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Residence Time Optimization in Continuous CrystallizersThanassi E. Fakatselis

Crystal Growth & Design, 2002, 2 (5), 375-379 DOI: 10.1021/cg020014b Publication Date (Web): 25 July 2002

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Delivered a t the Crystal E ngineering t o Crystal Growth: Designand Fu nction Symposium, ACS 223rd Na tional Meeting, Orlando,Florida, April 7-11, 2002

R e s i d e n c e T i m e O p t i m i z a t i o n i n C o n t i n u o u s

Cr ys t al l i z e r s

Thanassi E. Faka tselis*

Messo Inc., 563 North Oak, Hinsdale, Illinois 60521

Received April 16, 2002

ABSTRACT: The pr oduction ra te of a given crystallizer is defined, in pa rt, by t he r esidence time pr ovided by thecrystallizer vessel. Typically, this parameter is based on small-scale tests, which exaggerate the effects of secondarynucleation. Scale-up of crystallization equipment should allow for lower secondary nucleation, and this may, onoccasion, allow for lower residence time than that used in pilot testing. In scale-up, the attrition rate decreases withthe squ ar e of the vessel size increase, at constan t specific energy input , and crysta l-crystal cont act is more dependent

on crystal size, th an crystal nu mber. To determine the results of increasing production (lowering th e crystal residencetime), one n eeds t o consider specific cha racteristics of the crystal shape, har dness, britt leness, sources of att rition,stresses on the crystal structure, supersaturation, and type of equipment in use. A reduction in residence time isnot n ecessarily going to br ing about poorer crystal quality.

I n t r o d u c t i o n

One of the primar y design pa ram eters of a crysta llizeris the crystal residence t ime. This para meter impactson the product size to be obtained, embodies the crystalgrowth rate and the effective nucleation rate, and isusua lly determined by experimenta tion. The residencetime is a deciding factor in defining th e crystallizergeometric size, and as a result it has direct bearing on

the economics of a given crystallization system. Shortresidence times will define a smaller (less expensive)unit , but also one that may fail to produce crystals of sufficient size. As engineers, by na tur e, will err on t hesafe side, many operating crystallizers may be oversized,and their productivity may be increased under certaincondit ions. If th e specific application is examin ed closely,with a view to how the residence t ime is affected bycrystal characteristics and hardware configuration, itmay be possible to improve the units productivity withlittle penalty on crystal quality.

Figure 1 shows that the residence time of a crystal-lizer is, at least, dependent on certain macro effects ofth e su spension fluid m echan ics. The efficiency of mixing,

whether in terms of proper suspension, good distributionof the solids, and good mixing, will all affect the realresidence time of a crystallizer. The implication here isthat in a case of perfect mixing, the residence time isat some minimum value. This value is th en increasedin practice, to account for mixing inefficiencies.

The common concern, however, in increasing theproduction in an existing crystallizer is that because ofshorter residence time, it will bring about higher su-

persaturation, which in turn will reduce the averagepart icle size. Sometimes, to a void decreasing th e r esi-dence time, the magma density of the crystallizer willbe increased, but this holds the danger of increasedattrition, which will also result in a smaller product.The general expectation in connection with these orrelated a ctions is tha t th e secondary nu cleation ra te willincrease, while the effective growth rate of the crystalswill be reduced.

Therefore, th e general belief is that in increasingproduction (or providing shorter residence times for anew crystallizer) the average crystal purity or size willdecline. In the following sections, we will review eachof the parameters affected by increased production orshorter r esidence time in a continu ous crystallizer, an dhow they might a ctually affect crystal quality.

* Auth or correspondence. Tel: 708-672-1068. E-mail: t.fakat selis@messo.net.

F i g u re 1 . Suspension fluid mechanics effects on kineticprocesses in a crystallizer, categorized by scale (after ref 8).RTD is residence time distribution.

