Phase Transformation of Guanosine 5-Monophosphate in Continuous

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Phase Transformation of Guanosine 5-Monophosphate in Continuous Couette-Taylor Crystallizer: Experiments and Numerical Modeling for Kinetics Anh-Tuan Nguyen,† Jong-Min Kim,‡ Sang-Mok Chang,‡ and Woo-Sik Kim†,* † ‡

Department of Chemical Engineering, Kyung Hee University Seocheon-Dong, Giheung-Gu, 446-701 Yongin-Si, Korea Department of Chemical Engineering, Dong-A University 840 Hadan2-Dong, Saha-Gu, 604-714 Busan, Korea ABSTRACT: The phase transformation of guanosine 5-monophosphate (GMP) during drowning-out crystallization in a continuous Couette-Taylor (CT) crystallizer was studied experimentally and numerically. At a steady state, the phase transformation of the amorphous GMP into hydrate crystals was monitored along the axial direction of the CT crystallizer when varying the crystallization conditions, including the rotation speed of the inner cylinder of the crystallizer and the feed concentration. As a result, the phase transformation was significantly facilitated when increasing the rotation speed, due to the enhanced dissolution of the amorphous GMP, as well as the growth of the hydrate crystals. For the numerical modeling, simple material balances were derived for three kinds of GMP: the amorphous GMP, hydrate crystals, and GMP concentration in the solution, under the assumption of plug flow behavior for the fluid motion in the CT crystallizer. The simple model predictions matched well with the experimental profiles for the three kinds of GMP along the axial direction of the crystallizer, allowing estimates for the kinetics of the phase transformation, including the mass transfer coefficients for dissolution and growth. According to the model predictions, the rates of amorphous GMP dissolution and hydrate crystal growth were both competitive to control the phase transformation in the CT crystallizer, and about 10 times higher than those in a stirred tank crystallizer.

1. INTRODUCTION The phase transformation of polymorphic crystals during crystallization is very important with regard to product control for food additives, pharmaceuticals, and fine chemical materials, as different polymorphic crystals have different physical-chemical properties of solubility, hardness, stability, and bioavailability, and so forth.1-3 Thus, many studies have attempted to produce the desired polymorphs by controlling the phase transformation via the operating factors of the crystallization, such as the solvent, agitation speed, temperature, additives, initial solute concentration, pH, and seeding, and so forth, all of which are known as influencing factors.4-19 As such, according to Davey et al.,14 the phase transformation of 2,6-dihydroxybenzoic acid (DHB) was varied with the initial solute concentration. When increasing the initial feed concentration, more stable phase crystals were nucleated, which resulted in a larger surface area of stable crystals for the mass transfer, thereby promoting the phase transformation of DHB. Meanwhile, in the case of agitation, the phase transformation of taltireline was significantly facilitated when increasing the agitation speed, as the mass transfer for the dissolution of metastable crystals and growth of stable crystals were both enhanced.16 Mathematical modeling approaches have also been frequently used to investigate the phase transformation and estimate the influencing parameters for accurate control, design, and optimization of the phase transformation process.5-7,20 For example, Davey et al.5-7 used a mathematical model to predict the phase transformation under controlled conditions in an ideal batch crystallizer. By comparing the model prediction with a controlled experiment using a seed crystal mixture of metastable and stable r 2011 American Chemical Society

