냉각결정화기술의응용전략 -2 고려대화공생명공학과양대륙

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1 냉각결정화기술의응용전략 -2 고려대화공생명공학과양대륙

2 결정화공정의모델링 2

3 결정화모델의구성및활용 Seed properties: Size, shape, Operating conditions Nucleation and crystal growth kinetic parameters Measured final crystal size distribution Population Balance Or other model Optimization & design Simulated final crystal size distribution & yield Verification 3

4 Model for batch cooling crystallization Model for the crystallizer For modeling crystallization process, PBE is employed. f ( L, t) [ G( L, t) f ( L, t = )] f(0, t) = t L where, f is the population density of crystals, t is the time, L is the size of the particles, and G is the growth rate. (No breakage or agglomeration) B 0 G L = 0 The overall growth rate is given by G = k ( T, L) Δc g where Δc is the difference of the concentration in the solution, c, and the saturation concentration c*. And K g is the growth kinetic parameter. g 4

5 Model for batch cooling crystallization The growth kinetic parameter,k g Eg k g T, L) = k0 exp( )(1 + k RT where, f is the population density of crystals, t is the time, L is the size of the particles, and G is the growth rate. The mass balance dc dt ( 1 = ρ k where, μ 3 is the third moment of the CSD The third moment of the CSD v μ 3 d dt 3 μ3 = n L dl 0 L) k 2 5

6 Model for batch cooling crystallization The nucleation rate The nucleation occurs if the metastable limit is violated. The population density of crystals is expressed as following equation, The method which was suggested by Hu et al. [2] provides a means to reduce the PBE to a set of algebraic equations. L i,j+1 is given by f L, t 0 β B = k T Δc T ( i j+ 1 b ( ) ( ) f ( Li, t j ) ) G( L, t) 1+ L L G( L, t ) Δ+ + t L L= i, j 1 i, j j i, j L i Δt 6

7 Simulation results of static MSL model with PBE Simulation condition -20 /hr linear cooling In this results nucleation are not happened. 7

8 Crystal size distribution of static MSL model (CV = 34%) Simulation condition -20 /hr linear cooling Nucleation are happened in experimental results. 8

9 Dynamic MSL model parameters Saturation Temp.( ) k tau The parameter of MSL model are function of saturation temperature. 2.The value of parameter p is fixed at 2.2 from experimental results

10 Relation of model parameter & saturation temperature tau = 3.278e-3*exp(9.120e-2*Ts) k = 5.346e-5*exp(9.628e-2*Ts) 10

11 Simulation results of dynamic MSL model Simulation condition -20 /hr linear cooling Nucleation are happened. * So we can explain the experimental results of nucleation. 11

12 Simulation results of dynamic MSL model Simulation condition -16 /hr linear cooling In this results nucleation are not happened. 12

13 Crystal size distribution of dynamic MSL model (CV = 16%) Simulation condition -16 /hr linear cooling Nucleation are reduced. 13

14 Crystallization Applet Crystallization applet Developed for enhancing the understandings of the crystallization behavior. Effect of kinetic parameters Effect of agglomeration and breakage Effect of cooling strategy Applet program Platform independent Java runtime is required Interactive user interface No user installation Online/offline 14

15 Crystallization Applet 15

16 최적냉각곡선의도출 16

17 냉각결정화의냉각전략 기존이론 17

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19 Optimal Cooling Strategy Inside metastable region Δ T >Δ T > max 0 As possible as close to the metastable limit The higher supersaturation makes the higher crystal growth rate. Desired supersaturation level (η des ) The nucleation should be prohibited. Too close to the limit is dangerous. Desired supersaturation level η des <1. ΔT η = Δ T max 19

20 Objective function for optimal cooling curve Multi-step prediction is used. Objective is maximizing mean crystal size. Violation over desired supersaturation level η des works as penalty. min T( t ) k 1 T ( ) ( ) W( ) if η η < 0, then η η = 0 where ω Lt + η η η η N des des k des k des * T ( C) T ΔT η = = ΔT ΔT max max 20

21 Optimization based on Genetic Algorithm Characteristics of genetic algorithm (GA) GA is a search technique used in computing to find exact or approximate solutions to optimization and search problems. Genetic algorithms are categorized as global search heuristics. Genetic algorithms are a particular class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover. Advantages of GA The major advantage of GA is their flexibility and robustness as a global search method. They do not need gradient information and make relatively few assumptions about the problem being solved. They can deal with highly nonlinear problems and nondifferentiable functions as well as functions with multiple local optima. 21

