A New Heating-cooling System to Improve Controllability of Batch Reactors

7/30/2019 A New Heating-cooling System to Improve Controllability of Batch Reactors

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Pergamon C h e m i c a l En g i n e e ri n g S c i e n c e , Vol. 51, N o. I 1, pp. 3163--3168, 1996Copyr ight O 1996 E l s e v i e r S c i e nc e Lt dPr in ted in Or ea t Britain. All r igh ts r tmerved0009-2509/96 $15.00 + 0.00S0009-2509(96)00214-X

A N E W H E A T I N G - C O O L I N G S Y S T E M T O I M P R O V EC O N T R O L L A B I L I T Y O F B A T C H R E A C T O R SZ . L O U L E H , M . C A B A S S U D , M . V . L E L A N N , A . C H A M A Y O U a n d G . C A S A M A T T A

Laboratoi re de 06n ie Chimique - URA CN RS 192Ecole N ationale Sup6rieure d'Ing6nieurs de G6nie Chim ique18, Chemin de la loge - 31078 TOULOU SE Cedex - FRANCETel. : (33) 62 25 23 68 - Fax : (33) 62 25 23 18 - email : Michel.Cabassud@en sigct .frAbstract - T h e m a t h e m a t i c a l m o d e l l i n g a n d t h e d e v e l o p m e n t o f a n u m e r i c a l s i m u l a t o r o f ap i l o t - p l a n t b a t c h r e a c t o r a r e p r e s e n t e d . I n t h i s p a p e r , d y n a m i c s i m u l a t i o n a n d a d v a n c e d c o n t r o ls t r a te g y a r e g i v e n . T h i s w o r k p r e s e n t s t h e d e v e l o p m e n t a n d c h a r a c t e r i s a ti o n o f a m u l t i p u r p o s eb a t c h r e a c t o r w i t h a v a r i a b l e h e a t i n g / c o o l in g s t r u c tu r e f o r t e m p e r a t u r e c o n t ro l . T h i s s t r a t e g y i sb a s e d o n t h e u s e o f t h e t h e r m a l f l u x a s t h e m a n i p u l a t e d v a r ia b l e . T h e c o n t r o l l e r ( t h e G e n e r a l i s e dP r e d i c t i v e C o n t r o l l e r ) c o m p u t e s a t e a c h s a m p l i n g t i m e t h e t h e r m a l f l u x t o b e e x c h a n g e d w i t h t h et h e r m a l f l u i d f l o w i n g i n t h e j a c k e t t o a c h i e v e t h e d e s i r e d r e a c t o r t e m p e r a t u r e p r o f i l e . T h i si n f o r m a t i o n i s t h e n u s e d t o s e l e c t t h e t h e r m a l f l u i d o n t h e b a s i s o f t h e m a x i m a l a n d m i n i m a lt h e r m a l f l u x c a p a c i t i e s c o m p u t e d o n - l i n e f o r e a c h u t il i ty . T h i s m e t h o d o l o g y a l l o w s t o o v e r c o m et h e d i s c o n t i n u i t i e s d u e t o u t i l it y f l u id s w i t c h i n g f r e q u e n t l y e n c o u n t e r e d d u r i n g t h e b a t c h r e a c t o rope r a t i on .

