EFFECTS OF AGITATION RATE ON THE

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Memorias del XXXVI Encuentro Nacional de la AMIDIQ 5 al 8 de Mayo de 2015, Cancún, Quintana Roo, México

EFFECTS OF AGITATION RATE ON THE METASTABLE ZONE WIDTH IN SUGAR CANE BATCH CRYSTALLIZATION a

K. B. Sánchez-Sáncheza, E. Bolaños-Reynosoa, L. S. Galicia-Contrerasa, J. Lib, P. A. Quintana- Hernándezc División de Estudios de Posgrado e Investigación, Instituto Tecnológico de Orizaba. Av. Oriente 9 No. 852. Col. Emiliano Zapata, Orizaba, Veracruz, C.P. 94320, MÉXICO. b University of Waterloo, 
200 University Avenue We c Instituto Tecnológico de Celaya, Av. García Cubas 1200, Celaya, Guanajuato, C.P. 38010, MÉXICO. [email protected]

Abstract This work presents a study on the effects of temperature and agitation rate on the metastable zone width (MSZW) for seeded batch crystallization of sugar cane from aqueous solution. Temperature and agitation rate were selected as the main variables within crystallization operation due to their high impact on the final crystal properties. An experimental design of blocks in parcels divided with two replicates was conducted using three agitation rates: 150, 250 and 350 rpm, in a temperature range of 40 - 70 ºC. The MSZW were determined by applying a linear cooling trajectory with changes of 1 ºC (ΔT), and using an image-based approach to detect the first nuclei, while concentration changes during the process were monitored using a digital densimeter. An ANOVA analysis was performed and the results show that agitation rate has not statistical effect on the first and second metastable zone width, in contrast to those reported in literature for different solutes. Introduction Batch crystallization is an industrial important unit operation widely used for the production of chemical, pharmaceutical, agrochemical, and food products (sugar cane crystals) [1,2]. This operation offers several advantages over others separation techniques such as low operation costs, high purity (crystalline) products in a single (solid) stage and attractive final product appearance for commercial purposes [3]. The operating conditions have a major effect on crystallization quality in terms of crystal size distribution (CSD), polymorphism, and others. A high purity, a particular polymorphic distribution, and also a predefined CSD are the expected major properties of the crystal produced [4]. The latter properties are affected by the supersaturation (ΔC) trajectory that takes place in the batch time, and is it defined as the difference between the actual concentration (C) and the saturated concentration (C*, solubility). Supersaturation is also known as the driving force for nucleation, growth, and agglomeration phenomena that influence the crystal properties [5]. The supersaturation region is classified into different zones, usually called metastable zone width (MSZW), and is divided as follows: a) first metaestable zone (growth), b) second metaestable zone (nucleation), and c) labile zone (undesirable). The MSZW results from the specific characteristics of nucleation in a supersaturated solution of soluble substances and depends mainly on temperature, cooling rate, presence of impurity, mechanical effects, and the agitation rate has been recently considered [6]. The MSZW can be considered as a specific property of crystallization for each system. Also, it is an important parameter to analyze the specifications of the products obtained from the industrial crystallization processes [7]. The MSZW are represented commonly as curves within the solubility graph to represent the optimal operating window [8]. Concerning the operating conditions, it is well known that agitation rate has an important effect on the crystallization operation and becomes a key variable to control the CSD [6]. In the other hand, less effort has been done to study the effects on the MSZW and few works can be found that concludes