22 Optimization based on genetic algorithm Fitness function In order that the crystal growth rate is maximized while the nucleation rate is minimized, the operation should be close to MSL as possible and this problem can be formulated as an optimization problem. The objective function can be chosen as a function of the third moments of the CSD. For reality, cooling rate has upper and lower bound. Operation time and termination temperature sets to be identical for all types of the cooling strategies. min u( t) n ( μ 3 subject to 1 + w s ) μ 3 0 u( t) 50 22

23 Simulation Results (Linear cooling) (b) (a) Fig 2. (a) Evolution of CSD for the linear cooling curve, (b) The linear cooling curve and metastable limit, (c) Seed and newly formed crystal size distribution (c) 23

24 Simulation Results (Natural cooling) (b) (a) Fig 3. (a) Evolution of CSD for the natural cooling curve, (b) The natural cooling curve and metastable limit, (c) Seed and newly formed crystal size distribution (c) 24

25 Simulation Results (Optimal cooling) (b) (a) Fig 1. (a) Evolution of CSD for the optimal cooling curve, (b) The optimal cooling curve and metastable limit, (c) Seed and newly formed crystal size distribution (c) 25

26 Results Fig 3. Comparison of three types of the cooling curve (optimal, linear, natural curve) 26

27 Example 1: Linear cooling Experimental procedure Making up solution. (NH 4 ) 2 SO 4 H 2 O solution Concentration : (Ts=50 ) Keeping temperature as initial temperature for 1hr. RPM of agitator : 1000rpm Starting cooling experiment Adding the seed crystal when reactor temperature cross over the saturation temperature Seed crystal size : 462.5μm Seed crystal weight : 10g Filtering solution and drying the crystal 27

28 Estimating optimal initial temperature for linear cooling Experimental condition Solution concentration : [solute kg/ solvent kg] (T s =50 ) Cooling rate : 20 /h Processing time : 80 min. initial temperature : 51, 53, 55, 57 Expected results From 51 Crystal size : 1050 μm Total weight : 92.61g Broad crystal size distribution. From 55 Crystal size : 990 μm Total weight : 77.62g Narrow crystal size distribution. 28

29 Simulation results of linear cooling from 51 and μm (a) Linear cooling from 51, (b) Linear cooling from 53 29

30 Simulation results of linear cooling from 55 and μm (c) Linear cooling from 55, (d) Linear cooling from 57 30

31 Results of Experiment 2-1 Crystal size distribution Accumulated weight percent From 51 From 55 Mean crystal size ( μm ) Total weight (g) CV (%) CV (Coefficient of variance) under the 20% Implies uniform size distribution. CV L w 84% 16% = 100 2L L w 50% w 31

32 Example 2: Linear vs. Optimal Optimal cooling Strategy Experimental condition Solution concentration : [solute kg/ solvent kg] Processing time : 80 min. Initial temperature : 52.5 Final temperature : 23 Cooling curve Linear cooling : /h Optimal cooling : by simulated data» Maximum cooling rate : 25 /h» Maximum heating rate : 5 /h Expected results Optimal cooling Crystal size : 1050 μm Total weight : 92.61g Narrow crystal size distribution. Linear cooling Crystal size : 1050 μm Total weight : 92.61g Broad crystal size distribution. 32

33 Simulation results of linear cooling and optimal cooling (a) Optimal cooling line, (b) Linear cooling line 33

34 Results of Experiment Crystal size distribution (weight) Accumulated weight percent Optimal cooling Linear cooling Mean crystal size ( μm ) Total weight (g) CV (%) Crystal size distribution (Number of crystal) 34

35 Process Analytical Technology (PAT) 의응용 35

36 PAT Process Analytical Technology (PAT) 란? 온라인측정기를이용한결정화운전및제어기술 PAT 의목적은생산공정을이해하고제어하기위함. 왜중요한가? Quality can not be tested into products; it has to be built in by design. FDA 제품이동일한과정에의해생산되고품질이보증되어야함. PAT 의기대효과 효율향상 원가절감 균일한품질 36

