SciELO - Scientific Electronic Library Online

 
vol.18 issue4A THERMODYNAMIC MODEL TO PREDICT WAX FORMATION IN PETROLEUM FLUIDSRECOVERY OF CARBOXYLIC ACIDS FROM AQUEOUS SOLUTIONS BY LIQUID-LIQUID EXTRACTION WITH A TRIISOOCTYLAMINE DILUENT SYSTEM author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

  • Article in xml format
  • How to cite this article
  • SciELO Analytics
  • Curriculum ScienTI
  • Automatic translation

Indicators

Related links

Share


Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol.18 no.4 São Paulo Dec. 2001

http://dx.doi.org/10.1590/S0104-66322001000400007 

INDUSTRIAL CRYSTALLIZATION AND PRECIPITATION FROM SOLUTIONS: STATE OF THE TECHNIQUE

 

M.Giulietti1,2, M.M.Seckler1,3, S.Derenzo1, M.I.Ré1 and E.Cekinski1,4
1Instituto de Pesquisas Tecnológicas do Estado de São Paulo, IPT, Divisão de Química,
C.P. 0141, CEP 01064-970, São Paulo - SP, Brazil,
E-mail: giu@ipt.br, seckler@ipt.br, derenzo@ipt.br,
E-mail: mire@ipt.br, cekinski@ipt.br.

2
Universidade Federal de São Carlos, UFSCar, Departamento de
Engenharia Química, São Carlos - SP, Brazil

3
Delft University of Technology, TUDelft, Laboratory for Process Equipment,
Leeghwaterstr 44, 2628 CA, Delft, The Netherlands

4
Escola de Engenharia Mauá, EEM, São Paulo - SP, Brazil

 

(Received: April 24, 2001 ; Accepted: October 26, 2001 )

 

 

Abstract - Crystallization and precipitation from solutions are responsible for 70% of all solid materials produced by the chemical industry. Competing with distillation as a separation and purification technique, their use is widespread. They operate at low temperatures with low energy consumption and yield with high purifications in one single step. Operational conditions largely determine product quality in terms of purity, filterability, flowability and reactivity. Producing a material with the desired quality often requires a sound knowledge of the elementary steps involved in the process: creation of supersaturation, nucleation, crystal growth, aggregation and other secondary processes. Mathematical models coupling these elementary processes to all particles in a crystallizer have been developed to design and optimize crystallizer operation. For precipitation, the spatial distribution of reactants and particles in the reactor is important; thus the tools of computational fluid dynamics are becoming increasingly important. For crystallization of organic chemicals, where incorporation of impurities and crystal shape are critical, molecular modeling has recently appeared as a useful tool. These theoretical developments must be coupled to experimental data specific to each material. Theories and experimental techniques of industrial crystallization and precipitation from solutions are reviewed, and recent developments are highlighted.
Keywords
: Crystallization, precipitation, computational fluid dynamics.

 

 

INTRODUCTION

The continuous development of the chemical process industry has been accompanied by rising demands for product quality. Crystallization is one of the methods to produce particulate material in the chemical industry. In fact, crystallization is a separation technique which has been used for centuries. In the twenties, the first definition of crystallization as a unit operation appeared (Walker et al., 1923). This concept was used until the sixties when Randolph and Larson (1971) took population balance into account for mathematical treatment for crystallization analysis and design. After that, crystallization became recognized as a more complex field and as a part of the chemical engineering sciences. Many approaches appeared to establish the foundations of industrial crystallization, including chemical precipitation (Nielsen, 1964; Strickland-Constable, 1968; Nývlt, 1971; Mullin, 1972 and Garside, 1985). Presently, several textbooks on industrial crystallization are available: Jancic and Grootscholten (1984), Nývlt et al. (1985), Söhnel and Garside (1992), Myerson (1993), Mersmann (1994), Tavare (1995) and Mullin (1997).

Crystallization is often critical because it largely determines product purity and handling characteristics such as caking, wetting or losses due to dusting. Crystallization is employed in many cases as an energetically advantageous way to separate an individual compound from a mixture of substances represented by raw materials or by-products of reaction. Crystallization may occur as the formation of solid particles from a vapor, as solidification from a liquid melt or as the formation of dispersed solids from a solution.

The aim of this paper is to review the basic aspects of industrial crystallization from solutions for analysis and design purposes and to present its recent advances.

 

SOLUBILITY AND DRIVING FORCE

In a two-component system with two coexisting solid and liquid phases, assuming that one component crystallizes as a chemical entity, i.e., that it doesn't form solid solutions with the solvent, the thermodynamic condition for isobaric equilibrium can be expressed as the equality of chemical potentials of the component in both phases:

where m is the chemical potential of component 1 in the liquid (') and solid (") phases, for which:

We choose the pure anhydrous component at the temperature and pressure of the system as the standard state; a1 is its activity, g1 its activity coefficient and x1 its mole fraction in the solution. The solubility of component 1 in the solvent is the total amount dissolved at equilibrium state. In general solubility depends on temperature, so solubility curves or tables have been compiled (Seidell and Linke, 1958; Mullin, 1997; Nývlt et al., 1985). If the system is near ideal, concentration units can represent the relations above.

The solubility or saturation condition is experimentally determined by heating a suspension and observing the temperature at which the solids are completely dissolved. Above this temperature the solution is undersaturated. When again cooling this same solution, temperatures below that of saturation can be reached without the formation of any crystals. In this region the solution is called supersaturated. The difference between the concentration of the supersaturated solution, c, and the saturated concentration, c*, is the so-called absolute supersaturation, which is the driving force for the crystallization process:

Other important definitions are the supersaturation ratio, S, and the relative supersaturation, s:

If the solution mentioned previously is further cooled, a new solid phase is formed by nucleation at a specific point, which define the metastable zone, as indicated in Figure 1.

