

1011121314151617

18

19

20

DescriptionBase conditionsReboiler heat input increased 25y0

Reboiler heat input reduced 25Side-stream flow rate increased 25y0Side-stream flow rate reduced 25%Side-stream flow rate increased 0.05yoSide-stream flow rate increased 0 7y0Reboiler heat input increased 35y0Reboiler heat input increased 15%Reboiler heat input reduced 15%Reboiler heat input increased 5%Reboiler heat input reduced 5%33% feed rate increase20y0 feed rate reductionMole fraction benzene in feed in-creased 0 10Mole fraction benzene in feed re-ducrd 0 10+ lo benzene, -10% toluenechange in feed compn.. side-stream rate adjusted-10% benzene. + l o toluenechange in feed compn. , side-streamrate adjusted4-5y benzene. 7y0 toluene changein feed compn., side-stream rateadjusted

change in feed compn., side-streamrate adjusted1g / benzanc, +2% toluene

Mole Fraction BenzeneSide stream Bottoms0.999860.99993

0,993590.800080 999990,999440.999250.999930.999910,999470.999890.999810.999930,800090.999980.801410,99985

0.99988

0,99988

0,99993

0.89 x 10-40.18 x 10-40.66 x0 . 5 9 x 10-40.20540.44 x 10-40.41 X0.12 x 10-40.31 X0.49 x 10-30.59 X0.14 x 10-30,20540.26 x 10-50,20550.16 X0 . 13 x 10-30.96 X0.92 x 10-40.59 x 10-4

Side-StreamRate ,Moles/M i n u t e11.204011 ,2040

11 ,204014.0050

8.403011.209111.211411 ,204011 ,204011 ,204011.204011.204011 ,204011 ,204011 ,204011.204013.430

8.977

12,399

8.756

Theo.plate 21206.04(0.748)210.10(0.657)211.31(0.633)227.55(0.328)198.46214.82(0.558)216.48(0.525)212.20(0.611)208.10(0.701)206.69(0.734)206.55(0.736)205.81(0.753)201 .40(0.860)231.53(0.258)198.29(0.939)231 ,27(0.263)200.85(0.873)

212.96(0,596)202.13(0,842)208.89(0.685)

(0.934)

Temperature, .M o l e Fraction Benzene)Theo. Theo. Theo.plate 22 plate 23 plate 28

207.71(0.815)205.35(0.752)209.88(0.651)226.70(0,329)196.94(0.962)211.23(0.621)213.15(0.581)206.91(0.716)203.95(0.785)204.00(0.784)202.97(0,809)202.71(0.815)199.14(0.904)230.78(0.259)196.97(0,961)230.50(0.264)198.98( 0 . 9 0 9 )208.06(0,690)199.82(0.887)204.31(0,777)

200.14(0.870)201.50(0.833)208.44(0.671)226.04(0.330)195.88(0.978)207.55(0,691)209.57(0.646)202.50(0.808)200.64(0.855)201.60(0.831)200.10(0.868)200.14(0.867)197.45(0.936)230.18(0.260)195.98(0.976)229.88(0.265)197.51(0.935)

203,72(0.779)198.02(0.922)200.75(0.852)

193.34(0.986)193.27(0.988)199.53(0.824)223.33(0.333)192.86( 0 . 9 9 9 )194.76(0.947)195.38(0.931)193.30(0.987)193.26(0.988)194.01(0.968)193.30(0.988)193.44(0,983)193.06(0.993)227.40(0,264)192.90(0.998)227.09(0,269)193.17(0.990)193.53(0,981)193.18( 0 . 9 9 0 )193.23(0.989)

tray 28 as the control error measurement. a n entirely differentset of gain adju strr ents would be necessary. Th e use of thechromatograph can be a major aid in correcting this situation.

Thus, except for considerations in controller gain required,either tray 21 or 28 could serve as the l ocati on of a temperaturesensor for these latter upsets; only the boilup changes cau wthe anoma lous behavior described.

Th e anoira ly in respclnse obtained with boilup variations isdue to changes in the distribution of the heavier componentsabout t he feed plate. This results from the slight variations incolurrn liquid-vapor ralios present and causes correspondingchanges in colurrn operating te.i.perature. Since the vapor-liquid equilibrium betu.een benzene and toluene is extrer.elysensirive to re-nperature: changes in the disrribution of theheavier components can easily lead to a radical displacementof plate locations on the McCabe-Thiele diagram with acorresponding feed plate mismatch.