I N T R O D U C T I O NA l a r g e n u m b e r o f i n d u s t r i a l p r o c e s s e s , s u c h a s t h e p r o d u c t i o n o f p o l y m e r s , s p e c i a l i t y a n d f i n e c h e m i c a l s ,pha r m ac eu t i c a l s , b i opr od uc t s , a s w e l l a s o t he r p r oduc t s fo r w hi c h c on t i nuous p r odu c t i on i s no t f ea s i b l e , a r e ope r a t edb a t c h w i se . I n m a n y c a s e s t h i s m o d e o f o p e r a t i o n i s u s e d t o m a n u f a c t u r e a v a r i e t y o f p r o d u c t s t h a t n e e d s i g n i fi c a n t lyd i f f e r en t c ha r ac t e r i s t i cs suc h a s c onv e r s i on t i me , h ea t o f r eac t i on . . .e tc .G o od c on t r o l in suc h r eac t o r s i s qu i t e o f t en d i f f i c u l t t o ac h i eve ( J uba and H am er , 1986) due t o t he i r f l ex i b l e andm u l t i p u r p o s e c h a r a c t e r ( d i f f e r e n t o p e r a t in g c o n f i g u r a ti o n s a n d t h e u s e o f t h e s e r e a c t o r s f o r d i f f e r e n t p ro d u c t s ) . T og u a r a n t e e b a t c h - t o - b a t c h re p r o d u c i b i l i t y a n d i m p r o v e y i e l d s a n d s e l e c ti v i ti e s , a u t o m a t i o n o f b a t c h r e a c t o r s m u s t b ew i d e l y i n c r e a s e d . D u e t o t h e c o m p l e x i t y o f t h e r e a c ti o n m i x t u r e a n d t h e d i f f i c u l t y t o p e r f o r m o n - l i n e c o m p o s i t i o nm e a s u r e m e n t s , c o n t r o l o f b a t c h r e a c t o r s i s e s s e n t i a l l y a p r o b l e m o f t e m p e r a t u re c o n t r o l ( F r i e d r i c a n d P e m e , 1 9 95 ).M o r e o v e r , t h e c o n t r o l p e r fo r m a n c e s a r e m a i n l y d e p e n d e n t o n t h e h e a t i n g - c o o li n g s y s t e m a s s o c i a t e d w i th t h e r e a c t o r(Berber, 1995)T w o m a i n t y p e s o f h e a t i n g - c o o l i n g s y s t e m s a r e c o m m o n l y u s e d i n i n d u s t r y : th e a l t e r n a t e s y s te m o r m u l t i fl u i ds y s t e m a n d t h e m o n o f l u i d s y s t e m . T h e w e l l - k n o w n a l te r n a t e sy s t e m m a k e s u t i l i ty fl u i d s f l o w a l t e r n a t i v e l y i n t h ej a c k e t . T h e s e t h e r m a l f l u i d s a r e a v a i l a b l e a t g i v e n t e m p e r a t u r e ( p l a n t u t i li t ie s ) . It r e p r e s e n t s t h e m o s t w i d e l y u s e ds y s t e m i n i n d u s t r y ( m o r e t h a n 9 0 % ) d u e t o t h e r e l a t i v e e a s e o f d e s i g n a n d l o w c o s t ( d i r e c t u s e o f p l a n t u t i li t ie s ) .N e v e r t h e l e s s , b e s i d e s t h e w o r k u n d e r t a k e n i n o u r l a b o r a t o r y C Le L a n n e t a l . , 1 9 9 5 ) o n l y a f e w p a p e r s h a v e b e e np u b l i s h e d o n t h e s u b j e c t ( M a r r o q u i n a n d L u y b e n , 1 9 7 2 ; C h y l l a a n d R a n d a l l , 1 9 9 3) . T h e r e f o r e , t h e c o n t r o l t a s k o ft h i s t y p e o f p r o c e s s i s r a th e r d i f f ic u l t a n d c a n b e d i v i d e d i n t o t w o p a r t s : f i r s t ly t h e c h o i c e o f t h e r i g h t f l u i d a n ds e c o n d l y t h e a p p r o p r i a t e a c t i o n o n t h e f l o w r a t e o f t h i s u t i l i t y f l u i d i n o r d e r t o t r a c k s a t i s f a c t o r i l y t h e d e s i r e dt e m p e r a t u r e p r o f i l e . T h u s , t o g o f r o m h e a t i n g t o c o o l i n g , a c h a n g e o v e r o f f l u i d i s r e q u i r e d w h i c h r e s u l t s i n ad i s c o n t i n u i t y i n t h e o p e r a t i o n . A n a l t e r n a t i v e c o n f i g u r a t i o n is t h e m o n o f l u i d s y s t e m . T h i s s y s t e m u s e s o n l y o n ef l u i d w h o s e t e m p e r a t u r e c a n b e m o d i f i e d t o a c h i e v e t h e d e s i r e d r e a c t o r t e m p e r a t u re b y a n i n t e r m e d i a t e t h e r m a l l o o pw h i c h m a y i n c l u d e h e a t e x c h a n g e r s , p o w e r h e a t e rs , e t c . .. N e v e r t h e l e s s, t h e d y n a m i c s o f t h i s e x t e r n a l t h e r m a l l o o p sc a n b e p e n a l i s in g , e s p e c i a l l y i n t h e c a s e o f u r g e n t n e e d o f a r a p i d c o o l i n g o r h e a t i n g .I n t h i s p a p e r , w e d e s c r i b e a n e w h e a t i n g - c o o l i n g s y s te m w h i c h t a k e s a d v a n t a g e o f t h e l a r g e h e a t i n g ( c o o l i n g )c a p a b i l i ti e s o f s t e a m ( g l y c o l / w a t e r ) w h e n r a p i d h e a t i n g ( c o o l i n g ) i s n e e d e d . O n t h e o t h e r h a n d , f o r n o r m a l o p e r a t in gc ond i t i ons , t he u se a s i n g l e f l u i d c i r c u l a t ing a t a su f f i c i en t l y r ap i d f l ow - r a t e t o ensu r e g ood he a t t r ans fe r c oe f f i c i en t si s p r e f e r r e d . A n e w m e t h o d o l o g y f o r c o n t r o l a n d s u p e r v i s i o n h a s b e e n d e v e l o p e d . I t i s b a s e d o n t h e o n - l i n ec o m p u t a t i o n o f t h e m a x i m a l t h e r m a l f l u x c a p a c i t i e s o f e a c h c o n f i g u r a t i o n ( i . e . : s t e a m , i n t e r m e d i a t e f l u i d ,g l y c o l / w a t e r ) a n d t h e c o m p u t a t i o n b y t h e c o n t r o l l e r o f t h e t h e r m a l f l u x ( m a n i p u l a t e d v a r i a b l e ) n e e d e d t o t r a c k t h er e a c t o r t e m p e r a tu r e s e t - p o i n t .D Y N A M I C S I M U L A T I O N A N D P R E D I C T I V E C O N T R O L L E RT h e a c c u r a c y a n d c o m p l e x i t y o f t h e m a t h e m a t i ca l p ro c e s s m o d e l n e e d e d i n d e v e l o p i n g a c o n t r o l s y s t e m d e p e n d u p o nt h e p r o c e s s i n g o b j e c t i v e s , t h e c o n t r o l o b j e c t i v e s , a n d t h e d e g r e e o f a u t o m a t i o n r e q u i r e d . A d y n a m i c s i m u l a t i o n