 

 

The shift of the equilibrium state from one local energy minimum to another constitutes a first-order phase transition, induced by a change in a thermodynamic parameter such as temperature or concentration. The two states related to a first-order phase transition are distinct, occurring in separate regions of the thermodynamics configuration space (Callen, 1985).

In industrial practice, starting with a saturated binary solution, supersaturation can be generated in the following ways, depending on the solubility of the solute or more precisely on the slope of the solubility-temperature curve, dc*/dT (Figure 2):

 

 

i) For very soluble substances (C* > 0.2 g/g), by cooling the solution;

ii) For soluble substances (C* < 0.2 g/g), by cooling or evaporating the solution or by combining them by flash evaporation;

iii) For substances with a small dc*/dT (< 0.005 g/g.ºC), by evaporating the solution;

iv) For slightly soluble substances (C* < 0.01 g/g), supersaturation can be created by the chemical reaction of two or more reactants.

v) In all cases, the addition of a new solvent, miscible with the solvent present, where the solute is less soluble, can also be applied.

The choice of method for generation of supersaturation to crystallize a substance also depends on the product properties desired and economic aspects. In all cases, it is always possible to establish adequate mathematical expressions for the supersaturation in terms of known properties (Hurle, 1994).

 

ELEMENTARY PROCESSES

Nucleation

In a supersaturated solution, part of the solute tends to reorganize itself into the solid form. However, the formation of the solid phase (energetically favorable) implies the generation of an interface (energetically unfavorable). Therefore, if nucleation is to occur, an energy barrier has to be overcome. This barrier is particularly important in the early stages of the nucleation process, when only a few molecules or ions in solutions gather to form clusters with a high surface/volume ratio.

When nucleation from a clear solution takes place, it is known as primary homogeneous nucleation and is characterized by an exponential dependence on supersaturation as well as by very large metastable zone widths. One first defines the rate of primary nucleation, J, as the number of new particles, N, generated per unit time per unit volume of solution V (Volmer, 1939; Becker and Döring, 1935):

Starting with the basic Gibbs-Thomson relationship and with the definition of the Gibbs free energy, it is possible to obtain the equation for the homogenous primary nucleation rate which takes the following form (Mullin, 1997):

In industrial practice, this type of nucleation seldom occurs because solutions usually contain foreign particles that act as substrates for nucleation, known as primary heterogeneous nucleation. Due to the availability of a solid surface, the effective activation energy, geff, is lower for heterogeneous nucleation than it is for homogeneous nucleation (often geff = 1/2 to 1/3 of g) as is the pre-exponential term, Ahetero (Nielsen and Söhnel, 1971):

The metastable zone width is large, and due to the exponential dependence on supersaturation, the process is explosive and difficult to reproduce and should thus be avoided wherever possible in industrial practice. It always takes place in the early stages of unseeded batch processes. For other operating modes, primary heterogeneous nucleation occurs when the rate of supersaturation generation is higher than the capacity of the system to absorb it through crystal growth (Nývlt et al., 1985).

When a supersaturated solution is in contact with particles of the crystallizing compound, secondary nucleation occurs. Particles collide with the agitator blades, with the crystallizer walls and with each other, thereby promoting their abrasion. Tiny crystals under 100 mm in size that behave as nuclei are thus generated. Attrition takes place preferentially at specific locations on the crystal surface such as the edges and corners. For high supersaturations, more of these preferential locations appear, since the crystal surfaces become atomically rough, macro-steps or even dendritic growth may occur (Denk and Botsaris, 1972). There are many empirical expressions that correlate the secondary nucleation with crystallization parameters. The most accepted is given by (Nývlt et al., 1985)

where B0 is defined as the secondary nucleation rate similarly to the primary nucleation rate, J. The average power input from the agitator, e (k = 0.6 to 0.7), is associated with the collision energy, and the solids concentration, M, is related to the frequency of crystal-crystal collisions (j=2) or crystal-impeller and crystal-wall collisions (j=1). The dependence on supersaturation, b, is usually in the range of 1 to 3. Supersaturation is important not only because it defines the surface characteristics of the crystals, but also because it determines whether secondary nuclei survive: these small crystals frequently have internal stresses which make them more soluble than their parent crystals so that they dissolve if the supersaturation is not high enough (Nývlt et al., 1985).

Secondary nucleation is particularly important for coarse products (sizes of 500 mm and above) due to the enhanced collision energy of larger crystals. On the other hand, if crystals are smaller than the Kolmogorov length scale (which defines the smallest eddies in a turbulent field, usually 50 to 150 mm within agitated reactors), they are encapsulated within the viscous limits of the Kolmogorov eddies and do not generate secondary nuclei.

Crystal Growth

If crystal size is characterized by a characteristic dimension, L, we can define its linear growth rate, G, and the mass growth rate can be defined as

Crystal growth involves transport of the so-called growth units (molecules or ions of solute) from the bulk solution to the surface of the crystal and their incorporation into the crystal lattice. For growth controlled by diffusion (e.g., some cases of crystallization of compounds with a high solubility, static crystallization and crystallization from viscous solutions) the growth rate becomes

The mass transfer coefficient, kd = D/d, can be derived from several correlations for the Sherwood number, Sh = kdL/D, such as Sh = 2 + 0.6 Re1/2 Sc1/3.

For growth controlled by surface integration, the three mechanisms shown below can be distinguished (Mullin, 1997).

