CRYSTALLIZATION AND PRECIPITATION ENGINEERING

Alan Jones, Rudi Zauner and Stelios Rigopoulos

Department of Chemical Engineering University College London, UK

www.chemeng.ucl.ac.uk

Acknowledgements to: Mohsen Al-Rashed, Andreas Schreiner and Terry Kougoulos; EPSRC, EU and GSK Outline of talk

! Introduction to crystals and crystallization ! The ideal well-mixed crystallizer ! Prediction of Crystal Size Distribution ! Mixing effects in real crystallizers ! Precipitation processes ! Crystallization processes ! Scale up ! Scale out ! Conclusions Crystallization Processes ! Crystallization is a core technology of many sectors in the chemical process and allied industries

! Involves a variety of business sectors, e.g.

– Agrochemicals, catalysts, dyes/pigments, electronics, food/confectionery, health products, nano-materials, nuclear fuel, personal products & pharmaceuticals

! Processes can involve complex process chemistry together with non-ideal reactor hydrodynamics

– Hence can be difficult to understand and scale-up from laboratory to production scale operation

! Crystallization also forms part of a wider process system Crystallization Process Systems

Water

Feed ‘Clean’ air

Liquor Recycle to recycle Liquor to recycle

Slurry

Convey Liquor to recycle

Screen Mill Hot air oversize

PRODUCT CRYSTALS

Mix, convey, etc.

Jones, A.G. Crystallization Process Systems, Butterworth-Heinemann, 2002 CRYSTAL CHARACTERISTICS

Crystals appear in many: ! sizes, ! shapes and ! forms, Which affect both: ! performance during processing, and ! quality in application Phase Equilibria

Understanding phase equilibria is crucial to crystallizer operation

! Undersaturated - crystals will dissolve

! Metastable - crystals will grow

! Labile - solution will nucleate spontaneously

Solubility-supersolubility diagram Supersaturation

! Thermodynamically, solute in excess of solubility ∆µ Supersaturation = RT where µ = chemical potential

!For practical use

∆c = c − c * or S = c / c *

where c = concentration of solution c* = saturation concentration

Supersaturation, ∆c, is sometimes called the concentration driving force Crystallization Kinetics

! Nucleation rate - rate of formation of new crystals dN = B = k ∆cb nuclei/s m3 dt n where b = 'order‘ of nucleation B = nucleation rate –rate of increase of crystal number

! Crystal growth – rate of increase of crystal dimension dL = G = k ∆c g m/s dt g where g = 'order’ of growth G = growth rate rate – rate of increase in crystal size

Corresponding expressions exist for crystal agglomeration and breakage. Thus particle formation processes all depend upon supersaturation The Well-mixed Crystallizer

IN OUT Precipitation reactions

! Reactants flow into vessel

and form a reaction zone

! Particles form from reacting

species via crystallisation

! Process kinetics can be

dominated by mixing process

! Can get undesired

product forms, e.g. solvates from solvent drown out Note: For batch operation: • Outflow of product is zero • Hydrodynamic ratio (W/D) varies as function of fill during reaction • Reactant mixing & hence precipitation kinetics require optimisation Designing for Crystal Size Distribution (CSD)

! Key goal: Characterise Kinetics inter-relationship between – reactor residence time – process kinetics – product CSD CSD ! Understand relationship as function of reactor scale size ! Design reactors and process operating conditions to yield Residence Time – desired CSD The Crystallization Triangle Conservation Equations

Mass balance ! ∆concentration (inlet - outlet) → Mass Yield ! Only gives crystal yield – not how mass distributed in crystal size – the CSD ! Need ‘crystal number’ balance – population balance

Population balance ! Accounts for number of crystals formed & their size ! Hence CSD & mean particle size can be predicted ! Incorporates terms for crystal nucleation, growth, agglomeration & breakage Population Balance Model (PBM) ! PBM (Randolph & Larson 1962) provides population of crystals as described by number density function n(L,t)

• L - crystal size and t -time • Represents probability to have crystals with size L at moment t ! Numerical solution of PBE produces Crystal Size Distribution (CSD)

∂n ∂ ( nG ) n − no + + = B − D + B − D + B ∂t ∂L τ a a d d 0 ! G - growth rate ! B & D - ‘Birth’ & ‘Death’ functions for agglomeration & breakage

! B0 - nucleation rate ! τ - residence time (for continuous crystallisation) ! Indices a, d & 0 relate to agglomeration, breakage & nucleation

A partial integro-differential equation solved by numerical methods eg finite element. For non well-mixed systems need to include velocity derivatives in addition to crystal growth rate. Problems with Reactive Precipitation

! Spatial variation in reactant concentration & crystallizer performance thus sensitive to – mixing conditions – processing scale size ! For fast supersaturation rises and large vessel sizes this gives variability in particle formation rates ! Scale-dependant fluid mechanics also effect process kinetics through its impact on secondary nucleation

! Mixing effects tends to be particularly pronounced for fast precipitation systems (Danckwerts, 1958)

Danckwerts, P. V., 1958. The effect of incomplete mixing on homogeneous reactions. Chemical Engineering Science., 8, 93-99. Computational Fluid Dynamics Why use CFD?

