109 Journal homepage: www.fia.usv.ro/fiajournal Journal of Faculty of Food Engineering, Ştefan cel Mare University of Suceava, Romania Volume XII, Issue 2 – 2013, pag. 109 - 114 SUCROSE COOLING CRYSTALLIZATION MODELLING Valeriy MYRONCHUK1, Oxana YESHCHENKO2, *Maryna SAMILYK3 1National University of Food technologies, Kyiv, Ukraine, mironcuk@nuft.edu.ua 2National University of Food technologies, Kyiv, Ukraine, oxayes@mail.ru 3National University of Food technologies, Kyiv, Ukraine, m.samilyk@ukr.net * Corresponding author Received April 8th 2013, accepted May 15th 2013 Abstract: Based on the material balance equations and understanding of the final-grade massecuite cooling crystallization process as the technology object, a simulation model of the process has been built by which the computational experiments have been conducted. By results of these experiments, analytical exponential dependences of the massecuite characteristics change during cooling crystallization have been obtained, namely, grain content, weight, purity and dry solids weight ratio of massecuite syrup. The constructed model has been used to study the industrial cooling crystallization process. It is proved that the results of the experiment of the developed simulation model fully reflect the nature of the industrial process of final-grade massecuite cooling crystallization of sucrose. Typical scheme industrial cooling crystallization with massecuite water or impure sugar solution dilution and authors’ scheme with an intermediate heat massecuite have been considered. It’s experimentally shown that the use of final-grade massecuite intermediate heating after cooling to 50- 52 ºC by 7-10 ºC increases the effect of crystallization to 8.4% by reducing the viscosity of massecuite syrup, the surface tension and alignment of the massecuite cooling rate at sucrose crystalization rate. Consequently, the exclusion of dilution of massecuite by water or impure sugar solution and its replacement by intermediate heating provides a more complete depletion of molasses and increases the amount sugar grains in the massecuite. Keywords: massecuite, syrup, grains, dilution, mixer-crystallizer, the intermediate heat. 1. Introduction Additional sucrose crystallization process by cooling has complex dynamics and depends on many factors [1] – [7]. That is why there are many difficulties in regulating the cooling of the massecuite [8]. In addition, the long duration of the process generates complex physical and chemical transformations of the system. Despite numerous studies in this area, today there are gaps in the optimal mode of heat and mass transfer in the crystallization of the massecuite in the mixer- crystallizers. The study of this process using physical modelling is difficult in large part due to its duration (more than 30 hours). This can be eliminated by the use of simulation [9] – [11]. The objective of our research was to create a mathematical model of the process of crystallization by cooling, the ability to regulate it, to bring the best mode in which the crystallization rate corresponds to the cooling rate. 2. Experimental We presented the crystallization process as a technology object (Fig. 1) with the input, control and output parameters. The basis of the mathematical description of the sucrose cooling crystallization Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava Volume XII, Issue 2 – 2013 Valeriy MYRONCHUK, Oxana YESHCHENKO, Maryna SAMILYK, Sucrose cooling crystallization modelling, Food and Environment Safety, Volume XII, Issue 2 – 2013, pag. 109 - 114 110 process accepts the material balance of the process. Figure 1. The sucrose cooling crystallization process in mixers-crystallizers as a technology object: input parameters: Mm – massecuite mass, DSm – massecuite dry solids weight ratio, G1 – grain content at the beginning of crystallization, Pm – massecuite purity; control parameters: t1 – the initial temperature of the process, t2 – the final temperature of the process, Hss – supersaturation coefficient, Hsi – solubility index; output parameters: G2 – grain content at the end of crystallization, Ms – syrup mass, DSs – syrup solids weight ratio, Ps – syrup purity. General material balance equation: 2211 sgsgm MMMMM  , (1) balance equation by sucrose: 222 111 gss gssmm MScM MScMScM   , (2) balance equation by nonsugar: 2211 ssssmm NsMNsMNsM  , (3) balance equation by dry solids: 222 111 gss gssmm MDSM MDSMDSM   , (4) balance equation by water: 2211 ssssmm WMWMWM  , (5) Where mM , 1gM , 2gM , 1sM , 2sM – massecuite mass, the mass of crystals in the massecuite and syrup