Particle Growth Kinetics of Calcium Fluoride in a Fluidized Bed Reactor

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  Chemical Engineering Science 62 (2007) 2958– Particlegrowthkineticsofcalciumfluorideinafluidizedbedreactor R.Aldaco ∗ ,A. Garea,A. Irabien  Departamento de Ingeniería Química y Química Inorgánica, Universidad de Cantabria, ETSIIyT, Avda. los Castros s/n, 39005 Santander, Spain Received 26 September 2006; received in revised form 14 February 2007; accepted 28 February 2007Available online 12 March 2007 Abstract Crystallization process in a fluidized bed reactor to remove fluoride from industrial wastewaters has been studied as a suitable alternative tothe chemical precipitation in order to decrease the sludge formation as well as to recover fluoride as synthetic calcium fluoride.In the modeling, design and control of a fluidized bed reactor for water treatment it is necessary to study the particle growth kinetics. Removalof fluoride by crystallization process in a fluidized bed reactor using granular calcite as seed material has been carried out in a laboratory-scalefluidized bed reactor in order to study the particle growth kinetics for modeling, design, control and operation purposes.The main variables have been studied, including superficial velocity ( SV  , ms − 1 ), particle size of the seed material ( L 0 , m) and supersaturation( S  ). It has been developed a growth model based on the aggregation and molecular growth mechanisms. The kinetic model and parametersgiven by the equation  G  =  ( 2 . 26  ×  10 − 10 +  2 . 82  ×  10 − 3 L 20 )SV  0 . 5 S   fits well the experimental data for the studied range of variables.   2007 Elsevier Ltd. All rights reserved. Keywords:  Crystallization; Kinetics; Mass transfer; Mathematical modeling; Fluidized bed reactor; Particle growth; Calcium fluoride 1. Introduction Crystallization in a fluidized bed reactor (FBR) has beenused in many water and wastewater treatment applications. TheFBR has been developed for water softening of drinking water(Graveland et al., 1983; van Houwelingen and Nooijen, 1993), phosphate removal (Seckler, 1994; Battistoni et al., 2000, 2001,2002, 2006), fluoride removal (Giesen, 1998; van den Broeck et al., 2003; Aldaco et al., 2005, 2006a,b, 2007), and heavy metal recovery from wastewaters (Zhou et al., 1999; Chen andYu, 2000; Guillard and Lewis, 2001, 2002; Costodes and Lewis,2006; Lee et al., 2004). When it is compared with the chemicalprecipitation, the major advantage of this technology is thedecrease of sludge formation, the simplification of the materialsrecovery and the reduction of solid wastes.In the modeling, design and control of a FBR for crystal-lization purposes, the particle growth kinetics is the main vari-able. The properties of the particles in a crystallization processdepend mainly on the growth and nucleation kinetics, whichcontrol the properties of the solid product. ∗ Corresponding author. Tel.: +34942201597; fax: +34942201591.  E-mail address: (R. Aldaco).0009-2509/$-see front matter    2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2007.02.045 Crystal growth is a complex mechanism that includes manyfactors depending on different variables: dispersion, supersat-uration, crystal size, solution velocity, admixtures, magneticfield, temperature, and pH. Models allowing the mathematicaldescription of the variables are complex and a general expres-sion of crystal growth is difficult to be established, especiallyfor sparingly soluble systems (Tai, 1999). This paper goes over the main points in the experimentalstudy of the growth kinetics of calcium fluoride using granularcalcite as seed material in a FBR. It has been studied the influ-ence of the main variables on the particle growth kinetics anda crystallization rate of particle growth has been proposed forcalcium fluoride in a FBR. 2. Theoretical background The two-step growth model is the common mechanismregarding crystal growth (Tai et al., 1999). Several authors have determined crystal growth rates from the two-stepgrowth model for several systems including sodium chloride(Al-Jibbouri and Ulrich, 2002), potassium pentaborate (Gürbüz et al., 2005), aluminum sulphate (Mullin and Gaska, 1969; Garside et al., 1972), nickel sulphate (Phillips and Epstein,   R. Aldaco et al. / Chemical Engineering Science 62 (2007) 2958–2966   2959 1974), magnesium ammonium phosphate (Hirasawa et al., 2002),calciumcarbonate(Taietal.,1999),ammoniumperchlo- rate (Tanrikulu et al., 1998), citric acid (Bravi and Mazzarotta, 1998) and calcium phosphate (Hirasawa and Toya, 1990). The model considers the crystal growth based on two steps:a diffusion process and a first-order reaction. The former con-siders the mass transport of solute molecules by diffusion orconvection from the bulk of the fluid phase to the solid sur-face. The later supposes the solute molecules arrange them-selves into the crystal lattice (Mullin, 1993). These two stages can be described by the equations:d m c d t  =  k d  A(C  −  C i ) ( mass transport ) , (1)d m c d t  =  k r A(C i  −  C ∗ ) r ( surface reaction ) , (2) m c  is the mass of solid deposited in time  t  ,  A  the surface areaof the crystal,  k d   the coefficient of mass transfer by diffusion, k r  a rate constant for the surface reaction process,  C  the soluteconcentration in the solution,  C ∗ the equilibrium saturationconcentration, and  C i  the solute concentration in the solutionat the crystal–solution interface.In order to eliminate the term  C i , difficult to measure, ageneral equation for crystal growth rate based on the overalldriving force  C – C ∗ can be written asd m c d t  =  K G A(C  −  C ∗ ) g , (3)where  K G  is an overall crystal growth coefficient and  g  isusually referred to as the order of the overall crystal growth.Considering the relationship between the crystal growth rate,expressed as a mass deposition,  R G , and the overall lineargrowth rate as the change of a characteristic dimension on thecrystal per time unit,  G , R G  = 1 A d m c d t  =  3  c G  =  3  c d L d t  (4)the overall linear crystal growth rate can be expressed as G  = d L d t  =  K g (C  −  C ∗ ) g , (5)where L is a characteristic size of the crystal and K g , the overallcrystal growth coefficient, is defined as: K g  =  3  c K G . (6)In Eq. (6)    and    are the volume and surface shape factors,respectively, and   c  is the crystal density.In addition, the effect of particle size and the superficialvelocity may be significant on the crystal growth (Tai et al.,2006; Myerson, 2001; Mullin, 1993; Garside, 1985). A empir-ical model has been proposed in order to take into account themain variables that influence on the particle growth process,i.e., the supersaturation, the particle size and the superficialvelocity (Bravi and Mazzarotta, 1998) in macroscopic systems: G  =  K g  ·  L m 0  ·  SV  n ·  S  j  , (7)where  L 0  is the size of the particle,  SV   the superficial velocity, S   the relative supersaturation, and  m ,  n  and  j   are the crystalgrowth orders referred to the particle size, superficial velocityand supersaturation, respectively. 3. Crystallization of calcium fluoride in a fluidized bedreactor: process description The chemistry of the process is a conventional precipitation.By dosing calcium hydroxide to the wastewater, the solubilityof CaF 2  is exceeded and fluoride is converted from the aqueoussolution to solid crystals according to the following reactions:H + +  F − 1 ↔  HF, (8)Ca 2 + +  2OH − ↔  Ca ( OH ) 2 , (9)Ca 2 + +  2F − ↔  CaF 2 ( s ) . (10)The main difference with the precipitation lies on the seedmaterial. The process is based on the crystallization of calciumfluoride on granular calcite grains instead of mass precipitationin the liquid phase.During the operation, the grains increase in diameter in theFBR and fluoride covered grains are removed from the bot-tom of the reactor and replaced by fresh seed grains. Fig. 1shows photographs and SEM microphotographs of the productfrom the crystallization process when granular calcite is used asseed material. Pellets of calcium fluoride from granular calciteas seed material show homogeneous white spherical particles.The growth of granular calcite–calcium fluoride takes place bymolecular growth and aggregation between the granular cal-cite grains