Product size distributions in continuous and batch sucrose crystallizers

PRODUCT SIZE DISTRIBUTIONS

IN CONTINUOUS AND BATCH

SUCROSE CRYSTALLIZERS

Stefan K. Heffels

TR diss

1519

PRODUCT SIZE DISTRIBUTIONS

IN CONTINUOUS AND BATCH

SUCROSE CRYSTALLIZERS

PRODUCT SIZE DISTRIBUTIONS IN

CONTINUOUS AND BATCH SUCROSE CRYSTALLIZERS

<y\N13Cr

j O prome

J £ ■• •■;-' l Ö> DtLi-1

PROEFSCHRIFT V>

ter verkrijging van de graad van doctor aan de Technische Universiteit Delft op gezag van de Rector Magnificus, Prof.dr. J.M. Dirken, in het openbaar te verdedigen ten overstaan van

een commissie aangewezen door het College van Dekanen op dinsdag, 16 december 1986 om 16.00 uur

•Volii-'.'iC'ï'i I "

door

STEFAN KARL HEFFELS

Diplom Ingenieur (TU) Verfahrenstechnik, geboren te Buffalo, N.Y., USA

TR diss

1519

STELLINGEN

Het verschijnsel dat grote suikerkristallen harder groeien dan kleine komt niet doordat ze harder groeien naarmate ze groter worden maar doordat hard groeiende kristallen groot worden en langzaam groeiende kristallen klein blijven.

Uit filtratie overwegingen is een eis aan het product over de hoeveelheid kristallen kleiner dan lOOum relevanter dan alleen de gemiddelde kristalgrootte en de spreiding,in kristalgrootte.

Verwijdering van, isolatie aan een wand boven de kookzone van een suiker-kristailisatör.is preventief' op het aankorsten.

Dé zwalttë'yan'dë/TÜ is dat zij?haar eigen sterkte niet kent.

Dé drang naar persoonlijk langer werken wordt nauwelijks beloond en meer beleinmerd door: de werktijdregeling aan de TU.

Nichts Tim; macht "auf: die Dauer unglücklich, denn wie Sartre richtig ausdrückte':" Wiréxistieren nur insofern, als wir unser Sein zu

rechtfertigenivermogen; dürch unsér Tun und Verhalten. Unser Sein ist .etwas, zu'-' L'eisfcendes" v 4'"^.

-Er komt,Vahvzelf méér werk wanneer men maar meer werkt.

Jeder, der im Ausland gelebt :hat," Wird dem Spruch von Antoine de Saint-Exupèry zustimmen: "Urn sich in einem Land, in einem bestimmten Milieu wohl zu fühïehi.niup man alle-Brauche und Konventionen anerkennen. Sie sind es die,üns Wurzeï schlagen lassen. Ohne Konventionen zu leben, macht sèhr melancholisch, man leidet gewisserma^en an einem Mangel an Wirklichkeit."

Het koopgedrag van de burgers ten aanzien van buitenlandse goederen is in strijd met hun politiek standpunt.

Fortune is the discovery of details.

Zolang zenders beloond worden op grond van hun kijkersdichtheid, zullen de door het kabelnet aangeboden progamma's niet veelzijdiger worden, maar steeds meer op elkaar lijken.

Meer kriminaliteit en andere wetsovertredingen zijn een gevolg van een steeds toleranter wordende overheid.

S.Heffels

Product Size Distributions in Continuous and Batch Sucrose Crystallizers van S.K. Heffels p.6 middle P.7 p.13 middle p.l8 bottom p.18 eq.2.1.23 p.18 p.23 line 3 p.57 bottom p.55 middle [12.13] vary experiments 2.1.11 / [95] (2.1.19) fig 2.2.22 [62] instead of [11,12] varies expeiments 2.2.13 [116] (2.2.11) fig 2.2.24 [63]

p.155 Engineering Group Development Group (Anlagenplanung)

Acknowledgement

This research project was sponsored by the "Coöperatieve Vereniging Suiker Unie U.A.".

SUMMARY

The o b j e c t i v e of t h i s study i s to obtain a b e t t e r understanding of the for­

mation of c r y s t a l s i z e d i s t r i b u t i o n s (CSD) i n s u c r o s e c r y s t a l l i z e r s . This

s h o u l d be h e l p f u l i n t h e development of models f o r p r e d i c t i n g CSDs when

cascaded continuous c r y s t a l l i z e r s are t o be designed. I t should help a l s o in

t h e o p t i m i z a t i o n of CSDs of batch and c o n t i n u o u s c r y s t a l l i z e r s , and i t

serves as a b a s i s for the development of new c o n t r o l s y s t e m s . The CSD i s

s t r o n g l y e f f e c t e d by t h e n u c l e a t i o n and growth k i n e t i c s , on both of which

d i s c r e p a n c i e s e x i s t in the l i t e r a t u r e . Therefore, the mass t r a n s f e r , c r y s t a l

g r o w t h , and nucleation a r e analyzed i n the f i r s t p a r t s (chapters 2 . 1 - 3 ) . In

the l a s t p a r t , the k i n e t i c s are applied to s i m u l a t e t h e f o r m a t i o n of CSDs

u s i n g a MODIFIED FRACTION TRAJECTORY CONCEPT. Experiments were performed in

a 1.4 m

3

evaporative c r y s t a l l i z e r to obtain system s p e c i f i c d a t a for numeri­

c a l c a l c u l a t i o n s and t o v e r i f y the s i m u l a t i o n and i n d i r e c t l y the k i n e t i c

r e l a t i o n s h i p s found i n bench s c a l e equipment.

The main r e s u l t s , conclusions, and t h e i r s i g n i f i c a n c e a r e given below:

- Experiments confirmed t h a t small c r y s t a l s grow i n a v e r a g e v e r y s l o w l y ,

much slower than l a r g e c r y s t a l s (chapter 2 . 2 ) . An influence of the mass

t r a n s f e r was noticed and the influence increased with i n c r e a s i n g c r y s t a l

s i z e . The measurements under the microscope proved t h a t growth of small

and l a r g e c r y s t a l s i s influenced s i g n i f i c a n t l y by t h e s u r f a c e r e a c t i o n

even a t 70° C i n c o n t r a s t t o previous r e p o r t s in l i t e r a t u r e . Growth r a t e

d i s p e r s i o n was observed, which means c r y s t a l s of t h e same s i z e grow a t

d i f f e r e n t v e l o c i t i e s even i n the same environment. Furthermore, the in­

fluence of the s u p e r s a t u r a t i o n , t e m p e r a t u r e , and c r y s t a l o r i g i n on the

growth r a t e was measured. The growth behaviour could be explained well

with a Burton, Cabrera and Frank model. If any s i m p l i f i c a t i o n s have t o be

made when s i m u l a t i n g t h e formation of CSDs, i t i s recommended to use a

growth r a t e d i s p e r s i o n model with c o n s t a n t growth r a t e s of i n d i v i d u a l

c r y s t a l s .

- The mass t r a n s f e r c o e f f i c i e n t of diffusion between c r y s t a l and s o l u t i o n

was determined by experiments in a c e l l under a microscope and i n a 0.8 1

s t i r r e d v e s s e l (chapter 2 . 1 ) . A dispersion i n d i s s o l u t i o n r a t e s was found

and c o u l d be e x p l a i n e d by t h e d i f f e r e n c e s i n c r y s t a l shapes. The mass

t r a n s f e r c o e f f i c i e n t in s o l u t i o n s with low p a r t i c l e c o n c e n t r a t i o n (e*1.0)

i n c r e a s e d s t e a d i l y with decreasing c r y s t a l s i z e . Consequently, the s i z e

dependency of the mass t r a n s f e r c o e f f i c i e n t c a n n o t e x p l a i n t h e a p p a r e n t

s i z e dependent growth which had been reported by o t h e r s . Experiments on a

p i l o t p l a n t s c a l e using a dense s l u r r y (e<1.0) support the Sherwood equa­

t i o n of Nelson and Galloway.

