Investigation, mathematical modelling and simulation of the crystallisation process in a circulation crystalliser

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1 Investigation, mathematical moelling an simulation of the crystallisation ocess in a circulation crystalliser Proceeings of European Congress of Chemical Engineering (ECCE-6) Copenhagen, 6- September 7 Investigation, mathematical moelling an simulation of the crystallisation ocess in a circulation crystalliser M. I. Dorofeeva, a E. M. Koltsova, a A. Lieb, b M. Kin b a Department of Cybernetics of Chemical Engineering, D. Meneleev University of Chemical Technology of Russian, Miusskaya pl., 9, 47 Moscow, Russia b Institute of Thermal Process Engineering (TVT), University of Karlsruhe (TH), Kaiserstr., Geb..9, 76 Karlsruhe, Germany Abstract The inustrial crystallisation of well soluble substances is often ominate by seconary nucleation, in particular contact nucleation, an crystal growth. In ifferent crystallisers types the attrition is mainly cause by the crystals impact onto stirrer blaes, pumps, etc. The ultimate objective is to quantitatively escribe a crystallization ocess, which is governe by the formation an growth of attrition fragments. Keywors: seconary nucleation, attrition, crystallization, mathematical moelling, ammonium sulphate. Introuction Circulation crystallizers are wiely use in a moern chemical inustry. They have high efficiency an ovie low supersatutations. Such conitions allow to receive large crystals an to reuce or to eliminate formation of incrustations. For maintenance of circulation in crystallizers it is more expeient to use the pump instea of a stirrer. Use of the pump allows to reach greater capacity at rather small power consumption an the best tightness of a crystallizer, i.e. an opportunity of its work at eeper vacuum. The crystallization kinetics is etermine basically by nucleation an growth kinetics. The main source of nucleation in circulation crystallizers is attrition of crystals ue to their impact onto stirrer blaes, pump, etc (seconary nucleation). The mechanism of the seconary nucleation is the least stuie. After ecaes of semi-empirical moelling apoaches, Gahn an Mersmann (Gahn an Mersmann, 999) ovie a quantitative apoach to the moelling of seconary nucleation base on scientific knowlege about attrition an breakage. The collision of the crystals with the stirring blaes is of particular consieration. The applicability of the moel is emonstrate

2 M. I. Dorofeeva et al. for continuous operation of a Draft-Tube Baffle Crystalliser an Draft-Tube Crystalliser (Neumann, ) an for continuous operation of a Force Circulation Crystalliser (Lieb an Kin, 4). Theoretical stuies examine further operty functions (Gerstlauer et al., ). The ultimate objective is to quantitatively escribe a crystallization ocess, which is governe by the formation an growth of attrition fragments. The calculations can be use to select optimum ocess conitions for a ouct of certain quality. In the future, experimental investigations an mathematical moelling may be helpful tool to esign an operate inustrial crystallisers.. Experimental set-up For the investigation of attrition an growth mechanisms a number of experiments have been carrie out with the crystallizing system ammonium sulphate in the labscale. They have been carrie out attrition an crystallization experiments uner various conitions in a continuously operate.8-liter-force Circulation Crystalliser (FC-Crystalliser). All experiments have been performe at the Institute of Thermal Process Engineering (TVT), University of Karlsruhe (TH), Germany. For the investigation of the crystals attrition the installation apparatus was built (Fig. ). See Figure : Sketch of a laboratory setup for attrition (-crystalliser,,4-pulsation ampers, -piston pump, -heat exchanger, 6-impingement evice, 7,-thermostats, 8-laser iffraction spectrometer, 9-solution level controller) Before the experiments the setup was fille with a hot ammonium sulphate solution. To circulate the suspension at minimal attrition of crystals a piston pump with a pleate bellow an ball-valves was use (QVF DN7A). In orer to event estruction of the crystals in the pleats of the bellow, the bellow was coate with a layer of silicon rubber. At the inlet an outlet of the pump, pulsation ampers,4 were installe to compensate the sinusoial strokes of the pump. The hot solution passe through heat exchanger, were it was coole to a temperature of C. This temperature maintaine constant throughout the experiment. Shortly before the temperature C was reache, g of see crystals - µm in size were ae to the crystalliser (Table ). The aition of the see crystals ensure a certain