phases in a batch crystallizer, they then estimated the kinetic parameters of the mass transfer coefficients for dissolution and growth during the phase transformation. In addition, a population balance equation (PBE) was combined with the model to predict the crystal size distribution and kinetic parameters of the phase transformation of citric acid crystals.20 The Couette-Talyor (CT) fluid motion induced in the gap between concentric cylinders by the rotation of the inner cylinder is interesting due to its unique hydrodynamic features and welldefined flow regimes. According to Taylor et al,21 an azimuthal flow is induced by the rotating inner cylinder and then changes to a unique periodic vortex when increasing the rotation speed of the inner cylinder, as the centrifugal force of the azimuthal flow becomes greater than the radial viscous friction and perturbs the flow stability, causing a radial fluid motion. The Taylor number (Ta), defining the relationship between the centrifugal and viscous forces of the hydrodynamics, is generally used to determine the flow regime, varying from a stable Couette flow to a turbulent Taylor vortex flow, when increasing the rotation speed of the inner cylinder.22,23 Above a critical Ta value, periodic vortices, called Taylor vortices, are induced, as shown in part a of Figure 1. Owing to the strong circulatory motion of the fluid, the Taylor vortices provide homogeneous and strong radial mixing with a small axial dispersion, allowing many advantageous applications in various areas, including crystallization,24 polymerization,25 Received: October 28, 2010 Accepted: January 19, 2011 Revised: January 6, 2011 Published: February 11, 2011 3483

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Figure 1. (a) Schematic picture of plug model description of Couette-Taylor crystallizer (1. stationary outer cylinder, 2. rotating inner cylinder, 3. Taylor vortices, and 4. plug flow crystallizer) and (b) experimental system for modeling GMP phase transformation (1. dc motor, 2. Pump StepDos, 3. GMP feed solution, 4. methanol solution, 5. damper, and 6. analysis).

membrane separation,26 photocatalytic reactions,27 filtration,28 and biological systems.29 For example, Taylor vortices have been applied to the continuous drowning-out crystallization of guanosine 5-monophosphare (GMP) and significantly facilitated the crystallization, including the pseudopolymorphic transformation of amorphous GMP to hydrate crystals.24 For example, a pure polymorphic product of hydrate GMP crystals was obtained within 5 min of the mean residence time of a Couette-Taylor (CT) crystallizer, even at a high feed concentration of 150 g/L and moderate rotation speed of 300 rpm. This result was 5 times faster than the crystallization of hydrate GMP crystals in a continuous MSMPR crystallizer with the same feed concentration and a much higher agitation speed of 1000 rpm, and attributed to the more effective promotion of the mass transfer by the periodic Taylor vortices than that by the random turbulent eddies from the agitation. In addition, the gas-liquid mass transfer in CaCO3 crystallization via the CO2-Ca(OH)2 reaction was also found to be markedly enhanced by Taylor vortices, resulting in much

smaller crystals with a more uniform size and shape in a continuous CT crystallizer than those obtained in a continuous MSMPR crystallizer.30-33 Accordingly, in contrast to previous studies that focused on the phase transformation in a controlled batch mode in a stirred tank crystallizer, the present study investigated the influence of Taylor vortices on the pseudopolymorphic transformation of GMP solids during continuous drowning-out crystallization. In experiments, the phase transformation during continuous drowning-out crystallization is measured at the axial position of the CT crystallizer in a steady state, while it is numerically predicted using a simple model based on the material balances of the amorphous GMP, hydrate GMP crystals, and GMP in the solution. On the basis of comparing the experiments and numerical predictions, kinetic parameters are estimated for the phase transformation, including the mass transfer coefficients for the dissolution of amorphous GMP and growth of hydrate crystals, according to various operating conditions of rotation speeds of the CT crystallizer and GMP feed concentrations. Then, it is 3484

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Figure 2. Typical dynamic profiles of GMP concentration in product solution and crystal fraction of GMP in product solid during drowning-out crystallization at 25 °C with 300 rpm rotation speed for inner cylinder, 150 g/L GMP feed concentration, 3 min mean residence time, and 5:5 feed ratio (GMP feed solution, methanol).

evaluated how fast the mass transfer for the phase transformation in the CT crystallizer is compared with that in a stirred tank crystallizer.

