Application of a recent FBRM-probe model to quantify preferential crystallization of dl -threonine

chemical engineering research and design 8 8 ( 2 0 1 0 ) 1494–1504

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Application of a recent FBRM-probe model to quantify preferential crystallization of dl-threonine F. Czapla a,∗ , N. Kail b , A. Öncül c , H. Lorenz a , H. Briesen d , A. Seidel-Morgenstern a,c a

Max-Planck-Institut für Dynamik komplexer technischer Systeme, Sandtorstraße 1, D-39114 Magdeburg, Germany BASF SE, Ludwigshafen, Germany c Otto-von-Guericke Universität, Magdeburg, Germany d TU München, Chair for Process Systems Engineering, Germany b

a b s t r a c t The process of preferential crystallization is controlled by crystallization kinetics. Thus a key to run the process satisfactorily is using a process monitoring system eventually combined with a process model. In this context information of the liquid phase composition as well as the time resolved particle size distributions are usually desired. In contrast to measuring the liquid phase composition the inline measurement of particle size distributions is often difficult. The Focused Beam Reflectance Measurement probe (Lasentec, Mettler-Toledo GmbH) is an inline monitoring tool that is capable of measuring so-called chord-length distributions (CLDs). However these CLDs are different to the desired particle size distributions (PSDs). In the presented study this problem is overcome using a recent rigorous mathematical model of the measurement technology to transform PSDs into CLDs. The study shows how the probe model can be adopted to the investigated system using a series of initial validation experiments. Chord-splitting seems to occur when using the Focused Beam Reflectance Measurement probe. A simple modification of the particle geometry is incorporated into the probe model in order to simulate the chord-splitting. The simulated CLDs are then compared to the measured CLDs of different preferential crystallization runs performed for the system d,l-threonine/water. More specifically, measured moments of the chord length distributions along with optical rotation trajectories are compared to calculated moments of a population balance model in order to estimate the kinetic model parameters. This way the presented case study gives a systematic approach on how to apply the used probe model to monitor a preferential crystallization process and parameterize a process model. © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Preferential crystallization; Population balance modeling; Crystallization; Parameter estimation; FBRMprobe

1.

Introduction

Preferential crystallization is a method for the separation of two enantiomers into the pure enantiomers by crystallization. It is also referred to as resolution by entrainment (Amiard, 1956; Jaques et al., 1994). Since the process is kinetically controlled and operated in a cyclic mode it calls for a suitable process monitoring eventually combined with a dynamic process model (Elsner et al., 2005). The model can be used further on in order to design the process and to enhance the yield and/or productivity, respectively (as

∗

shown for example in Angelov et al., 2008; Bhat and Huang, 2009). To obtain process data of sufficient quality for the monitoring and model parameterization, adequate measurement devices have to be used. One popular inline monitoring tool for the solid phase of crystallization processes is the so-called Focused Beam Reflectance Measurement probe (FBRM) (see for example Greaves et al., 2008). A problem regarding this measurement technique is that the device is not capable of measuring directly a particle size distribution (Tadayyon and Rohani, 1998). Instead it measures a so-called chord length

Corresponding author. E-mail address: [email protected] (F. Czapla). Received 24 August 2009; Received in revised form 28 February 2010; Accepted 10 March 2010 0263-8762/$ – see front matter © 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2010.03.004

chemical engineering research and design 8 8 ( 2 0 1 0 ) 1494–1504

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Nomenclature Latin B b Eb,sec

R s T t w w+ V

nucleation rate (#/s) exponent for the nucleation law activation energy for secondary nucleation (kJ/mol) activation energy for dissolution (kJ/mol) activation energy for crystal growth (kJ/mol) number density of the crystals (#/m) growth rate (m/s) exponent for the growth law nucleation constant for secondary nucleation (#/(s m3 )) nucleation prefactor for secondary nucleation (#/(s m3 )) growth constant (m/s) growth constant prefactor (m/s) shape factor characteristic coordinate for crystal size (m) mass of the enantiomers in the liquid phase (kg) gas constant (8.314 J/(mol K)) supersaturation, s = (wr /w+ r )−1 temperature (◦ C) time (s) mass fraction (kg/kg) saturation mass fraction (kg/kg) volume (m3 )