- I t was shown by experiments t h a t in the b o i l i n g zone of a sucrose c r y s t a l ­

l i z e r primary nucleation i s n e g l i g i b l e . Nuclei are formed due to c r y s t a l

-i m p e l l e r and c r y s t a l - w a l l -impacts, and not by f l u -i d shear. The n u c l e a t -i o n

r a t e c o u l d be reduced by coating the s t i r r e r blades with t e f l o n t a p e . The

e f f e c t of c r y s t a l s i z e , s t i r r e r speed, s u p e r s a t u r a t i o n , and temperature on

t h e n u c l e a t i o n r a t e was s t u d i e d i n d e p e n d e n t l y on bench s c a l e equipment

(chapter 2 . 3 ) . I t was shown t h e o r e t i c a l l y and experimentally t h a t n u c l e a ­

t i o n i s p r o p o r t i o n a l t o t h e f i f t h moment of t h e p o p u l a t i o n d e n s i t y

d i s t r i b u t i o n . I t d o e s n ' t depend on the s l u r r y d e n s i t y as was assumed so

f a r i n l i t e r a t u r e and on which power laws of secondary nucleation are

u s u a l l y based. Furthermore, i t appeared t h a t many i n v i s i b l e b u t s t a b l e

n u c l e i can e x i s t i n a s o l u t i o n within the metastable zone and c o n s t i t u t e a

persaturation on the amount of crystals to grow was measured independently of the total nucleation rate. It allowed to differentiate between total and effective nucleation rate.

- The second part as mentioned in the first alineas deals with a numerical calculation procedure called MODIFIED FRACTION TRAJECTORY CONCEPT (chapter 3.3)' It enabled to simulate the CSD for batch and continuous crystal-lizers without general, idealized assumptions. It permitted simulation of batch and nonstationary continuous crystallizers taking into account growth rate dispersion and size dependent growth rate, the presence of a nuclei stock, fines removal, and a supply of crystals in the feed. The simulations support the crystallization kinetics determined in bench scale equipment. Simulation of the CSD for batch and continuous crystallization supports clearly the growth rate dispersion model in combination with a stock of nuclei and not a size dependent growth rate model. The apparent size dependent growth reported in the literature results from a clas­ sification of crystals according to their growth rates. The few fast growing crystals become large whereas the many slow growing crystals remain small. It was shown that crystallization under a steady state con­ dition is not sufficient to derive the kinetics adequate for modelling the evolution of the CSD under nonstationary condition (chapter 3«5)- The simulated transient conditions in crystallizers depends strongly on the growth and nucleation rate model. The presence of a stock of nuclei damps fluctuations of the process conditions, with other words fines removal decreases the stability of process conditions. The nucleation rate con­ stant is difficult to predict because it depends on the stock of nuclei which is influenced by the inhomogenities in the supersaturation in crys­ tallizers. Experiments indicated that the effective nucleation depends on the operation of the crystallizer, namely the undersaturation of the feed and near the heat exchange surfaces. Therefore, informations for scaleup purposes should be obtained not only with similar equipment but also under similar operating conditions. From the results of the simulations it can be recommended that full seeding techniques should be applied also in continuous crystallizers as is being done in batch crystallizers. Controlled supply of fines allows operation at low supersaturation, where effective nucleation is negligible, and damps the dynamic behaviour of the process.

SAMENVATTING

Het d o e l van h e t onderzoek i s de k e n n i s t e vergroten over de vorming von

k r i s t a l g r o o t t e v e r d e l i n g e n (KGV). Deze k e n n i s kan g e b r u i k t worden voor de

m o d e l o n t w i k k e l i n g om KGV t e v o o r s p e l l e n w a n n e e r c a s c a d e s van

k r i s t a l l i s a t o r e n ontworpen moeten worden. Het moet ook h e l p e n KGV i n b a t c h

en k o n t i n u e k r i s t a l l i s a t o r e n t e optimaliseren, en d i e n t a l s b a s i s voor de

ontwikkeling van nieuwe regelsystemen. De KGV wordt i n grote mate b e ï n v l o e d

door kiemvorming en k r i s t a l g r o e i s n e l h e i d , waarover tegenstrijdigheden t e

vinden z i j n i n de l i t e r a t u u r . Daarom worden de s t o f t r a n s p o r t s n e l h e i d , de

k r i s t a l g r o e i s n e l h e i d en de k i e m v o r m i n g i n h e t e e r s t e d e e l van d i t

p r o e f s c h r i f t behandeld. In het l a a t s t e deel van d i t p r o e f s c h r i f t worden de

r e s u l t a t e n t o e g e p a s t b i j de simulatie van de zich ontwikkelende KGV in een

model genaamd "Modified Fraction Trajectory Concept". Experimenten aan een

l,4m

3

k r i s t a l l i s a t o r leverden systeem specifieke waardes voor het model en

v e r i f i e e r d e n de s i m u l a t i e en i n d i r e c t ook de k i n e t i e k r e l a t i e s u i t h e t

e e r s t e d e e l .

De voornaamste r e s u l t a t e n , c o n c l u s i e s en hun b e t e k e n i s kunnen a l s v o l g t

samengevat worden:

- Experimenten bevestigden dat kleine k r i s t a l l e n v e e l langzamer dan g r o t e

k r i s t a l l e n groeien (hoofdstuk 2 . 2 ) . Een invloed van de s t o f t r a n s p o r t s n e l

-heid op de groei i s wel aanwezig en de i n v l o e d neemt t o e met toenemende

k r i s t a l g r o o t t e . De experimenten onder de mikroskoop toonden aan dat de

g r o e i van k l e i n e en g r o t e k r i s t a l l e n s i g n i f i c a n t door de o p p e r v l a k t e

r e a k t i e worden b e i n v l o e d . G r o e i d i s p e r s i e werd waargenomen, h e t g e e n

betekent dat k r i s t a l l e n van g e l i j k e g r o o t t e onder g e l i j k e k o n d i t i e s met

v e r s c h i l l e n d e s n e l h e d e n g r o e i e n . V e r d e r werd de i n v l o e d v a n de

oververzadiging, t e m p e r a t u u r , en k r i s t a l o o r s p r o n g op de g r o e i s n e l h e i d

g e m e t e n . Het g r o e i g e d r a g kon met h e t B u r t o n , C a b r e r a en Frank model

verklaard worden. Als men voor de s i m u l a t i e van de KGV h e t groeimodel moet

gaan vereenvoudigen, i s het raadzaam een groeidispersiemodel t e gebruiken

met konstante groeisnelheden van individuele k r i s t a l l e n .

- De s t o f t r a n s p o r t c o ë f f i c i ë n t voor d i f f u s i e t u s s e n een k r i s t a l en een

o p l o s s i n g werden b e p a a l d middels e x p e r i m e n t e n i n een c e l l o n d e r de

m i k r o s k o o p en i n g e r o e r d e vaten (hoofdstuk 2 . 1 ) . Een d i s p e r s i e i n

k r i s t a l oplossnelheden werd geconstateerd en verklaard door v e r s c h i l l e n i n

k r i s t a l v o r m e n . De s t o f t r a n s p o r t s n e l h e i d i n o p l o s s i n g e n met een l a g e

d e e l t j e s c o n c e n t r a t i e (e

s

1.0) i s omgekeerd evenredig met de k r i s t a l g r o o t t e .

K l a a r b l i j k e l i j k kan de s t o f t r a n s p o r t c o ë f f i c i ë n t n i e t de door anderen

gerapporteerde lengteafhankelijke groeisnelheid v e r k l a r e n . Experimenten op

semitechnische schaal ondersteunen de r e l a t i e van Nelson and Galloway voor

e<1.0.

- Het werd e x p e r i m e n t e e l aangetoond d a t i n een kookzone van een suiker

k r i s t a l l i s a t o r primaire kiemvorming verwaarloosbaar i s . Kiemen worden door

b o t s i n g e n met r o e r d e r b l a d e n en met de wand gevormd en n i e t door

afschuifkrachten i n de oplossing. De kiemvorming wordt gereduceerd a l s men

de r o e r d e r b l a d e n met een z a c h t e T e f l o n t a p e c o a t . De i n v l o e d e n van

k r i s t a l g r o o t t e , r o e r d e r s n e l h e i d , o v e r v e r z a d i g i n g en t e m p e r a t u u r op de

kiemvormingsnelheid werden onafhankelijk van e l k a a r op laboratorium schaal

onderzocht (hoofdstuk 2 . 3 ) . Experimenteel en t h e o r e t i s c h werd aangetoond

d a t de kiemvorming e v e n r e d i g met h e t v i j f d e moment van de p o p u l a t i e

d i c h t h e i d i s . Deze i s n i e t evenredig met de s l u r r y d i c h t h e i d zoals dat t o t

nu t o e v e r o n d e r s t e l d werd en waarop de k i e m v o r m i n g s r e l a t i e s m e e s t a l

vormen een r e s e r v o i r van kiemen. P l a a t s e l i j k e hoge oververzadigingen zoals

z i j voorkomen i n e e n k r i s t a l l i s a t o r kunnen deze kiemen t o t g r o e i

aktiverèn. De invloed van de oververzadiging op de h o e v e e l h e i d g r o e i e n d e

k r i s t a l l e n werd onafhankelijk van de t o t a l e kiemvorming gemeten. Daardoor

kon men een onderscheid tussen de t o t a l e en effektieve kiemvorming maken.