2. MATHEMATICAL MODELING The mathematical model was to describe the phase transformation of amorphous GMP to hydrate crystals during drowningout crystallization in a steady-state Couette-Taylor (CT) crystallizer. To simplify the model, it was assumed that the supersaturation during the phase transformation was ranged between the solubility of the amorphous GMP (metastable solubility) and the solubility of the hydrate crystals (stable solubility). Thereby, the nucleation of the amorphous GMP and hydrate GMP crystals during the phase transformation was neglected. The above assumption was validated in a later experiment. In addition, the CT crystallizer was simplified as a plug flow crystallizer in a steady-state,34 as shown in part a of Figure 1. The model equations for the phase transformation was then derived from the mass balances of three kinds of GMP, the amorphous GMP, hydrate GMP crystals, and GMP in the solution, using, vdmA ¼ - kD SA ðmAðeqÞ - mS Þ dx

ð1Þ

vdmC ¼ kG SC ðmS - mCðeqÞ Þ dx

ð2Þ

vdmS ¼ kD SA ðmAðeqÞ - mS Þ - kG SC ðmS - mCðeqÞ Þ dx

ð3Þ

where mA and mC were the mass concentrations of the amorphous GMP and hydrate crystals in the suspension respectively, mS was the mass concentration of GMP in the solution, mA(eq) and mC(eq) were the solubility of the amorphous GMP and hydrate crystals respectively, v and x were the axial velocity and axial position in the CT crystallizer (part a of Figure 1) respectively, kD and kG are the mass transfer coefficients of the dissolution and growth processes respectively, and SA and SC

were the surface area of the amorphous GMP and hydrate crystals per unit mass of solids respectively, defined as35 SA ¼ kSA

SC ¼ kSC

nA 1=3 kVA

2=3

FA

2=3

nC 1=3 kVC 2=3 FC 2=3

mA 2=3

ð4Þ

mC 2=3

ð5Þ

where kSi and kVi were the shape factors for the surface area and volume of the amorphous GMP (subscribe A) and hydrate crystals (subscribe C), respectively, and FA and FC were the density of the amorphous GMP and hydrate crystals, respectively. When defining the dimensionless variables as MA = mA/mT, MC = mC/mT, MS = mS/mT, and δ = x/vτ, where τ was the mean residence time of the CT crystallizer, the model eqs 1-3 were rearranged as: dMA ¼ - KD MA 2=3 ½MAðeqÞ - MS ð6Þ dδ dMC ¼ KG MC 2=3 ½MS - MCðeqÞ dδ

ð7Þ

dMS ¼ KD MA 2=3 ½MAðeqÞ - MS - KG MC 2=3 ½MS - MCðeqÞ dδ ð8Þ Here, KD and KG were the dimensionless mass transfer coefficients of the dissolution and growth, respectively, expressed as, KD ¼

KG ¼ 3485

kD kSA nA 1=3 mT 2=3 τ kVA 2=3 FA 2=3 kG kSC nC 1=3 mT 2=3 τ kVC 2=3 FC 2=3 v

ð9Þ

ð10Þ



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Figure 3. Typical axial profiles of GMP crystallization at 25 °C with 300 rpm rotation speed for inner cylinder, 76.37 g/L GMP feed concentration, 5:5 feed ratio (GMP solution/methanol) and 3 min mean residence time: (a) dynamic profiles of GMP concentration and crystal fraction of product solid and (b) dynamic profiles of characteristic length LC.

where nA and nC were the number of amorphous and crystalline hydrate GMP in the suspension, respectively, estimated from mA and mC as mA = FAkVALA3nA and mC = FCkVCLC3nC respectively using the characteristic length scales of amorphous GMP (LA) and hydrate crystals (LC). The model equation set of eqs 6-8 was then simultaneously solved using the ode45 routine in MATLAB based on an explicit Runge-Kutta formula.36,37 The adjustable parameters of KD and KG could be estimated by comparing the model prediction with experimental data on the mass concentration profiles of GMP solids and GMP solution in the CT crystallizer.