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316 4 Z. LOULEH t a l .program me o f b a tch reac to rs f i tt ed ou t w i th a mu l t if lu id hea t ing -coo l ing s ys tem has b een dev e loped and p re s en tede l s ewhe re (Cab as s u d e t a l . , 1994) . I t i n teg ra tes b o th the mo de l l ing o f the dyn am ic b ehav iou r o f a j a ck e ted b a tchreac to r and the s u pe rv i s o ry con t ro l s t ra t egy fo r the ope ra t ion o f th i s hea t ing /coo l ing s ys tem and the t em pe ra tu recontrol by an adva nced control le r . In th is paper , the s imula ted jack eted reacto r correspon ds to a rea l p i lot p lant f it tedou t w i th the new he a t ing -coo l ing s ys tem u nde r considera tion . A d es cr ip tion o f the ove ra l l p roces s i s g iven in thefol lowin g sect ion.T h e d yn a m i c s i m u l a t i o n m o d e lThe s e t o f d if fe ren t ia l eq u a t ions rep re s en t ing the dynam ic b ehav iou r ha s b een e s t ab l i shed f rom m as s and ene rgybalances on the react ive m ixture with the description of the heat t ransfers be twee n the circula t ing f lu id in the jacket ,the jack e t w a l l and the reac t ive mix tu re . Da ta and m ode l s s u pp l i ed to the dynam ic s imu la to r inc lu de the reac t ionkinetics and the necessa ry corre la tions to ca lcula te the heat t ransfer co eff icients and the p hys ica l propert ies . I t shouldb e em phas i s ed tha t th is s imu la t ion s o f twa re a l lows s ca l ing -u p s ince i t i n teg ra te s the geom e t r i ca l s t ru ctu re o f thes imu la ted reac to r . The mode l ha s b een e s t ab l i s hed a s s u ming tha t the reac to r i s pe r f ec t ly mix ed wi th u n i fo rmtempera ture and conc entra t ion of reactants . T he com posi t ion of the react ion mixture , i ts tempera ture and the jacke twai l tempera ture are com puted by a numerical solu tion o f the sys tem o f dif ferentia l and a lgebra ic equations .T h e a d a p t i v e c o n t r o l a l g o r i t h mAn adapt ive and predictive control ler ( the Genera lised Predict ive Controller w ith Mode l Reference : GPC MR ) is usedto com pute the necessary f lux (manipula ted variable) to be exchan ged between the react ion m ixture and the jacke t ino rde r to t rack the de s i red reac to r t empe ra tu re p ro fi le . Th i s adap t ive con t ro l l e r i s b a s ed on the l inea r inpu t -ou tpu trepre sen ta tion o f the p roces s . The on- l ine e s t ima t ion o f the mod e l pa rame te rs a l lows to fo l low the chan ges in thedynam ics occu r r ing du r ing the d i f f e ren t s t eps : hea t ing , re ac t ion , coo l ing . I t is a l s o a p red ic t ive con t ro l l e r wh ichcom putes the manipula ted variable m inimis ing the square errors be tween the fu ture se t-points ( reference prof ile) andthe ou tpu t p red ic t ions ( t empe ra tu re in the reac to r ) on a reced ing hor izon . De ta i l s o f th is a lgo r i thm and i t s u s e fo rt empe ra tu re con t ro l o f b a tch reac to r can b e fou nd in L e L an n e t a l . , 1995.P R O C E S S D E S C R I P T IO NThe character ist ics of the s im ula ted reactor corre spon d to a rea l p i lot p lant cons is t ing o f a ba tch reactor , i ts jack etand the heat ing-coo l ing hyb rid sys tem described abo ve. The reactor is a 16 l i te rs -DeDietrich type glass- l ined reactorwi th a max imu m ope ra t ing vo lu m e o f 12 li te r s. Three u t i li ty f lu ids a re ava i l ab le a t g iven t empe ra tu re s : s t e am (6b a rs ), c o ld wa te r ( a t ab ou t 15 C) , mix tu re o f mo noprop y lene g lyco l /wa te r (50 /50 we igh t% a t a t empe ra ture o f -10C) . The in te rmed ia te f lu id i s ob ta ined b y d i rec t mix ing o f co ld wa te r and s t eam, wi th a max imu m reachab letempera ture of 70 C. The reactor has the fol lowin g phy s ica l specif ica t ions : in ternal d iam eter of 0 .3 m, externald iame te r o f 0 . 4 m, a he igh t o f 0 .3 m , a j a ck e t hea t t r ans f e r a rea o f 0 .2 m 2 , a j a ck e t v o lu m e o f 0 . 012 m 3 , a wa l lth ick nes s o f 0 .01 m wi th a the rma l con du c t iv i ty o f 0. 005 k ca l s -1 m ' l K -1 and a w e igh t o f 27 0 k g . A s k e tch o f thepi lot p lan t is g iven in Fig. 1 .