Temperature Of fsets on Test Trays a f terCorrect ion o f Var ious UpsetsSeveral additional calculations were made to establish the

degree of consistency between the final operating temperatu resof the test trays and product q uality a t altered operating condi-tions. In these calculations, the concentration of rhe in-dividual components in the feed \vas varied over a rode ra t erange, and the side-stream Lvithdrawal rate was adjusted toyield product com.positions appr oxim ating those obtainedunder the base conditions. Th e results are shown in iterrs 1 7through 20 of Table 111. The computed producc composi-tions illustrate the pronounced materi al balance behaviorof the co1um.n under the conditions of the study. In each case,the side-stream rate exployed was sirrply calculated on rheassumption that the benzene content of the product stream.s\vould be the sarre as that under the base conditions. Th eclose ag re er en t of ihe results de-ronstrates the high fracrionat-

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- 1 0 185 90 35 100 IO 110 115 120 125 130 135Percent of Base Case RebDiler Heat Input

Figure 3. Effect of reboiler heat input variations ontemperature of theoretical plates 20 to 24

T ime M i n u t e sFigure 5.curacy of computed distillation transientEffect of size of computation interval on ac-

Figure 4.perature of theoretical plates 25 o 29Effect of reboiler heat input variations on tem-

ing ability of the column under the given operating conditions.Items 1 7 through 20 show that very significant changes in

the steady-state temperatures occur at theoretical plates 21through 23 as a result of feed composition changes, whenprodu ct composition is maintained relatively constant. Again,only minor changes in t he steady-state values occur at theoret-ical plate 28 as a result of these changes.

T i m e -Figure 6. Method of estimating dead time

1.2.

Draw o tangent to the transient response at the inflection pointand extend the tangent to the initial value of transientPoint a i s the composition change a t intersection of the tangent withthe horizontal axis. Point b, 2.7180, is located on the graph at theident ical time valueA line p arallel to the tangent through point b locates the equivalentdea d time, T d

3.

Colum n Trans ients and The ir E f fec t on Cont ro lThe computation methods used in this study can readily

give both the transient response of a column to a particularupset and the steady-state condition of the column resultingfrom the same upset. As in all such stepwise computa tions oftransient conditions by digital computers (77) , care must betaken to choose the computation interval time small enough togive a true response while large enough no to waste machinetime. Figure 5 illustrates the effect of interval s ize on transient

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1.0

9Figure 8. Transient re-sponse of composi t ion 0 328, a n d 36 wi th s tep 0 7c h a n g e of s i de -s t ream irec t va lue -

>

of t heo re t i cal p l a t es 23, r

f l ow to 125yo of cor- 2 3 6L 0 5-cI 1 1

? 0.3cE 0.2

L 7

3. :

Figure 7. Transient re-sponse of composi t ion oft heo re t i ca l p l a t es 0, 10,a n d 18 w i t h s t epc h a n g e of s i de -s t reamf l ow t o 1 25% of correctva lue

col umn response to a typical upset. 4n interva l size of 0.10min ute or less must be used for accuracy.

However. in cases such as the present, where the trayefficiency is not loo%, some small but unknown inaccuracy isintroduced in the transient response calculations, since theseare based on theoretical plates rather tha n actual stages.

Distillation column responses to step inp uts usually have t heappearance sketched in Figure 6. Thus there is a definiteperiod of time (ap paren t dead time) during which a detect-ing device itould nor know that an upset had occurred. Toassign a definite number to it, the graphical procedure ofFigure 6 is often used 5, 74). The resulting number willvary greatly betxteen different plates in the column as shownby Figures - to 12. Figures 7 and 8 illustrate the determina-tion of the dead time for several plates in the column for thesame upset. one involving the imposition of a step change of aSyO ncrease in side-stream flow rate. Figure 9 summarizes

these data for the whole column ; Figures 10 and 11 showcorresponding data for differing sizes and directions of suchupsets. Dead time is confined to the end trays of the columnand is apparently larger for smaller upsets, in agreement withprevious work on column equilibration time 8 ) .

Since dead time can severely influence the stability andresponse of a control system (76, 79 , every effort must bemade to keep it as small as possible, Therefore, the tempera-ture-sensing tray for the column control scheme must bechosen to accomplish this while bearing in mind the tempera-tu re effects previously discussed. Thu s, tray 28 would againbe chosen since it is the first tray witho ut a temper ature-reversal effect and has the smallest possible dead time.