3. EXPERIMENTAL SECTION The Couette-Taylor (CT) crystallizer was composed of two cylinders: an inner cylinder of stainless steel and outer cylinder of lucite acrylic plastic. The diameters of the inner and outer cylinders were 4 and 5 cm respectively, the length of the crystallizer

was 40 cm, and its working volume was 1.13 L. As shown in part b of Figure 1, the crystallizer was placed horizontally to eliminate the hydrostatic pressure. A pair of inlet ports, separately positioned at 180° for injecting the GMP feed solution and antisolvent, were located at the axial ends of the outer cylinder, whereas three sample ports were installed along the axial direction of the crystallizer. For the Taylor vortex flow, the inner cylinder was rotated using a dc motor, where the rotation speed was controlled from 300 to 900 rpm. The raw GMP material (99.9% purity) was supplied by CJ Co. (Korea). The GMP feed solution was prepared by dissolving the raw GMP material in water at various concentrations ranging from 61 to 153 g/L. Methanol (ACS grade), purchased from Duksan Pure Chemical Co., LTD, (Korea), was used as the antisolvent for the drowning-out crystallization. The GMP feed solution and antisolvent were simultaneously injected into the CT crystallizer already filled with distilled water. The other experimental conditions of the crystallization were fixed, including 3486



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pump, and dried in a desiccator for one day. The mass fractions of amorphous GMP and hydrate crystals were then analyzed using FTIR (Perkin, System 2000, U.S.A.),24 whereas the crystal sizes and crystal shapes were observed using a video microscope (IT System, Sometech, U.S.A.).24 The filtered solution samples were also analyzed for the GMP concentration using UV-vis (JASCO, V-570, Japan).24

4. RESULTS AND DISCUSSION

Figure 4. Typical axial profiles of GMP products at 25 °C with 300 rpm rotation speed for inner cylinder, 76.37 g/L GMP feed concentration, 5:5 feed ratio (GMP solution/methanol) and 3 min mean residence time: (a) x/τv = 1/3, (b) x/τv = 2/3, and (c) x/τv = 1.

a temperature of 25 °C, mean residence time of 3 min, and drowning-out ratio (volume flow ratio between the feed solution and the antisolvent) of 1. At a steady state, suspension samples were taken from the three axial ports, quickly filtered using a vacuum

4.1. Phase Transformation of GMP. The typical transient behavior of GMP drowning-out crystallization was monitored in the CT crystallizer, as shown in Figure 2. When injecting the GMP feed solution and methanol into the CT crystallizer, the GMP concentration in the product stream at the outlet (x = L) increased quickly to initiate the nucleation of amorphous GMP, then decreased rapidly and approached a stable solubility after 4-5 times the mean residence time. Also, the hydrate crystal fraction in the product suspension monotonically increased and leveled off after 4-5 times the mean residence time. Therefore, these profiles of the GMP concentration and crystal fraction in the product suspension confirmed that a crystallization time of 5 times the mean residence time was enough for the CT crystallizer to reach a steady state. At a steady state, the GMP drowning-out crystallization was monitored according to the axial position in the CT crystallizer, as shown in Figure 3. For example, with a GMP feed concentration of 76.37 g/L, 300 rpm rotation speed, and 3 min mean residence time, the crystal fraction in the steady state crystallizer increased significantly from 62% to 72% according to the axial position, whereas the GMP concentration in the solution was only slightly reduced, as essentially the same amount of GMP consumed by the growth of the hydrate crystals was simultaneously supplied by the dissolution of the amorphous GMP (part a of Figure 3). Therefore, the experimental results confirmed the phase transformation of amorphous GMP into hydrate crystals along the axial direction of the crystallizer. Plus, the hydrate crystal size increased along the axial direction of the crystallizer (part b of Figure 3), indicating that the drowning-out crystallization proceeded quickly around the inlet port (x = 0) of the crystallizer, whereas the solute concentration detected at x = L/3 dropped below the metastable solubility and remained close to the metastable solubility beyond this position in the crystallizer, implying a greater driving force (ΔC) for the growth of hydrate crystals than for the dissolution of amorphous GMP. The phase transformation of GMP solids was also confirmed by microscopic images of the suspension solids according to the axial position in the crystallizer, as shown in Figure 4. The large fraction of amorphous GMP included in the sample suspension at x = L/3 clearly disappeared along the axial direction of the crystallizer, whereas the fraction of hydrate crystals increased, thereby supporting the phase transformation in the CT crystallizer. Thus, according to the above profiles of the solute concentration and fraction of hydrate crystals along the crystallizer, it is reasonable to assume for the purpose of modeling that the phase transformation proceeded without any further nucleation of amorphous GMP in the CT crystallizer beyond x = L/3. In addition, the further nucleation of hydrate crystals beyond x = L/3 would be negligible due to the amount of hydrate crystals already nucleated during the early CT crystallization around the inlet port (x = 0) and the insufficient solute concentration beyond x = L/3 for generating a significant amount of hydrate crystals. As 3487