- Het twede deel zoals aangekondigd i n het begin handelt over een numerieke

b e r e k e n i n g w i j z e , genoemd h e t g e m o d i f i c e e r d e f r a c t i e t r a j e k t model

( h o o f d s t u k 3«3)« Daarmee kan men de KGV v o o r b a t c h en k o n t i n u e

k r i s t a l l i s a t o r e n s i m u l e r e n z o n d e r t y p i s c h e g e ï d e a l i s e e r d e

v e r o n d e r s t e l l i n g e n . De s i m u l a t i e i s m o g e l i j k v o o r b a t c h en n i e t

s t a t i o n a i r e kontinue k r i s t a l l i s a t o r e n , rekening houdend met g r o e i d i s p e r s i e

en l e n g t e a f h a n k e l i j k e g r o e i , de aanwezigheid van een k i e m e n b u f f e r ,

kiemvernietiging en k r i s t a l t o e v o e r i n de voeding van de k r i s t a l l i s a t o r . De

s i m u l a t i e b e v e s t i g d de k r i s t a l l i s a t i e k i n e t i e k d i e b e p a a l d werd op

laboratorium s c h a a l . Vooral wordt d u i d e l i j k het g r o e i d i s p e r s i e model i n

c o m b i n a t i e met een kiemenbuffer en n i e t een lengteafhankelijk groeimodel

zonder kiemenbuffer ondersteund. De o g e n s c h i j n l i j k e l e n g t e a f h a n k e l i j k e

g r o e i z o a l s h i j i n de l i t e r a t u u r gerapporteerd wordt, komt voort u i t een

k l a s s i f i k a t i e van k r i s t a l l e n op grond van hun k r i s t a l g r o e i s n e l h e i d . Weinig

hard g r o e i e n d e k r i s t a l l e n worden g r o o t t e r w i j l veel langzaam groeiende

k r i s t a l l e n k l e i n b l i j v e n . Het werd aangetoond d a t k r i s t a l l i s a t i e onder

s t a t i o n a i r e c o n d i t i e s n i e t voldoende i s om kinetiek gegevens t e bepalen,

d i e bruikbaar z i j n voor het modeleren van de e v o l u t i e van de KGV i n een

n i e t s t a t i o n a i r e c o n d i t i e ( h o o f d s t u k 3 - 5 ) • De g e s i m u l e e r d e n i e t

s t a t i o n a i r e c o n d i t i e i n k r i s t a l l i s a t o r e n h a n g t af van de g r o e i en

k i e m v o r m i n g s m o d e l l e n . De a a n w e z i g h e i d van een k i e m e n b u f f e r dempt

f l u c t u a t i e s van p r o c e s c o n d i t i e s , met a n d e r e woorden, k i e m v e r n i e t i g i n g

r e d u c e e r t de s t a b i l i t e i t van een p r o c e s . De kiemvormingskonstante i s

moeilijk t e voorspellen omdat h i j a f h a n k e l i j k i s van de k i e m e n v o o r r a a d ,

welke door de inhomogeniteiten van oververzadigingen i n een k r i s t a l l i s a t o r

beinvloed wordt. De experimenten gaven aan dat de e f f e k t i e v e kiemvorming

van de b e d r i j f s c o n d i t i e s afhangen, z o a l s de o n d e r v e r z a d i g i n g van de

voeding en langs het verwarmend o p p e r v l a k . Daarom moeten gegevens voor

opschaaldoeleinden n i e t a l l e e n met s o o r t g e l i j k e apparatuur maar ook onder

vergelijkbare b e d r i j f skondi t i e s uitgevoerd worden. Uit de r e s u l t a t e n van

de s i m u l a t i e s wordt a a n b e v o l e n om " f u l l s e e d i n g " t e c h n i e k e n ook voor

k o n t i n u e k r i s t a l l i s a t o r e n t o e t e p a s s e n z o a l s h e t v o o r b a t c h

k r i s t a l l i s a t i e gedaan wordt. Gekontroleerd toevoegen van k l e i n e k r i s t a l l e n

maakt h e t m o g e l i j k b i j l a g e o v e r v e r z a d i g i n g t e k r i s t a l l i s e r e n , waar

n a u w e l i j k s e f f e k t i e v e kiemvorming optreed, en dempt het dynamisch gedrag

van het p r o c e s .

CONTENTS

Summary

Samenvatting

1 INTRODUCTION 1

1.1 Scope 1

1.2 The research program 2

2. KINETICS OF SUCROSE CRYSTALLIZATION 4

2.1 MASS TRANSFER IN SUCROSE SOLUTIONS 4

2.1.1 Abstract 4

2.1.2 Scope 4

2.1.3 Theory of mass transfer and determination of k, 4

2.1.4 The exponent of Re and Re dependency 9

2.1.5 Determination of Sh

0

11

2.1.6 Solution of differential equation 13

2.1.7 Influence of the stirrer speed in an agitated suspension 16

2.1.8 Application of the Sh-Equation for slurries in a 1.4m

3

stirred vessel 18

2.1.9 Discussion 21

2.1.10 Conclusions and recommendations 23

2.2 GROWTH OF SUCROSE CRYSTALS 24

2.2.1 Abstract 24

2.2.2 Growth rates of small crystals at 70°C 24

2.2.2.1 Scope 24

2.2.2.2 Fundamental aspects of crystal growth 25

2.2.2.3 Evaluation of existing measurement techniques 27

2.2.2.4 Experimental equipment and procedure 29

2.2.2.5 Experimental results 30

2.2.2.6 Discussion 36

2.2.2.7 Conclusions and significance 39

2.2.3 Growth rates of large crystals 40

2.2.3.1 Scope 40

2.2.3-2 Introduction 40

2.2.3.3 Experiments about growth dispersion 4l

2.2.3-4 Effect of partial dissolution on the surface reaction 44

2.2.3.5 Influence of mechanical contact and exposure to high

supersaturations on the surface reaction 45

2.2.3.6 Concentration pattern around a growing crystal 46

2.2.3.7 Conclusions 52

2.2.4 Modelling growth rate of small and large crystals 52

2.2.4.1 Scope and objective 52

2.2.4.2 Analysis of non ideal growth rate models 52

2.2.4.3 The two step growth model 55

2.2.4.4 Significance and conclusions 58

2.3 NUCLEATION 59

2.3.1 Abstract 59

2.3.2 Scope and objective 59

2.3.3 Theory of secondary nucleation 59

2.3.3.I Total and effective nucleation rate 59

2.3-4.1 Experimental equipment and procedure 66

2.3.4.2 Results 68

2.3-5 Quantification of the nucleation rate in bench scale

equipment 69

2.3.5.1 Influence of crystal size and stirrer speed 69

2.3.5.2 Supersaturation and the secondary nucleation rate 70

A. Falling crystal experiments 70

B. Experiments in a 0.81 stirred tank 71

2.3.6 Experiments in a 1.4m

3

crystallizer 75

2.3.6.1 Effect of local high supersaturations 75

2.3.6.2. Effect of stirrer speed 77

2.3-7 Discussion on the mechanism of secondary nucleation 78

2.3.8 Conclusions 8l

3 THE FORMATION OF CRYSTAL SIZE DISTRIBUTIONS IN CRYSTALLIZERS

82

3.1 The description of the pilot plant unit and its operation 82

3.2 Retention time measurements in the 1.4m

3

crystallizer 86

3.2.1 Scope and objective 86

3.2.2 Conclusions 86

3.2.3 The measurement technique 86

3.2.4 The determination of the turnover time 88

3.2.5 Velocities 89

3.2.6 Axial dispersion of flow velocities 89

3.2.7 Height and residence time of the boiling zone 90

3.2.8 The residence time during continuous crystallization 91

3.2.9 Discussion

$2

3.3 Modelling the crystal size distribution(CSD) 93

3.3.1 Characterizing CSD 93

3.3.2 Balances 94

3.3.3 Calculated CSD under idealistic circumstances 96

3.3.4 Complications in sucrose crystallizers 97

3.3.5 The modified fraction trajectory concept

9&

3.4 Modelling batch crystallization 101

3.4.1 Objective 101

3.4.2 Growth rate dispersion function 101

3.4.3 Seeds originating from an unseeded MSMPR crystallizer 102

3.4.4 Milled crystals used as seeds 103

3.4.5 Conclusions 105

3.5 Modelling continuous crystallization under stationary and

nonstationary condition considering growth rate dispersion 106

3.5.1 Objective 106

3.5.2 Initiation of simulation program 106

3.5.3 The transient CSD using a permanent growth rate

dispersion model 108

3.5.4 The transient CSD using a size dependent growth rate

model 112

3.5.5 Effect of growth rate dispersion on the average growth

3-5.6 Discussion 113 3.5.7 Conclusions 115 4 HOW TO OBTAIN SYSTEM SPECIFIC DATA FOR THE DESIGN AND OPERATION OF