! To investigate localised mixing effects and fluid hydrodynamics 1. Local velocities

2. Local energy dissipation (εloc) 3. Solid volume fraction* 4. Heat transfer and temperature profile* ! For the development of crystallizer compartmental modelling framework ! To facilitate modelling, scale-up and design

* Kougoulos et al., Scale-Up of Organic Crystallization Processes. In AIChE National Meeting, Recent Developments. In Crystallization and Evaporation. San Francisco, CA, USA, 16-21 November 2003, (New York: AIChE), Paper 310B Agitated Vessel Mixing ! Real agitated vessels are not well- mixed except at small

volumes and/or high power inputs, which may cause particle disruption ! Uniformity of mixing decreases as vessel size increases !Numerical solution of the Navier-Stokes Equations Some CFD and Precipitation Studies

! Seckler et al. 1993 Precipitation of calcium phosphate in a 2-D CFD jet mixer

! Van Leeuwen et al. 1996 Zonal CFD model of BaSO4 precipitation

! Wei and Garside 1997 Precipitation of BaSO4 in stirred tanks ! Al-Rashed & Jones 1999 CFD modelling of gas-liquid precipitation ! Bezzo et al. 2000 Integration of CFD and process simulation ! Baldyga and Orciuch, 2001 PDF CFD methods ! Zauner and Jones 2002 CFD-Segregated Feed Model ! Rigopoulos & Jones 2003 CFD-Reaction engineering model Mixing Effects in Gas-liquid Precipitation

1.4E-8

CFD 1.2E-8 Penetration Film 1.0E-8 )

ze / (m 8.0E-9 i S an e 6.0E-9 ystal M r

C 4.0E-9

2.0E-9

0.0E+0 0123456 Ti m e / ( s )

CFD + PBM simulations in qualitative agreement with experiment but v. slow ⇒ compartmentalisation

Al-Rashed, M.H. and A.G. Jones. "CFD modelling of gas-liquid reactive precipitation". Chem Engng Sci., 54 (1999), 4779-4784 Precipitated Calcium Carbonate Crystals

Note presence of agglomerates and fines – attrition? Mixing Effects: Segregated Feed Model

! Villermaux’s (1989) Segregated Feed Model (SFM) based on physically meaningful mixing parameters involving – diffusive micro-mixing time – convective meso-mixing time

! SFM particularly suitable for modelling mixing effects, as it combines advantages of both – compartmental model – physical model Segregated Feed Model (SFM)

SFM divides reactor into three

Qf1 Qf2 zones:

• two feed zones f1 and f2 reac tion u1,2 reaction • bulk b plume f1 plume f2 u1,3 u2,3 Feed zones exchange mass with each other & with bulk

bulk b Process depicted by flow rates

u1,2, u1,3 and u2,3 respectively

According to time constants

Qb characteristic for micro-mixing & meso-mixing Characteristic Mixing Times

Meso-mixing – bulk blending Micro-mixing – molecular diffusion Based on time constants (Baldega et al 1995) 1/ 2 1 3  ν  ε avg Q t =17.3×  t meso = A 4 micro   ε ε loc 3  loc  N d s

Time constants tmicro & tmeso can be regarded as inverse coefficients for mass transfer by diffusion & convention, respectively Energy dissipation rate (ε) predictable from CFD Precipitation Process: Scale-up Methodology

! Carry out laboratory scale Laboratory-scale experiments measurements (kinetics etc) ! Model hydrodynamics

Hydrodynamic Population balance model (CFD) via computational fluid dynamics (CFD)

Mixing model ! Use population balance (Segregated Feed Model SFM) model for particle properties (number/CSD) ! Link two models via segmented feed model (SFM)

Large-scale reactor ! Predict precipitation performance as function of scale size Process Scale-up: Semi-batch Precipitation

! Note small 1 l reactor, exp. !In contrast at 5 l reactor, exp. particle sizes at 30 25 l reactor, exp. high values of 1 l reactor, model low energy 25 5 l reactor, model energy input inputs 25 l reactor, model 20 breakage acts m] µ [

