FUNDAMENTALS OF INDUSTRIAL CRYSTALLIZATION AN OVERVIEW

1. FUNDAMENTALS OF INDUSTRIAL CRYSTALLIZATIONAN OVERVIEW Michel COURNIL, Department of Chemical Engineering (Centre SPIN), Ecole des Mines de Saint-Etienne (France) cournil@emse.fr www.emse.fr TU Wien 18. January 2002

2. Industrial crystallization Introduction Definition : "Crystallization"is a sequence ofphysical operations which allow to obtain in the form of a crystalline solid one or several substances initially contained in a liquid or gaseous phase • Crystallization is one of the oldest unit operations of thermal separationused to prepare or concentrate a substance in the solid state • Preliminarystepofcrystallizationprocess : = preparation of asupersaturated solution(= which contains "too much" dissolved solid) Two ways for this…. • Solvent elimination • Shift of the equilibrium sokid-liquid equilibrium via temperature variation Crystallization precipitation(involves chemical steps)

3. Industrial crystallization Introduction Diversity of shape and size…. Many physical, chemical, mechanical and rheological properties of solid materials depend on the grain size and shape examples : pigments for paintings (TiO2), catalysts, pharmaceuticals, food products, materials for electronics,...

4. Industrial crystallization Introduction The particle size distribution and the particle shapeof a solid productare essential criteriafor its commercial quality Meeting these industrial specifications is the objective of industrial crystallization • To this aim, it is necessary to defineand perform: • the necessaryphysico-chemical transformations, • thereactor type • theoperating conditions

5. Industrial crystallization A few fundamental aspects Relative supersaturation Equilibrium conditions Systemone grain (or crystal) + liquid solution C = Cs(T) T : temperature C: solute concentration in solution Cs:saturation concentrationsolubility C > Cs:supersaturatedsolution: crystal nucleation and growth C < Cs:non saturated solution : crystal dissolution

6. Industrial crystallization A few fundamental aspects C s > 0 s < 0 Solubility (kg of solute/kg ofsolvant) T Temperature (°C) T2 T1 Equilibrium conditions(continued) Cs(T) generally increases with temperature Principle of "cooling crystallization" : purely thermal transition from an undersaturation state (T1) to a supersaturation state (T2)

7. Industrial crystallization A few fundamental aspects Differential growth of the crystal faces Instability development Agglomeration-fragmentation Cristallography (notions) A crystal = regular sequence of ions, atoms or molecules The different crystalline systems (minimum energy) In practice : many deviations from the theoretical shapes : kinetic effects, instability, impurities, agglomeration-fragmentation,….

8. Industrial crystallization A few fundamental aspects (crystallography-continued) ess interaction : esl interaction : ell interaction : • Interfacial roughness notion • Characteristics of a crystal faceat the atomic scale smoothrough • Approachviastatistical physics : energetic interactions between "firstneighbours" Importance of "entropic factor" :

9. Industrial crystallization A few fundamental aspects (crystallography-continued) P1 P2 P3 Interfacial roughness (notion- continued) Statistical simulations(Monte-Carlo method) Principle :construction/destruction of the crystal interface bydiscrete random events the probability of whichdepends on the interactions between close neighbours (P1, P2, P3) Results : a < 3 : rough interface a > 4 : smooth interface

10. Industrial crystallization A few fundamental aspects (crystallography-continued) Interfacial roughness (simulation examples) From worksof Gilmer et Bennema)

11. Industrial crystallization A few fundamental aspects (crystallography-continued) Interfacial roughness(continued) The faces of a real crystal can be of different roughnesstype

12. Industrial crystallization A few fundamental aspects Particle size distribution A sample of granular solid = a huge number of grains of different shape and size Assumption: one size parameter – "mean" diameterD – of a crystalis characteristic of all its properties The crystal populationis described byfunction f(D) population density : f(D).dDis the crystal number per unit volume the diameterof which rangesbetween DandD + dD Large variety in particle size distribution ; for monomodal distributions, simple laws with two parameters are used : mean diameter and standard deviation (dispersion)