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u id

~ "'-~ntermed iate ]G ly co l/W a te r ~ f l u i d I

F ig 1 . Schem e o f the p i lo t p l an tA NE W M E T H O D O L O G Y F O R S U P E R V I S O R Y A N D C O N T R OL O F B A T C H R E A C T O R SA new s t ra t egy in teg ra t ing s u pe rv i s o ry and con t ro l toge the r i s p ropos ed . The con t ro l l e r (GPCMR ) compu te s thethe rma l f lu x neces s a ry to ach ieve the req u i red reac to r t empe ra tu re p ro f i l e . The max ima l and min ima l the rma lcapacit ies of each therm al f lu id (s team, intermedia te f luid , g lycol/water) a re then determ ined an d used to choo se the"right" f lu id accord ing to these therm al l imit capaci ties with a priori ty to the f lu id present in the jacket . T he l imitcapac it ie s o f hea t ing and coo l ing o f e ach the rma l f lu id a re ca lcu la ted on - l ine b y a p ro cedu re invo lv ing the reac t ion


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Controllability of batch reactors 3165mix tu re t empe ra tu re , the jack e t in l e t and ou t l e t t empe ra tu re s , t he phys ica l p rope r t i e s o f the f lu ids and theman ipu la ted va r i ab le v a lu e de l ive red b y the con t ro l le r . W hen th is de s i red f lu x ove rs hoo t s the l imi t capac i t ie s o f thep re s en t f lu id , a chang eove r o f the rma l f lu id is pe r fo rmed . A n a i r pu rge o f the jack e t i s ca r r i ed ou t b e fo re f eed ing thejack e t w i th the " r igh t " f lu id . In com par i s on wi th m os t o f the p rev iou s work s , the ch ange ove r o f f lu ids i s thu s no tpe r fo rm ed accord ing to a p rede f ined t empe ra tu re a l a rm s y s tem b u t accord ing to the phys ica l capac i ty o f the hea texchanges.M o r e o v e r , t o o v e r c o m e t h e s t r o n g d i s c o n ti n u it i es d u e t o t h e c h a n g e o v e r f r o m h o t t o c o l d u t il it ie s a s d o n et rad it iona lly wi th mu l t i f lu id s ys tems , we p ropos e to u s e an in te rmediate s ys tem ob ta ined b y m ix ing co ld w a te r ands team. Th i s new hea t ing -coo l ing s ys tem i s an hyb r id conf igu ra t ion (Cab as s u d e t a L , 1995) which integra tes theadvan tages o f b o th the mon of lu id and mu l ti fluid s ys tems :- during norm al condit ions, a unique f lu id ( intermedia te f luid) ci rcula tes a t a f ixed f lowrate (high eno ugh to ensuregoo d hea t t r ans f e r coe f fi c i en t s ) and i ts t empe ratu re i s mod i f i ed accord ing to the req u i red the rm a l f lu x com pu ted b ythe con t ro l l e r b y ac t ing o n the q u an t i ty o f in jec ted s t eam.- f o r ex t reme t em pe ra tu re cond i t ions s t e am o r g lyco l /wa te r a re d i rec tly u s ed ( a s in the m u l t i flu id s ys tem) ; t heut il i ty f lowrate is ch ang ed accord ing to the required thermal f lux .I t may b e no ted tha t the advan tages o f th i s s t ra t egy , b a s ed on s u pe rv i s o ry con t ro l a ccord ing to the rma l f lu xl imi t s, no t on ly mak es the hea t ex change ca pac i ty va ry con t inu ou s ly b u t enab le s an adeq u a te chang e o f s ys temconf igura t ion , f rom mu lt i f lu id to mon of lu id configurat ion.At each s ampl ing pe r iod the fo l low ing two s t eps p rocedu re i s pe r fo rmed : in a f i r s t s tep , the the rm a l f lu x l imi tcapacit ies in each conf ig ura t ion are com puted (s team, intermediate fu i d , g lycol /w ater) . This leads to the cho ice ofthe " r igh t " f lu id . Then , in a s econd s t ep , the rea l con t ro l a c t ion va lu e (va lve open ing degree fo r s t e am andglycol/water) is com puted depe nding on the u t il i ty involved.M o d e l b a s e d s u p e r v i s o r y c o n t r o lTh e therm al flux del ivered by the thermal f lu id to the reactor is expressed b y : Q1 = f Cp(TJin-Tjout) (1)The the rma l f lu x ex changed b y the therma l f lu id and the reac to r i s g iven b y : Q2 = Ua A0m (2)A0 m is the m ean tempera ture dif ference between the jacket and the reactor :

a 0 m = {(Tjin - Tr ) + (Tjout - Tr)} (3)2The who le m e thod o logy re li e s on the a s s u mpt ion tha t b o th the rma l f lu x a re eq u a l : Q1 = Q2D e t e r m i n a t i o n o f t he t h e r m a l f l u x l i m i t c a p a c i t i e s f o r e a c h u t i li t y fl u idIn this case, the therm al fluid inlet temperature (Tjin) and its f low-ra te (f) a re k nown.I t s max imu m va lu e co r re s ponds to a ze ro f lowra te s o : Qm ax g w = 0 (4)The m in im u m v a lu e co r re s po nds to the m ax im u m f lowrate , fmax g w, o f the g lyco l /wa te r s t re am ava i lab le a t atempera ture Tug w (-10 C in practice).Th e f lowrate ( f ir) of the intermedia te f lu id is obta ine d by mixing the co ld water s t ream (f ixed f low rate fcw) with f i lesteam flowrate : f if=fcw+fst (5)I t i s a s s u me d tha t the in te rmed ia te f lu id ha s the s am e p rope r t i e s (Cp) a s the co ld wa te r (m a in wa te r) . The s t e amflowra te fs t is com puted as fol lowin g : f s t =1~.c v s . ~ s t - P c w (6)whe re Ps t is the s team pressure (6 bars in pract ice) , Pcw is the pressure of the co ld water (m ain water), 13 the va lveop enin g degree, cvs the valv e characteristic coefficient.Th e intermedia te f lu id tempera ture (after mixing) is g iven by:

f st ( C p c w [ T u s t - T u cw ] + L v )Tim Tucw-~ (7 )C p c w f i fwhe re Tucw is the inle t tempera ture of cold water (main water , in pract ice abou t 15C) . Tus t is the tempera ture ofthe inle t s team (boi l ing tempera ture a t Ps t).{ Tif [ 2 f i f . C p c w - U . a ] + 2 T r . U . a }Fro m Eq. (1) , (2) and (3) we obta in Tjout : Tjout = (8)(2 . f i r . Cp c w + U . a )

Qm axif is de termined for f i fmax c orrespo nding to fs lmax, i . e . 13=1. In pract ice , the s team c ontro l va lve has beenchos en in o rde r to ge t a max im u m temperature o f 7 0 C .The m inim um therm al f lux corresponds to the case where on ly cold water is used as in termedia te f luid , so :Qm inif = fcwC pcw (Tucw-Tjout) (9)s t e a mThe the rma l f lu x ex changed b y s t eam in the jack e t and the reac to r mix tu re i s p ropor t iona l to the l a t en t hea t o fcondensation :


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3166 Z. LOULEHet aLQ st = fs t L v (10)W e have a l so t he hea t exc han ge expr es s i on : Q s t = U .a (T j s t -Tr ) (11)

Th e s team f low rate i s giv en by : fs t =[~. cvs . NVP-~ - Pj (12)T h e m a x i m u m v a l u e i s o b t a i n e d f o r [ 3 = l. T h e p r e ss u r e P j c a n b e d e r i v e d f r o m t h e p r e s s u r e o f a i r i n t h e j a c k e t a n dt he pa r t i a l p r e s su r e o f t he s t eam i n t he j ac k e t ac c or d i ng t o :

p j = Pa i r ' T j s t + PJ st (T j s t ) (13)293T h e s t e a m t e m p e r a t u r e in t h e j a c k e t , T j st , i s d e t e r m i n e d a s t h e b o i l i n g t e m p e r a t u r e c o r r e s p o n d i n g t o t h e p a r t i a lp r e s s u r e P J st in t h e j a c k e t . S o , t o d e t e r m i n e t h e s t e a m t e m p e r a t u r e c o r r e s p o n d i n g t o t h e m a x i m u m f l o w r a t e o fs t eam, w e ha ve t o so l v e a non- l i ne a r func t i on by an i t e r a t i ve p r oc edu r e .T h e m i n i m a l t h e r m a l f l u x i s o b t a i n w h e n t h e v a l v e i s c l o s e d : Q m i n s t = 0 ( 14 )C o m p u t a t i o n o f t h e t h e r m a l f l u i d f l o w r a t eD i f f e r e n t m a n i p u l a t e d v a r i a b l e s h a v e t o b e c o n t r o l l e d . T h i s p r o b l e m i s s o l v e d b y c a s c a d i n g t h e c o n t r o l l o o p . T h em a s t e r c o n t r o l l e r c o m p u t e s t h e h e a t i n g / c o o l in g f l u x t o b e d e l i v e r e d / r e m o v e d t o t h e r e a c t i o n m i x t u r e . T h i s v a l u e i st h e n u s e d , in a s l a v e - l i k e l o o p , t o e v a l u a t e t h e o p e n i n g v a l u e o f t h e c o n t r o l v a l v e . T h i s c o m p u t a t io n i s m a d e i n t w os t eps : in t he f i r s t one , i t i s de t e r mi n ed w he t he r t he t he r m a l f l ux c an be f ea s i b l y r ea l i s ed w i t h t he f l u i d c i r c u l a t ing i nt h e j a c k e t o r w h e t h e r a c h a n g e o v e r t o a n o t h e r f l u id i s n e e d e d ; in a s e c o n d s t e p , t h e c o m p u t a t io n o f t h e c o n t r o l v a lv eo p e n i n g d e g r e e i s c a r d e d o u t.T h e f l u x t o b e e x c h a n g e d b y t h e c h o s e n t h e r m a l f l u id ( E q . 1 f o r li q u i d fl u i d , E q . 1 1 f o r s te a m ) i s c o m p u t e d b yt h e c o n t r o l l e r ( Q c o n 0 . T h u s , c o n t r a r y t o t h e p r e v i o u s p r o c e d u r e , t h e o b j e c t i v e o f t h e c o m p u t a t i o n i s t o d e t e r m i n et h e f l o w r a t e o f t h e f l u i d b y u s i n g t h e e q u a t i o n s g i v e n a b o v e . L e t u s r e c a l l th a t , f o r t h e i n t e r m e d i a t e f l u id , t h i sf l o w r a te c o r r e s p o n d s t o t h e a m o u n t o f i n j e c te d s t e a m i n t h e c o l d w a t e r. T h e a c t u a l m a n i p u l a t e d v a r i a b l e is t h e v a l v eopen i ng d egr ee c om pu t ed ac c or d i ng t o t he c a l i b r a t ion c ha r ac t e r i s t ic s o f t he va l ve .R e c y c l i n g o f h o t w a t e r a t t h e o u t l e t o f th e j a c k e tE n e r g y c a n b e s a v e d b y r e c y c l in g t h e i n t e r m e d i a te f lu i d a n d t h e r e f o re b y u s in g e x a c t q u a n ti ti e s o f s t e a m o r c o l d w a t e rn e c e s s a r y t o g e t t h e d e s i r e d t e m p e r a t u r e a t t h e j a c k e t i n l e t . In t h i s c a s e , a c o m p a r i s o n b e t w e e n t h e c a l c u l a t e d in l e tt emper a t u r e , T j in , a n d t h e m e a s u r e d o u t l e t j a c k e t t e m p e r a t u r e T j o u t a l l o w s t o c h o o s e t h e f l u i d t o b e i n j e c t e d a n d t od e t e r m i n e t h e c o r r e s p o n d i n g v a l v e o p e n i n g d e g r e e . M o r e o v e r , i n p r a c t i c e t h e f l o w r a t e o f t h e i n t e r m e d i a t e f l u i d i skep t c ons t an t ( f i fc ) by a t r ap .- I f T jou t _> Ti f i n j ec t i on o f c o l d w a t e r i s needed . The f l ow o f f r e sh c o l d w a t e r ( fw ) t o be i n t r oduc e d i s g i ven by :