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Table 1. Initial Values of GMP Solids and Solution Products Used for Modeling rotation speed of inner cylinder [rpm]

feed concentration (mT) [g/l]

300

76.37

mA,i [g/l]

mC,i [g/l]

mS,i [g/l]

LA,i [μm]

LC,i [μm]

24.31

39.67

12.39

42.0

55.6

500

22.50

41.79

12.08

40.3

53.5

700

19.32

45.07

11.98

40.1

52.7

900

14.90

49.87

11.60

38.2

51.7

30.50

1.02

19.39

10.09

36.8

55.3

45.82

2.85

32.73

10.24

37.2

54.4

61.10

7.52

42.60

10.98

38.8

53.3

76.37

24.31

39.67

12.39

42.0

51.8

300

Figure 5. Typical experimental and mathematical modeling results for GMP phase transformation at 25 °C, 5:5 feed ratio (GMP solution/methanol) with different crystallization conditions, and 3 min mean residence time: (a) amorphous fraction in solid product, (b) crystal fraction in solid product, (c) GMP concentration in liquid product, and (d) characteristic length of crystalline hydrate.

a result, this allows a simple model of the phase transformation in the CT crystallizer in terms of the material balances of three kinds of GMP, the amorphous GMP, hydrate GMP crystals, and GMP concentration in the solution, according to the axial position in the crystallizer (x = L/3 = ∼L), as depicted in eqs 1-3. Thus, the experimental data on the amorphous GMP, hydrate crystals, and

solute concentration at x = L/3 were considered as the initial conditions for modeling the phase transformation in the CT crystallizer, as summarized in Table 1 according to various rotation speeds for the inner cylinder and GMP feed concentrations. 4.2. Modeling of Phase Transformation. The phase transformation of GMP in the CT crystallizer was compared with the 3488



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Figure 6. Influence of rotation speed of inner cylinder and feed concentration on lumped mass transfer coefficient of GMP phase transformation at 25 °C, 5:5 feed ratio (GMP solution/methanol), and 3 min mean residence time: (a) effect of rotation speed with 76.37 g/L GMP feed concentration and (b) effect of feed concentration with 300 rpm rotation speed.

model predictions under various crystallization conditions, as shown in Figure 5. Matching the experimental results, the modeling predictions included a phase transformation decrease in the fraction of amorphous GMP in the suspension along the axial direction of the crystallizer (part a of Figure 5), and a corresponding increase in the fraction of hydrate crystals. Also, the profile predictions of the solute concentrations and crystal sizes in the crystallizer matched well with the experimental results (parts c and d of Figure 5). As the phase transformation in a solution is based on recrystallization processes, including the dissolution of metastable solids and growth of stable ones, it depends intrinsically on the

mass transfer at the solid-liquid interface. Thus, the hydrodynamic conditions are frequently a key influencing factor on the phase transformation. Therefore, in the present study, it was predicted that the fraction of amorphous GMP would be lower at a high rotation speed of 700 rpm than at a low rotation speed of 300 rpm due to the stronger vortices promoting the phase transformation. Correspondingly, the fraction of hydrate crystals was predicted to be higher at 700 rpm than at 300 rpm. 4.3. Kinetic Parameters. By comparing the model predictions and experimental results for the amorphous GMP and hydrate crystal fractions, solution concentrations, and crystal sizes in the crystallizer, the kinetic parameters of the phase transformation 3489