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that agitation rate has a direct effect on the MSZW [9,10]. Unfortunately, in many sugar cane industrial processes, crystallizations are carried out in stirred vessels without any optimization of the hydrodynamic conditions mainly due to lack of knowledge related to MSZW. Therefore, in order to produce crystals with high purity and specified CSD at minimum cost, it is necessary to operate the crystallizer with the optimal operating conditions within the appropriate supersaturation level, e.g. carry out the seeded crystallization process within first metastable zone. The aim of this work is the experimental measurement of MSZW for sugar cane solutions, taking into account the effects of agitation rate and temperature, which represents a key novelty since this is the first work that use both variables. The results will yield better understanding of the phenomenological behavior occurring in sugar cane crystallization. This will improve the operation conditions at industrial crystallization and also will allow to specify optimal operating trajectories, which increases the overall process performance to achieve strict requirements in the final product quality, and reduce environmental impact by reducing pollutant materials. Methodology The MSZW of sugar solutions were measured using the procedure reported by Akrap et al. [9], described as follow. Saturated solutions of commercial sugar cane (high purity) at different equilibrium temperatures (40, 50, 60 and 70 ºC) were prepared in a cooling batch crystallizer (see details in Table 1). The saturated solutions preparation was realized following an experimental design of blocks in parcels divided, being carried out four solutions, each one tested with three agitation rates (150, 250 and 350 rpm), with two replicates, given 24 experiments. The established weight of each solution was 4500 g (g sugar/ml water), so that the sampling was not an importance variable to consider and to be able to handle the system as a solution constant volume. The detailed quantities used to prepare the saturated solution are presented in Table 2. Table 1. Detailed devices of the experimental setup

Quantity Device 1 Glass crystallizer 6 L, heating-cooling jacket 2.55 L crystallizer dimensions: height 35 cm and internal diameter of 14.4 cm, lower dome height of 1.8 cm. 1 Generic variable speed motor, direct transmission from 0 to 1.500 rpm, 60 Herz, 127 VAC and 760 W, stirring arrow 14 in (length) and 1/4 of diameter with 316 stainless steel. 1 Impeller of 4 rectangular rings with 90 ° of separation between each crossing. Blades with 2 in length and 1 in width. 316 stainless steel. 2 Thermocouple J type. 0 to 760 ºC, wire-rope, 3m. 1 Programmable recirculating bath Julabo F-34 with temperature range of - 34 at 200 °C, with recirculation pump 15 L/min, bath volume of 14-20 L, 120 VAC / 60 Hz. 1 Densimeter DMA-4500 Anton-Paar, measurement range of 0-3 g/cm3, measurement error in the temperature 0.1 °C and 1x10-5 g/cm3 in density. Serial port connection RS-232. 1 Professional microscope: Carl Zeiss, model 37081, Primo Star iLED. 1 Digital microscope camera AxioCam ERc5S. CMOS sensor. USB connectivity and HDMI. 1 Programmable tachometer. Range from 50 – 999,999 rpm. 1 Optical sensor for distances of 3 ft. Range 1 – 150,000 rpm. 1 PC Intel QuadCore, 4 Gb RAM.

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Table 2 Quantities used for each saturated solution

Temperature of saturation [°C] 70 60 50 40

Weight of solution [g azúcar / ml agua ] 4500 4500 4500 4500

Mass of sugar [g] 3440.83 3334.97 3220.32 3096.91

Volume of water [ml] 1059.17 1165.03 1279.68 1403.09

Once the solution reached the saturation concentration without crystals, according with solubility curve expressed in Eq. (1), the solution was cooled down at a given linear cooling rate in intervals of 1 ºC. For each temperature stationary state, a solution sample was taken to measure the concentration (density (g/cm3)) using a densimeter model DMA 4500 Anton Paar (see Table 1). (1) To identify the first metastable zone, 5 ml of solution without filtering was sampled and images were acquired with the support of an images acquisition system using a 10X objective in order to observe the appearance of small crystals (nuclei), indicating the limit for the first metastable zone. After identifying the first nuclei, the solution was cooled down again until reach 10 ºC less than initial temperature. Then, CSD was measured using the image-based approach reported by Bolaños et al. [6] to quantify the temperature where the CSD’s dispersion has a sudden increase and the appearance of agglomerates, which indicate the limit for the second metastable zone. Finally, an ANOVA analysis (95% confidence interval) was performed to quantify statistically the effects of the agitation rate on the MSZW and a curve fitting was done to model the MSZW. The statistical software NCSS® and MATLAB R2014b® were used in this final stage. Results Figure 1 shows a sequence of images that represents each metastable zone. In Figure 1a, the saturated solution is free of crystals, meaning that the concentration is within the first metastable zone. Next, Figure 1b shows the appearance of the first visible nuclei, representing the second metastable zone. Finally, the appearance of agglomerates in Figure 1c gives the end for the second metastable zone, and the beginning of the labile zone. Defining the limit for the second and labile zone is complicated, and the CSD analysis should be taken in consideration. Is worth mentioning that special care was taken to keep the sample at the same temperature to prevent the sudden formation of nuclei in the process of measurement of concentration and CSD.