and the formed calcium fluoride in the liquid phase(nucleated precipitation). The molecular growth and aggrega-tion on the granular grains takes place while competing withprimary and secondary nucleation in the liquid phase (discreteprecipitation) and mineral layer abrasion.Primary and secondary nucleation and abrasion of the grainsin the fluidized bed lead to smaller particles (referred to asfines), which leave the reactor from the top and form, togetherwith the remaining fluoride in solution, the fraction of the flu-oride that is not possible to recover in the reactor. The set-upof the reactor and streams is described in Fig. 2.Low supersaturation leads to nucleated precipitation. On thecontrary, when the system is operated at higher supersaturation,primary nucleation occurs, leading to the formation of manynuclei (discrete precipitation), which are not possible to retainin the reactor. Under these conditions, the efficiency of the pro-cess is lower increasing the turbidity of the effluent. A fluo-ride concentration of 100mgL − 1 leads to 8% of fines, whilea concentration of 300mgL − 1 leads to 51% of fines. Froma technical point of view, a fluoride concentration lower than150mgL − 1 needs to be introduced in the reactor in order toavoid the formation of fines (Aldaco et al., 2005, 2006a).Appropriate supersaturation conditions at the inlet of thereactor are not possible when the fluoride wastewater has ahigh fluoride concentration. To get a fluoride concentrationlower than 150mgL − 1 starting from a concentrated wastewater  2960  R. Aldaco et al. / Chemical Engineering Science 62 (2007) 2958–2966  Fig. 1. Photography and SEM microphotography of (a,c) granular calcite and (b,d) pellets of calcium fluoride. F inlet -F grains-F outlet-    d   i  s  o   l  v  e   d   F   f   i  n  e  s seeds Ca 2+ solutionFluidized Bed Fig. 2. Fluidized bed reactor. water recycling needs to be applied to dilute the fluoride con-centration in the feed stream of the reactor. Consequently, theeffluent concentration is lowered and it is possible to control thesupersaturation in the reactor according to the previous results.However, secondary nucleation seems to be the srcin of the new fines formation in the reactor decreasing the nucle-ated precipitation. The use of a sand filter bed improves theefficiency of the process when recycling of the effluent is neces-sary. The efficiencies of the continuous process can be reachedusing a filter bed to avoid secondary nucleation (Aldaco et al.,2006a). 4. Materials and methods 4.1. Laboratory-scale FBR The reactor consists of a methyl methacrylate cylindricalvessel 350mm height and a diameter of 20mm partially filledwithgranularcalciteasseedmaterialinwhichthefluoridewaterand the calcium reagent solution are pumped upward throughthe reactor at a velocity allowing the fluidization of the pelletsso that the cementing of grains is prevented. The flow is suchthat the seed material will not settle down and flow out of thecrystallization vessel.The FBR is provided with two inlet nozzles.The main nozzle(6mm in diameter) is located vertically at the symmetry axisof the reactor. The calcium solution is pumped into the reactorthrough a secondary nozzle (6mm in diameter) placed horizon-tally at the wall at 15mm from the bottom of the reactor.The calcium reagent and fluoride solutions were injected intothe FBR using different peristaltic pumps (WATSON MAR-LOW 323 and 313S).The experimental facility is completed with several regula-tion valves and flowmeters.   R. Aldaco et al. / Chemical Engineering Science 62 (2007) 2958–2966   2961Table 1Experimental conditionsRun no  L 0  C F, in reactor  S F  F, in reactor  F  ca , in reactor  SV  (mm)  ( mgL − 1 )  (dimensionless)  ( mLmin − 1 ) ( mLmin − 1 ) ( mh − 1 ) CG-1 0.30–0.35 150 19.2 103 69 33CG-2 0.55–0.60 150 19.2 103 69 33CG-3 0.25–0.30 150 19.2 103 69 33CG-4 0.45–0.50 150 19.2 103 69 33CG-5 0.30–0.35 50 6.4 103 69 33CG-6 0.30–0.35 300 38.5 103 69 33CG-7 0.30–0.35 150 19.2 67 45 21CG-8 0.30–0.35 150 19.2 141 94 45 M  calcite /V  reactor  637kg  ×  m − 3 ;  ( Ca / F ) in  1.1. 