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Figure 7. Influence of agitation speed and feed concentration on mass transfer coefficient of GMP phase transformation at 25 °C, 5:5 feed ratio (GMP solution/methanol), and 3 min mean residence time: (a) effect of rotation speed with 76.37 g/L GMP feed concentration and (b) effect of feed concentration with 300 rpm rotation speed.

were estimated, including the dissolution coefficient of the amorphous GMP and growth coefficient of the hydrate GMP crystals, as shown in Figure.6. Thus, the dimensionless mass transfer coefficients for the dissolution (KD) and growth (KG) were predicted to vary with both the rotation speed of the inner cylinder and the feed concentration. When increasing the rotation speed of the inner cylinder, this enhances the intensity of the Taylor vortices, thereby increasing the dimensionless mass transfer coefficients, KD and KG, as shown in part a of Figure 6. The dimensionless mass transfer coefficients, KD and KG, also increased when increasing the feed concentration, as shown in part b of Figure 6. In contrast to real mass transfer coefficients, which are independent of the chemical potential (concentration), the predicted dimensionless mass transfer coefficients, KD and KG,

varied with the feed concentration. This can be explained in terms of the variables: total mass concentration (mT) and numbers of amorphous GMP (nA) and hydrate crystals (nC), included in the definition of the dimensionless mass transfer coefficients, which depend on the feed concentration. That is, when increasing the feed concentration, more GMP solids were crystallized-out, involving higher numbers of amorphous GMP and hydrate crystals in the phase transformation, thereby increasing the dimensionless mass transfer coefficients, as depicted in eqs 9 and 10. Interestingly, the dimensionless mass transfer coefficient for growth (KG) was always 5-7 times greater than that for dissolution (KD) across the whole range of rotation speeds and feed concentrations. On the basis of the model estimation of the dimensionless mass transfer coefficients, KD and KG, the actual mass transfer 3490



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Table 2. Physical Parameters of GMP Solid Products Used for Modeling (Ref ) items

amorphous GMP hydrate GMP crystals

solubility: mA(eq), mC(eq) (g/l)