CRYSTALLIZERS 116 Appendices

Al Shape factors of sucrose crystals 118 A2 Diffusion constant in concentrated sucrose solutions 122

A3 Energy transfer rate to crystals in collisions 128

A4 Filtration of sucrose crystals 131 A5 Data of experiments on

A5•1-nucleation A5.2-crystal growth

A5.3~retention time (chapter 3-1)

A5.4-pilot plant experiments 136

A6 [Physical properties 1^1

Notation 1^3 References 146 Curriculum Vitae 155

1. INTRODUCTION 1.1 Scope

World productions of sucrose or saccharose ( C ^ H J I O ^ ) amounted to ap­ proximately 100 mio. tons in 1984/85 [ 6 ] . Thus it is one of the largest crystallized industrial bulk products. But unlike sodium chloride, another such product, it is still mostly produced in batch operations.

Continuous sucrose crystallizers would have the following advantages [7]: -Peaks in power and steam demand are avoided and related installations and

associated costs can be eliminated.

-Storage tanks before the crystallizers -are superfluous because all other facilities except centrifuges are operated continuously already.

-The product quality for crystallization under steady condition would be stable.

-A factory can be operated at optimal condition for each stage.

Two problems are still delaying the introduction of continuous operating mode in the sugar industry:

1. Incrustations. These develop on the walls of the crystallizer, in pipes etc. Thus existing continuous and batch crystallizers especially of white sugar have to be cleaned regularly . The use of continuous crystallizers is mainly restricted to sugar solutions of lower grade B and C because firstly the problems with incrustation and nucleation are more severe in a solution of high purity which are needed for white sugar production. 2. The demand on the product quality, namely the average crystal size,

spread in size and of impurity concentration is higher for white sugar than for B and C sugar grade product. The latter is redissolved and recycled to the A sugar crystallizer. For any product a coarser product is desired because it is easier and more efficient to filtrate, which in turn reduces impurity levels, and can be dried more efficiently.

The spread in crystal size is inevitable worse in continuous crystal­ lizers because the residence time distribution is worse. In lowly viscous systems a classified product removal or fines removal system based on sedimentation is widely used. But sucrose suspensions are too viscous for such a technique.

Fig. 1.1

Residence time d i s t r i b u t i o n for

a c a s c a d e o f N i d e a l l y mixed

tanks

2

-The r e s i d e n c e time d i s t r i b u t i o n can be narrowed by arranging vessels i n

s e r i e s for approaching a plug flow (fig. 1.1). Calculations p r e d i c t t h a t a t

l e a s t 6 e q u a l and i d e a l l y mixed v e s s e l s are necessary to achieve a c o e f f i ­

c i e n t of v a r i a t i o n of 30-35%- These c a l c u l a t i o n s assume constant temperature

and other i d e a l conditions, namely, t h a t n e i t h e r growth r a t e d i s p e r s i o n , nor

size dependent growth, n o r c o n g l o m e r a t i o n , n o r n u c l e a t i o n t a k e s p l a c e .

Whether t h e s e a s s u m p t i o n s a r e v a l i d f o r multiflash evaporation (see f i g .

1.2) remains t o be proven.

Fig. 1.2

One concept of multi stage flash evaporation, others in [3i4]

Steam

Reviews by Wright [ 8 ] , Austmeyer [ 9 t l 0 ] and Bruhns [11] cover s e v e r a l design

c o n c e p t s of continuous sucrose c r y s t a l l i z e r s . The Five-Cail Babcock type i s

devided i n t o many compartments with d i f f e r e n t volumes. Steam i s i n j e c t e d i n

o r d e r to keep t h e s u s p e n s i o n i n m o t i o n . A new l a y o u t drawing increasing

a t t e n t i o n i s t h e BMA tower, i n which f o u r t a n k s a r e p l a c e d i n a v e r t i c a l

t u b e . S t i r r e r s are used to i n c r e a s e the heat t r a n s f e r c o e f f i c i e n t for l a r g e

s l u r r y d e n s i t i e s .

In f a c t a l l types b u i l t so far are continuous c r y s t a l growers. Furthermore,

c r y s t a l l i z a t i o n in sucrose s o l u t i o n s i s not i d e a l and t h i s n e c e s s i t a t e s up

to 24 v e s s e l s in s e r i e s . The s e e d s f o r the c a s c a d e s a r e s t i l l prepared

batchwise up t o a mean s i z e between 200 and 500pm. These r e v i e w s r e v e a l a

l a c k of understanding i n the formation of c r y s t a l s i z e d i s t r i b u t i o n s neces­

s a r y for t h e d e s i g n of an o p t i m a l c o n t i n u o u s s u c r o s e c r y s t a l l i z e r .

Techniques have to be developed i n which c r y s t a l s up to 500 um are produced

continuously as w e l l .

1.2 The Research Program

Previous research on o t h e r systems has shown t h a t i t i s r i s k y t o d e s i g n

i n d u s t r i a l s c a l e c r y s t a l l i z e r s based s o l e l y on experiments i n bench s c a l e

equipment. Therefore, a p i l o t plant was b u i l t comprising a 1.4 m

3

e v a p o r a ­

t i v e c r y s t a l l i z e r . Previous s t u d i e s [12,13] on sucrose c r y s t a l l i z a t i o n did

not enable y e t s a t i s f a c t o r y simulation of the CSD i n c r y s t a l l i z e r s . In addi­

tion problems of i n c r u s t a t i o n were not overcome. This has lead t o a for t h i s

study as shown schematically in figure

1.3-This t h e s i s focusses on modelling the CSD which i s mainly influenced by the

k i n e t i c s , namely the nucleation and the c r y s t a l growth r a t e . The f i r s t chap­

t e r ( 2 . 1 ) d e a l s w i t h the mass t r a n s f e r of diffusion which i s claimed to be

c o n t r o l l i n g growth. I t i s followed by t h e growth of c r y s t a l s of v a r i o u s

sizes (2.2). The third chapter (2.3) covers mechanism of nucleation and the influence of some relevant parameters such as crystal size, stirrer speed, supersaturation, and temperature. They have been studied in a mini cell, bench scale equipment, and 1.4m' crystallizer and by using a microscope, interferomentry, a Coulter Counter or sieving as measuring techniques. In the second part the modelling of crystallizer performances is presented with emphasis on the formation of CSD applying the results of the first chapters.

( seeding techniques in series parallel operation botch-continuous cooling-evaporative process param. >y

N,S.MSL|~T,V J plate material wall temperature pourous material problems paramours O units r^-s^l measuring techniques I I results design X tanks in sciie concept

Fig. 1.3 Schematical illustration of the research program

The calculations are compared with experiments in a 1.4 m3 pilot plant crys­

tallizer. At first, its operation is described (3-1) • Next, the results are given of the retention time measurements performed under various process conditions (3-2). The simulation served as a feed back for further experi­ ments and modifications in the theoretical model (3-3)• Finally, some aspects are treated in detail: batch crystallization (3-4) and the dynamic behaviour of CSD in a continuous crystallizer using a crystal free feed (3.5)• The presentation finishes with recommendations for the improvement of the CSD in sucrose crystallizers and with recommendations for further re­ search. Incrustation above the boiling zone was studied by the author in the pilot plant crystallizer and is published elsewhere [14]. Incrustation below liquid level was studied also in a tube yielding criteria for the design and operation of crystallizers [15]» The incrustation problem, therefore, is not treated in this thesis.

A feed back from industry is helpful for carrying out relevant research. The Suiker Unie was prepared to support most of the apparati of the project financially and to transmit technical data of industrial crystallizers.