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I t i s r ecognized t hat t her e ar e m any appli cat i onswhere the desired crystal product is not the largestpossible, th at sometimes, small crystals are requiredexpressly, and that on occasion, agglomerated solids isthe desired form. In the aut hors opinion, h owever, th e

majority of industrial crystallizers is called upon toproduce as large a p roduct as possible, within t he u nitsdesign limitations, and it is for t his reason, tha t in t hispaper the concept of better crystals is often usedinterchan geably with larger crystals.

I n c r e a s e d S u p e r s a t u r a t i o n

A crystallizer is usu ally provided with some mixingmechanism to control the supersaturation (c) gener-ated by the crystallization process. The supersaturationlimit is u sually described by the meta stable zone width(MZW); after that l imit has been surpassed, primarynucleation, with detriment al effects on crystal size, is

expected to occur. The mixing, therefore, provides ameans to maintain the local supersaturation to someoptimum level, an d definitely, to a level below th e limitset by t he MZW.

For a given operating crystallizer, increases in pro-duction mean an increase in the c value within whichthe crystallizer operates, given tha t th e mixing ra te doesnot chan ge. The optimum level of super sat ura tion is notknown in most cases, because it is not a para meter t hatcan be easily quan tified: tests ar e usua lly carr ied outin small scale (lab) units, which do not correspond wellt o t he dynam i c s yst em of t h e equi val ent i ndus t r ialcrystallizer. As a result, an increase in c is consider eddangerous, because there is little actual knowledge of

how far into the MZW the unit may already be operat-i ng. T he f ear exi s t s t hat t he hi gher c value mightexceed the MZW.

However, th ere a re several exceptions to th is line ofreasoning. Increasing supersaturation might result inlarger crystals, due to agglomera tion,1 given, of course,t hat t he i nt ens it y of m i xi ng w il l be s uch t hat s uchagglomera tes will not be broken u p. In some cases, suchas in drowning-out precipitation or cooling crystalliza-tion of potassium sulfate,2 t h e g row th r a t e c a n b eindependent of crystallizer volume size, crystallizergeometry, a nd mode of agitat ion (Figure 2). In certa infast-rate crystallization reactions, as production in-creases in the crystallizer, micro- or meso-mixing be-

comes a critical parameter. In such cases, the crystal-l izer r equi r es m or e i nt ens e m i xi ng t o count er t heincrease in c, an d t o avoid t he occur ren ce of excessiveprimary nucleation. As an example, Torbacke 3 foundthat the average crystal s ize in reacting hydrochloric

acid with sodium benzoate increased with increasedcirculation and increased feed point mixing intensity(Figure 3).

The above illustrate that a higher c in an operatingcrystallizer, or a higher c allowed in a new design (asopposed t o previous pra ctice) does n ot necessar ily implya requirement for increased m ixing, to compensa te forthe resultant supersaturation. A well-defined MZW anda bett er u ndersta nding of the crystallization kinetics ofa given process may allow for such an increase in thec with n o discernible penalty.

C ry s t a l C h a r a c t e r i s t i c s

The need t o dissipate a higher level of supersatu rat ionnormally leads to increasing the crystallizers mixingrat e or inten sity. A more esoteric approach t o reducingt h e c is to increase the magma density in the crystal-lizer, so that the available crystal surface area compen-sates for the increase in supersaturation. Increasingagit at i on i nt ens it y or m agm a densi t y i s t hought t oincrease the attrition rate of the crystal, and thus leadto redu ced overall crystal size. While this is generallytrue, the degree to which these phenomena are experi-enced in a specific system is not th e same, a nd m ay n otbe as severe as one might expect.