3 Investigation, mathematical moelling an simulation of the crystallisation ocess in a circulation crystalliser initial concentration of the soli phase in the solution for measuring the initial particle size istribution function. The circulating suspension passe through special impingement evice 6. The impingement evice was esigne as a hollow cyliner within which there was another, orthogonal an symmetrical positione cyliner (See Figure ). The crystals are accelerate in a nozzle an impact onto the inner cyliner. a b l b Figure : Photograph (a) an schematic (b) of the impingement evice ( =. m, D =.4 m, b =. m, l =.7 m) At the outlet an impingement evice, the particle size istribution function an the mass meian size of the forming particles were continuously measures with the help of a laser iffraction spectrometer (Mastersizer, Malvern). They have been carrie out attrition experiments for ifferent see crystals in size uner variation of the volumetric flow an, as a result, uner variation of the impingement velocity of the crystals. For all experiments the mass concentration of the solution was.44 kg/kg an the ensity was kg/m. vacuum LC Prouct Проба TI 9 TI m 6 4 Figure : Sketch of the laboratory FC-Crystalliser (-crystalliser,,4-pulsation ampers, -piston pump, -heat exchanger, 6-impingement evice, 7,9-thermostats, 8,- solution level controller, -feestorage evice, -fee evice, -pump, 4-feeimput controller, -temperature controller, 6,7-stirrers, 8-conenser, 9-conensate storage evice) 7 4 M FIC TIC el. LC

4 M. I. Dorofeeva et al. 4 For the investigation of the crystals growth with their attrition the FC-Cristalliser was built (Fig. ). The crystallization apparatus consists of a fee valve, which is capable to operate uner vacuum, a piston pump, an impingement evice 6, a heat exchange, witch are escribe above, a ouct removal evice an a vacuum system. At the inlet of the piston pump the hot ammonium sulphate solution (saturation temperature 4 C an concentration.48 kg/kg) continuous was impute from the fee evice with the help of the pump. Cooling of the circulate solution to the temperature of C was guarantee by the heat exchanger. At regular intervals ( min), reesentative samples were taken. The position for the sample removal was selecte carefully in orer to guarantee a reesentative ouct removal. When exceeing the filling level in crystalliser 8, the tube is cleane automatically with comesse air. After this oceure, an outsie valve opens an the ouct is remove. Since the crystalliser is operating uner vacuum, the ouct removal evice must have the same essure conition. The samples were filtre, washe with acetone an rie for h at C. Then the particle size istribution function an the mass meian size of the crystalls were measure with the help of a laser iffraction spectrometer. The supersaturation of the solution was obtaine via ensity measurement (DMA, Paar). They have been carrie out crystallization experiments uner variation of volumetric flow, nozzle iameter an fee rate. For all experiments size of see crystals was - µm.. Mathematical moeling an simulation of the crystals attrition The mathematical moel of the attrition consists of only one zone the attrition. The moel is base on the theoretical consieration of Gahn an Mersmann (Gahn an Mersmann, 999). It was assume, that the crystals flow with the same velocity as the liqui phase an the parent crystal an the forming fragments ha the same shape, characterize by the volume shape factor k V =π/8. For the escribe cylinrical target the nozzle iameter was still smaller, then the iameter of the inner cyliner, so that the geometric target efficiency is % (η geo =). Another possibilities an limitations of the moel can be foun in Gahn an Mersmann (Gahn an Mersmann, 999). A iscussion about the assumptions mae an the mathematical erivation of the moel can be foun in Gahn (Gahn, 997). One of the main results of this work is the chouse of the equation of particle number conservation: n ( t, A( t, n ( t, in = n ( t, n ( t, L = t h h L = L * ( W ( W ) δ ( L L ( ) p p,min ( ) ( W ( W ) n ( t, z( h L ( p p,min τ z( n ( t, L + ( L ) N ( q ( L, fr,max fr,min This equation take into account, that crystals of ifferent sizes have ifferent attrition velocities A an, because if this, leave the phase of sizes L (the secon term on the left-han size of the equation). The equation consier, that a impact of the crystals in etachment of a large number of fragments from it N fr, which are characterize by the istribution q fr (the penultimate term in the equation) an each impact of the crystal leaves not only small fragments, but also a large piece of size L*, slightly smaller than the parent crystal (the penultimate term in the equation). fr fr fr L ()