37 PAT Tool 의기대효과 Multivariate data acquisition/analysis 중요공정변수를파악하기위한 Design of Experiment Process analyzers Off-line, at-line, on-line, in-line, non-invasive Process endpoint monitoring and control 공정을모니터링하고원하는조업조건에유지 최종생산물에대해반응또는결정화시간대신보다명확한물성을이용한결정가능 Continuous improvement/knowledge management 사후관리및공정개선의과학적자료축적 37

38 Process Analyzers 전통적인측정방법 Temperature, pressure, ph, turbidity, probes Mass flow meter Volumetric gas uptake/evolution 최근의측정방법 In situ real-time (Operando) spectroscopy (midir, NIR, UV-vis, Raman, acoustic) In situ real-time particle analyzer (FBRM, PVM, ) 미래에나올방법들 Advanced data management software package Remotely controlled in situ real-time process sensors with high sensitivity New process sensors (combo probe, diode laser frequency modulation spectroscopy, ) 38

39 과포화도의측정 Attenuated Total Reflection Fourier Transform Infrared (ATR-FTIR) spectroscopy degree of supersaturation의측정 39

40 결정의분포측정 Conventional methods (Offline) Sieving: μm Microscopy: μm In-process Ultrasonic spectroscopy 주파수가 1-150MHz 범위의초음파가 1mm-5cm의 path를통과하는동안에고체의농도에따라초음파의강도 (intensity) 가변화하는것을측정결정크기가 0.1μm-100μm 사이인경우 30%-70% 사이의 solid 농도측정온도별, 농도별강도의 Attenuation에따른 calibration 필요 40

41 In Situ Particle Size Analyzer (PSA) Laser beam을조사하여반사되는것을측정해입자의수나크기를측정 (Focused Beam Reflectance Measurement, FBRM) 입자의형태에따라어려운 calibration 필요절대적측정값보다는상대적변화의측정에적합 41

42 In-process Video Microscopy (PVM) 반응기내의한지점에서시간에따른결정사진 capture 결정의크기나모양의변화, agglomeration, breakage등을눈으로확인자체적인측정값을내보내지않음 In situ PSA와같이사용하는것이일반적예 ) 10분간격으로측정된그림 42

43 결정구조및 Morphology 의측정 Raman spectroscopy 결정구조측정 In-process XRD (X-Ray Diffraction) Polymorph에따라다른위치에서나타나는 X-ray 회절의강도에의해 polymorph의농도측정 PVM 반응기내의결정에대한사진을통해결정 43

44 대표적 Example Polymorph 제어의목적 순도화학적불순물 (reagents, by-products) 잔류용매 solid forms (polymorphs, solvates, hydrates) 물성결정도와결정구조결정의 morphology crystal size distribution (CSD) 결정표면적, 밀도등안정성 생산성수율생산시간 - crystallization, filtration, drying 부피당생산량 - g/l, kg/batch 조업효율 인건비등 ( 출처 : J. Wang, C. Loose, J. Baxter, D. Cai, Y. Wang, J. Tom, and J. Lepore, Growth promotion by H2O in organic solvent selective isolation of a target polymorph, J. of Crystal Growth, 283, (2005) 44

45 유효성분 (API) 이두가지 polymorphs 를가짐 Drowning-out 에의해생산 Form I 이 Form II 보다안정적 공정상문제점 불가피한 Form II 의생성 ( 전형적으로 2~10%) 매우느린 Form I 성장속도 ( 기존방법으로 18 시간이상소요 ) 매우느린 Form II 에서 Form I 로의변환속도 ( 특정용액에서몇일정도 ) 40ºC 이상에서분해 ( 낮은온도에서조업 ) Form I 세척에많은세척수필요 (<500 L/m2/hr) 공정개선의주안점 Form I 의선택적성장을위한중요파라미터의파악 순수한 Form I 의생산을위한강건하고효율적인공정의설계 45

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50 관찰사항 중요파라미터도출 Anti-solvent addition rates Solvent composition Seed quality and loading 개선결과 확대된순수한 Form I 생산영역 Cycle time 단축 (2~4 hours vs. 18 hours) 여과효율향상 (~ 400 L/m 2 /hr vs. <500 L/m 2 /hr) 단위부피당생산성향상 (~60 g/l vs. ~20 g/l) 50

51 Thank you! 51