fw = f i f e . T j i n - T j u t (15)Tucw - Tj in- I f T jou t < T i f , t he quan t i t y o f s t eam t o be i n t r od uc ed i s g i ven by :

T j in - Tjoutf s t f i f e . C p c w ' [ L v _ C P cw (Tj i n - Tus t ) ] (16)S I M U L A T I O N R E S U L T ST o d e m o n s t r a te t h e g o o d p e r f o r m a n c e o f t h is n e w m e t h o d o l o g y , s i m u l a t io n s t u d i es h a v e b e e n p e r f o r m e d . T h es i m u l a t e d re a c t o r c o r r e s p o n d s t o t h e p i l o t p l a n t p r e v i o u s l y d e s c r i b e d . T h e r e a c t o r i s a s s u m e d t o b e f e d w i t h 1 2 1 o fw a t e r a t 22 C . R eac t o r t emp er a t u r e c on t r o l , ac c or d i ng t o a 4 s t eps t emper a t u r e s e t - po i n t p r o f i l e , ha s been s t ud i ed fo rva r i ous c ond i t i ons :

- 1s t pha se : hea t i ng f r om 2 2 C t o t he des i r ed tem per a t u r e i n 1500 s- 2 ri d pha se : c ons t an t tem per a t u r e s e t - po i n t du r i ng 4500 s- 3 r d phase : c oo l i ng t o 30 C i n 2800 s- 4 t h phase : c ons t an t t em per a t u r e s e t po i n t a t 30 C du r i ng 1200 s .T h e f i r s t s i m u l a t i o n ru n d e a l s w i t h a d e s i r e d c o n s t a n t t e m p e r a t u r e o f 4 5 C ( T c o n s ) . F i g u r e 2 g i v e s t h e t im ee v o l u t i o n o f t h e r e a c t o r t e m p e r a t u r e , t h e s e t - p o i n t a n d t h e a c t u a l m a n i p u l a t e d v a r i a b l e ( th e v a l v e o p e n i n g d e g r e e ) .L e t u s r e c a l l t h a t t h e r e i s n o t u n i q u e v a l v e b u t f o u r : o n e f o r t h e s t e a m w h e n i t i s u s e d a l o n e , o n e f o r t h e s t e a mi n j e c ti o n i n c o l d w a t e r , o n e f o r c o l d w a t e r w h e n t h e i n t e r m e d i a t e f lu i d i s r e c y c l e d a n d f i n a l l y o n e f o r g l y c o l / w a t e r.The p l o t t ed va l ve open i ng deg r ee (~) c o r r e spond s t o t he s i mu l a t i on r un pe r fo r m ed w i t h r ec yc l e d in t e r med i a t e f l u id .F i g u r e 3 g i v e s t h e t i m e e v o l u t i o n o f t h e i n l e t a n d o u t l e t j a c k e t t e m p e r a t u r e s . I n F i g . 4 , t i m e e v o l u t i o n s o f t h el i m i t c a p a c i t ie s f o r e a c h f l u i d a n d o f t h e t h e r m a l f l u x r e q u i r e d ( Q c o n t c o m p u t e d b y t h e c o n t r o l l er ) a r e p l o t te d . T o g e ta m o r e r e a d a b l e f ig u r e , t h e m a x i m a l s t e a m t h e r m a l f l u x h a s n o t b e e n p l o t t e d ( ~- 5 k e a l / s ) . T h e s e t w o f i g u r e s s la o wt h a t t h e i n t e r m e d i a t e f l u i d is u s e d d u r i n g a l m o s t t h e e n t i r e p r o f i l e . J u s t a t t h e e n d o f t h e p r e h e a t i n g s t e p ( a r o u n d1 7 50 s ) , a c h a n g e o v e r o f u t i li t y h a s b e e n p e r f o r m e d f r o m i n t e r m e d i a t e f lu i d t o s t e a m , a s t h e r e q u i r e d t h e r m a l f l u xc o m p u t e d b y t h e c o n t r o l le r o v e r s h o o t s t h e m a x i m u m c a p a c i t y o f t h e i n t e r m e d i a t e fl u i d ( F ig . 4 ) . T h i s c h a n g e o v e r i sa c c o m p a n i e d b y a n a i r p u r g e w h i c h c o r r e s p o n d s t o a n i n l e t j a c k e t t e m p e r a t u r e o f 2 0 C ( F i g . 3 ). A s s o o n a s t h ec o n s t a n t t e m p e r a t u r e s t e p i s r e a c h e d , t h e c o m p u t e d t h e r m a l f l u x b e c o m e s n e g a t i v e ( F i g . 4 ) . T h u s , t h e r e i s a n o t h e rc h a n g e o v e r f r o m s t e a m t o i n t e r m e d i a t e f l u id w i t h a n a i r p u r g e ( F i g . 3 ). W h e n t h e i n t e r m e d i a t e f l u id i s u s e d , o n e c a nn o t i c e a s m o o t h e v o l u t i o n o f t h e i n l e t j a c k e t t e m p e r a t u r e ( F i g . 3 ) . T h i s e x a m p l e s h o w s t h e d o u b l e r o l e o f t h e