Greek i 

ith moment of the population (mi ) density of the crystals (kg/m3 )

Indices r

enantiomer r = 1, 2

Ed Eg F G g kb,sec kb,sec,pre kg kg,pre kv L mL

Fig. 1 – Illustration of the chosen procedure for parameter estimation based on FBRM-data. et al., in press) and model parameterization of preferential crystallization processes (see for example Wang and Ching, 2006; Czapla et al., 2008). However this study is the first to exploit the mentioned transformation model for a parameter estimation in the field of preferential crystallization. This is done after an initial step by step validation of the technique that could be followed by other researchers interested in application of the probe model. The single one publication also using this probe model for a parameter estimation is to the authors knowledge the PhD thesis of Kail (Kail, 2009). Before performing the parameter estimation the probe model is tested using a series of validation experiments where no crystallization phenomena are occurring. These phenomena could masque measurement effects that would have to be attributed to the probe or the optical properties of the particles. This way effects such as chord-splitting (Kail et al., 2007) and the proportionality between particle number and size and the predicted measurement can be investigated. The approach followed is illustrated schematically in Fig. 1.

2. distribution (CLD). The typically resulting problem is to relate the CLD to the actual particle size distribution of the crystals (Grover et al., 2009; Hobbel et al., 1991; Ruf et al., 2000; Worlitschek et al., 2005; Wynn, 2003). This problem is typically mathematically ill-posed and therefore prone to errors (Wynn, 2003). A recent method to overcome the mentioned difficulties in this transformation is to use a mathematical model of the probe and its optical properties along with a wire frame model of the measured particles to transform a calculated particle size distribution into a chord length distribution within reasonable calculation time (Kail et al., 2007, 2008a,b, 2009). The novelty of this model is that it imitates the chord discrimination algorithm used in the FBRM-probe taking also the laser intensity profiles as well as optical aperture of the probe into account. Note that in their principle very similar approaches have been presented before by other authors (for example Kovalsky and Bushell, 2005; Ruf et al., 2000; Kempkes et al., 2008). Nevertheless these works did not model the FBRMprobe measurement and the optical phenomena occurring during the measurements to the extent as in the model used in this work. The chord length distribution delivered is then compared to a measured chord length distribution together with comparing experimental and theoretical optical rotation signals ˛. The FBRM-probe has been used before in monitoring (Czapla

Preferential crystallization

The basic concept of preferential crystallization will be explained for the typical case of a conglomerate. dlthreonine/water belongs to this type of system. The concept is illustrated in Fig. 2 in a ternary phase diagram. At point A the solution contains a slight excess of the enantiomer L. This

Fig. 2 – Schematic illustration of a preferential crystallization process in a ternary phase diagram for a conglomerate forming system.

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solution is cooled down to TEnd . During the cooling the system is inside a metastable zone. This means that the solution is supersaturated but no crystallization will occur for a certain amount of time. At this point enantiopure seed material of L is added to the vessel. These seeds will induce a crystallization of the L enantiomer. Since molecules of L are consumed from the mother liquor the concentration of the liquid phase will decrease along the trajectory A–B until point B is reached. At B the process is stopped and the crystals of L are harvested via a solid–liquid separation. Since the overall process is cyclic the mother liquor is heated up and a defined quantity of eutectic material is added to the solution so that after complete dissolution point C can be reached. Starting from point C the solution is cooled down again into the metastable zone and seeds of D are added. D crystallizes and the composition changes along a trajectory C–D until point D is reached. There the D crystals are harvested via a solid–liquid separation. With the addition of eutectic feed material the solution reaches again point A and the cyclic process scheme can be started again. Thus, with two sequel batches, a certain amount of eutectic feed material can be separated into pure D and L crystals. The stopping points of the process depend on the width of the metastable zone that is usually influenced by many factors (temperature, cooling rate, concentration, surface area present, etc. see also for example Mersmann, 1995). Therefore determining the kinetics of the process is of major importance for its understanding and design.