(a) Spiral Growth (Figure 3)

For small supersaturations, growth units are incorporated only at kinks on the crystal surface: first a defect has to be generated on the surface and then growth proceeds layer by layer upon this defect so that a spiral dislocation forms; this spiral is self-propagating and never dies. The surface is thus smooth at the atomic level (Burton et al., 1951).

 

 

(b) Growth by Two-Dimensional Nucleation (Figure 4)

For relatively larger supersaturations, two-dimensional nucleation appears on the crystal surface, thereby generating the necessary kinks for further growth. If the rate of lateral growth of the 2D nuclei is high in comparison to the nucleation rate, the surface is smooth. For higher supersaturations the nucleation rate dominates the process and the surface becomes rough (Nielsen, 1984).

 

 

Rough Growth (Figure 5)

For even higher supersaturations, growth units attach anywhere on the crystal surface (terraces, steps or kinks) so the crystal surface becomes rough. For organic compounds, the transition between smooth and rough growth can be achieved by increasing not only the supersaturation, but also the temperature.

 

 

Growth controlled by surface integration can be described by the general empirical equation (Mullin, 1997)

Theoretical considerations show that spiral growth at very low supersaturations results in g=2 and for large supersaturations, g=1. For a 2D nucleation mechanism, g is greater than 2 and for rough growth, g=1. Experimental determination of the growth kinetics supported by microscopic examination of crystals often allows the determination of the prevailing growth mechanism. The most frequently found mechanism is spiral growth. As mentioned in the nucleation section, the rough regime should be avoided wherever possible, as it results in excessive secondary nucleation. Whichever the prevailing growth mechanism, the constant, kg, is proportional to solute concentration, i.e., soluble compounds grow faster than slightly soluble ones (G values in the ranges 10-7-10-8 and 10-9-10-10 m/s, respectively).

As noted before, small crystals generated by secondary nucleation may have varying degrees of mechanical stress, so they have a higher solubility and thus lower growth rate than larger crystals. They heal as they grow so their growth behavior becomes similar to that of the larger crystals. This behavior explains two phenomena commonly observed during mass growth of crystals: growth rate dispersion, whereby different individual crystals show varying growth rates and size-dependent growth, whereby smaller crystals grow slower than large ones.

 

MODE OF OPERATION AND MATHEMATICAL REPRESENTATION

Continuous operation is usually applied for large capacities. It offers good control of average product size. Continuous processes are easier to operate than batch ones, requiring less manpower and less physical space for the same production capacity. They are not recommended for products with a strong scaling tendency. Continuous processes can be represented by a simple mathematical treatment that takes population density (n), defined as the number of crystals of a specific size per unit volume of crystallizer as the basic variable. The mass balance in the crystallizer can be obtained using the equilibrium data (solubility curve) and definition of the moments of distribution as pointed by Randolph and Larson (1988). The third moment of the distribution correspond to the mass of crystals produced in the crystallizer. A population balance for the crystallizer is coupled to mass balance as well as to crystallization kinetic parameters as shown in Figure 6, where the population balance does not take into account breakage and agglomeration processes.

 

 

For an MSMPR (Mixed Suspension, Mixed Product Removal) crystallizer without agglomeration and breakage, operating at steady state, the solution of population balance is (Randolph and Larson, 1988)

A straight line on a mono log scale (Figure 7) can represent this. The slope is (-1/Gt) where G is the growth rate and t is the average crystal residence time. From the intercept with the y-axis, no, it is possible to estimate the nucleation rate (B0) from

 

 

With this formulation, the average product size for any operational condition can be easily obtained.

Batch operation is usually preferred for small-scale production, but there are exceptions. Batch operation normally involves simpler equipment and the same crystallizer can be used for more than one product. Batch is the recommended mode of operation for crystallization of substances with low growth rates. Good practices for batch operation involve a sound selection of cooling profiles and seeding procedures since they influence product quality (Giulietti et al., 1995; Giulietti et al., 1996; Derenzo et al., 1996; Giulietti et al., 1999a).

Cooling Profile

Curve 3 in Figure 8 shows a typical cooling curve found in industrial practice derived from a constant flow rate of the cooling fluid. Several families of particles are generated by sequential nucleation bursts due to higher supersaturation in the early stages of the process, resulting in a product with a wide crystal size distribution (CSD) and a large number of fines. Also, the CSD changes from batch to batch due to excessive primary nucleation. All these problems can be avoided if only one nucleation step (or seeding) occurs at the beginning of the process. This situation can be achieved with the cooling profile shown by curve 1 in the same figure. This curve was theoretically derived, assuming that only growth (no nucleation) dominates the process (Nývlt et al., 1985). A similar curve can be obtained for evaporation crystallization. This "ideal cooling", however, is expensive in practice due to the control hardware and the high cooling capacity required (van Rosmalen, 1999). Curve 2 in Figure 8 shows a linear cooling profile, an intermediary situation, which is a reasonable compromise between the "ideal" and "industrial" situations.

 

 

Seeding is frequently applied to avoid the supersaturation peak at the beginning of the process. The chosen mass of seeds is around 0.5 to 2% of the crystal mass to be obtained (Myerson, 1993). Seeds are normally obtained by screening the product in a narrow range. A good seeding procedure involves pre-washing the crystal seeds with a nearly saturated solution to dissolve small particles adhering to their surfaces. Seeds should be fed into the crystallizer during the cooling process just after the solution has become supersaturated. When seeding a large quantity of crystals, a large surface area is provided for solute incorporation, lowering the average supersaturation of the batch process and resulting in a product with a narrow CSD (Jagadesh, 1996).