13. Industrial crystallization A few fundamental aspects Particle size distribution(continued) f(D) Log-normal normal D Shape of classical laws of size distribution Different representations of the population size distribution By number, by weight or volume : f(D).D3.dD, by surface area : f(D).D2.dD

14. Industrial crystallization A few fundamental aspects Particle size distribution(continued) Light scattering Laser beam scattering Microscopy Settling Sieving 0.01 100 1000 10000 Dinmm 0.001 0.1 1 10 Overviewof the different methods of particle sizing They depend on the sizing operating mode : off-line, on lineor in situand on thesize domainof the crystals Off-line :sieving, settling, image analysis,… On line : optical methods (light scattering), visualization In situ : a few of the previous methods Size range :

15. Industrial crystallization The different steps of the crystallization process Nucleation : crystal creation from a supersaturated solution Crystal growth : increase of the crystal size up to the desired size by growth from supersaturated solution Dissolution : in non-saturated solution Ostwald ripening : slow ageing (size evolution with time) of a crystal population in the vicinity of the saturationn Agglomeration : formation of crystal clusters linked by crystalline bridges (in supersaturated solution)

16. Industrial crystallization The different steps of the crystallization process Nucleation • The first step of the crystallization process : crystal birth • Decisive influence on the crystalnumber and size(given mass quantity to be crystallized) • Several mechanisms of new crystal (nuclei) production : • - in the absence of crystals("clear" solution) : primary nucleation • - in the presence of crystals : secondary nucleation • A transitionstep : the least understood crystallization tep • The crystallization step is the most difficult to characterize experimentally : small nuclei, ill-known structure, widely non reproducible process, intimately linked to growth

17. Metastability zone C 2 Glycine diffusivity 1 T 0 Supersaturation (s + 1) Industrial crystallization The different steps of the crystallization process Primary nucleation A few experimental aspects… - existence of an induction period (delay) at average supersaturation level and a metastability zone (no nucleation) at low supersaturation level • the supersaturated media contain aggregates (clusters) of solute (2 to several hundreds of units in each cluster) • Experimental evidence : spectroscopy, « anomalies » in the diffusivity values,…

18. Industrial crystallization The different steps of the crystallization process Primary nucleation Kinetic models of homogeneous primary nucleation Ai + A1 Ai+1 (Ri) (i  1) A1is a single atom (solute monomer), Aiaggregate of i atoms Ri two opposite reactions Ai + A1  Ai+1 (Fi) Ai+1Ai + A1(Bi+1) Vfi = fiCi Vbi = bi+1Ci+1 • transformation rate of Aito Ai+1 : Ji = fiCi - bi+1Ci+1 • mass balance of Ai

19. Industrial crystallization The different steps of the crystallization process Primary nucleation Kinetic models of homogeneous primary nucleation (continued) as   constant fi et bi+1determination  kinetic theory of gasesfi=bsi(i > 1) b C1si = s1 i2/3  no model to calculate bi+1howeverat equilibrium :Ji = 0 for all i Problem of calculation of the equilibrium concentrations….

20. Industrial crystallization The different steps of the crystallization process Primary nucleation Kinetic models of homogeneous primary nucleation (continued) DGi xi minimum andDGi maximum for : xi i i* Problem of calculation of the equilibrium concentrations ….iA1 = Ai (critical nucleus)

21. Industrial crystallization The different steps of the crystallization process Primary nucleation Kinetic models of homogeneous primary nucleation (continued) Back to the nucleation rate calculation… Metastability zone J  s Assuming steady state…. : constant CiandJi independent fromi :

22. Industrial crystallization The different steps of the crystallization process Primary nucleation Kinetic models of homogeneous primary nucleation (continued) atlow supersaturation level, the nucleation process is very slowand even can be blocked in the vicinity of the critical nucleuswithout reaching zone i>i* no nucleation : "metastability zone" the induction period is the time taken by the system to cross the critical zone ; in many cases, the nucleation rate (number of nuclei produced per unit time and volume) is considered as inversely proportional to the induction period The nucleation rate is often expressed in the simpler mathematical form :JK'sn ; parametersK' andnaredetermined from curve-fitting of experimental data