3.

Fig. 3 – Experimental setup for the 1.5 l plant.

Experimental setup

The experiments are performed in a 1.5 l lab scale crystallizer filled with 1 l of solution. The details of the setup and the inline, online and offline analytical instruments are presented in the following. The basic setup is already described in Alvarez Rodrigo et al. (2004) and was improved to be suitable for a polythermal process mode (Elsner et al., 2005). One major improvement was the addition of probes to monitor the solid phase (FBRM and PVM, see below for details). The setup is depicted schematically in Fig. 3. The main part of the setup is the double walled glass vessel labeled as “crystallizer”. It is equipped with a Teflon® coated propeller stirrer (3 blades, 72 mm diameter) and thermostated with the programmable thermostat1 (Lauda, edition 2000). For the online analysis a solid free sample is drawn through a porous frit (0.45 ␮m pore size) and pumped with a peristaltic pump (Heidolph, 5201) through a Polarimeter (Polarmonitor, IBZ Messtechnik GmbH, Hannover, 50 mm cell) and a densitometer (DE40, MettlerToledo) and then back into the vessel. The insulated pipeline is thermostated with thermostat2 (Julabo, F32) at 54 ◦ C for all experimental runs in the dl-threonine/water system. The volumetric flow rate of the solution in this measurement circuit is set at 10 ml/min and kept constant during all experimental runs. The stirring speed was also kept constant for all experimental runs at 500 rpm.

Fig. 4 – Illustration of the necessary input data for the probe model in order to transform a measured PSD into a CLD. During the crystallization experiments a linear cooling using a constant cooling rate is employed. The seed crystals are added to the vessel after the starting temperature TStart is reached. The experimental conditions for the three experiments carried out and used for the kinetic parameter estimation are given in Table 1.

4.

Probe model

The recently developed model for the FBRM-probe (Kail et al., 2007, 2008b) is used as a means of a forward transformation of the calculated PSD to a CLD (Kail, 2009). The FBRM-probe model relies on the implemented geometry of the particles to be measured. All necessary inputs to the model are illustrated in Fig. 4 in order to give an overview. To illustrate the method and the problem of the implementation of a particle geometry typical crystals of the amino acid dl-threonine, used in this case study, are depicted in Figs. 5 and 6. The crystals are modeled as a simple elongated rectangle which should provide a good representation of their actual appearance. Important

Table 1 – Experimental conditions of the experimental data sets used for the parameter estimation procedure. Exp. 1 2 3

wl-thr [g/gSol ] 0.09815 0.1128 0.1197

wd-thr [g/gSol ] 0.09757 0.1115 0.1191

TStart [◦ C] 36 47 57

(dT/dt) [K/h] −18 −11 −13

TEnd [◦ C] 18 31 40

Mass of seeds [g] 3.5 5 2.2

Volumetric shape factor kv Eq. (1) 0.08 0.177 0.177

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Fig. 5 – Threonine crystals of the sieve fraction 150–212 ␮m. in this context is the ratio between length and width of the crystals. As can be seen in the pictures the particles are usually quite elongated. For the sieved crystals an average ratio of length to width of approximately three to one has been measured. For the actual seed crystals and crystals inside the process an average length to width ratio of approximately six to one has been found. These geometries are an important input to the model. Another input variable that has to be provided is the refractive index of the medium. For the calibration experiments (see next chapter) the refractive index of ethanol, used as the liquid phase, has been inserted (n = 1.36). For the crystallization system the refractive index depends on the mass fraction of threonine in solution. It has been set to a value of n = 1.36 corresponding to a mass fraction of 15% dl-threonine dissolved in water, measured at 30 ◦ C (MettlerToledo refractometer). Luckily here the refractive index of the calibration system is quite similar to the actual crystallization system (actual values: ethanol: 1.3614, threonine/water (15% threonine content): 1.358). The ratio of length to width can be quantified by use of the volumetric shape factor kv : Vsolid = kv L3