Ploss4 found tha t crystals break when a certain st ressthreshold is exceeded, and not (as generally thought)

as a function of energy input to the slurry by the mixingdevice. Furt her, in industrial-size crystallizers, thecontr ibution to the overall nu cleation ra te by crystal-crystal collisions, ra th er t ha n p ropeller collisions, is thedeci di ng fact or , and cr yst al s hape i s an i m por t antcriterion on how stresses will be distributed within th elatt ice of a given crystal . I t follows that in largercrystallizers, estimat ing crystal brea kage involves someunderstanding of the hardness and brit t leness of thecrystal , rather than the effect of the energy input byth e mixing device. The effect of mixing energy inp ut onnu cleat ion is, in an y case, diminished a s th e crystallizersize increases, simply due to the larger volume of theslurry being mixed.

F i g u r e 2 . Dependence of overall growth rate constant onprevailing supersaturation for two different crystallizer vol-umes, 300 and 3850 mL (after ref 2).

F i g u r e 3 . Dependence of average crystal size on ratio of feedsupersat ura tion to mixing intensity in r eaction crystallization(after ref 3).

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A combination of high mixing rate and high magma

density is generally th ought to produce conditionssimilar to those in a crystal grinder, as the probabilityof a crystal being hit by the mixer increases in time andin intensity. However, Cra wley5 found that crystals donot necessarily break into progressively smaller ands m all er par t s as t hey ar e s ubject ed t o cont i nuousagitation; ma ny fines reatt ach themselves to largercrystals, others agglomerate into larger particles, andthe resulting effective secondary nucleation is muchlower than theoretically expected. In combination,Gahn 6 notes that as crystal s ize increases, the prob-ability th at a crysta l will contact t he impeller decreases,becaus e t he i ner t i a of a l ar ger m as s w il l al low t hecrystal to follow flow-lines, rather than be caught in

mid-flight by the mixer blade (Figure 4). This meansthat larger crystals are actually subjected less fre-quently to impact forces, an d th e result is erosion, ra thert han at t r i t ion. T hi s explai ns w ell t he fact t hat t hetypical shape of most large crystals made in continuouscrystallizers is spheroid.

The above illustra te th at increasing the a gitation rat eis not necessarily a detrimental action in maintaininga given crystal size, while increasing crystallizer pro-duction. Such parameters as the crystal physical prop-erties (hardness, shape, elasticity, etc.), as well as theactual crystal size distribut ion should be considered indeciding whether to increase the mixing intensity in thecrystallizer.

Scal e-U p

Under the best-hoped-for conditions, the averagecrysta llizer unit ha s been designed on th e basis of small-scale (1- to 6-L) test u nits. Typically, th e residen ce timeus ed i n t he s cal e-up i s ver y clos e t o t hat found asoptimum in the testwork. Optimum residence t ime isthought to be that at which crystal growth is maximized,while att rition, erosion, a nd generally, secondary n ucle-at ion is m inimized, to produce a la rge crystal. However,it is well-known that small-scale equipment provideshigher levels of secondary nucleation, than the samesystem in its scaled-up version.

Several methods for scale-up from a laboratory crys-tallizer to an industrial-size unit have been proposed,and are used, on the basis of what the designer mightconsider important attr ibutes of a particular crystal-l ization operation. In short , these methods address

mostly physical or fluid-dynamic va riables a s powerinput, mixing intensity, tu rbulence, geometr ic similar-ity, etc. There is, by the nat ure of the problem, very littleknown on the scale-up characteristics for residence time,growth and nucleation rate for a particular system.

Synowiec7 s h ow s t h a t w h ile t h e a t t r it ion d u e t otur bulent forces caused by fluid m otion is independentof vessel size, the maximum contribution to the totalnumber of fragments would be in the 30-40% range.He further elaborated that at constant power input perun it volume, as a un its volume is scaled up, the r elativeattrition rate (the ratio of attrition in the larger unit totha t of the pilot u nit) drops exponent ially as the scale-up factor increases (Figure 5).

Jones2 found lower nucleation rates for larger crys-tallizer volumes of the same crystallization system whileno effect of crystallizer size wa s n oted on growth rat e(Figure 6).