23. Industrial crystallization The different steps of the crystallization process Primary nucleation The heterogeneous primary nucleation foreign surface Experimental evidence : nucleation is facilitated by the presence of impureties, dust, walls,…. Interpretation: the nuclei appear on foreign supporting surfaces which decrease their formation DGi:DGhet = f. DGhom f : heterogeneity factor 0<f<1 q : contact angle

24. Industrial crystallization The different steps of the crystallization process Primary nucleation The heterogeneous primary nucleation • similar form of kinetic law • DGhet < DGhom • concentrations in different aggregates are increased • heterogeneous nucleation is faster than homogeneous nucleation • reduced metastabilityzone

25. Industrial crystallization The different steps of the crystallization process Secondary nucleation definition : the secondary nucleation consists of the formation of new crystals in presence of crystals of the same nature ("parents") in a stirred supersaturated solution • the secondary nucleation rate depends on the properties of the "parent" crystalsas well as onthe crystallizer operating conditions • possible atlow supersaturation level (in these conditions, primary nucleation would be impossible) • in the continuous industrial crystallizers, nucleation is essentiallysecondary

26. Industrial crystallization The different steps of the crystallization process Secondary nucleation (continued) Potential secondary nuclei solution clusters Parent crystal Mechanisms of secondary nucleation : • initial breeding :release into the solutionof small particles of crystalline dust • contact nucleation : • crystal-wall • The shockscrystal-stirrerproducenew fragments (nuclei)crystal-crystal • "true" secondary nucleation : the layer adjacent to the parent crystal surfaceacts as a stock of nuclei liable to be released

27. Industrial crystallization The different steps of the crystallization process Secondary nucleation (continued) Rate of secondary nucleation : • The nuclei production ratedependson : • - theinput powerof the stirring device • - theconcentration in solidof the suspension • - thesupersaturation • Only empirical laws : BII = ksbSjwd • BII : number of nuclei produced per unit volume and time • s : supersaturation level, w : stirrer rotation rate ; S, surface areaof the parent crystals, with b = 0.5 - 2.5 ; j = 1 ; d = 0 - 8 (2 - 4)

28. Industrial crystallization The different steps of the crystallization process Crystal growth step Adsorbed species kink terrace  In crystallization, growth plays an essential influence on the crystalsizeandshape The growth of a cystal face results from the progressive integration of atoms or ions into the crystal lattice The growth kinetic processis divided in several consecutivesteps The growth rate is determined by the slowest step(rate-determining step) Representation of the crystal surface : Different adsorption sites :terrace(1 bond), step (2 bonds), kink (3 bonds)

29. Industrial crystallization The different steps of the crystallization process Crystal growth (continued) The different steps of the growth mechanism 1- Transport (bulk diffusionof the solute ions or molecules towards the crystal face) 2- Adsorptiononto the crystal surfacepotentialgrowth units 3- Bi-dimensionaldiffusionof the growth units on a terrace 4- Adsorption of the growth unit onto a step 5- Unidimensionaldiffusion alonga step 6-Adsorption of the growth unit onto a kink  integrationto the crystal lattice Consequence :progressive filling of the step by growth units, progression of the step on the surface, formation of the crystal lattice layer by layer

30. Industrial crystallization The different steps of the crystallization process Crystal growth (continued) Growth rate= mole or mass flux orrate of linear growth kdexpressed from correlations :example Sh = = 2 + 0.81 Rep1/2Sc1/3(Sh : Sherwood number ; Sc : Schmidt number) Crystal growth mechanisms : akineticassumption (whatrate-determining step?) and amorphologicalassumption(roughorsmooth interface?) A few typical cases of growth rate laws Growth rate with rate-determining bulk diffusion :(no influence of morphology…) Growth rate diffusion flux concentration gradient in the interfacial layer  kd (C - Cs)  kds; kdmass-transfer coefficient