(1)

Apart from the implementation of the crystal geometry and the setting of the refractive index there are not many further possibilities to adjust the FBRM-probe model. The remaining free parameter inside the probe model is a velocity factor accounting for the relative velocity between laser (2 m/s nom-

Fig. 7 – Cumulative absolute velocity distribution of particles of 500 ␮m length in a stirred vessel (calculation with FLUENT, based on 10 randomly inserted particles, 3.5 s calculation time, 3 blade propeller stirrer at 500 rpm).

Fig. 8 – Cumulative absolute velocity distribution of particles of 1000 ␮m length in a stirred vessel (calculation with FLUENT, based on 10 randomly inserted particles, 3.5 s calculation time, 3 blade propeller stirrer at 500 rpm). inal scanning speed) and crystals suspended in the vessel. Since the stirring speed in the experiments performed is quite high (500 rpm) calculations have been performed in order to estimate the average crystal velocity in the stirred vessel. A standard CFD-calculation has been performed using FLUENT with ten crystals of different sizes (500 ␮m and 1 mm length, respectively) inserted at random points inside the vessel in order to approximate the average crystal velocity. The resulting velocity distributions are given in Figs. 7 and 8. From the calculations an average particle velocity in the vessel of 1 m/s can be estimated. Therefore the velocity factor is set to 0.5 as the particle velocity is approximately half of the nominal laser rotational velocity. In the model a normal distribution of relative velocities between the obtained minimal and maximal velocities is assumed. It is used to generate the according scattering profiles of the particles (Kail et al., 2009).

5. Preliminary experiments for model validation Fig. 6 – Product crystals of threonine harvested from a preferential crystallization batch experiment.

In order to check the basic validity of the approach for the investigated system some preliminary experiments using l-

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Fig. 9 – Cumulative particle size distributions obtained from microscopic image analysis of the three sieve fractions used for the “calibration” of the FBRM-probe.

threonine crystals suspended in ethanol are performed. Since threonine is nearly insoluble in ethanol the particle size distribution of the suspended crystals should not be altered significantly after their introduction into the vessel. After some time breakage of the crystals due to crystal–stirrer or crystal–crystal collisions could alter the particle size distribution. However this fact was neglected due to the fact that the measured CLD-moments did not change significantly over time (except for the largest sieve fraction). During all measurements the CLD data provided by the FBRM-probe is sorted into 50 linear channels in the range from 1 to 1000 ␮m. Experiments were carried out in order to “calibrate” the probe similar to the procedures presented in (Vaccaro et al., 2007; Wynn, 2003). A goal of this calibration procedure was to find a correlation between the measured CLD and the CLD resulting from a transformation of the PSD measured with the optical microscope using the probe model. To find this calibration three additional experiments have been carried out. The experiments were done in the same 1.5 l vessel used for the crystallization experiments. Instead of using a dl-threonine solution sieved fractions of l-threonine crystals were suspended in ethanol. The stirring rate was set to 500 rpm for all experiments. The sieve fractions used were 63–90 ␮m, 90–150 ␮m and 150–212 ␮m. The particle size distributions of these three fractions obtained with microscopic image analysis are given in Fig. 9. The crystals of each of the sieve fractions were added in portions of approximately 5 g to the vessel. The exact amounts added are given in Table 2. In the stirred vessel the chord length distribution was measured by the inserted FBRM-probe. Additionally a sample of each of the sieve fractions was measured using microscopic image analysis. The measured particle size distribution (PSD) for the three sieve fractions is given in Fig. 10. The measured

Fig. 10 – PSDs for the three sieve fractions used for probe calibration. The distributions were scaled to a mass of 15 g.