a) b) c) Figure 1 - MSZW identification, a) First metastable zone, b) Second metastable zone and c) Labile zone

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a)

b)

a) Figure 2 – Experimental data for temperature vs density: a) 150 rpm, b) 250 rpm and c) 350 rpm

It is possible to see that the behavior of the density is uniform for all saturation temperatures. Special care was taken to avoid the presence of crystals in the saturated solution before starting each experiment. It was also sought to start each experiment when the density was as close as possible to the solubility curve. In all graphs in Figure 2, it is observed that the densities for each saturation temperature and agitation rate tends to increase as the temperature decreases, confirming that cooling the crystallizer promotes the crystallization phenomena. The identified limits for the MSZW are presented in Table 3.

First metastable zone Second metastable zone

Agitarion rate (rpm)

Table 3. Limits of MSZW for sugar solution

150 250 350 150 250 350

Saturated Saturated solution at 40 ºC solution at 50 ºC Temp. Density Temp. Density [ºC] [g/cm3] [ºC] [g/cm3] 27.5 1.34089 47 1.34551 30 1.34013 46 1.34711 31 1.33949 47 1.34738 26 1.34178 44.5 1.34765 27.5 1.34202 44 1.35001 29 1.34085 45.5 1.34900

Saturated Saturated solution at 60 ºC solution at 70 ºC Temp. Density Temp. Density [ºC] [g/cm3] [ºC] [g/cm3] 56.5 1.35491 69 1.36118 58 1.35343 68.5 1.36185 57.5 1.35427 68 1.36180 54.5 1.35607 67.5 1.36251 56.6 1.35483 66.5 1.36258 55.5 1.35569 67 1.36390

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From the ANOVA results (Tables 4 and 5) performed for the data shown in Table 4, it can be observed that there is not a value of F 0 for replications since this value is excluded for being a block (restrictions to randomization), the same occurs for AB, AC and ABC, this is because there is no interaction between the block and the factors. The temperature factor (B) showed a significant effect (high F 0 ) for the variation in the amplitude of the concentration zones. This result is expected because the tests were carried out at different temperatures, which affects the density during crystallization of sugar cane. The agitation rate factor (C) and interaction (BC) have no statistical effect (low F 0 ) on the limits both metastable zones. This study allows to demonstrate that agitation rate has not a defined effect on the MSZW for sugar solutions, which differs from that reported by Akrap et al. [9] and Sanders et al. [10], where the MSZW decrease with increasing the agitation rate. Table 4. ANOVA analysis for first metastable zone Source of variation

Degree of freedom

A: Replication 
 B: Temperature AB 
 C: Agitation rate AC 
 BC 
 ABC 
 S Total (Adjusted) Total

1 3 3 2 2 6 6 0 23 24

Sum of squares

Mean squares

F0

3.248704E-06 1.551387E-03 1.912546E-06 6.815834E-08 2.212908E-06 8.954642E-06 5.439492E-06 0 1.573224E-03

3.248704E-06 ------5.171291E-04 811.16 6.375153E-07 0.03 3.407917E-08 1.65 1.106454E-06 ------1.49244E-06 ------9.065819E-07 -------

Prob. Level ------0.000073* 0.970120 0.279995 -------------------

Table 5. ANOVA analysis for second metastable zone Source of variation

Degree of freedom

A: Replication
 B: Temperature AB 
 C: Agitation rate AC 
 BC 
 ABC 
 S Total (Adjusted) Total

1 3 3 2 2 6 6 0 23 24

Sum of squares

Mean squares

F0

2.012604E-06 1.541882E-03 5.534246E-06 1.172708E-06 1.156111E-05 1.322386E-06 7.633592E-06 0 1.58302E-03

2.012604E-06 ------5.139606E-04 278.61 0.10 1.844749E-06 5.863542E-07 1.73 5.780554E-06 ------2.203976E-06 ------1.272265E-06 -------

Prob. Level ------0.000363* 0.907906 0.260503 -------------------

Based on the statistical result, if a polynomial fit is applied to all experimental data to model the first and second metastable zone regardless the agitation rate, a good correlation should be obtained. Eq. (2) and (3) represent the limits for the first and second metastable zone, respectively. The curve fitting assistant in MATLAB R2014b® was used.