-4-2. KINETICS OF SUCROSE CRYSTALLIZATION 2.1 MASS TRANSFER

Mass transfer coefficients have gained special interest in crystallization because diffusion of solute to the crystal surface is one of the steps in crystal growth. Size dependent growth was explained in the past by a size dependent mass transfer coefficient [12,13.16,21]. This, however, was not sufficient for explaining crystal growth rate measurements particularly for small crystals.

Another area in which mass transfer coefficients are required is the modell­ ing of dissolution, which is controlled by mass transfer. Fines dissolution is applied commonly to improve crystal size distributions. In this chapter the mass transfer of diffusion will be determined from dissolution experiments. It is widely accepted that dissolution is solely rate control­ led by volume diffusion and is a first order reaction [17,18].

Growth is influenced by diffusion and surface reaction. Growth experiments will not be carried out because the conditions cannot be created in order to obtain a fully diffusion controlled growth rate. Even a small contribution of the surface reaction can be of strong influence on the overall mass transfer coefficient.

2.1.1 Abstract

The mass transfer coefficient of diffusion can be described well with the Sherwood equation according to Nelson and Galloway. It is supported by various experiments using single crystals (20-1500 um) in undersaturated solutions and by a few batch dissolution experiments in 1.4 m3 crystallizer.

An influence of stirring on the mass transfer coefficient was noticed in bench scale equipment but was small in the large vessel. The results indic­ ate that size dependent growth cannot be explained by the size dependency of the mass transfer. It was found that a dispersion in dissolution rates ex­ ists due to differences in shape.

2.1.2 Objective

The equations using dimensionless numbers for the mass transfer coefficient of diffusion even in the same system differ remarkably among authors.

The objective of this study is, therefore, to interprete the dissolution rates observed during this study for the derivation of a suitable Sh-equation in a sucrose-water system. This will be preceded by an analysis of measurements of other authors for the mass transfer coefficient at crystal solution interfaces.

2.1.3 Theory of Mass Transfer and Determination of k,

Experiments in other systems indicate that the relations for the mass trans­ fer rate of diffusion during dissolution can also be applied to the mass transfer rate of diffusion during growth [18]. It has been shown that the dissolution is a first order reaction and can be expressed by:

R

^i = f ^ T = k , (c - c j (2.1.1)

d A dt d eq b ' '

2

i n which A = k.L (2.1.2)

m = p k L

3

(2.1.3)

p v

c = concentration per volume of c l e a r s o l u t i o n

The d e f i n i t i o n s of the concentrations are important since the transformation

i n t o o t h e r d i m e n s i o n s can lead t o non l i n e a r r e l a t i o n s h i p s . According to

thermodynamics, the d r i v i n g force o i s the difference i n chemical p o t e n t i a l

between t h e s u b s t a n c e i n t h e s o l u t i o n u and a t the c r y s t a l u , where the

Q.

solution is close to saturation.

u - u Tc'

a

= v m

-eq ~-eq ~-eq

S =

-

^ - vln ^ — ^ ~ — c' in [kg

s

/kg

w

] (2.1.4)

If one assumes that the activity coefficients T are independent of the con­

centration and that supersaturation is low, then equation (2.1.4) is valid.

According to Van Hook [19], equation 2.1.4 is valid for sucrose solutions up

to |S| ~ 1.1.

Apart from Ac it is a problem to calculate the value of k, .For the diffusion

mass transfer coefficient k, a general model was proposed by Nelson and

Galloway [22,25] in suspensions using a Sh-number and taking into account

the interference of particle boundary layers in the diffusion process

2 5/e

m

♦ [

2

W ' >

2

W

1

/* - 2] tanh

( 5

/c

m

)

Sh - (1 - ( l - e )

1

^ )

2 { 2 1 5 )

^ r ^ - tanh (£/

em

)

1 - (l-e)

1 / 3

in which

d - o

1 / 3

^

a, m = coefficients of the system, usually m = 0!

They assumed that there is a definite concentric boundary layer around a

spherical particle in a multi particle system beyond which the concentration

gradient is zero. In an infinite medium the concentration gradient is zero

only at infinity, which leads to a limiting value of Sh = 2 . This limiting

value is reached when crystals are dissolving to very small sizes as the Re­

number becomes very small. If the particle is in an infinite medium (e = 1),

equation (2.1.5) is simplified to a common Frössling-type equation:

(e * 1.0): Sh = Sh + a Re

b

Sc

c

(2.1.6)

o

p

°

r

D

k. = r^ [Sh

t a ( £ ^ ^ )

b {

-n-)

c

]

d L

l

o n p ID

J

c

-6-A discussion about the parameters D, v and L w i l l follow n e x t .

I t must be remembered t h a t D i s the mass diffusion con§_tant^ in F i c k ' s law

and valid for d i l u t e s o l u t i o n s . Frequently, the values of D are extrapolated

r i g o r o u s l y t o high c o n c e n t r a t i o n s , for which D i s d i f f i c u l t to determine.

Dealing with high c o n c e n t r a t i o n s , however, F i c k ' s law does not hold, because

t h e d r i f t of s o l u t e i n t h e boundary l a y e r t h e o r y cannot be n e g l e c t e d

anymore. Nevertheless, F i c k ' s d i f f u s i o n c o n s t a n t , a c c o r d i n g t o e q u a t i o n

( 2 . 1 . 5 ) can be used, however, i f the diffusion coefficient i s corrected for

the mass concentration (w = Bx/100) of s u c r o s e in s o l u t i o n a c c o r d i n g t o

(Garside, Wesselingh, [26,27])

D

r

= — (2.1.7)

C 1 - w

This diffusion coefficient may not be correct, if the structure of the solu­ tion is not homogeneous. Measurements in 1965 [28,29] indicate cluster formation in highly concentrated sucrose solutions. It has been recently reported to be present in supersaturated solutions in four other aqueous systems [30] as well. The sucrose clusters were estimated to be about 8 nm in size. Therefore, this diffusion coefficient should be regarded as an effective D (see also Appendix A2). In nearly saturated sucrose solutions at 80°C, w= 0.8, the diffusivity will be about five times larger than predicted by neglecting the drift. The correction has not been taken into account so far in the literature for calculations in the sucrose water system (for details see review in [11,12]) .

The relative velocity y^ between particle v and fluid v_ as given by the usual form for hindered settling of monodisperse particles at low Re numbers

(Re < 1)

! (P " Px) S d l

v

■

v P

-

v

i ■ i s - * — r

f

—

F ( e ) { 2

-

1

-

8 )

For applying the equation to sucrose crystals it is necessary to use the diameter of a sphere with an equivalent volume as the crystal with a charac­ teristic size L. Experiments with sucrose crystals (0.4<L<1 mm, 10 <Re <1, TI* 0.1-0.15 Pas) have revealed that d ~ 1,09 L and n = 5.1 [12,32,33]. For a single particle in an infinite medium (e =1.0) the function accounting for the particle concentration F (e) = 1 and equation (2.1.8) turns into Stokes law.

In dense monodisperse systems Richardson and Zaki [31] proposed:

F (e) = en (2.1.9)

In c r y s t a l l i z e r s c r y s t a l s a r e u s u a l l y p o l y - s i z e d . According to Masliyah [34]

the following g e n e r a l i z e d e q u a t i o n should be used i n t h i s c a s e f o r t h e

v e l o c i t y of the i t h s p e c i e s :

V -

v

l

=

Ï8 ^ ' n V

8

" ^

g

V

F (e) (2

-

1

-

10)

Note t h a t t h e d e n s i t y d i f f e r e n c e between p a r t i c l e and suspension i s used.

With equation ( 2 . 1 . 1 0 ) he could e x p l a i n t h a t , for example, i n a c l o s e d

p o l y d i s p e r s e system very small p a r t i c l e s can move upward (v .< 0) while

l a r g e p a r t i c l e s sedimentate (v .> 0 ) . These s t r a n g e e f f e c t s a r e i n f l u e n c e d

by t h e p o r o s i t y and a r e caused by the displacement of volumes. The upward

movement of the displaced solution can be g r e a t e r than the s e d i m e n t a t i o n of

small p a r t i c l e s .