Fina lly, working with st irred ta nks, Rielly8 confirmedthat the frequency with which a crystal is hit by thepropeller is a function of the crystal size. He found thatcrystal size distributions for generally smaller crystalsreflect h igher rat es of breaka ge by the pr opeller, due t othe higher probability that the propeller will hit mostcrystals in such a system. However, when the samecompound is crystallized in a larger volume, i t willproduce a somewhat larger average particle (because

F i g u r e 4 . Relationship between relative speed (crystal andpropeller); propeller characteristic length T ) B [sin( - R)], afunction of blade width B , blade angle [], and crystal pathincident angle [R]; crysta l size; and probability of contact (afterref 6).

F i g u r e 5 . Effect of scale-up factor on overall attrition rate(ref 7).

F i g u r e 6 . Nucleation rate vs growth rate for 50 m K2SO 4crystals, cooling crystallization (after ref 2).

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nucleation in the larger unit is generally lower), thelarger pa rticle, in tu rn, will be less prone to be dam agedby the propeller. He concluded that s t irred tanks arenot to be considered well mixed, and that using thatmodel to predict MSMPR crystallization kinetics isfraught with difficulties, because average values areused, which are not reproducible in other systems.

T h e a b ov e (a s w ell a s ot h er ) w or k le a ds t o t h econclusion that in most industrial crystall izers t he

residence time u sed in the vessels origina l design isver y l ikely a cons er vat ive es t im at e, and a cer t ainamount of production increase may be possible withoutany penalty in crystal quality.

I t i s i m por t ant t o cons ider , however , t he act ualcont ribut ors to the un its effective nucleat ion ra te, an dthe type of geometric configuration employed. Thisapproach would safegua rd a gainst a n overly optimisticappr oach to the sa fety factor inher ent in a crysta llizersresidence time.

A ttri ti on

T her e ar e t hr ee s er i ous s our ces of at t r i t i on i n an

industr ial crystallizer: att rition du e to crystals hit bythe propeller of the mixer, at tr i t ion from one crystalstr iking a nother, and attr i t ion from a crystal s tr ikingcrystallizer part s (vessel wa lls, van es, supports, etc.).The two first are the most important contributors tooverall crystal attr i t ion, and each will be addressedseparately.

A ttri ti on: C rystal-I m p e l l e r . As discussed ear lier,a common concern to increasing the production ra te ofa crystallizer is the effect that higher supersaturationwill have on n ucleation ra te a nd scaling tendency withinthe crystallizer vessel. The usua l solution t o problemsstemming from high supersaturation is to increase theagitation in the crystallizer. However, there is fear that

in increasing the mixing intensity in an existing crys-tall izer, or using a higher mixing intensity in a newdesign, one might bring about higher rates of crystalbreakage. There are, h owever, several situa tions wherethis fear may be groundless.

Nienow9 showed that the impact efficiency (the prob-abili ty of a given crystal hit t ing the impeller) dropsdramat ically with increasing vessel s ize. Therefore,although one might expect some effect from increasedagitation in a large-scale crystallizer, it is likely that itwill not be a s severe as th eory might predict. The overalleffect of increased agitation on crystals is small, accord-ing t o Synowiec7 who developed equat ions sh owing th atwhile crystal-impeller contacts are a strong function

of crystal size (fifth order dependence), they are onlylinear ly dependent on ma gma density an d power input.Fur t her , Synow iec developed dat a t hat i ndi cat ed asignificant reduction in the number of fragments gener-ated by the impeller, if the impeller surface hardnesswere to be reduced. Combining the above, one mightconclude that increasing mixing rate in a crystallizer,w hi l e at t he s am e t i m e changi ng t he m i xer s ur f acemat erial, may result in only small increases in second-ary nucleation.

Zwietering10 shows that given geometric similarity,the specific energy input (kW/kg of crystal) from a mixerdecreases exponentially with increasing scale-up r at ios.Therefore, the breaka ge detected in pilot plan t work is

most likely far greater than what will be experiencedin a larger unit. Combining this finding with Synowiecswork we may state that increasing mixing intensity ina crysta llizer, as we a lso increa se th e crystallizers size,should result in little or no adverse effects on crystalsize.