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Density limit for first metaestable zone with R2 = 0.9845: r first = 1.338 - 0.000113 ´ T + 6.824E - 06 ´ T 2

(2)

Density limit for second metaestable zone with R2 = 0.9855: rsecond = 1.336 + 8.516E - 05 ´ T + 4.85E - 06 ´ T 2

(3)

Again, as a result of the good correlation obtained, it is confirmed that agitation rate has no effect on the MSZW. This behavior can be attributed to the difference in chemical composition with the solutes employed by Akrap et al. [9] and Sanders et al. [10], and also the crystallization kinetics that are specific for each mixture of solvent – solute. Conclusions Agitation rate has a high impact on CSD, due to mechanical interactions with the impeller, crystallizer geometry, and viscosity. However, the agitation rate does not exhibit a statistical effect on the MSZW for sugar solutions (sugar cane - water). Therefore, selection of an optimal agitation rate is independent of MSZW and should be based from their influence upon other variables such as the CSD. The mathematical models presented can be used with great precision to track the evolution of concentration in the sugar cane crystallization process. References 1. Bolaños-Reynoso. E.; Xaca-Xaca O.; Alvarez-Ramirez J. J.; López-Zamora L. “Effect analysis from dynamic regulation of vacuum pressure in an adiabatic batch crystallizer using data and image acquisition”, Ind. Eng. Chem. Res., Vol. 47, p. 9426-9436, 2008. 2. Zoltan K. Nagy; Gilles Fevotte; Herman Kramer; Levente L. Simon. “Recent advances in the monitoring, modelling and control of crystallization systems”, Chemical Engineering Research and Design. Vol. 91, p. 1903-1922, 2013. 3. Stefan Schorsch; David R. Ochsenbein; Tomas Vetter; Manfred Morari; Marco Mazzotti. “High accuracy online measurement of multidimensional particle size distributions during crystallization”, Chemical Engineering Science. Vol. 105, p. 155-168, 2014. 4. Q. Hu; S. Rohani; A. Jutan. “Modelling and optimization of seeded batch crystallizers”, Computers and Chemical Engineering. Vol. 29, p. 911-918, 2005. 5. H. Hojjati; M. Sheikhzadeh; S. Rohani. “Control of supersaturation in a semibatch antisolvent crystallization process using a fuzzy logic controller”, Ind. Eng. Chem. Res. Vol. 46, p. 1232-1240, 2007. 6. Bolaños R. E.; Sánchez S. K. B.; Urrea G. G. R.; Ricardez S. L. A. “Dynamic modeling and optimization of batch crystallization of sugar cane under uncertainty”, Ind. Eng. Chem. Res., Vol. 53, p. 13180-13194, 2014. 7. Kwang-Joo Kim; Alfons Mersmann. “Estimation of metastable zone width in different nucleation processes”, Chemical Engineering Science. Vol. 56, p. 2315-2314, 2001. 8. Kadam, S.S., Vissers, J.A.W., Forgione, M., Geertman, R.M., Daudey, P.J., Stankiewicz, A.I., Kramer, H.J.M. “Rapid crystallization process development strategy from lab to industrial scale with PAT tools in skid configuration”, Org. Proc. Res. Dev. Vol. 16, p. 769–780, 2012. 9. Akrap M.; Kuzmanić N.; Prlić-Kardum J. “Effect of mixing on the crystal size distribution of borax decahydrate in a batch cooling crystallizer”, Journal of Crystal Growth, Vol. 312, p. 3603-3608, 2010. 10. Aleksandra Sander; Jasna Prlić Kardum. “Pentaerythritol crystallization – Influence of the process conditions on the granulometric properties of crystals”, Advanced Powder Technology. Vol. 23, No. 2, p. 191-198, 2012.

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