Fig. 11 – Measured and calculated scaled CLDs using the model from Kail et al. (2008b) after the first addition of crystalline material. CLD of the suspended crystals and the CLD resulting from the model transformation of the measured PSD after the first addition of crystals are displayed in Fig. 11. A scaling based on total particle number was done in order to compare the added samples with the measured samples (same number of particles). The resulting CLDs after the subsequent additions of crystalline material are given in Figs. 12 and 13. When comparing the resulting CLDs with the measured CLDs it is obvious that the fit is unsatisfying. Thus, the model is not capable of describing the chord length distribution for all three fractions and for the different amounts of crystals added (5, 10, and 15 g). The size region of the chord sizes is predicted quite accurately, but the weighting of the chord counts is shifted towards larger sized crystals. In order to solve this problem it was assumed

Table 2 – Masses of ethanol and crystals used in the three additional calibration experiments are given. Versuch 1 2 3

Ethanol [g]

Add 1 [g]

Add 2 [g]

Add 3 [g]

750 750.15 750

5.01 5.01 5

5 5.01 5.01

5.02 5 5.02

The volumetric shape factors (Eq. (1)) of the different fractions are also given.

Volumetric shape factor kv 0.14 0.11 0.28

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Fig. 12 – Measured and calculated scaled CLDs using the model from Kail et al. (2008b) after the second addition of crystalline material.

Fig. 13 – Measured and calculated scaled CLDs using the model from Kail et al. (2008b) after the third addition of crystalline material. that the particles are mainly transparent and only generate a reflection around the edges. This phenomenon is sometimes referred to as chord-splitting (Tadayyon and Rohani, 1998). It was incorporated into the model assuming that the particles are a quarter as thin as the actual particles. The approach followed is illustrated in Fig. 14. Thereby more elongated particles are incorporated into the model in order to generate reflections at the particle edges only. Therefore for every particle two reflections are generated with a smaller size as the original particle which simulates a particle that is half transparent with respect to its surface area. Due to the scaling the effect of generating two chords per par-

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Fig. 15 – Measured and calculated scaled CLDs using the model from Kail et al. (2008b) after the first addition of crystalline material. It was assumed that the particles are measured twice in order to simulate chord-splitting.

Fig. 16 – Measured and calculated scaled CLDs using the model from Kail et al. (2008b) after the second addition of crystalline material. It was assumed that the particles are measured twice with an opaque center in order to simulate chord-splitting. ticle can be neglected. Comparing the quality of the fits from Figs. 15–17 the agreement gets slightly worse with an increase in particle size. This can be attributed to the fact that the further used assumption of exactly half opaque particles might hold for the smaller particles but not for the larger particles. There the edges already have significant widths which might be too large in comparison to the actual edge widths seen by the laser. The fit of the model to the experimental data has significantly improved so that the model can be tested for analyzing the three actual crystallization experiments in order to estimate kinetic parameters.

6. Process model for preferential crystallization

Fig. 14 – Illustration of implemented alternative geometry that is used to simulate chord-splitting. The small particles on the edges are the substitute for the original particle.

For modeling crystallization processes typically the population balance approach is chosen (Randolph and Larson, 1988; Ramkrishna, 2000; Gerstlauer et al., 2006; Ramkrishna and Mahoney, 2002). The goal is typically to describe the changes in the distributed system with a mathematical model containing

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The crystallization kinetics describe the rates for the different phenomena that govern the dynamics of the particle size distribution Fr . There exist a multitude of empirical, semiempirical and physically based expressions to model different kinetic phenomena (Mersmann et al., 2002). For the models used in this work the kinetics of crystal growth and secondary nucleation are needed: Crystal growth: Gr = kg

 w r wr,sat

g

−1

(5)

Secondary nucleation: Br = kbsek Fig. 17 – Measured and calculated scaled CLDs using the model from Kail et al. (2008b) after the third addition of crystalline material. It was assumed that the particles are measured twice with an opaque center in order to simulate chord-splitting. integro-differential equations and algebraic equations. Furthermore, changes of the particle size distributions can be coupled via a mass balance to changes of the fluid phase concentrations. Inside the model algebraic expressions for the underlying kinetic phenomena have to be formulated (see Mersmann et al., 2002; Garside and Shah, 1980 for overviews). A simplified version of the partial differential equation describing the one-dimensional case is: ∂Fr (L, t) ∂(Fr (L, t)) = −Gr ∂t ∂L