13.1

9.5

density: FA, FC (kg/m3) volume shape factor: kVA, kVC

1685 0.52

1625 0.04

surface area shape factor: kSA, kSC

3.14

1.25

coefficients, kD and kG, were calculated using eqs 9 and 10, as shown in Figure 7. In the calculation, numbers of amorphous GMP (nA) and hydrate crystals (nC) were assumed to remain constant during the phase transformation in the crystallizer. The number of amorphous GMP and hydrate crystals were then calculated using the initial conditions of mA,i, mC,i, LA,i, and LC,i at δ = 1/3 (x = L/3) in Table 1. Meanwhile, the other physical parameters, including the densities, volumes, and surface area shape factors, of the amorphous GMP and hydrate crystals were separately measured using microscopic images, as summarized in Table 2. Here, the shape factors were extracted under the assumption of the spherical habit of amorphous GMP and rectangular plate of hydrate crystals, as suggested in our previous study.35 The mass transfer coefficients for dissolution and growth, kD and kG, were both promoted as much as 2.5 fold when increasing the rotation speed from 300 to 900 rpm, due to the intensified Taylor vortices effective for the mass transfer. Meanwhile, as expected, the mass transfer coefficients were independent of the feed concentration. Interestingly, the mass transfer coefficients for dissolution and growth remained almost the same across the whole range of experimental conditions, indicating the competitiveness of both the amorphous GMP dissolution and the hydrate crystal growth in controlling the phase transformation of the GMP solids. 4.4. Comparison between Couette-Taylor and Stirred Tank Crystallizers. The mass transfer coefficients for the phase transformation of the GMP solids in the CT crystallizer were compared with those in a typical stirred tank crystallizer designed based on a standard Rushton mixing tank.38 Here, it should be mentioned that the hydrodynamic features of the CT and stirred tank crystallizers were different, as the fluid motion in the CT crystallizer was induced by the rotation of the inner cylinder, whereas the turbulence in the stirred tank crystallizer was driven by impeller agitation. Thus, to express the two different hydrodynamic features using a single quantity, the energy dissipation indicating the turbulent intensity of the fluid motion was used.38-40 As shown in Figure 8, the energy dissipation in the CT crystallizer was always much greater than that in the stirred tank crystallizer, as the large contact surface of the inner cylinder in the CT crystallizer was more efficient for viscous dissipation than the inertia-driven turbulence from the impeller in the stirred tank crystallizer. Therefore, the mass transfer coefficients in the CT crystallizer were predicted to be higher in order of magnitude than those in the stirred tank crystallizer. As such, the mass transfer coefficients in the CT crystallizer changed from 1.3 10-5 to 3.2 10-5 m/s when increasing the rotation speed from 300 to 900 rpm. In contrast, in the stirred tank crystallizer, the mass transfer coefficients ranged from 6.0 10-7 to 3.2 10-6 m/s when varying with the agitation speed from 200 to 1000 rpm.35 Also, when comparing with other literature values (3.4 10-8 to ∼2.1 10-7 m/s) obtained from the phase transformation of L-histidine in a stirred tank crystallizer,41 the results

Figure 8. Comparison of mass transfer coefficients in Couette-Taylor and stirred tank crystallizers for estimating turbulent motion effectiveness. (Sherwood No correlation in CT crystallizer (ref 42), Sherwood No correlation in stirred tank crystallizer (ref 43)).

confirmed the increased facilitation of the mass transfer in a CT crystallizer. The predicted mass transfer coefficients for the CT crystallizer also agreed quite well with the Sherwood number correlation,42,43 suggesting that the simple model is effective for describing the phase transformation in a CT crystallizer. Here, the Sherwood number correlations describing the mass transfers on the solid-liquid interfaces in both CT and stirred tank crystallizers and were implicitly expressed in terms of the energy dissipation. Because of the simplification of modeling, some deviation of the model prediction of mass transfer coefficients from the Sherwood correlation was caused. However, the modeling predictions in both CT and stirred tank crystallizers consistently described the influence of the hydrodynamic conditions on the phase transformation as the Sherwood correlations in both crystallizers, as shown in Figure 8.

5. CONCLUSIONS The phase transformation of GMP solids along the axial direction in a steady state CT crystallizer was monitored and successfully modeled using the simple material balance of three kinds of GMP: the amorphous GMP, hydrate GMP crystals, and GMP concentration in the solution. Using this model for the GMP phase transformation, the predicted profiles of the amorphous GMP, hydrate crystals, and solute concentrations according to the axial position in the crystallizer agreed quite well with the experimental results across a whole range of crystallization conditions, including the rotation speed of the inner cylinder (300-900 rpm) and feed concentration (30.5-76.37 g/L). In addition, the proposed model also provided the kinetics of the phase transformation, including the dissolution rate of the amorphous GMP and growth rate of the hydrate crystals, allowing a fully predictive process design for the drowning-out crystallization of GMP, including the phase transformation. It was found that the dissolution and growth of GMP solids were both competitive for control of the phase transformation of GMP. Due to the highly effective hydrodynamic motion in the CT crystallizer, the mass transfers for the phase transformation were much faster than those in a stirred tank crystallizer. Therefore, 3491


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’ AUTHOR INFORMATION Corresponding Author

*Tel.: þ82-31-201-2970. Fax þ82-31-273-2971. E-mail wskim@ khu.ac.kr.