In normal operation, product size can vary from batch to batch. The best way to have a more stable size is to control the time from the beginning of supersaturation to the end of the cooling process, the real crystallization batch time. Figure 9 shows an overview of the effect of average supersaturation on nucleation and growth rates and on average product size. In a faster crystallization, average supersaturation increases (Nývlt, 1985). Therefore, for each system, the adequate minimum batch time has to be observed in order to produce a more or less stable average crystal size.

 

 

Due to the transient nature of batch processes, their mathematical description is not as simple as that of the continuous mode of operation. A typical batch population density distribution is shown in Figure 10. It is composed of an initial family of crystals from the seeds combined with another generated during the process to give the final distribution.

 

 

Experimental Determination of Crystallization Kinetics

Growth and nucleation kinetics can be measured either simultaneously or independently. By operating an MSMPR at steady state, with a varying degree of supersaturation (e.g., by changing the crystal residence time and temperature), nucleation and growth parameters, g and kg and n and kN, can be estimated using the plot of ln n against L (Fig.7). In this method, it is necessary to confirm that steady state was achieved before sampling. Generally this occurs within 8 to 16 residence times from the beginning of operation (Garside et al., 1990).

In batch mode, nucleation and growth kinetic parameters can be derived by monitoring at least supersaturation or CSD and ideally both (Gutwald and Mersmann, 1990; Myerson, 1993). Supersaturation can be monitored in an indirect way, i.e., using any solution property, such as refractive index, density, conductivity, etc. (Nývlt et al., 1985; Garside et al., 1990). Monitoring CSD allows estimation of the growth rate and population density (Myerson, 1993). If the only monitored variable is the CSD at the end of the run, the average growth and nucleation kinetics throughout the run could be obtained (Nývlt et al., 1985). In this case more than three experiments at varying batch time or average supersaturation are needed. The conditions should be in the range of unstable operation shown in Figure 9 so that substantially different average crystal sizes are experimentally derived (Derenzo, 1994).

Independent measurement of the growth kinetics is achieved in a fluid bed crystallizer: a known number or mass of uniformly sized crystals is fluidized in a solution of known supersaturation for a fixed time. At the end of the experiment, average product size or total mass is measured again to calculate the size increment (Garside et al., 1990). Nucleation kinetics may be independently determined by induction period measurements, defined as the time required after saturation of the solution to observe the formation of the first crystals when cooling the system at a linear rate. At least three experiments are needed with different cooling rates (Nývlt et al., 1985).

 

BASIC DESIGN

The design of industrial crystallizers has been sometimes called an art rather than a science due to the high complexity of the system: simultaneous heat and mass transfer with a strong dependence on fluid and particle mechanisms; multiphase and multicomponent system; concentration, particle size and size distribution that could vary with time; scarcity of data; low reproducibility in the experiments to determine both nucleation and growth rates; secondary effects like agglomeration and the effect of impurities that can alter the morphology and the quality of the crystalline product. Some authors have proposed methods for design of crystallizers, among them Mullin (1997), Randolph and Larson (1988), Nývlt et al. (1985), Jancic and Grootscholten (1984), Mersmann (1994) and Toyokura et al. (1976). The strategy of basic design of industrial cristallizers can be divided into three steps: choice of the solvent, basic design and detailed design.

Choice of the Solvent

The solvent chosen should give the desired polymorph and the optimal shape of the crystals. In general this choice is made based on experimental tests, but also using molecular modeling techniques. The use of additives often helps to change the crystal shape or the crystallization kinetics. The textbooks of Nývlt and Ulrich (1995) and Myerson (1999) give detailed information on the effect of additives on several systems of industrial interest.

Basic Design of the Process

This design involves the following steps: definition of design specifications and information, crystallization method (cooling, evaporation, flash, precipitation or second solvent addition), mode of operation (batch or continuous, single or multistage), type of industrial crystallizer and estimation of the basic dimensions of the crystallizer. This basic process design is the traditional way of designing an industrial crystallizer (McCabe et al., 1993).

Some design specifications are defined first: the yield, the mean crystal size (for a good estimeted value, this specification must be defined by laboratory tests or taken from the literature) and the final purity of the product. At this stage, other specifications such as polymorphs and crystal inclusions are not taken into account.

In addition, some design information is needed: the feed composition, temperature, concentration and presence of crystals; physical and transport properties for solute and solvent, such as densities, viscosities, heat conductivities and heat capacities and their dependence on temperature; thermodynamic properties such as solubility curve and other phase diagrams; and for systems with more than one solvent, the mutual solubility.

After these definitions and a survey of the data, a number of design decisions have to be made. The crystallization method is in general chosen on the basis of the physical and thermodynamic properties of the solute and solvent and the required purity of the final crystalline product (van Rosmalen, 1999). Chemical reaction or anti-solvent crystallization is chosen when the solute is slightly soluble in the solvent (c*<0.01). An adequate choice of reactant and solvent can result in a good yield and purity of the final product (Giulietti and Danese, 1993).

The second criterion for the choice of the crystallization mode is based on the solubility curve. For highly soluble materials (c*>0.2) with a low dependence on temperature (dc*/dT <0.005), evaporative crystallization is recommended. In other cases (c*>0.2 and dc*/dT >0.005), the cooling mode is recommended.

The choice of mode of operation follows. Multiple effect crystallizers are used to save energy and to provide products with a narrower CSD. Investment costs can play an important role in this decision.

The type of industrial crystallizer can be selected from the mean crystal size specified. Some well-known textbooks (Mullin, 1997; Myerson, 1993; Jancic and Grootscholten, 1984; Nývlt, 1992; Mersmann, 1994; Toyokura et al., 1976) give detailed information on industrial crystallizer types and selection criteria.