Figure 12 gives the dead times found from the response to astep change in feed composition. These results are very similarto the responses to side-stream take-off ra te changes, exceptthat a feed composition upset affects both ends of the column.

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Figure 9. Dead timecharacteristics of columnwith step change ofside-stream flow to125 of correct value

Figure 10. Dead timecharacteristics of columnwith step change of side-stream flow to 1 1 2 5y0of correct value

Use of Analyzer and Other Cons idera tionsWith the establishment of the best position for the tempera-

ture-sensing element and the determination of the penaltiesinvolved with the use of this and other locations, one canevaluate the best method of using the analyzer sampling theside-stream prod uct composition. Should it be used to resetthe temperature controller? Or: to reset the side-stream flowcontroller itself along with the temperature controller to com-pensate for possible insensitivities in that element? These twopossibilities ar e illustrated by Figure 13.

In the case of a tray 21 location for the temperature element,the steady-state temperature offsets tested in Table I11 must heremoved by an integral action on the part of the analyzercontroller. Since a large dead time is present a t the side-stream location, along with an appreciable analysis time formany analytical devices such as chromatographs, this correc-

T h e o r e ti c a l P l a k N u m b e i

tion is a long process at best. In addition, systems with theselong dead times often exhibit an oscillatory behavior . Th earrangement of Figure 13 (upper) would be necessary for anadequate use of the analyzer controller to correct the opera-tion of the temperature controller.

Since the tray 28 response is so one-sided, the best use of theanalyzer controller is to compensate for this effect-that is,allow the temperature controller to correct for decreases in feedrate and feed composition where large errors in temperatureoccur, but use the analyzer controller set at a high gain tocorrect for increases in feed rate and feed coinposition wherethe temperature controller is very insensitive. To accomplishthis, the analyzer controller must be set to take positive com-position errors only; otherwise, i t will tend to overcorrect forthose cases where the composition should fall below the desiredside-stream value. Th e arrangement of Figure 13 (lower)

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-=i 10.0c-

7 5

5 0I

R e b o i l e r ~ yg; y5

C ; I3 4 6 8 IC 12 I4 ;6 I8 20 22 24 26 28 3 3 35 j6T h e o r e t i c a l P l a l e N u m b e r

Figure 1 1 . D e a d t i m echaracter i s : i cs of columnwi th s tep chang e o f s ide-s t ream f low to 75y fcorrect va lue

/0 ~

2 4 6 8 I 12 I4 16 I8 2 24 26 28 30 32 34 j6T b e o r e t i c a cla e N u T i e r

would thus give the most satisfactory performance where tray28 temperature responses were being used.

ConclusionsWhen temperature is being considered as the primary

sensing element for control of large distillation columns, thefollowing must be kept in mind in choosing the correct tray formounting the sensing element:

1. Th e possibility of an anomalous temperature response oftrays near the feed plate, where the presence of minor com-ponents can upset the normal column-tempe rature patte rnand alte r the vapor-liquid equilib ria between the keys.The magnitude of steady-state offsets in plate tempera-ture in correcting for operating conditions away from thedesign case. Korm ally , these offsets decrease as one movesfurther away from the feed plate.

2.

3. For columns with a large number of plates, dead timein column response profiles m ay seriously affect controllability.Kormally, large dead time effects are confined to plates nearthe ends of the column. Thi s \yould direct the movement of thetemperature-sensing element to a tray near the feed tray-incontradiction to the statements above.1 The best compromise is, therefore. the lowest tray(nearest the feed) which satisfies the requirements of items 1and 2.5. The addition of the chromatograph to the control loopas a secondary sensing element provides the possibility of twouses of this information.In case of an incorrect temperature element tray location forany reason, it can act as a set point changer to correct for thetemperatur e offset at a new steady-state operating condition.For correct temperature sensor locations, it can act as a'f in e tuner of side-stream take-off rates to compensate forpossible errors in take-off flow rates due to instrument drift.etc ., in particul ar for correcting side-str eam or product take-offrates \vhen an upset has increased product composition.