5 Investigation, mathematical moelling an simulation of the crystallisation ocess in a circulation crystalliser The size of the parent crystal s remnant after the attrition event is a function of the parent crystal s size ior to the collision an the volume of the attrition fragments forme by that collision an is etermine from the volume balance equation: * L Vattr ( ) ( L = L () k V In the equation () h enotes the Heavysie function, δ enotes the Dirac istribution:, x = x, x x δ ( x x ) =, ( x), x < h = (), x The initial an bounary conitions for Eqs. (): in n ( t =, = n (, n ( t, L = ) = (4) The other necessary exessions an the material operties of the ammonium sulphate can be foun in Gahn an Mersmann (Gahn an Mersmann, 999). Table : Calculate an experimental values of the meian sizes for ifferent operating conitions of the attrition Operating conitions Experiments results Calculation results L see, υ, M mat, τ, v ax, v, t, L in, L en, t, L,in, L en, µm l/h kg/h s m/s m/s min µm µm min µm µm * * * * * * * a stable state was not reache. L, µm мкм 6 4 эксперимент experiment модель calculation Computers calculations were performe from ifferent ocess conitions. It was obtaine, that the higher volumetric flow rate an corresponingly impact velocity v, smaller nozzle iameter an target size the smaller size of the crystals obtaine. а t, t, min мин ln(n, m - m) ln(n,м - м - ) 4 Figure 4: Comparison of the experimental (points) an calculate (lines) values of the mass meian crystal sizes (a) an values of the natural logarithm of the particle size istribution function at ientical moments of time (b) for the conitions of experiment (Table ) Meian crystals size an particle sizes istribution have been calculate for all experiments conitions an compare with the experimental finings. Foun in the 4 мин min мин. min эксперимент experiment мин. min модель calculation мин. min эксперимент experiment мин. min модель calculation b L, µm мкм

6 M. I. Dorofeeva et al. 6 calculations an experiments stable-state characteristics are esente in the Table for all experiments conitions. The comparison of calculate an experimental results for the conitions of experiments from the Table is given in Fig. 4. Simulations were performe for ifferent conitions of the attrition ocess. It was obtaine, that the higher volumetric flow υ an, corresponingly, the higher impact velocity v, the smaller nozzle iameter D an inner cyliner size (target size) b the smaller size of the crystals obtaine. 4. Mathematical moeling an simulation of the crystallization in a laboratory FC-Crystallizer While mathematical moeling the crystallization ocess with crystals attrition was subivie in separate zones: in mixing, cooling, attrition (impingement evice), growth an sampling zones. Mass an energy balances have been esente for each zone, population balances for attrition an growth zones. In this work three variants of the growth rate exessions were consiere: G G ( k = c( + + c( ck k r k r k r ( ) ( ) ( ) ( ) L k L k L k L, () k ( ) ( L ) k r c( L ) L =, (6) c ( k ( L ) + k ) k r G ( L ) = k ( ) g g c L. (7) Assuming a combine mass transfer an secon orer surface reaction controlle growth, the growth rate of a crystals is efine as the exession (), in the case of the first orer surface reaction controlle growth as the exession (6). For the case of any orer of the growth rate epenence on supersaturation can be use the empirical equation (7). The riving force for the crystal growth is efine by: * Γ k c ( L ) = c c exp (8) RTL Each crystal, especially the small fragments, have a lower iniviual solubility, which epens on their respective strain energy. The ouct of the strain energy na the crystal size is in oportion to the surface relate energy Г k. This parameter nees to be etermine by experiment. The mass transfer coefficient is: k ( 4 D εl v l =.8 + L vl D Mean specific power input in FC-Crystalliser. W/kg (Gahn an Mersmann, 999). Growth rate exession an growth parameters of the ammonium sulphates crystals have been selecte in the ocess of calculations. It was obtaine, that for the ammonium sulphates crystals can be use exessions () an (6) with parameters Г к =. (J m)/kmol, k r =.4 m 4 /(kmol s) an Г к =.6 (J m)/kmol, k r =.8 m 4 /(kmol s) corresponingly. All calculations results, witch are esente below, were performe using the exession (). Meian crystals size, supersatutation an particle sizes istribution have been calculate for all experiments conitions an compare with the experimental (9)