4.2. Materials The fluoride solution used as feed stream was obtained bydiluting a concentrated hydrofluoric acid solution. Syntheticfluoride solutions in the range 80–500mgL − 1 were used in theexperiments.Chemical grade reactants (a dissolution of hydrated lime inwater as calcium reagent with a concentration from 270 to1600mgL − 1 )anddemineralizedwaterwereused.Severalstud-ies show the hydrated lime as an adequate source of calciumto the neutralization of fluoride containing wastewater (Saha,1993; Yang and Smith, 1990). In addition, the Ca ( OH ) 2  sus-pensions are likely to dissolve along the bed length, distribut-ing the supersaturation more evenly throughout the bed whenhigh fluoride concentration is necessary to treat (Seckler, 1994). However, the efficiency of the process and the pellets growthcould be influenced by the hydrated lime suspension and disso-lution. The influence of the calcium hydroxide suspension onthe crystallization process requires further experimental work.Silica sand has been used as seed material in the crystal-lization process of metals and anions in a FBR (Aldaco et al.,2006a; Battistoni et al., 2006; Chen and Yu, 2000; Gravelandet al., 1983; Guillard and Lewis, 2002; Seckler, 1994). How-ever, silica content in the synthetic calcium fluoride obtainedfrom the crystallization process is an important drawback toreuse the calcium fluoride as raw material in the HF manufac-ture (acid grade CaF 2 , content of SiO 2  < 1%). Granular calcitewas used as seed material in order to avoid silica content in thecrystallization product (Aldaco et al., 2007). 4.3. Experimental procedure A typical run consists of adding about 70g of sieved gran-ular calcite as seed material and controlling the solution ve-locity so that the solids are uniformly suspended in the FBR.The experimental conditions in order to establish the influenceof the variables on the calcium fluoride growth in a FBR areshown in Table 1. The superficial velocity in the reactor was in the range between 21 and 45mh − 1 . The seed size of granularcalcite was between 0.25 and 0.60mm. Finally, the supersat-uration, through the fluoride inlet concentration in the reactor(50–300mgL − 1 ) , was between 6.4 and 38.5.Levels of supersaturation in aqueous solutions of sparinglysoluble electrolytes are expressed in terms of the solubilityproduct as S   =   IP K a  1 /  , (11)where  IP istheionactivityproductofthelatticeionsinsolution, K a  is the activity solubility product of the salt, and    is thenumber of ions in a formula unit of the salt (Mullin, 1993). The supersaturation can be defined for the calcium fluoridesystem at room temperature (20 ◦ C) as S   =  [ Ca 2 + ][ F − ] 2 3 . 4  ∗  10 − 11  1 / 3 . (12)The seed material mass increases due to the precipitation of calciumfluorideuponthegranularcalcite.Asaresultofthis,theseed material increases in diameter.The duration of a run variesfrom 20 to 37h, depending on the conditions of supersaturationand the superficial velocity. This is sufficient to reach steadystate in the liquid phase, after 30min (Aldaco et al., 2005). During the experiments, samples of fluoride-coated calcitegrains (pellets) were removed from the bottom of the reactorat different times. The pellets were air dried and the particlesize was determined by Laser-Ray Diffraction (Mastersizer S,Malvern Instruments). 5. Results and discussion Figs. 3–5 show the dimensionless particle size of the pelletsas a function of time when the supersaturation, the particlesize of the seed material and the superficial velocity changesaccording to the experimental conditions shown in Table 1. Itis observed that the crystal growth of the pellets of calciumfluoride depend on the particle size of the seed material.The crystal linear growth rate  G  has been determined asthe ratio between the size increment between two given in-stants and the elapsed time. The overall linear crystal growthrates of the calcium fluoride for several runs are shown inTable 2. Three important remarks may be noted: (i)  G  variesfrom about 8 . 19 ×  10 − 10 to 1 . 16 ×  10 − 9 ms − 1 as the solutionvelocity ( SV  ) increases from 21 to 45mh − 1 ; (ii)  G  raises from
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