improving safety and productivity of isothermal semi-batch ... - EPFL

IMPROVING SAFETY AND PRODUCTIVITY
OF ISOTHERMAL SEMI-BATCH REACTORS
BY MODULATING THE FEED RATE
PAR
Olivier UBRICH
lngdnieur chimiste ENSSPICAM
de nationalit6 franqaise
acceptbe sur proposition du jury:
Prof. F. Stoessel, directeur de thhe
Prof. D. Bonvin, rapporteur
Prof. K. Hungerbijhler, rapporteur
Prof. G. Kille, rapporteur
Dr Th. Meyer, rapporteur
Lausanne, EPFL
2000

Version abregee
Depuis la prise tle conscience cies risques que penvent erltrairrer urle production
cllimique ma1 gkrke, dc nornbrcuscs cntrcprises sc sont penchkes sur la si.curit6 thcrmiquc
dcs procCd6s. Ces dernihrcs annkcs, le contrale des r6actions cst devcnn nn
dcs soucis ~najcrlrs dcs indr~strics. Afin d'avoir un mcillc~~r contrblc, Ics proc6diis dc
chimie fiue sent la plupart du temps rBalisCs en mode serni-batch. De nlClnle, pour des
raisoms de selectivit6, Ic mode isothcrmc cst souvcnt Ic lr~ode utilise. Ainsi, normalt:ment,
les reactions se dCroulent sans incidents. Cependant, occasior~nellement, elles
s'ernballent parce que des materiaux inadecluats out kt6 utilisb, parce que les conditions
operatoires ont chaugCt 011 encore parce qne les Cqnipemer~ts sont d6fect11e1~u.
Lors dc toutc 6tudc dc scaleup, dc~uc questions fondamentalcs doivent Btrc posbcs. La
prcmihrc cst relative aux conditions normalcs dc fonctio~nicmcnt. I1 cst n6ccssaire dc
v6rificr que le systhmc dc refroidisscmcnt soit capablc dc maintcnir la tempkraturc sltr
la trajectoire dksirke. Pour cela, il faut vBrifier sorl aptitude ii Bvacuer ii tout instant
la cl~aleur produitc par la rkaction chirnique. Ainsi, lc systkme est capable de rester
en mode isotherme. La deuxikrne est relative ii I'Bvolution de la nlasse r6actionnelle
en cas de dysfonctionnernent. I1 est r~kcessaire de vkrifier que la rBactio11 ne puisse
p~s cor~duire ti une situatior~ critiqne en cas de parlne ~ Isysterr~e I tle refroidissetnent.
Avant tolitc mise cn production d'un nouvcan procbd6 scmi batch, tmc 6t1ldc
dc s6curitB est rkaliske. La plupart du temps, clle sc bornc h vkrificr In faisabiliti: du
prockdi! pour un flu d'introductior~ de reactif cot~sti~t~t. Ut1 tel flux est utilise pour
des raisons pratiqucs: il cst cn cffct Ic 11l1ts fitc.ilt9 .:I ri-i~list.~.. II c~sistc~ elor~c c.11 cc poi~~t
precis n~atiere ii am6lioratior1 tiit lit ~)~.t~cI~~c~ti\~ili.. I

sance cfcs contraintcs A chaque instant pcrn~ct de d6finir uric fonction d'introduction
optimale. I1 cst alors possi1)le de ddtcrminer explicitenlent nnc fonction d'ajont compos6c
de diffkrcntes scgmcnts kvcntucllcnlcnt approchks par unc succcssion dc diffbrcnts
palicrs. Dc mgmc, lcs temp dc basculcment entre ces diffhrcntes scgmcnts
sont connus. En fait, il existe deux rnani6res de r6aliser l'implaritation de la m6thode:
soit en boucle fermke, soit en boucle ouverte.
La m6thode va 6tre app1iqui.e datis un premier temps en boucle ouverte. Dar~s
cc cas il est ndccssairc de trouver dc facon cxplicite la cinetiquc de la reaction 6tudiCe
avant de po~~voir rdaliscr l'optiniisation. Cctte btude cir16tique B 6tk r6alisi.c cn couplant
la calorinlbtrie ct la spcctroscopie (infrarougc ct Raman) lors de m6mes expbricnces.
Une fois la cinetique Ctablie, l'optimisation est test6e expbrimentalement:
les rdst~ltats sont compards avcc dm sin~i~lations thCoriques. La nlkthodc s'av&rc efficace,
rriais est trh dkpendante de la precision de I'etude cinktique. De plus, elle peut
s'avkrer probl6rriatiyue lors de son implantation si la cinktique ne corresporid pas li
celle deterrninee en laboratoire.
Dc cc fait, la mbthodc d'optimisation utilisant une boilclc ferm6c revet des avantages
ddtermiriants. Afin de pouvoir implanter la mbthode en boucle fcrrnbc, il a 6t6
necessairc dc modifier un calorinlbtre commercial dc maniere a determiner l'dcart de
la trajcctoirc par rapport a la contrainte active et de l'y maintcnir. L'installation
a bt6 utiliske pour optimiser une r6action aux parametres cin6tiqucs inconnils. Elle
permettra kgalement de prouver l'importance de I'utilisation de boucles fernlees en
se niontrant trks robuste vis a vis de l'utilisation de produits plus ou moins purs.
Ainsi, ce travail met en kvidence l'importance de l'utilisation d'une fonction
ti'ajout non 1int.aii-e pour des procdes semi batch r6alisi.s en mode isotherme. Elle
pcrrnct uric arnklioration de la productivitk tont en 6vitant les risques thcrrniques
en conditions normales de fonctionnement, conime en cas de panne du systen~e de
refroidissemcnt.