7 Investigation, mathematical moelling an simulation of the crystallisation ocess in a circulation crystalliser finings. Stable-state characteristics for all experiments conitions are esente in the Table. The comparison of the ynamic behavior of these characteristics is given in Fig. for the conitions of experiments - from the Table. 7 L, мкм L, µm 4 Table : Calculate an experimental results for ifferent operating conitions of the crystallization Operating conitions Experiments results Calculation results Т mat, M f, υ, M mat D, v ax, v, L en, σ L en, σ C kg/h l/h kg/h m m/s m/s µm µm the parameter was not measure эксп. эксп. эксп. модель calculation 4 6 t, мин σ t, min,4,,, а ln(n, m - m) ln(n,м - м - ) 4 Figure : Comparison of the experimental (points) an calculate (lines) values of the mass meian crystal sizes an relative supersaturation (a) an calculate values of the natural logarithm of the particle size istribution function (b) for the conitions of experiment - (Table ) мин min мин min 7 мин min мин min 6 мин min 7 7 L, мкм L, µm b b. Mathematical moeling of the crystallization in a inustrial FC-Crystallizer The mathematical moel of the inustrial crystallization ocess in a FC-Crystalliser has been esigne, because the purpose of the moeling is an opportunity to eict the meian crystals size an the particle size istribution. For this purpose it was escribe continuous cooling FC-Crystalliser (Fig. 6). The volume of the growth zone is.6 m, the volume of the pump.4 m. Cooling the suspension occurs in crystalliser.

8 M. I. Dorofeeva et al. 8 4 LC TI Prouct removal Отбор продукта Подача исходного Fee раствора Figure 6: Schematic reesentation of inustrial crystallization ocess in 4-m FC-Crystalliser (-crystalliser, - triple-blaes axial pump, -thermostats, 4-solution level controller) L, мкм M а, мкм f =. kg/s, x f =.4 n n R, min - R = min -, µm L, µm, x f =.4 kg/kg b M f, kg/s t, мин L, мкм, µm a t, мин t, min t, min M f =. кг/c, n R = c L, мкм, µm M f =. kg/s, n R = min t, мин Figure 7: Calculate values of the meian crystals sizes for ifferent operating conitions (a-ifferent pumps opeller frequency, b-ifferent fee rate, c-ifferent opeller blaes number, -ifferent fee concentration) The mathematical moel of the inustrial crystallization ocess is similar to the mathematical moel of the laboratory crystallization ocess. It inclues mixing, 4 x f, kg/kg t, мин t, min t, min