5/6

Controllability of batch reactors 3167i n t e r m e d i a t e f l u id w h i ch ca n b e u s e d b o t h f o r h e a t in g a n d co o l i n g . I n F i g . 5 , t h e f l o w r a t e o f s t e a m i n j e c t e d i n w a t e rt o p r o d u ce t h e i n te r m e d i a t e f l u i d h a s b e e n p l o t t e d f o r b o th co n d i t i o n s ( w i t h a n d w i t h o u t r e cy c l e ) . I t ca n b e n o t i c e dt ha t th e r e cy c l e a l l o w s h i g h e n e r g y s a v i n g s . I n a dd it io n , t h is a r r an g e m en t e n a b l e s a g o o d a d j u s t m e n t o f t h e h o t w a t e rt em p e ra tu re a t t he j a ck e t i n l e t b y f e e d i n g s m a l l a m o u n t s o f s t e a m o r co l d w a t e r a s a f u n c t i o n o f t h e r e qu ir e d t h er m a lf l u x .

Temperature (*C) valv e opening 155 0 F - - ~ - - ~ - - ~ - ~ . . . * . ~ . ~ . ~ . . ~ r ~ ` . ~ . - ~ - ~ - - - - r - ~ - . ~ . ~ . ~ . : ~ . ~ : ~ ~ 1

/ - - - - T c o n s X I ; ! 0 . 63 0 3 5 ! / . . . . . . [~ '!~ "~ J ', ~ 0 . 4

i / ii h i" ~ - - 4 : .i : V t . , . . . . . . . . . . . . . . ! . . . . . . . i 00 2 0 0 0 4 0 0 0 6 0 0 0 S0 0 0 1 0 0 0 0Figure 2 : Temperature and manipulated variable

Temperature ( C )80 " . . . . . . . . . . . . . . . . . ' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . r . . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . .0605040302010

time s)' ' '2--000' ' ' ~ . . . . . . . . . . .0 0 0 6 0 0 0 8 0 0 0 10000

Figure 3 : In le t and o ut le t jac ke t temperatures

Th e r mal f lu x (kcal . s - t )2; ' : - ; , - , -

1 ,5 k . . . . . Q m ~ x\ I . . . . . K r m m . f ~ . . . . . .1 .~ % ~ - - i n ' . . " "

o - ~

t i m e ( s )- 1 0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0

Figure 4 : Limits and con tro l va lue o f the thermal f lux

1. 61. 41. 21.(30 .80 .60 .40 .2

S te am f lowr ate in j e c te d in th e in te r me d ia te f lu id (k g / s ) x 1 0 "

- - w i t h o u t r e c y c l e I~ ] . . . . recycle I!

t............ ~ ~ . : n . . , _ ~ . g ~

F i g u re 5 : F l o w r a t e o f s t e a m w i t h a n d w i t h o u t r e cy c l eT o s t u d y t h e f l e x i b i l i t y o f t h i s s t r a t e g y , a n o t h e r s i m u l a t i o n r u n h a s b e e n p e r f o r m e d f o r a d i f f e r e n t co n s t a n t

t e m p e r a t ur e s e t - p o i n t : 6 0 C . L e t u s n o t i c e t h a t a ch a n g e o f t h i s te m p er a tu r e i m p l i e s g r e a t e r he a t i n g a n d c o o l i n grates . F ig . 6 shows that the reactor temperature fo l lows perfect ly the se t -point prof i l e . As prev ious ly ment ioned , theo p e n i n g v a l v e d e g r e e ( 6 ) c o r r e s p o n d s t o t h e fo u r di f f er e n t v a l v e s a n d t o t he ca s e o f r e cy c l e d i n t e r m e d i a te f lu id . F i g .7g i v e s t h e e v o l u t i o n o f t h e r m a l f l u x l i m i t s f o r e a ch u t i l it y fl u i d a n d t h e th er m a l f l u x ca l cu l a t e d b y t h e co n t r o l l er . A sexpec ted , due to the h igher temperature lev e l , the required capac i t ie s o f heat ing and coo l ing are larger. Com pared tothe previous c ondi t io ns (F ig . 5 ) , a l l the d i f ferent ut i l i ty f lu ids hav e had to be used . In particu lar , dur ing the heat ingphase , s tea m i s required ins tead o f intermediate f lu id. S im i lar ly , a t the end of the coo l ing phase (around 800 0 s ) , theh i g h e r co o l i n g r a t e i m p l i e s a ch a n g e o v e r f r o m i n t e r m e d i a t e f l u i d t o g l y co l / w a t e r . T h e s e ch a n g e o v e r s o f f l u i d s a r edecide d automat ic a l ly by the supervi sory contro l s trategy based on the thermal f lux c omputat ion .