Increasing m ixing inten sity in an existing crystallizer

can be a chieved by speeding up the existing stirrer, byincreasing the stirr ers diameter , or chan ging its pum p-ing efficiency (changing the impeller type). The secondchoice may be the optimum: Wichterle11 found that theshear r ate of a centrifugal pump impeller (and t hus t hesecondary nucleation produced by it) is directly relatedto impeller speed (Figure 7). Figure 7 illustrates thatthe sa me tu rbulence (Reynolds num ber) can be obtainedat several combinations of shear rates and impellerspeeds. As a result, a carefully chosen impeller (largerdiameter will produce the same flow at lower speed) mayavoid excessive n ucleation at higher pumping rates.Naturally, changing the impeller type (improving thepumping efficiency) is an even bett er solution, which,

however, is usually not feasible because of mechanicallimitations of the stirrer in use.

On t he ba sis of th e above sampling of published work,i t m ay be s een t hat i ncr eas ing m i xi ng i nt ens it y athigher production rates should be seriously considered,as it may be more beneficial than generally expected.

A tt r i t i o n : C ry s t a l -C rystal . A typical way to in-crease production, while ma inta ining a constan t (beforeand after t he pr oduction increase) residence time, is toincrease th e ma gma den sity (kg of crystals/m3 of slur ry)in th e crystallizer. Conventional th eory indicates tha t,in such case, the secondary nucleation should increase,because of increased probability of crystal-crystal col-

lisions. Fu rth er, th ere a re limitations to th e level of suchan i ncr eas e, due t o s us pens ion l im i t at ions by t hecrystallizer stirrer.

In scale-up, however, at constant specific energyinput, the attr i t ion rate decreases with the square of the vessel s ize increase; crystal-crystal contact iseight h-order dependen t on crystal size, and only second-order dependent on crystal number, according to thework of Synowiec.7 Therefore, increasing magma densityto compensa te for residence time lost to an increase inproduction m ay be accepta ble in cases where t he crystals ize i s s m all , and t he s t ir r er has t he capabil it y of maintaining suspension of the crystals in a heaviermagma density.

F i g u r e 7 . Normalized shear rate (shear rate/rotation rate)vs local Reynolds number for disks (diameters of 80-160 mm)and impeller (160 mm diameter), after ref 11.

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C ry s t a l l i z a t i o n E q u i p m e n t

The t oleran ce for increased agitat ion, increased ma gmadensity, and reduced residence t ime, resulting from

production increases is a function of (among otherthings) the type of crystallizer being employed. Themain types of crystallizers used in the industry forcontinu ous operation a re the forced circulation (FC)cr yst al li zer , w hi ch i s equivalent t o a t ank w it h anexternal circulation loop; the draft tube baffle (DTB)crystallizer, which combines a settler with an MSMPRsection ( the st irrer is located within a draft tube forimproved m ixing efficiency); an d t he OSLO (or growth)crystallizer, which employs a fluidized bed of crystalsto eliminate crystal-to-stirrer at trition. What follows a resome of the special characteristics of industrial scalecontinu ous crystallizers, in conn ection to increasedproductivity:

(i) In a draft tube baffle (DTB) crystallizer equippedwith fines destru ction capa bility, increased n ucleationdue to higher magma density, higher circulation rates,or h igher supersat ura tion m ay go unnoticed if the finesdestruction equipment is so large th at i t will destroythe new (additional) fragments.

(ii) Kneule12 found that for MSMPR units (the forcedcirculation crystallizer is considered to approximateMSMPR operation) the mass t ran sfer (and th us growthrate) may be improved dramatically by increasing the

NRE , for certain ranges of operation, and for certainagitator power numbers (Figure 8).