The influence, of L on k , i s of s p e c i a l i n t e r e s t t o the formation of c r y s t a l

s i z e d i s t r i b u t i o n during d i s s o l u t i o n and growth. The s i z e dependency of L i s

complex and depends on the values of Sh , ' a ' and the exponent b . k w i l l

be

1

independent of s i z e only for l a r g e c r y s t a l s i f b = 1/3 and Sh << a Re

Sc . In t h e l i t e r a t u r e a v a r i e t y of s i z e d e p e n d e n t r e l a t i o n s h i p s are

l i s t e d f o r k , . The v a l u e s of a and b v a r i e s s t r o n g l y in sucrose solution:

0.3 < a < 4.3 and 1/3 < b < 2 / 3 , assuming Sh = 2 and c = 1/3 i n e q u a t i o n

( 2 . 1 . 6 ) ( s u r v e y i n [ 1 2 ] ) . The d e t e r m i n a t i o n of Sh have r a r e l y been at­

tempted although i t i s very important i n modelling growth and d i s s o l u t i o n of

f i n e s . Austmeyer [35] has measured the mass t r a n s f e r i n suspensions (e < 1)

e x p e r i m e n t a l l y and s u p p o r t s the t h e o r y of Nelson and Galloway [ 2 2 ] , I t

p r e d i c t s t h a t k , w i l l d e c r e a s e w i t h d e c r e a s i n g s i z e as Sh reaches zero.

This i s i n c o n t r a s t to the assumption t h a t Sh = 2 because t h i s l e a d s t o an

i n c r e a s e of k , ( k , ~ 1/L) . Furthermore, i t i s (often) unclear whether the

s t r o n g influence or concentration on the physical p r o p e r t i e s D, n, and p in

s u c r o s e s o l u t i o n s a r e taken into account properly when f i t t i n g experimental

d a t a .

In t h i s t h e s i s t h e Sh r e l a t i o n s h i p i s reexamined taking i n t o account the

values of 1, p, n and v properly [ 3 5 i 3 7 ] , in the f i r s t i n s t a n c e for e = 1.0,

f o r which a s i z e d e p e n d e n t growth was n o t i c e d , t o o . Assuming e q u a t i o n

(2.1.6) i s c o r r e c t 'a* and b are s t i l l t o be determined.

F i r s t 'a* and b w i l l be determined. The shape of a c r y s t a l k. and k changes

during d i s s o l u t i o n from a cornered p a r t i c l e a t f i r s t i n t o an e l l i p s o i d and

f i n a l l y i n t o a sphere. By others t h i s was avoided by the measurement of the

mass t r a n s f e r perpendicular to a plane s u r f a c e . T h i s , however, i s an a r t i f i

-c a l -c o n d i t i o n f a r from r e a l i t y . Interferometry along -c r y s t a l s of 0.5 mm in

s i z e had r e v e a l e d t h a t t h e boundary l a y e r as w e l l a s t h e c o n c e n t r a t i o n

g r a d i e n t i s s p h e r i c a l (see chapter 2 . 2 . 3 - 6 ) . The radius of the c r y s t a l will

very l i k e l y influence the mass t r a n s f e r r a t e , and thus t o b , ' a ' , and Sh .

T h e r e f o r e , a microscope technique w i l l be used i n t h i s study. The change of

the c r y s t a l geometry w i l l be measured i n time (L, , L. , L, = f ( t ) ) , while

v a r y i n g Ac, v .. , and t h e i n i t i a l s i z e from r u n t o run. This allows the

determination of IK = f ( t ) and m = f ( t ) u s i n g t h e shape f a c t o r s from the

a p p e n d i x Al and c a l c u l a t i o n of k , according t o equation ( 2 . 1 . 1 ) . I f the

term Sh D /L can be ignored, the v a l u e of b i s g i v e n by t h e s l o p e of the

l i n e i n a l o g k , v e r s u s l o g v diagram a c c o r d i n g t o _fquation 2 . 1 . 1 1 . The

e r r o r of ignoring Sh i s l e s s than 10# i f k > 2.7*10~^ (L = 300 um) and

k

d

> 2'10~

5

m/s (L = §00 um)

d

-8-HJ a E

log(k -

jf- Sh

Q

) = logf-j^) + C log(Sc)

C

+ b log(j^) + b log v (2.1.11)

c

The value of 'a' can be calculated easily for Re = 1 because log Re =0.

Sh will be determined by measuring the dissolution rate of small crystals

o . .,,.,■

in a dilute liquid (e = 1) . As the second term a Re Sc can be neglected

equation (2.1.13)

c a n

be solved. Using an average k and k. and assuming

them to be being independent of size the integration leads to:

(L » - L') 3 P k

Sh = — S - j : - - . , (2.1.12)

o t 2 ID k. Ac

c A

Measurements wili provide the relationship between L and t, which can be

modelled by the solution of equation (2il.l3). It is obtained after insert­

ing equations (2.1.2), (2.1.3). and (2.1*6) into equation (2.1*1) and

rearranging:

1

L 3pk dL t

h' ir-'— :—Tb ITS

= / dt (2

-

1

-

13)

L A Sh D a D pvL

T\

'

J o

o o c c

i \ t \

"IT"

+

—

{

—

]

^W

]

c

The equation (2.1.13) can be solved analytically for the two cases:

i) that the relative velocity is constant, thus independent of crystal

size. Then the equation descibes the experiments under the microscope

and in a stirred solution using crystals glued to ah impeller blade.

ii) that the velocity is size dependent according to equation 2.1.8 and 9»

The calculation will be proven by additional measurements of the total

dissolution time for crystals sedimentihg in a solution and for crystals

freely floating in an agitated solution. On top of that, experiments

will be carried out in a 1400 1 batch crystallizer using a mixed suspen­

sion in order to testify the validity for slurries (e < 1 ) .

In summary, the exponent of Re and the value 'a' will be determined first

followed by the determination of Sh and solving the integral of equation

2.1.13.

2.1.4 The Exponent of Re and Re Dependency

The Microscopic Technique:

A seed crystal is glued on a needle with silicon adhesive and placed in a microcell, illustrated in fig. 2.1.1 and similar to the one used by Garside in 1979 [38]. Through the bottom chamber thermostated water and through the upper chamber sucrose solution is flowing.

i

Fig. 2.1.1. Schematic diagram of the micro cell

Legend: 1: thermo-couple in sucrose solution, 2: thermo-couple in water, 3: water inlet and outlet, 4: sucrose solution inlet and outlet, 5' glass cover slips, 6: support rod on which crys­

tals is attached, 7: plexi-glass ring placed in the solution chamber.

Thermocouples are present in both chambers. The sucrose solution is sucked out of a 0.8 1. storage vessel through the micro cell. The solution was prepared by dissolving a desired quantity of refinery sugar in demineralized water of 90°C. The solution was never in use for more than one day.

The relative velocity of the solution passing the crystal was derived from the measured volume of solution v used over a given time interval.

v= f- (2.1.14)

Two thermostats are used during an experiment. The one which is connected all the time to the storage vessel is kept at the desired temperature for dissolving the seed crystal in the micro cell. The other is fixed at a tem­ perature to enable growth of the seed crystal. With the help of two three way valves one of the thermostats controles the temperature of the micro cell. (fig. 2.1.2). The condition can be changed within 15 s. from a super-saturation to a desired undersuper-saturation and vice versa.

-10-O

2 ^ 1 (M) r KV • 3 — T l -cH-a \ ) ^

f

* D

/ = » - v C7 ] (XI

Ö

^ i

i , f T 2 1 1

v _

x^

—1

Fig. 2.I.2. Schematic diagram of the measurement set up

Legend: 1: micro cell, 2: microscope, 3: storage vessel, Tl, T2: thermostats

Experimental Results:

A typical run with the microscopic technique is listed in table 2.1.1. As expected it was noticed that with decreasing size the crystal is dissolving faster. For each measurement point the mass and crystal surface was calcu­ lated with the shape (see Appendix Al) taken into account. By using equation 2.1.1 k, was determined. k, increased steadily for crystals below 600 um. The crystal surface got rougher while dissolving.

Table 2.1.1 A typical run observing the dissolution of a single crystal

T t L, L L. M A M A dt d 1 b h cornered ellipsoid min mm mm' mm mg mm2 mg

_mm'

ellipsoid mg/min 10 m/s Bx=77-8# v=2.3 mm/3 -Ac=-22.6kg/m: 78 81 83 82 81. 82, 0 5 11 15 20 25 1088 575 1025 563 950 500 813 450 750 363 588 275 425 413 413 363 313 250

0.300

0.268

0.212

0.143

0.092

0.043

68 56 35 04 O.78 0.48 0.220

0.197

.162 .110 0.070 0.033 0. 0. .28 .18 .00 • 77 • 58 35

28 250 125 100 0.003 0.09 0.0025 0.06

29

0

0

0

0

0 0 0

-0.024 13.8

-0.0125 17-8

-0.010 7.4

-0.008 7.7

-0.0075 9.5

-0.0060 12.6

-O.OO5 61.5

0

Since the scattering of the measurement points was least between L *300 um and 400 um and ageed best with the trend expected the k , was determined at 300 um and 400 um for all experiments with the average velocity varying from run to run.