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Y

Figure 13. Uses o f ana lyzer cont ro l le ras secondary cont ro l element in co lumncont ro l

Upper. Resett ing of t e m p e r a tu r e s et p o i n t

l o w e r . Fine tuning of f low con t ro l

l i terature Cited(1) Archer, D. H., Rothfus, R. R., Chem. Eng. Progr. Symp. Ser.(2) Berger, D. E., Campbell, G. G., Chem. Ens. Progr. 51, 348-52(1955).(3) Berger, D. E., Short, G. R., Znd. Eng. Chem. 48, 1027-30(1 956).4)Hoyt, P. R., Stanton, B. D., Petrol. Refiner 32, 115-19 (October1953).(5) Oldenbourg, R. C., Sartorius, H., The Dynamics of Auto-matic Control, pp. 99-1 57, American Society of MechanicalEngineers, New York, 1948.(6) Rademacher, O., Rijnsdorp, J. E., Dynamics and Control ofContinuous Distillation Columns, Proceedings of 5th WorldPetroleum Congress, Paper 5, Section VII, May 1959.(7) Rijnsdorp, J. E., Maarleveld, A. Use of Electrical Analoguesin the Study of the Dynamic Behavior and Control of Distilla-tion Columns, pp. A63 ff., Symposium on Instrumentation andComputation in Process Development and Plant Design, May1959, Institution of Chemical Engineers, London.(8) Rose, A, , Johnson, C. L., Williams, T. J., Znd. Ens. Chem.(9) Rose, Arthur, Sweeney, R. F., Schrodt, V. N., Zbid., 50, 737-40(1958).(10) Rose, A,, Williams, T. J., Ibid., 47, 2284-9 (1955).(11) Rosenbrock, H. H., Brit. Chem. Ens. 3, 364-7, 432-5, 491-4(1 958).(12) Rosenbrock, H. H., Tran s. Znst. Chem. Ens. London 35, 347-51(1957).(13) Rosenbrock, H. H., Tavendale, A. B., Storey, C., Challis,J. A, , Transient Behavior of Multicomponent DistillationColumns, Preprints of Papers, International Federation of Au-tomatic Control Congress, Moscow, June 27 to July 7, 1960,pp. 1277-82, Butterworths, London, 1960.

57, NO. 36, 2-19 (1961).

48, 1173-9 (1956).

(14) Smith. 0 J. M., ZSA J . 6 , 28-33 (February 1959).(15) Williams, T. J., Znd. Ens. Chem. 50 , 1214-22 (1958).(16) Williams, T. J., ZSA J . 9, 39-42 (July 1962).(17) Williams, T. J., Harnett, R. T., Chem. Eng. Progr. 53, 220-5(19.57).(18) Williams, T. J., Harnett, R. T., Rose, A,, Znd. Ens. Chem.(19) Williams, T. J., Min, H. S., I S A J . 6 89-93 (September48, 1008-19 (1956).1959).

RECEIVEDor review September 26, 1962ACCEPTED arch 8, 1963Division of Industria l and Engineering Chemistry, 142nd meeting,ACS, Atlantic City, N. J., September 1962.

PROCESS OPTIMIZATION B YSEARCH TECHNIQUES

D . M . H I M M E L B L A U Department of Chemical Engineering, The University of Texas, Austin 12, Tex .An ad ap t i v e sea rch t echn i que is p roposed t o so l ve the f o l low i ng t yp e o f p rob l em: Max i m i ze o r m i n im i ze anob ject i ve funct ion sub ject to l i near or non l inear const ra in ts of t he f o rm G i X I , x2 .. ,) = 0 5 i 5 m;m < n . An examp l eappl i ca t io n i s presented f or a s im pl i f i ed butane i som er izat ion process.

The ob ject i ve funct ion i t se l f ma y be l inear , non l inear , o r expr essed as some in t egra l .

HIS REPORT s concerned with the general prob lem of findingTa solution to a set of m simultaneous equations with nunknowns, \\.here the n unknowns can be subject to constraints.Of special interest here is the case where the number of un-knowns is greater than the number of independent equations,and consequently a best solution can be obtained only if acriterion of best is available as some objective function.

While a wide choice of methods of solution is availablewhen all the equations and the objective function are linear,the same cannot be said if the equations and/or the objectivefunction are nonlinear. Certainly there is ampl e room in thisarea for new suggestions as to iterative or other techniques toresolve such difficult problems with simplicity and speed. Anew method of handling this problem is described, that of an

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Control of a Distillation Column For