’ ACKNOWLEDGMENT This study was financially supported by the NRF (Korea, 2010-0017993) and KETEP (Korea, 2010-2020100030). ’ REFERENCES (1) Bernstein, J. Polymorphism in Molecular Crystals; Oxford University Press: New York; 2002. (2) Hilfiker, R. Polymorphism: in the Pharmaceutical Industry; WILEY-VCH: New York, 2006. (3) Brittain, H. G. Polymorphism in Pharmaceutical Solids; Marcel Dekker. Inc: New York, 1999. (4) Mullin, J. W. Crystallization, 3rd ed; Butterworth-Heinemann: Woburn, MA, 1993; pp 257-260. (5) Davey, J. R.; Garside, J. From Molecules to Crystallizers; Oxford University Press: New York, 2000; pp 44-52. (6) Davey, J. R.; Cardew, P. T. The Kinetics of Solvent-Mediated Phase Transformations. Proc. R. Soc. London 1985, A398, 415–428. (7) Davey, J. R.; Cardew, P. T. Rate Controlling Processes in Solvent-Mediated Phase Transformations. J. Cryst. Growth 1986, 79, 648–653. (8) Scholl, J.; Bonalumi, D.; Vicum, L.; Mazzotti, M. In Situ Monitoring and Modeling of the Solvent-Mediated Polymorphic Transformation of L-Glutamic Acid. Cryst. Growth. Des. 2006, 6, 881–891. (9) Qu, H.; Kohonen, H.; Louhi-Kultanen, M.; Reinikainen, S. P.; Kallas, J. Spectroscopic Monitoring of Carbamazepine and Phase Transformation in Ethanol-Water Solution. Ind. Eng. Chem. Res. 2008, 47, 6991–6998. (10) Caillet, A.; Rivoire, A.; Galvan, J. M.; Puel, F.; Fevotte, G. Crystallization of Monohydrate Citric Acid. 1. In Situ Monitoring through the Joint Use of Raman Spectroscopy and Image Analysis. Cryst. Growth. Des. 2007, 7, 2080–2087. (11) Kitamura, M. Strategy for Control of Crystallization of Polymorphs. CrystEngComm. 2009, 11, 949–964. (12) Wikstrom, H.; Rantanen, J.; Gift, A. D.; Taylor, L. S. Toward an Understanding of the Factors Influencing Anhydrate-to-Hydrate Transformation Kinetics in Aqueous Environments. Cryst. Growth. Des. 2008, 8, 2684–2693. (13) Qu, H.; Kultanen, M. L.; Rantanen, J.; Kallas, J. SolventMediated Phase Transformation Kinetics of an Anhydrate/Hydrate System. Cryst. Growth. Des. 2006, 6, 2053–2060. (14) Davey, R. J.; Blagden, N.; Righini, S.; Alison, H.; Ferrari, E. S. Nucleation Control in Solution Mediated Polymorphic Phase Transformations: The Case of 2,6-Dihydroxybenzoic Acid. J. Phys. Chem. B 2002, 106, 1954–1959. (15) Mukuta, T.; Lee, A. Y.; Kawakami, T.; Myerson, A. S. Influence of Impurities on the Solution-Mediated Phase Transformation of an Active Pharmaceutical Ingredient. Cryst. Growth. Des. 2005, 5, 1429– 1436. (16) Maruyama, S.; Ooshima, H.; Kato, J. Crystal Structures and Solvent-Mediated Transformation of Taltireline Polymorphs. J. Chem. Eng. 1999, 75, 193–200. (17) Alvarez, A. J.; Singh, A.; Myerson, A. S. Polymorph Screening: Comparing a Semi-Automated Approach with a High Throughput Method. Cryst. Growth. Des. 2009, 9, 4181–4188. (18) Kurotani, M.; Hirasawa, I. Polymorph Control of Sulfamerazine by Ultrasonic Irradiation. J. Cryst. Growth 2008, 310, 4576–4580.

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