The exponent of Re was determined from the log k, versus log v plot (fig 2.1.3) according to equation 2.1.11^and was found to be 0.4.. 0.5 (r = 0.94)

by a least square fit for v>4 10~ m/s.

10" S 10 -5 2 io -6 o L O O O I I » * L«400tia * " " bO.fcO

.

«2--a . . i «-<. 10 -3 10" 10 -1 Relative velocity v fm/s]

Fig. 2.1.3. The influence of the relative velocity on the mass transfer coefficient of crystal sizes of 300 and 400 um at 80"C.

The value of 'a' can easily be calculated if Re=l. Equation 2.1.6 is reduced to equation 2.1.15. By calculating the velocity for crystals with L 300 um or 400 jam for Re=l, kd can be obtained from fig 2.1.3. Sh = k,L/D was found

to be ~ 108. Obviously Sh ^ 2 in equation 2.1.6 and can be neglected. This 1/3 leads to a * 2 since Sc = 46.6. Sh - Sh Re = 1 Sc 1/3 (2.1.15) 2.1.5 Determination of Sh

Now we are able to calculate the maximum crystal size for which Sh deviates less than 10% from Sh .

o

1.5 R e1 / 2 S c1 / 3 £ 0.1 Sh _(2.1.16)

-12-In a series of experiments varying Ac from run to run small crystals (L ~ 20 um) were dissolved (L-»0) in a slightly undersaturated stirred solution. Using equation 2.1.12 Sh was calculated from the time necessary to dissolve

80% respectively 95% of the number of seeds.

A new technique was used to check the efficiency of the fines removal.The dissolution rate of fines was measured in the 11 double-walled glazed vessel containing sucrose solution (0.8 1) at controlled undersaturation levels at 80°C. Small crystals with sizes below 20 um can not be sieved and were formed by cooling down some ml of solution while stirring in a separate beaker. The size and amount of crystals, which were formed spontaneously, were estimated under a microscope. With the help of syringe the solution containing small crystals was injected into a well stirred undersaturated solution in the measuring vessel. Afterwards, samples were taken with a pipet each minute and placed on a microslide under a cover glass, which in turn were held at 60°C by resting on a thermostatically controlled plate. It corresponds to a supersaturation of 1.25 which should enable growth of all crystals present. This was found to be the best practical way to prove whether fines are really destroyed or not. The amount of crystals did not increase significantly after one hour. A sample was also taken from the unseeded solution as reference. The saturation temperature of the solution at which crystals are rounded was measured beforehand with a saturoscope. Since the sizes of all seeds were not uniform and the amount of seeds not equal for all runs, the number of fines removed was related to the amount of crystals in the first sample in each run.

Table 2.1.2 Experiments on the dissolution of fines

3

P

K

S P D cl c (kg/m3) (m2/s) 0.995 1365-7 3-52.10 ^ 0.99 1365-2 3.55.10 1"

0.98 1364.0 3-59.10 J-JJ

0.97 1362.9 3.64.10 u

The results give a global impression for the time necessary to dissolve 80% respectively 95# of the seeds. Times necessary to dissolve 80# and 95$ of crystals (L * 20um) as a function of undersaturation are illustrated in fig. 2.1.4. It can be seen that the amount of crystals disappears strongly during the first minutes and with increasing undersaturation. The values of Sh are listed in table 2.1.2 using equation 2.1.12 (L = 20 um, k = 2.16 and k =

o a v 0.47 assuming an ellipsoid LiSL, = 1.5:1). Within the accuracy of the

results it can be concluded that Sh is greater than zero and most likely to be two (Sh = 2 ) .

-Ac

(kg/m3)

1.6

3-2

6.4

9-7

2 D(ü 7.93. 3-92. 1.93. 1.26. Lc)kA 101 1 101 1 11 10 11 10 %!<*» (sec)

95

50

20

15

I) Sh0 (80%) 3.45 3.15

3-9

3-45

W*

95

**

(sec)

I65

80

65

40

Sh0 (95%) 1.95 1.95

1.2

1-35

3

ï

2

Tim e o -\ \ 1 ^ ^^^s^O ° - - 9 5 % — - ? — 8 0 % . .= J i (U e t— 60 UQ 20 , / / <v^ / ^ _ 1 1 1 1.00 0.98 0.96 Supersaturation S 2 10~2 K 10~2 6 10"2 Supersaturation At'lm'/kg]

Fig. 2.I.4. Times necessary to dissolve 802 (x) and 95% («) of the seeded crystals (L ~ 20 pm) as a function of the

supersaturation.

Fig. 2.1.5- Total dissolution time versus the inverse of

the supersaturation Ac

2.1.6 Solution of Differential Equation

Now the values of 'a', b, and Sh are determined the integral of equation2.1.13 can be solved. The dissolution rate was calculated and tested by approppriate expeiments for the following cases: v= const ( microscope experiments), vsL2 ( settling crystals), v in stirred solutions and in dense

suspensions.

Under the reasonable assumption that the undersaturation is constant in time the solution of the differential equation (2.1.13) will result in a inverse proportionality between the total dissolution time and undersaturation. The experiments shown in fig. 2.1.5 prove that it is indeed correct to assume a first order reaction for dissolution (equation 2.1.1).

For b = 1/2 equation 2.1.13 can be solved analytically. The integration was performed for two cases.

1st case: v = f(L)

This case agrees with t h e e x p e r i m e n t s performed w i t h f i x e d c r y s t a l s and c o n s t a n t r e l a t i v e v e l o c i t y . The time necessary t o d i s s o l v e c r y s t a l s with L down t o s i z e L i s : t_ JL r 2 L £ L _ h___ 3C, 2JL n 3 ^ j - l n (UC1fL)rL (2.1.17) in which C, = -r- . (&—) l d n 1/2 (a _ , i / 3

-14-c„ =

2 D .k Ac c a 2 3P .k p v

The curve 1 in fig. 2.I.6. shows that equation 2.1.17 corresponds well with the observed change in size during the dissolution experiments under the microscope. Curve 2 in fig. 2.1.6 represents the dissolution of similar crystals with common geometrical proportions of their axis (1^:1^:1^ = 2:1:0.8) whereas curve 3 (1.5:1:0.6) and 4 (1:1:0.4) correspond to crystals of other shapes, which are also present, during crystallization. The

dis-1 " 300

Simulation 1

Fig. 2.1.6. Simulation of the change in size during dissolution using equa­ tion 17 for an experiment at a constant relative velocity. 1. simulation of the experiment

2.

3-4.

Ll: Lb: Lh 2:1:0.8 Ln:L.:L, = 1.5:1:0.6 1 b h Ll: Lb: Lh 1:1:0.4

s o l u t i o n time v a r i e s up t o 30% of the average d i s s o l u t i o n time. This means

t h a t c r y s t a l s of the same c h a r a c t e r i s t i c s i z e L

b

r e v e a l a d i s p e r s i o n of

d i s s o l u t i o n r a t e s due t o d i f f e r e n c e s i n s h a p e . The adequacy of equation

2.1.17 in r e p r e s e n t i n g the r e a l s i t u a t i o n was t e s t e d by simulating the t o t a l

d i s s o l u t i o n time of other experiments and i s i l l u s t r a t e d in f i g 2 . 1 . 7 - The

p o i n t s indicated with M were performed i n t h e c e l l under t h e m i c r o s c o p e

whereas t h o s e i n d i c a t e d with an N are performed in an a g i t a t e d v e s s e l with

the c r y s t a l s glued to an impeller blade a t d i f f e r e n t r a d i i . The b l a d e was

50 : 4» 30 20 10 0 -. -f

■ 1

■I

8 l 9 11 11 measurement • (M) simulation ö i i • » > !