(iii) Bennet t 13 theorized that the coefficient of varia-tion of crysta l size distribut ions of ma ny forced circula-

tion crystallizers is less th an the ideal 50% becau se ofpoor mixing. Improving t he mixing in a n forced circula-tion crystallizer would thus utilize crystallizer volumethat was, hereto, idle, and thus the crystallizer wouldgain production capa bility without a penalty in crystalquality.

(iv) Gahn 6 determined tha t, for a DTB (on potassiumnitrate production), an increase in magma density hadlittle effect on crystal size, after a certa in t hresh old is

passed (Figur e 9). From field experience, we have foun dthis to be true for other compounds as well.

(v) Gahn,6 Synowiec,7 and ot her s ha ve over t i m esuggested that the agitator or pump impeller may bed es ig ne d i n s u ch a w a y t h a t on e m a y r e d u ce t h eprobability of crystal to impeller impa ct. Such designshave begun to be industrially available, and can be usedin operation upgrades.

(vi) Increasing the capacity of an OSLO crystallizercan be m ade with some geometric changes, to improveits clarification capa bilities a t h igher thr oughput rat es.However, as such improvements have physical limita-tions, OSLO un its that are pushed very hard will tendto operat e as FCs, with the a tten dan t effects on crystalsize (smaller crystals).

C o n c l u s i o n s

The increase of production in an existing crystallizermay, under certain conditions, be achieved with mini-mal impact on the crystal quality. The crystall izeroperation should be reviewed in very specific terms forthe crystal tolerance to attr i t ion, the mixer type, theflexibility of the crystallizer type in use, the supersatu-rat ion involved, and the type of operat ion (salting out,reaction, evaporative or surface cooling, etc.). On thebasis of this paper, one may develop a strategy that

could include special propeller types, specific m ixingintensity, magma density increase, etc., t hat wouldallow in combination the increase in crystal productionwithout an undue penalty on the product crystal s izefrom higher attrition or nucleation rates.

R e f e r e n c e s

(1) David, R.; Bossoutrot, J .-M. Chem. Eng. Sci. 1996, 51 (21),4939-4947.

(2) Jones, A. G.; Mydlarz, J. Chem. Eng. Res. Des. 1989, 67,283 -293.

(3) Torbacke M.; Rasmuson A . Chem. Eng. S ci. 2001 , 56, 2459-2473.

(4) Ploss, R.; Mersman n, A. Chem. Eng. Tech . 1989, 12 , 137-146.

(5) Cra wley, G. M.; Gruy, F.; Cour nil, M. Chem. Eng. S ci. 1996,51 (20), 4537-4550.

(6) Gahn, C. In Die Festigkeit von Kristallen und ihr E influssauf die Kinetik in Suspensionskristallisatoren ; Universityof Mun chen, Thesis , 1997.

(7) Synowiec, P.; J ones, A. G.; Ayazi Sh amlou, P . C h em. En g .S ci. 1993, 48 , (20), 3485-3495.

(8) Rielly, C. D.; Marquis, A. J. Chem. Eng. S ci. 2001, 56, 2475-2493.

(9) Nienow, A. W. Trans. Inst. Chem. Eng. 1976, 54 , 205-207.(10) Zwietering, Tr. N. C h em. En g . S ci. 1958, 8, 244-253.(11) Wichterle, K.; Sobolik, V.; Lutz, M.; Denk , V. C h em. En g .

Sci. 1996, 51 (23), 5227-5228.(12) Kneule, F. Chem ie-Ing. T ech . 1956, 3, 221-225.(13) Bennett, R. C. Chem. E ng. Prog. 1962, 58 (9), 76-80 .

CG020014B

F i g u r e 8 . Mass tran sfer in a flat-bottom agitated tan k as afunction of Reynolds number, for benzoic acid, salt, bariumchloride, naphth alene, in aqueous, or methanol, or othersolutions (after ref 12).

F i g u r e 9 . Potassium n itra te in a DTB crystallizer, residencetime of 2.2 h , specific energy input of 1 W/kg (after ref 6).

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