At this stage, design calculations are performed in order to obtain the general dimensions of the crystallizer, making use of mass (overall and component) and energy balance equations. The solution of these equations provides the feed and product flow rates, the heat duties for the heat exchangers and the evaporation or cooling rates for the crystallization process. If product purity needs to be considered, impurity balances must be done. Using an adequate distribution factor, the purge stream is derived to ensure the required impurity level of the magma. The mean residence time of the magma in continuous crystallizers can be estimated by using the equation

where Lm is the mass mean crystal size of the product and Gm the mean crystal growth rate. For rough calculations, Lm can be assumed to vary from 200 to 1000 mm for highly soluble materials and Gm in the range of 4.10-8 to 10-7 m/s. For practical purposes, the fraction of solids in the magma suspension ( can be assumed to be in the range of The volume (V) of the crystallizer can be calculated by multiplying the production rate by the mean residence time. Assuming that the cylindrical crystallizer vessel has a height/diameter ratio of 3/2, its diameter becomes

For the calculation of the heat exchange area, the mean temperature difference between the exchange fluid and the magma should be between 1 and 3°C for cooling and from 10 to 30°C for evaporation surfaces. The mean heat transfer coefficient can be assumed to be in the range of 800 to 1100 W/m2.K. These average values were taken from Seckler (2000). The mixing inside the crystallizer is important and will be discussed later in this paper.

The method presented above is a practical short-cut method to evaluate the main parameters of the industrial crystallizer that allows an initial estimate of the investment cost of the plant. A complete basic design procedure can be found in Nývlt (1992) and Mersmann (1994).

Detailed Crystallizer Design

The detailed scale design of the industrial crystallizer can be based on the required product quality. Extended models can be used to describe the interactions of hydrodynamics and to include the crystallization kinetics in different parts of the industrial crystallizer, where non-uniform conditions occur (Bermingham et al., 1998; Eek et al., 1995; Gahn and Mersmann, 1997; Neumann et al., 1998). Molecular modeling can be used to predict the shape of the crystals, the possible formation of polymorphs and the influence of additives on the characteristics of the final product. At this stage, the optimization of the global process can be an important tool to improve product quality. The CSD can be manipulated by using process actuators like fines removal and product classification, which in many cases have a great effect on the crystallizer's process dynamics (Neumann et al., 1998).

 

MIXING OF SUSPENSIONS IN CRYSTALLIZATION

The design of the mixing system interferes with crystallizer behavior in several ways. Since it is impossible to obtain a perfectly homogeneous suspension, differences in solid and liquid residence times arise. In addition, regions of high solids concentration consume solute more eagerly and thus have a lower supersaturation. Part of the mixing power introduced into the crystallizing medium is consumed in collisions between the particles, thus generating secondary nucleation, so low power inputs and low blade tip velocities are preferred. For precipitation systems, effective liquid mixing on the molecular level (micromixing) is often required at the location where reactants are added to reduce variability in product quality.

The main goal of solid-liquid agitation in crystallizing systems is to keep crystals in suspension and to promote interphase mass transfer by inducing turbulence in the liquid phase. To date, the most widely used basis for the design of solid-liquid suspension systems is the critical speed, which corresponds to the minimum agitation speed for complete off-bottom solid suspension, Njs. Under this condition, the surfaces of all the particles are exposed to the fluid, thereby ensuring that the maximum surface area is available for mass transfer.

Considerable attention has been devoted to determining this minimum agitation speed. Zwietering (1958), who was the first to apply this criterion, determined the minimum impeller speed at which complete suspension is achieved, with the aid of dimensional analysis and experiments with a wide range of impeller types, sizes and off-bottom clearances, vessel sizes and physical properties of fluid and solid.

Many other works like Baresi and Baldi (1987), Wichterle (1988), Rao et al. (1988), Thring (1990), Rewatkar and Joshi (1991), Janzon (1994) and Myers (1994), Armenante (1998) have been published on this subject. Despite these, it is recommended that Zwietering's correlation be used for small-scale predictions except (a) where special geometries are involved and (b) where the correlations of others have been based on experimental conditions well away from those covered by Zwietering (Harnby, 1992).

This correlation takes the following form

For paddle stirrers with D/W=2, the dimensionless constant S can be calculated from the following equation, adapted from the original work of Zwietering (1958):

 

PRECIPITATION

Precipitation is a subclass of crystallization that has been characterized by one or more of the following features: formation of a slightly soluble compound, generation of supersaturation by chemical reaction, fast processing, and production of small particles. All these features are in fact connected. For a compound with a very low solubility, it is possible to generate a very high supersaturation almost instantly, e.g., by mixing two reactants. At high supersaturation, precipitation proceeds rapidly and a large number of nuclei are generated so a fine product results. This effect is enhanced by the fact that compounds with low solubility grow slowly (see the section on crystal growth).

Precipitation processes proceed according to the same elementary steps presented earlier for crystallization of highly soluble compounds. Supersaturation is usually achieved by chemical reaction, addition of an anti-solvent, addition of a saline solution (salting out), or a change in pH. Due to high supersaturation, heterogeneous primary nucleation is usually dominant, and in some cases even homogeneous nucleation can take place. Crystal growth often follows the rough growth mechanism identified by irregular crystal surfaces. Besides these elementary steps, other secondary processes play a very important role in determining final product properties.

