Chemical Engineering Science 62 (2007) 2958 – 2966 www.elsevier.com/locate/ces Particle growth kinetics of calcium fluoride in a fluidized bed reactor 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 2007 Available 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 to the 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. Removal of fluoride by crystallization process in a fluidized bed reactor using granular calcite as seed material has been carried out in a laboratory-scale fluidized 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 parameters given by the equation G = (2.26 × 10 -10 + 2.82 × 10 -3 L 2 0 )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 been used in many water and wastewater treatment applications. The FBR 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 and Yu, 2000; Guillard and Lewis, 2001, 2002; Costodes and Lewis, 2006; Lee et al., 2004). When it is compared with the chemical precipitation, the major advantage of this technology is the decrease of sludge formation, the simplification of the materials recovery 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 process depend mainly on the growth and nucleation kinetics, which control the properties of the solid product. ∗ Corresponding author. Tel.: +34 942201597; fax: +34 942201591. E-mail address: aldacor@unican.es (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 many factors depending on different variables: dispersion, supersat- uration, crystal size, solution velocity, admixtures, magnetic field, temperature, and pH. Models allowing the mathematical description of the variables are complex and a general expres- sion of crystal growth is difficult to be established, especially for sparingly soluble systems (Tai, 1999). This paper goes over the main points in the experimental study of the growth kinetics of calcium fluoride using granular calcite as seed material in a FBR. It has been studied the influ- ence of the main variables on the particle growth kinetics and a crystallization rate of particle growth has been proposed for calcium fluoride in a FBR. 2. Theoretical background The two-step growth model is the common mechanism regarding crystal growth (Tai et al., 1999). Several authors have determined crystal growth rates from the two-step growth 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,