(2)

Herein Fr stands for the number density distribution of each of the two enantiomers (r = 1, 2), L for the particle length and G for the crystal growth rate. Appropriate boundary and initial conditions have to be formulated in order to model the birth and death of particles. These boundary and initial conditions depend on the process scheme chosen. For the seeded preferential crystallization process scheme the boundary and starting conditions are: Fr (L, t = 0) = Fr,Seed Fr (L = 0, t) =

Br Gr

(3) (4)

The boundary condition presented in Eq. (4) implies the assumption of zero size nuclei. Eq. (3) contains the particle size distribution at the beginning of a batch. In order to solve the partial differential population balance (Eq. (2)) suitable discretization schemes have to be used. There are a number of sophisticated discretization schemes available (Hu et al., 2005; Motz et al., 2002; Qamar et al., 2008, 2007, 2006; Ramkrishna, 2000). The method of characteristics (MOC) can be easily applied when it can be assumed, as in our work, that no nucleation of the counter enantiomer takes place. It offers the advantage of no numerical dispersion, high computational speed along with numerical stability using coarse grids. 50 nodes on a linearly discretized grid from 0 to 1 mm were used in our calculations. Details of the numerical scheme used can be found in (Kumar and Ramkrishna, 1997). For discretizing the time domain the Matlab® solver “ode15s” was used (Shampine and Reichelt, 1997).

 w r wr,sat

b    3,r

−1

kv

V

(6)

The temperature dependence can be modeled, if necessary, with an Arrhenius type law. This type of law holds for the prefactors of the crystal growth and the dissolution rates as well as for the secondary nucleation rates (see for an example reference Hu et al., 2004): kg = kg,pre e−Eg /RT

(7)

kb,sek = kb,sek,pre e−Esek /RT

(8)

The chosen expression for the crystal growth rate as well as the rate equation for the secondary nucleation are classical semi-empirical formulations that are frequently used (Mersmann et al., 2002; Elsner et al., 2005; Randolph and Larson, 1988; Tadayon et al., 2002). Inside these kinetic equations there are six free parameters that have to be estimated: b, kb,sek,pre , g, kg,pre , Eb,sek , and Eg . The shape factors kv of the crystals where determined initially using microscopic image analysis and are therefore fixed for each crystal population used.

7.

Parameter estimation

The chosen objective function used for the parameter estimation (Eq. (9)) incorporates two parts to be minimized. One part of the objective function presented in Eq. (9) consisted of the difference between calculated and measured CLDs. A second additive part of the objective function consisted of the difference between the optical rotation values ˛ also measured in the three runs and the corresponding values calculated using the model and a polarimeter calibration function. In Fig. 18, the measured CLD trajectories for the seeded experiment 1 were plotted over time and channel length. Already from the CLD-distribution it can be seen that the process is dominated by nucleation. The number of counts increases heavily along the experimental run. Fig. 19 shows the chord length distribution fitted to the experimentally determined one using Eq. (9) as the objective function. Instead of using the full CLD-distribution the zero moment of the CLD-distribution is used in order to fit the model to the experimental data. It showed that using the zero moment of the chord length distribution gave a comparable quality of the fit of the model to the experiment. This is far superior to fitting the whole distribution in terms of calculation times and assignment of weights to the objective function. Additionally, the assignment of weights to the objective function, which would have been necessary in order

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Fig. 18 – Measured CLD trajectories for the seeded experiment 1 from Table 1. Fig. 21 – Comparison between calculated and measured optical rotation for experimental run 1.

Fig. 19 – Calculated best fit CLD trajectories for the seeded experiment 1 from Table 1. to scale the two parts when using full distributions, would have been more complicated and would result in introducing additional parameters.