Polymorphism occurs when there is more than one possible arrangement of solutes in a crystalline lattice. Polymorphs are thus chemically identical compounds, but with different crystalline structures. Polymorphs behave differently in terms of their solubility, nucleation and growth rates, etc. Calcium carbonate, for instance, can precipitate as aragonite, valerite and calcite, all having the chemical formula CaCO3. For ionic salts, pseudo polymorphs, i.e., salts containing varying amounts of hydration water, occur. Due to their large sizes, organic molecules and biomolecules have many polymorphs, wich are often very similar to each other, so precipitation products are frequently mixtures of polymorphs. When supersaturation is high enough, precipitation is so fast that the building units of the crystal do not have enough time to adequately arrange themselves according to a thermodynamically stable configuration, and a partially or fully amorphous product results. The degree of crystallinity may often be correlated with synthesis conditions (Seckler et al., 1999a; Seckler et al., 1999b).

A practical rule that holds true for most precipitation systems is the Ostwald rule of stages, according to which the first phase formed is the most soluble. This derives from the fact that polymorphs with higher solubilities precipitate faster (Calmanovici et al., 1996). After being formed, the polymorph redissolves as new phases of decreasing solubility are formed. At the end, only the polymorph with the lowest solubility survives. All precursors are called metastable phases, and the surviving polymorph is the only thermodynamically stable phase.

In industrial practice, one should conduct precipitation at a sufficiently low supersaturation in order to avoid the presence of difficult-to-handle colloidal amorphous phases. In addition, the choice of precipitation conditions should take into account the solubilities of the possible polymorphs so that only the desired phase is formed. For instance, if a salt with only a few water molecules is required, precipitation should be conducted at a high temperature. When it is not possible to isolate the desired compound on the basis of solubility differences, the precipitation time should be adjusted: a short time is preferred if the desired polymorph is a metastable phase, whereas a long time may be used to obtain stable modification.

Aging

The thermodynamic stability of a solid compound arises from the ordered arrangement of its molecules in a crystal lattice in an infinite medium. For particles of finite size, the average particle stability is an average of its volume and surface contributions. Since surfaces have a low stability, the smaller the particle, the lower its stability, i.e., the high its solubility.

This effect is important for particles of 1 m m or less. In late stages of batch precipitation, when supersaturation is low, smaller particles tend to redissolve (Söhnel and Garside, 1992). The residual supersaturation is slowly consumed by larger particles. Aging can take days or even months, and in general, it helps to improve product quality as it results in larger crystal sizes and improved product crystallinity.

Agglomeration is present in almost all precipitation processes and in some crystallization systems as well (Derenzo et al., 1996), particularly during start-up, where higher supersaturations prevail (Eek, 1995). When solid-liquid separation is critical, agglomeration is desired since it leads to larger, easy-to-filter particles. When products of high purity are needed, however, agglomeration should be avoided since agglomerates trap impure mother liquor in their interstices. For low solids contents (below 1 vol%) in the precipitator, agglomeration of these solids on large seeds in a fixed or fluid bed can be advantageously applied (Seckler et al., 1996a,b,c; Seckler et al., 1995).

The process of agglomeration starts with the transport of particles towards one another. When the particles have enough kinetic energy to overcome the repulsion due to their surface potential, they collide. If they remain in contact long enough for growth to take place and thereby bind the particles together, an agglomerate is formed. Having this picture of agglomeration in mind, one understands the variables affecting agglomeration during industrial precipitation. Mixing intensity improves the particle collision frequency and thus agglomeration. However, a mixing intensity that is too high promotes particle disruption. Solids concentration also increases the collision frequency to the second power (since two particles are involved in each collision). pH has a very strong effect on the surface potential, for every compound there is a pH where the particle surface is electrically neutral (the isoelectric point). At this pH, particle-particle repulsion vanishes and agglomeration is highest. A high ionic strength depresses the double layer, thus stimulating agglomeration. A high supersaturation decreases the time needed for binding particles together, thereby facilitating agglomeration.

Jones et al. (1996) review quantitative descriptions of agglomerative precipitation systems using population balance based models. Since such models are computationally intensive and parameter fitting is difficult, Seckler (1994) proposed a simple model based on the moments of CSD. The model was successfully applied to the agglomeration of amorphous calcium phosphate. Recently, Hounslow et al. (1999) have proposed a universal model for agglomeration with a population balance structure coupled a phenomenological dimensionless number. Hounslow and coworkers have been studying agglomeration of calcium oxalate and calcium carbonate for several years. In this model, it is assumed that solid bridge is formed before its rupture by fluctuations in flow field. They propose the non-dimensional number M:

The parameter d* derives from parameters of limited usefulness: the material mechanical resistance, a factor that relates bridge growth rate and crystal growth rate and a bridge shape factor. The agglomeration efficiency y is defined as the ratio between experimental agglomeration rate and average collision rate. It was found that the reactant concentration does not affect agglomeration and that a slight positive effect of particle size is present. The mixing intensity was inversely proportional to the agglomeration rate for both systems studied. The authors postulate that agglomeration mechanism for both compounds is identical.

Mixing

Precipitation is often conducted either by chemical reaction or anti-solvent processes. In both cases, mixing has to take place on the molecular level before precipitation proceeds. Since many precipitation processes are conducted at very high supersaturations, the characteristic reaction time is of the same order of magnitude or even smaller than the mixing time. When this situation prevails, the course of the mixing process helps to determine the course of supersaturation. This explains why mixing conditions affect crystal shape, purity, crystallinity, and in some cases, even the phase modification (e.g., polymorph) that is formed. When one wishes to produce large crystals of high crystallinity and purity, precipitation should be conducted at low supersaturation. Therefore, reactants should be added near areas of high mixing intensity, and as far as possible from each other, i.e., a good dispersion of the concentrated reactant with the reactor contents should be stimulated. If fine particles with a narrow size distribution are desired, intense mixing should provide rapid contact between concentrated reactants. Mersmann et al. (1994) give a nice review on this topic and Tosun (1988) showed how the proper selection of addition points can be effective in controlling the particle size of barium sulfate crystals.