Temperature ( C ) v a l v e o p e n i n g 1370 t . . . . . . . . . t . . . . l ~ " ' ' i 1t ~ T r I ~ [[ . . . . . T c o n s | t l I60 L ~ .~ .~ i - ~ o 8_ l , . ~ ,, o i ! 4 , 6t i i \ t ~ , , Io f / , f l .io ,,

~ / I , ! t i " k . ; i I3 og v ! [ i i ! , i ! L i jzv~^ r J i , " ~ s _ . . . . . . . . . . . . k d . . . . . ':.iv ' L . :' ^0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 uFigure 6 : Temperature and m anipulated variable

Th e r mal f lu x l imi t s (kcal . s t )2 " - - ~ " - , . . . . . . . . . r " ' ~ ' ' ~ . . . . . . . . r ' ' ~ ' ' ~ . .. . .. .. r ' " ~ ' " ~ ' " ~ " ' r . .. . .. .. . " ' " ~ " "

I - - Q c o n t1 , 5 ~ [ . . . . Q m a x i t' t I . . . . Q m a x1 " [ ~ f ~ . . . . . Q m m . - " . . . .I N I 4 - - Q m i n , ,, " " , 1 L '= " i0 , 5 " . . , . . . ~ "

- 0 , 5 " " " " " , " 4 ~. . . . . . . . . . . . . t i m e { s )

- 1 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 10000Figure 7 : Lim its and contro l va lue o f the thermal f lux


6/6

316 8 Z. LOULEHet a l .C O N C L U S I O NT h i s s t u d y d e m o n s t r a t e s t h e f e a s i b i l i t y o f t h e d e v e l o p e d s u p e r v i s o r y c o n t r o l s t ra t e g y b a s e d o n t h e t h e r m a l f l u xc o m p u t a t i o n . T h e r e s u l t s e x e m p l i f y t h e m u l t ip u r p o s e c h a r a c te r o f t h e p r o p o s e d m e t h o d o l o g y w h i c h i s a n e c e s s a r yc ond i t i on fo r a suc c es s fu l au t oma t i on o f ba t c h c hem i c a l r eac t o r s .T h e s t r a te g y p r e s e n t s t h e a d v a n t a g e s o f a m u l t i - fl u i d th e r m a l s y s t e m ( p o s s i b i l i ty t o u s e u t i l i ty f l u id s d i r e c t l ya v a i l a b l e o n a p l a n t ) a n d t h o s e o f m o n o f l u i d t h e r m a l s y s t e m ( c h a r a c t e r i s e d b y h i g h d y n a m i c p e r f o r m a n c e a n dc o n t i n u i t y o f t h e r m a l c o n t r o l ) . T h e m o d e l b a s e d s u p e r v i s o r y c o n t r o l a l l o w s a n a d e q u a t e c h a n g e o v e r o f t h e r m a lu t i l i ty f l u i d a s a func t i on o f t he f e a s i b l e c apac i t y o f t he t he r m a l c onf i gu r a t i on .N O T A T I O N-a- C p- c v s- f- L v- Pcw-P j- Ps t-Q- Q c o n t- Q m a x , Q m i n- T-x j- T r- T u- U

hea t t r ans fe r a r ea (m 2)spec i f i c hea t (kc a l K g -1 K -1)va l ve spec i f i c a t i on (kg s - 1 ba r 1 / 2)ma ss f l ow r a t e (kg s - 1 )l a t e n t h e a t o f s t e a m ( k c al k g - 1 )m a i n w a t e r p r e s s u r e b a rs t e a m p r e s s u r e i n t h e j a c k e t b a rfeed s t eam pr es su r e ba rt he r ma l f l ux exc hang ed be t w een j ac ke t f l u i d and r eac t i on mi x t u r e (kc a l s - I )t he r ma l f l ux c om pu t ed by t he c on t r o l l e r (kc a l s - I )m a x i m a l a n d m i n i m a l v a l u e s o f t h e t h e r m a l f l u x ( k c a l s - 1 )t emper a t u r e (K )j ac ke t t emper a t u r e (K )r eac t i on mi x t u r e t emper a t u r e (K )sou r c e t emp er a t u r e o f u t i l it y f l u i d (K )hea t t r ans fe r c oe f f i c i en t (kc a l m - 2 s - 1 K - 1 )

G r e e k c h a r a c t e r s-8- AOmS u b s c r i p t scwg wifino u ts t

v a l v e o p e n i n g d e g r e emean t emper a t u r e d i f f e renc ec o l d w a t e rg l y c o l / w a t e ri n t e r med i a t e f l u i di n l e to u t l e ts t eam

(% )(K )

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