at the beginning and at the end of the cooling crystallization process, kg; mSc , 1sSc , 2sSc , mNs , 1sNs , 2s Ns , mDS , 1sDS , 2sDS , mW , 1sW , 2sW – sucrose, non-sugars, dry solids and water weight fractions in the massecuite and molasses at the beginning and at the end of process, %/ The mathematical description of the sucrose cooling crystallization is necessary to determine the sucrose amount in the syrup. It is determined from equation   sssiwss HPtHM ScM m , %100  , (6) Then   %100 , s sssiw s M HPtHM Sc m , (7) where sM – the syrup mass, kg, sSc – sucrose weight ratio in syrup,%, mw M – water mass in the massecuite, kg,  PtH si , – solubility index of sucrose as a function of temperature and purity, ssH – supersaturation coefficient of the massecuite. Variation of sucrose solubility index with temperature and the solution is determined by the regression equation of the third order, we have received the least square method:   25 26 36 36 3 23 25 10821,2 10317,8 10244,5 10429,6 101505,4 10926,6 10084,6 01827,0 1903,00502,1, tP Pt P t tP P t P tPtH si                 , (8) Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava Volume XII, Issue 2 – 2013 Valeriy MYRONCHUK, Oxana YESHCHENKO, Maryna SAMILYK, Sucrose cooling crystallization modelling, Food and Environment Safety, Volume XII, Issue 2 – 2013, pag. 109 - 114 111 Where t – the product temperature, ºC, P – sugar solution purity, %. We believe that in the cooling crystallization process water and non- sugars content in syrup remains unchanged. Then at the beginning of cooling crystallization, we have Syrup mass:   %100%100 , 111 mmmm sssiws WMNsM HPtHMM m   , (9) Grain mass: 11 smg MMM  , (10) Grain content in the massecuite: %10011 m g M M G  . (11) Similarly, we find the syrup and crystals masses at the end of the cooling crystallization process:   %100%100 , 222 mmmm sssiws WMNsM HPtHMM m   , (12) 22 smg MMM  , (13) %10022 m g M M G  . (14) In general, for any temperature in the cooling process massecuite 21 ttti  we have   %100%100 , mmmm ssiisiws WMNsM HPtHMM mi   , (15) ii smg MMM  , (16) %100 m g i M M G i . (17) The sucrose, non-sugars, dry solids and water mass fractions in the syrup, and its purity were determined by the equations:   %100 , i m i s ssiisiw s M HPtHM Sc  , (18) %100 i i s mm s M NsM Ns  , (19)   %100 , i m i s mmssiisiw s M NsMHPtHM DS   , (20) %100 i m i s wm s M MM W  , (21) %100 i i i s s s DS Sc P  , (22) Equations (15)–(22) is a mathematical description of the model of sucrose cooling crystallization process. On the basis of computational experiments on the model (15)–(22) we have obtained analytical dependence of the massecuite characteristics (grain content, mass, purity, and the dry solids weight ratio of syrup) on time and massecuite purity:          mG PcmGmGm ePbPaPG , , (23)          mмM м м Pc mM mM ms ePb Pa PM    1 , , (24)          msP s s Pc mP mP ms ePb Pa PP    1 , , (25)          msDS s s Pc mDS mDS ms ePb Pa PDS    1 , , (26) Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava Volume XII, Issue 2 – 2013 Valeriy MYRONCHUK, Oxana YESHCHENKO, Maryna SAMILYK, Sucrose cooling crystallization modelling, Food and Environment Safety, Volume XII, Issue 2 – 2013, pag. 109 - 114 112 Where c i     – the relative time, i - current time, c - the total cycle time, mP – massecuite purity. 3. Results and Discussion The above model we used to simulate the industrial sucrose cooling crystallization process in the mixer-crystallizers, which requires water or impure sugar solution dilution of massecuite. Although this method to some extent, can improve the crystallization conditions, the water addition in the massecuite violates isohydric conditions of crystallization. This reduces the final crystallization effect, increases the molasses amount, and hence the sucrose content in it, as well as energy costs in sugar house. For this reason, it is advisable to carry out massecuite heated to a definite temperature instead of water dilution. The constructed sucrose cooling crystallization model is used to study the process of industrial sucrose crystallization in two modes, flow graphs of which are presented in Fig. 2. The amount of water or impure sugar solution for dilution of massecuite is calculated as:   dmd mdmm d DSDS DSDSM M    , (27) Where Md – mass of water or impure sugar solution for dilution of massecuite, Mm – masscuite mass, DSd, DSm, DSdm – dry solids weight ratio of sugar solution for the dilution, of massecuite before and after dilution, respectively; if massecuite is diluted with water, then 0dDS . a b Figure 2. Flow graph of the