Summary
In recent decades, a more profound understanding has been realized that 1111controlled
chemical processes can lead to accidents with severe conscqnences. Many
chemical corripanies became active in research on thermal risks. For chemical engineers,
the control of chenlical reactions becarrie one of the most important concerns.
Thus, for a better control, most fine chemical processes today are performed in a
semi-batch mode. Also, isothermal operating conditions arc often employcd for inlproved
sclcctivity. As a rule, the chcrr~ical reactions proceed without problems, 1~1t
in some rare cases unfortunately a runaway situation is encolintered, because wrong
mat,crial havc been uscd, opcrating conditions havc changed, or cquipmcnt has been
deficient.
In any scale-up from laboratory or pilot to full-scale operation, two cluestions must
be answered. The first one relates to the normal operating conditions. Indeed, it will
always be necessary to verify that the reactor temperature can be niaintained along
the dcsircd path. In other words, it mnst be verified that the capacity of the cooling
system will at all ti~nes be able to ncntralizc cxccss heat gcr~cratctl ar~ywhcrc within
the rcactor by the chcrnical reaction. The system will thcn function isothcrn~ally.
The second cllicstion relates to the bchavior of rcactor tcmpcratnre in thc c=c of
technical failures. It will bc ncccssary to verify, for instancc, that a critical situation
can be avoided when the cooling breaks down.
Thermal studies are realized, therefore, before any new semi-batch process is put in
operation. With respect to reaction cornponent feed, such studies gerierdly tent1 to
cvalnatc the fcasibilit,~ of the process under coiidit,ior~s of a st,rict,ly linear ii~t,rod~iction
of one componcr~t into the reacting system. Such a fed function is uscd for practical
rcasons like case of implcmcntation. Howcvcr, no fnndamcntd rcasons spcak against
using a nonlinear fccd function. Lifting thc limitation to lincas fccd frlnctions may
actnally opcn up ways to improvc the productivity. Physical and safety constrain1,s
rnust of course be respected just as rigorously when using a nonlinear feed function.
It was the airn of this work to define a method that can be applied to run isotherrn:il
semi-batch reactors while using a controlled nonlinear feed rate. This method should
yield scnsit)ly reduced cyclc timcs while fiilly acco~~~rr~odating all irnposctl coristraints.
Thc n~odnlation of fccd rate rnust be such that thcsc objjectives can 1)c achieved.
Toward this aim, a preliminary mathematical study of nonlinear systems ha< first
1)cen realized. A simple mcthod is presented in this part of the work which allours

one to recognize whether a given chernical reaction model will be influenced by the
feed of one of the components. In systems defined a? being "feedback linearizable",
the production optimum depends on the constraints alone. This means that the optimlmm
feed rate can be defined fiom a mere knowledge of the dominating constraint as
a function of time. It will then be possible to explicitly deterrniue the function as a
composite of different consecutive segments, each depencling on an active constraint.
The switching times Getweer1 the different segn~erlts can also be defined. Implementation
may occur in ;in opo~ or in n closccl loop.
In a first np~)ro;lc:l~. lilt: IIII~I~IIII~ \\.;is ~~li~I~orii~(~l li~r o1)(:11-1001) S~S~CIIIS. As a prercq~~isilc
to ol)ti~r~iz;~~io~~.
t111a. IIIII>I ~.s~~Ii~.itl\ II~-II,~III~II(! 11~: kinet;ics of the chemical
sys11~111 (,ol~siIit~rI~l. *r11i> \\;L\ I ~ ~ I I ill I ~ . t11t. ~II..I;IIII.I, t)f' it i~~~~)r(!scl~t.;lti~~c reaction, by
o i I r i ~ I ~ ~ r t t t i ( it t i ' i ~ I l I I I ) ~csren~ents. Usil~g
tllc, ki~~c-tia. I)~II.~IIII~~II.I~ tIt.11'1 111i11tll1 ill IIIIW. IIII~~I~II~I~IIIL'II~S, the optirrlization was
~xrSvr~~~erl. 'I'II(w (.~l)I:ri~l~ta~~l . l1i14 1.4 WIII 11i1vc I,~~.II cor~~pared with theoretical
si~~ruli~tio~is. T~II* IIII~I~IIII~ I)~II\IYI III \)I. t~liic:iciit, I~ut also strongly cfepenclent on the
accnracy of thc ki~ict.ic. cl;lt;l. Tlicrclbrc, apart from below-optinl~nn process conditions,
hazartloi~s sitliatio~~s I I I IJ)C ~ ~ CIICOIIII~~~C~, for instance, as a result, of changes
in reaction kinetics caused by conta~nination of the reaction medium. Hcrc an 011line
optimization implementing a closed-loop optimization algorithm presents strong
advantagw.
For the work involving closed systerns, it was necessary to use a rnodified reaction
calori~r~eter allowing the trajectory divergence to be evaluated relative to the active
constrai~lt, and coutrol the systerr~ accordingly. This i~~stallation was utilized for the
optinlizatio~~ of a chenlical reaction for which the kinetic parameters were unknown.
The si~periority of thc closed loop was also demonstrated by revealing its robustness
with regard to a contamination of the reaction system by an impurity affecting the
kinetics.
In conclusion, it was shown in this work that 1~y using a modulated rextant feed
function for serni-batch processes performed isothermally under constraints one can
sigr~ificantly improve the productivity, and at the same time avoid severe consequences
of incidences such a? a cooling failure.