31. Industrial crystallization The different steps of the crystallization process Crystal growth A few typical cases of growth rate laws(continued…) Rate-determining interfacial steps Two different cases according to the surfaceroughness • rough interface : • an adsorption sitea kinkonly step 6 of the mechanism growth rates • smooth interface : Growth is possiblein spite of the absenceof steps and kinks • Two explanations... • • in the case ofhigh supersaturation levels :many atoms are adsorbed on the terraces temporary aggregatesbi-dimensional nuclei

32. Industrial crystallization The different steps of the crystallization process Crystal growth A few typical cases of growth rate laws(continued…) • smooth interfaceandhigh supersaturation level(continued) Different situationsof growth of the bidimensional nucleus • smooth interfaceandlow supersaturation level • microphotographs showstepsin form ofspirals

33. Industrial crystallization The different steps of the crystallization process Crystal growth A few typical cases of growth rate laws(continued…) • smooth interface and low supersaturation level (spiral growth- continued) • Screw-dislocations source of new steps (Burton-Cabrera-Frank "BCF" model) • Spatial structuresand stationary processes Simplification : G s (high supersaturation) G s2(low supersaturation) • growth rate law :

34. Industrial crystallization The different steps of the crystallization process Crystal growth Influence of the impurities (additives) on crystal growh 0 ppm 35 ppm 5 ppm 50 ppm 6,5 ppm Experimental evidence : KH2PO4growth in presence of impurity Al3+

35. Industrial crystallization The different steps of the crystallization process Crystal growth Influence of the impurities (additives) on crystal growh The shape of a growing crystalis defined by the relative valuesof the growth rate of its different faces ; The more rapid the growth in a direction, the lower the lateral developmentof the face normal to this direction Foreign atoms adsorbed on a terrace can reduce to a large extent the proceding rate of the steps A foreign atom or molecule can enter intocompetitionwith a "normal" atom as far asadsorptionon a site is concerned and thusblockorreducethe growth rate Molecular dynamics calculations adsorption abilityof a molecule on a face Possibilityof select or define and synthetize “ tailor-made ” additives to obtaina well-defined crystal shape

36. Industrial crystallization The different steps of the crystallization process Agglomeration Agglomerate Agregate Definitions : Aggregation : formation of a clusterof crystalslinkedbyweak cohesion forces(van der Waals) Agglomeration : collision then aggregationbetween crystalsfollowedby the formation ofcrystalline bridges(in supersaturated solution)

37. Industrial crystallization The different steps of the crystallization process Agglomeration(continued) Particle size In turbulent medium :significance of the ratio Kolmogorov scale = size of the smallest eddies (about50 mm) Kolmogoro v microscale R = 0,2 mm Interaction range : van der Waals Electrochemical double- layer Hydrodynamic interactions • mechanismsof collision • Submicronic particles(brownian motion) • collisions dueto the flow  interactions between solid particles

38. Industrial crystallization The different steps of the crystallization process Agglomeration(continued) attractive(London-Van der Waals) : potential : A : Hamaker constant ; R : particle radius ; h : separation between particles • répulsive(electrochemical double layer (in water)) potential : • F0 : electrostatic surface potential (assimilatedtoz potential) ; k-1 : Debye-Hückel length + + - - + + + + - - + + + + - - + + - - + + + + + + - - + + hydrodynamic interactions: liquid draining-off between approaching particles  interactions between solid particles

39. Industrial crystallization The different steps of the crystallization process Agglomeration(continued) quasi-fractalmodel: iprimary particles of radiusa1  aggregateof outer radiusai agglomerate morphology • Compactagglomerates • equivalentsphere models • Ramified agglomerates quasi-fractal models Df :fractal dimension consequences on : collision frequence, hydrodynamic interactions and fragmentation