massecuite cooling crystallization process: a – with water or impure sugar solution dilution, b – with an intermediate heat, RM – reception mixer, MC – mixer-crystallizer, H – heater, C – centrifuge. Temperature range of the cooling crystallization process is described by dependencies: When massecuite is diluted with water or impure sugar solution:     1 1 1 1 ceb a t   (28) When intermediate heating is used               heatingafter , 1 heatingbefor , 1 2 1 2 2 1 1    c c eb a eb a t . (29) Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava Volume XII, Issue 2 – 2013 Valeriy MYRONCHUK, Oxana YESHCHENKO, Maryna SAMILYK, Sucrose cooling crystallization modelling, Food and Environment Safety, Volume XII, Issue 2 – 2013, pag. 109 - 114 113 35 40 45 50 55 60 65 70 75 80 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 ti/tc t, o C Figure 3. Temperature range of final massecuite cooling crystallization: – with an intermediate heat, – to the standard mode. It stands to reason that the water dilution not only reduces the grain content in the massecuite at the end of crystallization, but also increases syrup purity (Fig. 4). For bringing of massecuite to a given dry solids weight ratio impure sugar solution for dilution of its must be much more than water. This may explain the smallest content of the grains in the massecuite after dilution and at the end of crystallization for the scheme with the impure sugar solution dilution. Besides that decrease the purity syrup in this case is not achieved at the expense of its desugarization, but due to high content of non-sugars which were added during dilution (Fig. 4). 24 26 28 30 32 34 36 38 40 42 44 4045505560657075 t, oC G , % a. 84,0 84,5 85,0 85,5 86,0 86,5 87,0 87,5 88,0 88,5 4045505560657075 t, oC D S s, % b. 52 54 56 58 60 62 64 4045505560657075 t, oC S c s , % c. 63 64 65 66 67 68 69 70 71 72 73 4045505560657075 t, oC P s , % d. Figure 4. Changing massecuite technological characteristics during the cooling crystallization process: – with water dilution; – with impure sugar solution dilution; – with an intermediate heat; а – grain content in the massecuite; b – dry solid weight ratio in the syrup; c –sucrose weight ratio in the syrup; d – syrup purity To analyze the effectiveness of intermediate heating final massecuite in the mixer-crystallizers we carried out a series of research in which besides the addition of Food and Environment Safety - Journal of Faculty of Food Engineering, Ştefan cel Mare University - Suceava Volume XII, Issue 2 – 2013 Valeriy MYRONCHUK, Oxana YESHCHENKO, Maryna SAMILYK, Sucrose cooling crystallization modelling, Food and Environment Safety, Volume XII, Issue 2 – 2013, pag. 109 - 114 114 dilution water massecuite or molasses, massecuite intermediate heating by 5, 7, 10 and 12 °C has been used. The results suggest that the best effect is got when the temperature of the intermediate heating of massecuite in the mixer-crystallizers after cooling to 50-52 ºC is 7-10 °C (Fig. 4). In this case, the viscosity of the syrup is reduced almost by half, the surface tension is also reduced. Decreases the viscosities of syrup increases the sucrose molecules diffusing from solution to the crystal surface, and reduce the surface tension increases the rate of crystallochemical reaction at the phase interface during the transition of sucrose dissolved in the crystal. Crystallization effect in this case is 8.4%. In addition, we found that if the purity of the initial massecuite decreases, the temperature of its intermediate heating must be increase. Also a significant improvement in the sugar grains size moves up in fractions of 0.63-1.0 mm and greater than 1.0 mm 4. Conclusion Alternative water dilutions of final massecuite in the cooling crystallization process in mixers-crystallizers is to use an massecuite intermediate heating by 8 ºC-10 ºC after reducing its temperature by 50-52 ºC. The use of massecuite intermediate heating reduces the syrup viscosity and the surface tension at phase interface "solution" – "solid", which increases the intensification of sucrose crystallization. In this case greater molasses desugarization and better grain size of sugar crystals in the final massecuite are achieved. 5. Acknowledgments We thank Elena Vygran for assistance in translation. 6. References [1] S. OUIAZZANE, B. MESSNAOUI, S. ABDERAFI, J. WOUTERS, T. BOUNAHMIDI. Estimation of sucrose crystallization kinetics from batch crystallizer data // Journal of Crystal Growth, Volume 310, Issue 4, 15 February 2008, Pages 798-803 [2] Lie-Ding SHIAU. 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