43 as size-reducing ! Results from L 15 local zones with process 10 high levels of 5 !This leads to supersaturation 1E-3 0.01 0.1 1 10 smaller particles & nucleation Specific power input ε [W/kg]

Calcium Oxalate Precipitation: Particle Size vs Power Input

Zauner, Rudolf and Alan G. Jones. "Scale-up of continuous and semi-batch precipitation processes." Ind Engng Chem Res, 39, (2000). 2392-2403. Precipitation in Bubble Columns

! The formation of a solid product via a gas-liquid reaction

! Common applications: inorganic salts (e.g. CaCO3, CaSO4), fine chemicals

! Apart from yield, the Particle Size Distribution (PSD) of the product is very important Conventional Approaches to Bubble Column Modelling and Scale-up

! Experimental approach - use of empirical correlations – Limited validity of correlations, often lead to contradictory conclusions

! Hydrodynamic approach - entirely based on CFD – Not yet possible to couple with the non-linear dynamics of fast reactions and crystallisation mechanisms that occur at the gas-liquid interface A Trade-off: Hybrid CFD - Dynamic Reaction Engineering Model

Hydrodynamic scale (mesoscopic) C

x Bulk scale Interfacial (macroscopic) scale (microscopic) Model Assumptions

! Isothermal operation

! Only primary processes of particle formation (i.e. no secondary processes that involve particle-particle interactions such as agglomeration)

! Dilute suspension, i.e. negligible influence of solids presence on hydrodynamics

! Homogeneous bubbly flow, i.e. no bubble coalescence CFD Modelling of Gas-liquid Flow in a Bubble Column

! Captures the gross 10 hydrodynamic effects riser, model that determine the 8 riser, experiment downcomer, model overall long-time- downcomer, experiment average gas hold-up and 6 liquid circulation 4

2 ! Eulerian-Eulerian two- gas hold-up in riser, % dimensional dynamic 0 model considered 0246810 adequate for that gas flowrate, m3/s (x10-4) purpose

! Use of CFX flow solver CFD and experimental gas hold-up

Rigopoulos, Stelios and Alan G. Jones. "A hybrid CFD - reaction engineering framework for multiphase reactor modelling: Basic concept and application to bubble column reactors". Chem. Eng. Sci., 58, (2003), 3077-3089. Case Study: CaCO3 Precipitation via CO2 Absorption in Ca(OH)2 Solution

Equilibrium concentrations 1

n CO3

o 0.8 i 0.6 act

r HCO3

f 0.4 l 0.2 mo CO2 0 35791113 pH

CO2 (g) → CO2(aq) absorption - - CO2(aq) + OH ↔ HCO3 sub-reaction i - - = HCO3 + OH ↔ CO3 + H2O sub-reaction ii ++ = Ca + CO3 → CaCO3(s) crystal formation Time Course of Concentration Profiles

13 ) 30 3 m /

12 l 25 o

11 m 20 (

n CO2 o

10 i 15 pH CO3 at r 9 t 10 HCO3

cen 5

8 n

7 co 0 0 204060 0204060 time (min) time (min) Evolution of Supersaturation

4.5 ) 3 4 CO3= gmol/m3 m /

l 3.5 o

m 3 Ca++ gmol/m3 g 2.5 on ( i 2 Supersaturation at r 1.5 ent 1 nc o

c 0.5 0 0246810 time (min) Evolution of Nucleation Rate )

c 1E+15 e s / i 1E+13 e l 1E+11 nuc ( e

t 1E+09 a 1E+07 on r i 100000 eat l 1000

og nuc 10 l 0246810 time (min) Experimental Results and Model Predictions

13 1.4E-06 12 1.2E-06

11 Agglomerate ) 1.0E-06 m ( e

10 z 8.0E-07 i s pH

9 le

6.0E-07 ic t r 8 a 4.0E-07 P

7 2.0E-07

6 0.0E+00 0246810 time (min)

pH (model) pH (exper.) Size (model) Size (exper.)