40. Industrial crystallization The different steps of the crystallization process Agglomeration(continued) F1collision frequencebetween two particlesof radiiai et aj: For example :F1 =  (caseof a turbulent medium) e : dissipated turbulent power ; ai et aj : particle radii agglomeration dynamics Ai + AjAi+j Population balance in an agglomerating system Agglomeration kernelKi,jproduct of two factorsF1 et a  atakes into accountthe physico-chemicaland hydrodynamic interactions;it is called "capture efficiency factor"

41. C Ca Stirrer Cf Tf, Cf , crystals : f(D) Tf Ta T Industrial crystallization The crystallization reactors The continuous crystallizers Feed ; Ta ; Ca ; flow-rate : W ; no crystals Steady feed Steady operating characteristics Removal ; Tf ; Cf ; flow-rate : W ; f(D)

42. Industrial crystallization The crystallization reactors Thecontinuous reactors : the MSMPR model Mixed suspension mixed product removal reactor • Simplifying assumptions of the MSMPR model • Steady state • The same shape for all crystals • One grain size parameter : L • Growth rate independent from the size • Constant volume of the suspension Volume /Flow-rate = V/W = t (residence time) • Perfectly mixed reactor • Isokinetic removal( no classification) • No crystalin the feed pipe • No ripening, no agglomeration, no fragmentation • New crystals (nuclei)appear with a zero initial size

43. Industrial crystallization The crystallization reactors The continuous crystallizers : population balance The population balanceis an extension of the notion and the approach of classical (mass, energy,…) balances to the extensive variable"number of entities"of a population characterized by one or several properties This approach can be applied to the MSMPR crystallizer and its crystal population of densityf(D) Variation in the numberof grains of size ranging betweenDandD + DDduring time interval Dt V Df. DD = [f(D, t).G(D, t).Dt - f(D+ DD, t).G(D+ DD, t).Dt]V -W.f(D, t) DD. Dt + (B(D, t) -D(D, t)). V. Dt. DD B(L):"birth"contribution (nucleation, agglomeration,...) D(L) :"death"contribution (agglomeration, fragmentation,...)

44. Industrial crystallization The crystallization reactors The continuous crystallizers : population balance (continued) Intercept : f0 Log(f) Slope = -1/(Gt) D In the case of the MSMPR at the steady state : B(D) = 0 except forD = 0 Integration  f(D) = f0 exp(-D/Gt)with :f0 = B0/G (B0  B(0))

45. Industrial crystallization The crystallization reactors The continuous crystallizers : population balance (continued) From the semi-log representation off(D), the most significant parameters of the crystallization process : B0and G, can be easily determined • Distribution : • by number • by diameter • by surface area • - by weight other characteristics f = 6 kv r n0 (Gt)4 fvolume fraction in solid L50 = 3.67 Gt mean size by weight : 4 Gt

46. Industrial crystallization The crystallization reactors The continuous crystallizers : the MSMPR limitations Log(f) Classified product removal Poor mixing Agglomeration Fragmentation Classification D Example : potassium sulphate size distribution (continuous crystallizer) The real crystallizers present many deviations from the MSMPR assumptions and characteristics, however the MSMPR model is often taken as reference

47. Industrial crystallization The crystallization reactors The continuous crystallizers : the MSMPR limitations A large population of fine crystals…..= problems for filtration, agglomeration, safety,… The continuous crystallizers : influence of the operating variables Feed supersaturation : crystal number :  and mean size :  Residence time: less influence than expected : growth counterbalanced by fragmentation (attrition)

48. Corresponding particle size distribution Experimental principle Industrial crystallization The crystallization reactors A partial solution to the large population of fine particles : the fine dissolution loop

49. Industrial crystallization The crystallization reactors Conclusion Three unit operations around the crystallizer:  crystallisation/precipitation  solid /liquidseparation drying Characteristicsof the industrial crystallizers • Reactor volume : 4 -2800 m3 • Particle mean size : 1/10 - 10 mm • Residence time : 1 hr -10 hr • Stirring rate : 3-250 rpm • Input power of the stirring device : 0,1-1 W/kg • Large crystallizers production per hour > 10t-100 t/hr