 2   ˛(i, j) measured − ˛(i, j)calculated



Ndata

Fgoal =

j=1

˛(i, 0)measured

+

Fig. 22 – Calculated best fit PSD trajectories for experiment 1 from Table 1.

(i, j)0,scal,CLD,measured max((i)0,scal,CLD,measured )

In Fig. 20, the measured and calculated CLD-distributions at the end of the batch are compared. In Fig. 21, the measured and

Fig. 20 – Comparison of calculated and measured chord length distributions at the end of the first experimental run.

−

(i, j)0,scal,CLD,calculated max((i, j)0,scal,CLD,calculated )

2  (9)

calculated optical rotation trajectories are displayed. For both trajectories a relatively good agreement between model and experiment is obtained. The calculated PSD, that is the basis for the determination of the CLD presented in Fig. 19, is given in Fig. 22. A significant occurrence of secondary nucleation can be seen. In order to evaluate the quality of the estimated parameters and of the method applied the fit was made using all three experiments performed at different conditions (Table 1) simultaneously. The calculated and measured CLD-distributions at the end of the individual runs are plotted in Fig. 23. For an easy illustration of the course of the chord lengths of the particle population along the three experimental runs also the zero moments based on the measured chord length distributions are plotted in Fig. 24. The corresponding optical rotation trajectories of the three runs are given in Fig. 25. For matters of comparison also the trajectories of the zero moments of the PSD are given in Fig. 26. Obviously there is still some potential for improvement. For this reason it was tried to improve the implementation of the

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Fig. 23 – Calculated and measured chord length distribution for three seeded experiments (experiments 1–3 from Table 1) at the end of the experimental run.

Fig. 26 – Comparison between calculated and measured zero moments of the particle size distribution. Table 3 – Resulting kinetic parameters after fitting the model simultaneously to the data provided by experiments 1–3 (Table 1).

Fig. 24 – Comparison of calculated and measured zero moments of the chord length distributions for three seeded experiments (experiments 1–3 from Table 1). geometry further by considering the exact morphology of a dlthreonine crystal as presented in (Kumar et al., 2006). However, it turned out, that the performance of the model could not be improved significantly by the addition of two edges. When a closer look is taken on the numerical values of the parameters obtained after fitting the model simultaneously to the data obtained from experiments 1 to 3 (Table 3), param-

Parameter

Value

b kb,sek,pre g kg,pre Eb,sek Eg

2.9 2.1 × 1016 [#/(m3 s)] 1 5.6 × 10−8 [m/s] −11 [kJ/mol] −319 [kJ/mol]

eter values are obtained for the orders and prefactors that lie in the range expected (compare for example Garside and Shah, 1980 and Elsner et al., 2005) for values on the system dl-threonine water). However, as often the case in crystallization experiments, the physical significance of the parameters is not fully convincing. Especially the values for the activation energies appear to be less reliable. In particular Eg is atypically high. The presented approach using FBRM-data along with a suitable probe model and information regarding the fluid phase composition seems to be feasible to identify parameter values. Parametric uncertainties where not calculated in this study due to a lack of time. The implementation of procedures for calculating uncertainties as can be found in literature (Bard, 1974; Czapla et al., 2008; Diez et al., 2006; Dochain and Vanrolleghem, 2001) could be an addition to evaluate the presented application of the probe model.

8.

Fig. 25 – Comparison between calculated and measured optical rotation (experiments 1–3 from Table 1).

Summary and conclusions

A recently developed model of the FBRM-probe is applied to parameterize a process model for preferential crystallization of dl-threonine. Measured CLD trajectories along with optical rotation trajectories of actual separation runs in the system dl-threonine/water provide experimental data for the parameterization. The presented study shows how the probe model can be adopted in order to accurately transform calculated PSDs into CLDs. The calculated CLDs of actual separation runs could be fitted successfully to the measured CLDs. A simple method was introduced into the probe model to account for chord-splitting that was suspected to occur with the used system. When comparing the model calculations with the measured data of three individual process runs a relatively good agreement between model and measurement could be achieved.

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