 

NEW TRENDS IN INDUSTRIAL CRYSTALLIZATION

The recent developments in industrial crystallization from solutions are considerable (Price, 1997). The commercial availability of software for molecular modeling (Myerson, 1999) has led to new advances in the use of alternative solvents in crystallization of organic materials as well as to the development of tailor-made additives for the modification of the crystal habit (Winn and Doherty, 1999). Additives have been receiving increased attention (Nývlt and Ulrich, 1995; Myerson, 1993) due to the possibilities they offer of changing the crystal habit (Giulietti et al., 1999a; Leão et al., 1996), inhibiting scaling and product caking (Veiga et al., 1999).

Continuous research efforts are being devoted to the field of secondary nucleation. Ó Meadhra et al. (1996) have set a new approach for the scale-up of this phenomenon. Gahn and Mersmann (1999) have developed a detailed mechanistic model for secondary nucleation. The model was applied within the framework of a population balance based model to successfully describe the steady state behavior of a 1 m3 crystallizer (van Rosmalen and Kramer, 1999).

Computational fluid dynamics (CFD) is becoming an important tool for describing solid-liquid mixing in crystallization. This technique allows the prediction of flow patterns, local solids concentration and local kinetic energy values, taking into account vessel as well as agitator shape. It has been used to assess the effect of mixing variables and system geometry on mixing performance. As an example, Figure 11 shows the distribution of solid phase concentration within an industrial scale vessel originally agitated by paddle impeller and after optimization of agitation parameters, with 45º pitched blade impeller. It is possible to see that after optimization the degree of homogenization is much higher. For precipitation, CFD has been successfully applied to describe local concentrations (Seckler et al., 1995; van Leeuwen et al., 1996); however, new developments are needed to better describe the distributed micromixing behavior in precipitators.

 

 

Mathematical modeling of crystallization processes by neural networks has been successfully applied to batch systems (Giulietti et al., 1999b) and is a promising alternative for improving control of industrial crystallizers by prediction of CSD based on plant's historical data.

The action of external fields on crystallization has shown promising results in recent years. Ultrasound waves applied to crystallization magma reduce agglomeration and create a narrower CSD (Martinez et al., 1999). Sonochemistry is an emerging field of research that can offer an enormous contribution to industrial crystallization development (Thompson and Doraiswamy, 1999). Despite their exoteric character, magnetic fields seem to open up new possibilities for the control of the solubility and the kinetics of crystallization of diamagnetic materials (Freitas et al., 1998; Freitas et al., 1999) in view of their industrial applications.

New techniques for the production of spherical particles, such as quasi-emulsion crystallization (Ré and Biscans, 1999), are promising alternatives for obtaining particles with special properties and characteristics, especially for the pharmaceutical, cosmetic and fine chemistry industries.

Downstream processing in biotechnology offers new challenges for the separation and purification of biomolecules such as enzymes and proteins by crystallization (Miranda and Berglund, 1995). Chernov and Komatsu (1995) have reviewed the fundamentals of this type of process.

Improvements in the understanding of the fundamental aspects of crystallization have led to the successful solution of problems found in industrial practice, such as a reduction in process variability and improvements in product quality (crystal shape, product handling, downstream processing performance, etc.). Often such gains are achieved by the mere adjustment of operational procedures with no need for investment.

The developments just presented show that the technology of industrial crystallization and precipitation is becoming more and more exciting and challenging in the world of chemical engineering.

 

NOMENCLATURE

A  area, m2
B

 weight of solids/weight of fluid x 100, dimensionless

B0 

secondary nucleation rate, #/m3.s

c

concentration, mol/m3

d

particle size, m

D

crystallizer diameter, m

D

impeller diameter, m

crystal growth rate, m/s

gravitational constant, 9.81 m/s2

g

order of crystal growth kinetics

J

 ate of primary nucleation, #/m3.s

K

Boltzmann constant, 1.3805x10-23 J/K

k

constant of crystallization kinetics

kd

mass transfer coefficient, mol/m2.s

L

crystal size, m

M concentration of solids in suspension, kg/m3
M dimensionless agglomeration number
m mass, kg
n

order of nucleation kinetics

n

population density, #/m4

Njs

minimum agitation speed for complete off-bottom solid suspension, 1/s

Q

volumetric flow rate, m3/s

R

gas-law constant, 8.3130 J/mol.K

Re

Reynolds number

S dimensionless constant
S supersaturation rate
Sc Schmidt number
Sh Sherwood number
T/C off-bottom clearance ratio
T/D  impeller ratio
T temperature, K
t time, s
V crystallizer volume, m3
Vm molecular volume, m3/mol
Wi stress energy in the crystal, J
x  mole fraction

Greek Letters

y  agglomeration efficiency
u  kinematic viscosity, m2/s
Dr  density difference between particle and fluid, kg/m3
D  difference
a  activity, mol/m3
e  agitator power input, J/kg and solid fraction in suspension
g  activity coefficient, interfacial tension, J/m2 and shear stress, J/m2
m  chemical potential, J and, dynamic viscosity, kg/m.s
r  density, kg/m3
s  relative supersaturation
t   residence time, s

Subscripts

1 component, solute
a area
cryst crystallizer
eff effective
g growth
i impeller
in inlet
L liquid
M mean
N nucleation
o initial
out outlet
T total
v  volume

Superscripts

0 standard
' liquid phase
'' solid phase

 