9 Investigation, mathematical moelling an simulation of the crystallisation ocess in a circulation crystalliser attrition (axial-pump), growth (crystallizer) an sampling zones. In this case the attrition is cause by the crystals impact onto pump blaes. An the mathematical moel of the attrition zone inclues relation of a volumetric flow rate with the pumps opeller frequency, relations from axial, tangential an relative velocities, angle of apoach, geometric target efficiency of the pump blaes ege an face, the characteristic length of ege an face (target sizes), perpenicular collision velocity with the targets. All parameters in this zone (attrition rate, nucleation rate, number ensity function) are obtaine by their integrating over the pump raius. Using the mathematical moel, computer calculations for ifferent operating conitions were performe. The results of calculations are esente in Figure 7. During calculations it has been reveale, that change of a ouct characteristics has oscillatory character (See Fig. 7). It was obtaine, that the higher pumps opeller frequency, opeller blaes number, fee rate an smaller fee concentration the smaller size of the crystals an smaller oscillations amplitue obtaine, that the higher pumps opeller frequency an fee rate the higher oscillations perio obtaine. With the help of calculations ocess optimisation for the reception a ouct 6-8 µm in size at a minimal power input have been one. The operating moe of the triple-blaes axial-pump has been chosen, the pump has been picke up an its operating moe has been chosen. The chosen operating moes of the pump an calculate results are esente in Table. Table : Pump operating moes an calculate results l m, m Operating conitions n R, υ, ε, min - m /s W/kg a M f, kg/s x f, kg/kg L en, µm Results σ G Kr, kg/s For the calculation of all consiere ocesses a Delphi 7. ogram has been evelope. The ogram allows executing calculations for ifferent crystal's system an operation conitions 9 6. Conclusions An experimental set-up for attrition ocess an for continuous crystallisation was introuce. The attrition an growth of the ammonium sulphate crystals were investigate. The mathematical moels of the attrition ocess an of the crystallization ocess in the FC-Crystalliser have been evelope. Influences of volumetric flow, nozzle iameter an target iameter on ouct characteristics have been eterminate. The mathematical moel of the inustrial crystallization ocess in the FC-Crystalliser has been evelope. Influence of pumps opeller frequency, opeller blaes number, fee rate an concentration on ouct characteristics an on oscillation parameters have been eterminate. The computer ogram for simulation of three variants of ocess for ifferent crystal's system an operation conitions has been evelope.notation a opeller blaes number A attrition rate. m/s b cyliner size, m c molar concentration, kmol/m

10 c k molar ensity, kmol/m c supersaturation, kmol/m iameter of the pump, m l inner iameter of the tube, m cyliner iameter, m D binary iffusion coefficient, m /s D nozzle iameter, m g exponent of growth G growth rate, m/s G Kr cristalliser efficiency, kg/s h Heavisie function k mass transfer coefficient, m/s k g growth rate constant, m/s k r integration rate constant, m 4 /kmol s k V volume shape factor l clearance in impingement evice, m L parent crystal size, m L * size of the parent crystal s remnant after the attrition event, m L mass meian crystal size, m M mass flow, kg/s - n size istribution function at the outlet in the impingement evice, m - m n R pumps opeller frequency, s - N fr total number of fragments q fr number ensity istribution of the fragments, m - R ieal gas constant, J/kmol K t time, s T temperature, K v velocity, m/s V attr volume of the fragments, m W p impact energy. J x mass concentration of the solute in the solution, kg/kg z impact frequency, s - Г k surface relate energy, J/m δ Dirac istribution, m - ε specific power input, W/kg η geo geometric target efficiency ν l kinematics viscosity, m /s σ relative supersaturation υ volumetric flow, m /s τ resience time in impingement evice, s Subscripts an superscripts ax axial en final f fee in initial mat motherly max maximal min minimal impact see see * equilibrium M. I. Dorofeeva et al.

11 Investigation, mathematical moelling an simulation of the crystallisation ocess in a circulation crystalliser Acknowlegements This work was supporte by grant of PRO e. V. (Pro ocess engineering expertise network) an grant RFBR a. The authors woul like to thank all partners an colleagues for their continuing support an helpful iscussions. References Cerstlauer, A., Mitrovic, A., Mots, S., Gilles, E.-D., () Chemical Engineering Science, 6, -66. Gahn, C., Die Festigkeit von Kristallen un ihr Einfluss auf ie Kinetik in Suspensionkristallisatoren, PhD Thesis, Muenchen University of Technology, Germany (997). Gahn, C., Mersman, A., (999) Chemical Engineering Science, 4, 7-9. Lieb, A., Kin, M., (4) Power Tehnology, 4-44, Neumann A.M., Characterizing inustrial crystallizers of ifferent scale an type, PhD Thesis, Delft University of Technology, The Netherlans ().