Contents
Nomenclature
1 Introduction
2 Bibliography
2.1 Iritroduction ................................
2.2 Thcr~nal stability .............................
2.2.1 In 11or111al operating .......................
2.2.2 Coolir~g failure ..........................
2.3 Optirnizatiom of thc proccss .......................
2.3.1 Optimization without any constraints ..............
2.3.2 Optimization under constraints .................
2.4 Organii~at~ion of thc thcsis ........................
3 Characterization of the optimal solution
3.1 Introduction ................................
3.2 Preliminaries ...............................
3.2.1 Nonlinear systems . ........................
3.2.2 Short introduction to Lie algebra ................
3.2.3 Feedback linearization ......................
3.3 Forrr~ulatiorl of the optimization problern ................
3.3.1 Problern forniulation .......................
3.3.2 Optirnurn of a feedback linearizable system ...........
3.3.3 Singular regions . .........................
3.3.4 Characterization of optimal input for feedback linearizable systerns
................................
3.3.5 Formulation of constraillts ....................
3.3.6 Shapc of thc optimal solution ..................
3.4 Proposcd methodology for finding an optimal solutior~ .........
3.5 Kinetic models in isothcrmal mode ...................
3.5.1 Case of consecutivc reactions ...................
3.5.2 Case of diffcrcnt ordcr parallel reactions ............

CONTENTS
3.5.3 Case of same order parallel reactions .............. 55
3.5.4 Case of nth-order reactions with impurity in feed ........ 56
3.5.5 Case of consecutive parallel reactions, case number one .... 58
3.5.6 Case of consecl~tive parallel reactions. casc number two .... 60
3.5.7 Case of nth-order reactions with decomposition . ........ 63
3.5.8 Recapitulation ........................... 64
3.6 Qualitative comparison wit11 the method used in industry ....... 67
3.7 Conclusions ................................ 69
4 Off-line feed control: Case study
4.1 Int~oductior~ ................................
4.2 The reaction ................................
4.2.1 The model reaction examined ..................
4.2.2 Plailsibility check for the reaction being 2nd order .......
4.2.3 Can the selected reaction be considered as a 2nd order reaction?
4.3 Identificatiorl of kinetic pararrieters ...................
4.3.1 Results of thc spectroscopic measurements ...........
4.3.2 Results obtained by calorimetry .................
4.3.3 Evaluation of the activation energy and of the frequency factor
4.3.4 Calorimetry or spectroscopy: advantages/disadvantages . ...
4.4 Optimization: experinlerital results ...................
4.4.1 Spectroscopic results .......................
4.4.2 Calorimetric results ........................
4.5 Optimum constar~t feed rate: experirnerltal results ...........
4.6 Comparisons ................................
4.7 Conclusion
.................................
5 On-line feed control: Case studies 97
5.1 Introduction ................................ 97
5.2 Experirnentalset-up ........................... 98
5.3 The second-order reaction: experirncntal results ............ 101
5.3.1 Calibration ............................ 101
5.3.2 On-line results . .......................... 102
5.3.3 Cornparkon with constant feed rate . .............. 104
5.3.4 Limitation of the method . .................... 105
5.4 A more complex reaction system: experimental rcsillts ........ 105
5.4.1 The reaction . ........................... 106
5.4.2 Heat of mixirlg .......................... 107
5.4.3 Heat of rcaction .......................... 108
5.4.4 h/lodulated feed method with pure product: experimental results109
5.4.5 Parametric sensitivity ...................... 114
5.4.6 Adiabatic experiments ...................... 116

CONTENTS 13
5.4.7 Cornparison with constant feed ratc ............... 118
5.5 Modulated feed mcthod with impure product ............. 119
5.5.1 Constant feed rate expcrimc~lt .................. 120
5.5.2 Modrilated fced mcthod: cxpcrimental results ......... 120
5.5.3 Cornparisor1 ............................ 121
5.6 Conclusiori ................................. 122
6 Conclusions 125
6.1 Summary ................................. 125
6.2 Perspect;ives ................................ 127
7 References 129
8 Annex 137