Reasonable agreement up to the onset of agglomeration SEM Micrographs of Calcium Carbonate Crystal Agglomerates: Effect of Crystal Agglomeration

3 3 21 litres Ca(OH)2 = 3 mol/m ; 0.00001 : 0.0001 m /s CO2: N2 Current Work

!Compartmental model of batch cooling crystallization at high solids content………… Batch Cooling Crystallization

Pre-processing Simulations

!CFX-Promixus !Multi-Fluid Model (MFM)

!Multiple Frames of Reference !Modified Drag coefficient (Brucato, 1998)

!Monodisperse particle sizes

!Standard k-ε turbulence model

!Heat transfer (estimated liquid side heat transfer coefficient) Computational Fluid Dynamics at High(er) Solids Content

CFD clips of [1] velocity profile development and [2] particle concentration

[1] Shows flow dampening [2] Shows solids segregation

Illustration based on 5L batch cooling crystallizer operating at 300 rpm 200 µm 5 v/v% (7 % w/w) Compartmental Model – Flow (Rushton turbine)

8 7

9

1 2 3 6 5 4

[1] [2]

[1] Shows overall flow pattern on different horizontal planes [2] Overall flow pattern on vertical scale 45o angle to baffles Compartmental Model –Heat (Rushton turbine)

1. Heat transfer coefficient Nu = hd = C Re a Pr b µ c k Uniform Bulk Temperature Cooling Zone 2. Simulate linear cooling profile Cooling Zone (353K to 293K at -1oC min-1) 3. ‘Cooling zones’ evident 4. Cooling profile influences temperature gradients

Temperature profile after 360s simulation Compartmental Model – Slurry (Rushton turbine)

Q7,8 8 7

Q 8,9 Network of Zones

Q 9,1 Q3,9 Q 9 3,7 Green: Bulk Zone

Q 9,2 Orange: Cooling Zone

Q1,2 Q2,3 1 2 3 Blue: Impeller Zone Q 5,1 Q4,2 Q Q Q 6,1 5,2 3,4 Red: High Solids Content Zone 6 5 4 Q5,6 Q4,5

Based on CFD modelling at different crystallizer scales using a Rushton impeller Process Modelling

! gPROMS (Process Systems Enterprise Limited)

1. Dynamic Simulations

2. Compartmental facility available

3. Batch crystallization process can be simulated

4. Optimisation can be carried out

5. Population balance with crystallization kinetics

! New technology

1. CFD (Fluent) and gPROMS interface

2. Simultaneous CFD simulation & modelling in gPROMS Simulations

w/w) 6 % ! Initial boundary conditions ( 5 Theoretical CSD Prediction 4 1. Seed distribution 3 Experimental CSD

2. Supersaturation distribution 2 3. Temperature 1 Mass 0 0 50 100 150 200 250 300 Crystal Size, (µm) ! Define time steps for batch process

! Define parameters, variables & algebraic expressions

! Population, mass and energy balances are ODEs A better way…..?

Scale out, rather than up Segmented Flow Tubular Reactor (SFTR). After Lemaître et al.

Reagents are mixed and formed into well-mixed mini crystallizer droplets within a segmenting fluid, which are subsequently separated

Donnet, M., P. Bowen, N.Jongen, J. Lemaître, H. Hofmann, A. Schreiner, A.G. Jones, R. Schenk, C. Hofmann and S. De Carlo. “Successful scale-up from millilitre batch optimisation to a small scale continuous production using the Segmented Flow Tubular Reactor. Example of calcium carbonate precipitation”. In Industrial Crystallization, 15-18 September 2002, Sorrento, Italy. Chemical Engineering Transactions, 3, (2002), 1353-1358. Interdigital Micro Mixer. (After Schenck et al. )

Schenk, R., M. Donnet, V. Hessel, H. Hofmann, N. Jongen and H.Löwe, 2001. Suitability of various types of micromixers for the forced precipitation of calcium carbonate, In 5th International Conference on Microreaction Technology (IMRET 5), Strasbourg, France 27-30 May 2001. Predicted Mean Particle Sizes of Calcium Carbonate

7 m (seeds) = 0 mg / L 6 m (seeds) = 0.1 mg / L ] m (seeds) = 7.5 mg / L m 5 µ m (seeds) = 10 mg / L [

1,0 4

3

2 mean size d 1

0 0.001 0.01 0.1 1 initial concentration [mol/l]

Schreiner, A. and A. G. Jones. “Precipitation in the Segmented Flow Tubular Reactor (SFTR)”. In Industrial Crystallization, 15-18 September 2002, Sorrento, Italy. Chemical Engineering Transactions, 3, (2002), 1245-1250. Crystals From the SFTR

a). Vaterite b). Y-Ba oxalate.

(Courtesy www.bubbletube.com) Conclusions

! New computational techniques for the analysis and design of systems for the manufacture of particulate crystals have become available

! The more complex precipitation processes whereby crystallization follows fast chemical reactions have also been analysed more deeply

! This progress has been aided by the growing power of the population balance and kinetic models, CFD and mixing theory, respectively

! Further progress may reasonably be expected in the development of computer models, software and hardware

! Alternative techniques are under development to avoid mixing problems and obtain efficient processes and high quality products