I

■ i

I-l N

S i

_ l 1 10 10 10 „-3 -2 Relative vetocity v [m/s] 10 -1

Fig. 2.1.7. Simulation of the total dissolution rate for experiments at each constant relative velocity, but using equation (2.1.17) varying the initial size and undersaturation from run to run.

inclined 45° in in order to stir the solution. Of course the size of the crystals could not be measured once the crystals were entered into the solution. The experiments could only reveal the time necessary to dissolve the crystals. These experiments were carried out in order to check the results of the microscopic technique, with its uncertainties in the velocity of the solution passing the crystal. The velocity of the crystals glued to the impeller blade which was rotating at constant speed was;

2n r.N (2.1.18)

2nd case: v ÖL2

According to equations 2 . 1 . 9 and 2 . 1 . 1 0 , a s i z e dependent v i s considered in e q u a t i o n 2 . 1 . 1 3 . T h i s c a s e i s s i m i l a r t o t h e c o n d i t i o n s i n suspensions. Under the assumption t h a t n ( e q u a t i o n 2 . 1 . 9 ) i s i n d e p e n d e n t of s i z e the f o l l o w i n g e q u a t i o n can a l s o be u s e d f o r hindered s e t t l i n g of c r y s t a l s in s u s p e n s i o n s . t=

IFJL

Ü3

3 c0

[4

In +/3arctan

2/L- ' j r

I r

7T

Co

3J

73

180 8 0J JL (2.1.19)

-16-(2.1.19) in which C_ as in equation 2.1.17 and

c

3

= f M P

p

- P ) g 0.065- (Jg) i/3

Since e * 1 P = P =P i • _susp rcl

This equation was able to simulate the experiments in which the dissolution time was measured of crystals sedimenting freely at an undersaturation of 0.8 at 82°C (zie fig. 2.1.8)

5

-= 3

-£ 2

Sucrose water solution T=82*C, S=0.8

0 100 500 Initial crystal size L (urn)

Fig. 2.1.8 Simulation (straight line) of the total dissolution time versus initial size of free falling crystals using equation (2.1.19)

2.1.7 Influence of the Stirrer Speed in an Agitated Suspension

Experiments were performed in a vessel where a solution was seeded with a few crystal at a time. Their dimensions had been measured under a microscope. The stirrer speed and initial crystal size were changed from run

to run. Again, only the total dissolution time was measured. The results are listed in table 2.1.3. It was found that the crystals dissolve much faster than

TABLE 2.1.3 Influence of the stirrer speed on the constant a in the Sh-equation (L0=1.85 mm, S=0.97, T= 8l°C) run No

8

10 11

12

13 14 "opl min

8

8.9 12 14.3 17-4 19 25.2 20.1 16.1 12.1 8.5 7-9 5.7 4.7 N rpm 340 300 260 220 l60 100 90 170 220 260 90 170 220 260 Res 381 336 291 247 180 112 101 190 246 291 223 421 544 643 a 50 61 51 43 34 31 20 29 38 51 55 58 85 107

predicted by equation 2.1.19 for sedimenting crystals. Since the dissolution time of small crystals is assumed not to be influenced by the stirrer speed, only the second term in the Sh-equation should be adjusted. With the assump­ tion that the power of Re remains uneffected (b=0.5) equation 2.1.22 was used to simulate the experiments by adjusting the value of 'a'. Even at a low stirrer speed (90 rpm, D=6 cm) the value of a will be ten times higher than for free settling crystals (a ). Attempts were made to correlate the ratio a/a with the dimensionless Re-number, which takes the stirrer-speed

o into account:

pN D* Re = &

-s n (2.1.20)

D = diameter of the stirrer (= 6 cm)

Any correlation of a and Re must guarantee that for Re 0 the value of a is equal to a for sedimentation:

l i m Re -»o s 10 10 10' / X ,x'/ y O X / K/'t.

(2.1.21)

Re * 1 s 10J

F i g . 2 . 1 . 9 . The i n f l u e n c e of s t i r r i n g (Re ) on the constant (a) i n the

Sh-equation in comparison to the a of free s e t t l i n g c r y s t a l s .

-18-Re was correlated with a/a as illustrated for the 3 experimental sizes in s o

fig. 2.1.9 °n a logarithmic scale. The curves indicate that the power jS is

not constant.

a = a (1 + a1 Re )P (2.1.22)

With a1 = 1 even at low stirrer speed the influence of Re is very strong

since Re >> 1. This influence can be reduced by deceasing the value of a1.

So far it was assumed that the influence of the stirrer speed is not crystal size dependent. An increase of the relative velocity v by stirring may be expected. The following equation could be used for the relative velocity in Rep [39]:

vr = ƒ f ( Ns)2 + vt 2 (2.1.23)

If this is true, the stirrer speed influences the effect of sedimentation velocity (v ) on k,. Consequently Re ~L does not hold any longer and equa­ tion (2.1.19) can not be used to evaluate our dissolution experiments. Evidently, more experimental data are necessary to derive a suitable cor­ relation between k, and L taking Re into account. Sh- equations for the mass transfer in stirred solutions fail in a sucrose water system, where the conditions are influenced by a laminar flow around settling crystals and by conditions between laminar and turbulent flow due to stirring. Therefore, the constant a was adjusted as necessary to simulate the dissolution rate observed experimentally. Experiments were performed next to determine the value of 'a' and to prove whether this size dependency is also observed in a pilot plant crystallizer with a suspension representative for industrial operations.

2.1.8 Application of the Sh Equation for Slurries in a 1.4m3 Stirred Vessel

Batch crystallization was performed in a 1.4 m3 crystallizer, containing a

draft tube and a 3 bladed marine impeller. The pilot plant unit is discribed in detail elsewhere ([12] and chapter 3-1) • After achieving a crystal con­ tent of 22 wt% the solution was heated to 83°C (S>0.93) in order to dissolve

the crystals. Slurry samples could only be centrifuged each 30 minutes for determining the CSD by sieving.

The population density distributions were simulated with the use of a frac­ tion trajectory concept ([116] and chapter 3-3) applying both, models: Nelson and Galloway equation (2.1.5) and the Frössling-equation (2.1.6) for a=10. Figure 2.1.10 shows the CSD formed by dissolving a batch produced CSD, whereas figure 2.1.13 shows a CSD formed by dissolving a CSD created by continuous crystallization. Both models simulate the CSD well for crys­ tals, larger than 100 um. For small crystals, however, the Nelson and Galloway equation seems to be more appropriate. A Frossling equation using Sh =0 simulates the CSD fairly well, too.

32 E * c c 30 28 26

£ 24

■ o | 22 ia

I 20

- - Sh=2*10Re1/2Sc1/3

— Nelson & Galloway a=10 200 500 1000 Size L [umi 1500

F i g . 2 . 1 . 1 0 . S i m u l a t e d CSD a f t e r d i s s o l v i n g

b a t c h w i s e a CSD w h i c h was

produced i n a batch c r y s t a l l i z e r .

E ♦ 34 32 30 28 26* 24 22 | 20 i/> e "3 o

a.

-Sh=10Re1 / 2Sc1 / 3 --Sh=2+10Re1/2Sc1/3

— Nelson & Galloway a=10 ■ 200 500 1000 Size L [urn] 1500

Fig. 2 . 1 . 1 1 . S i m u l a t e d CSD a f t e r d i s s o l v i n g

b a t c h w i s e a CSD w h i c h w a s

produced i n a continuous

MSMPR-C r y s t a l l i z e r .

2 0

-Fig 2.1.12 shows a p l o t of the cumulative population d e n s i t y d i s t r i b u t i o n , a f t e r d i s s o l u t i o n and a f t e r subsequent growth. The h o r i z o n t a l d i s t a n c e be­ tween the l i n e s i s not uniform i n d i c a t i n g a s i z e dependency of growth and d i s s o l u t i o n . Curve 1 r e p r e s e n t s a batch formed CSD which was p a r t i a l l y d i s ­ solved to r e c e i v e c u r v e 2 . I t shows t h a t c r y s t a l s (550<L<650) d i s s o l v e slower than small c r y s t a l s (L<350pm) and l a r g e r c r y s t a l s (L>770 pm). The

30 310pm e 25 20 I T *C S -MA pir CA X Kc '/. t 69 1.14 608 34 22 Q au 0.93 518 29 10 A 78 1.03 739 28 19 0 100 500 1000 Size L [MID] 1500

Fig. 2.1.12. Cumulative number size distribution after dissolving batchwise a CSD which was produced in a batch MSMPR-Crystallizer.

crystals were allowed to grow again. Large crystals grow faster than small crystals. Partial dissolution has improved the CSD because the spread in size of curve 3 is less and the average size greater than the initial curve. It shows that the number of small crystals is reduced.

Forced convection around a falling crystal as well as stirring is bound to increase k^. In a small vessel (0.8 1) it was found that the influence of

stirring on k is very strong. Attempts were made to consider the effect of the stirrer speed in the Sh-equation. Presumably., the relation will be valid, however, only for the agitated solution, in which the experiments were performed.

Industrial sucrose crystallizers can be devided into several zones [40]: a. sedimentation zone of the downcomer

b. bubbling zone