BIBLIOGRAPHY

Armenante, P. M., Nagamine, E. U. and Susanto, J., Determination of Correlations to Predict the Minimum Agitation Speed for Complete Solid Suspension in Agitated Vessels, Can. J. Chem. Eng. 76, 413-419 (1998).        [ Links ]

Baresi, A. and Baldi, G., Solid Dispersion in an Agitated Vessel. Chem. Eng. Sci. 42 (12), 2949-2956 (1987).        [ Links ]

Becker, R. and Döring, W., Kinetische Behandlung der Keimbildung in übersättigten Dämpfen, Ann. Phys., 24, 5, 719-752 (1935).        [ Links ]

Bermingham, S.K., Kramer, H.J.M. and van Rosmalen, G.M., Proceedings of Escape 8, May 24-27, Brugge (1998).        [ Links ]

Burton, W.K., Cabrera, N. and Frank, F.C., The Growth of Crystals and the Equilibrium Structure of their Surfaces, Phil. Trans., A243, 299-358 (1951).        [ Links ]

Callen, H.B., Thermodynamics and an Introduction to Thermostatistics, John Wiley & Sons, New York (1985).        [ Links ]

Calmanovici, C.E., Biscans, B., Gilot, B., Laguerie, C. and Giulietti, M., Stable and Metastable Modifications Relates with Solid Formation from Solutions, Proc. 13th Symposium on Industrial Crystallization, Toulouse, France, 349-354, 16-19 September (1996).        [ Links ]

Chernov, A.A. and Komatsu, H., Principles of Crystal Growth in Protein Crystallization, in Science and Technology of Crystal Growth, van der Eerden, J.P. and Bruisma, O.S.L. (eds.), Kluwer Academic Publ., Dordrecht (1995).        [ Links ]

Denk, E.G. and Botsaris, G.D., Fundamentals Studies in Secondary Nucleation from Solution, J. Crystal Growth, 13/14, 493-499 (1972).        [ Links ]

Derenzo, S., Estudo da Cristalização do Ácido Adípico em Escala de Laboratório em Regime Descontínuo, por Resfriamento, Master's Diss., Escola Politécnica da Universidade de São Paulo, São Paulo (1994).        [ Links ]

Derenzo, S., Seckler, M.M. and Toste, E.M., Agglomeration Study of Adipic Acid from Aqueous Solution Crystallization, Proc. 13th Symp. Ind. Crystallization, Toulouse, 16-19 Sept., 425-430 (1996).        [ Links ]

Derenzo, S., Shimizu Günther, P.A. and Giulietti, M., On the Behavior of Adipic Acid Aqueous Solution Batch Cooling Crystallization, Crystal Growth of Organic Materials, ACS- Conference Series, Myerson, A., Green, D. and Meenan, P. (eds.), American Chemical Society, Washington D.C., 145-150 (1996).        [ Links ]

Eek, R.A., Dijkstra, S. and van Rosmalen, G.M., AIChE J., 41, 3, 571-584 (1995).        [ Links ]

Eek, R.A., Control and Dynamic Modelling of Industrial Suspension Crystallizers, Ph.D. Thesis, Delft University of Technology (1995).        [ Links ]

Freitas A.M.B., Seckler M.M., Landgraf F.J.G., Derenzo S. and Giulietti M.M. Effect of Magnetic Field in Crystallization from Solutions, XIII Intern. Cong. of Chemical and Process Eng., CHISA '98, Prague, Czech Republic (1998).        [ Links ]

Freitas, A.M.B., Landgraf, F.J.G., Seckler and M.M., Giulietti, M., The Influence of Magnetic Field on Crystallization from Solutions, Proc. 14th Int. Symp. Ind. Crystallization, Sept. 12-16, Cambridge, UK (1999).        [ Links ]

Gahn, C. and Mersmann, A., Brittle Fracture in Crystallization Processes, Part A, Attrition and Abrasion of Brittle Solids, Chem. Eng. Sci., 54, 1273-1282 (1999).        [ Links ]

Gahn, C. and Mersmann, A., Trans I. Chem. E, 75(A), 125-131 (1997).        [ Links ]

Garside, J., Industrial Crystallization from Solutions, Chem. Eng. Sci., 40, Nº 1, 3-26 (1985).        [ Links ]

Garside, J., Mersmann, A. and Nývlt, J., Measurement of Crystal Growth Rates, European Federation of Chemical Engineering, Working Party on Crystallization (1990).        [ Links ]

Giulietti M., Seckler, M.M., Derenzo, S., Schiavon L.H., Valarelli, J.V. and Nývlt, J., Effect of Selected Parameters on Crystallization of Copper Sulphate Pentahydrate, Cryst. Res. Techn., 34, 959-967 (1999a).        [ Links ]

Giulietti, M. and Danese, M., Potassium Sulfate Production By Reaction and Precipitation in Aqueous Ethanol Solution, Proc. 12th Symposium on Industrial Crystallization, Poland, Vol. 2, 5-151 (1993).        [ Links ]

Giulietti, M., Derenzo, S., Nývlt, J. and Ishida, L.K., Crystallization of Copper Sulfate, Cryst. Res. Techn., 30, 177-183 (1995).        [ Links ]

Giulietti, M., Terra, L.R. and Guardani, R., Modeling Batch Cooling Crystallization by Means of Neural Networks, Proc. 14th Int. Symp. Ind. Crystallization, Sept. 12-16, Cambridge, UK (1999b).        [ Links ]

Giulietti, M., Seckler, M.M., Derenzo, S. and Valarelli, J.V., Changes in Copper Sulfate Crystal Habit During Cooling Crystallization, J. Crystal Growth, The Hague, 1089-1093 (1996).        [ Links ]

Gutwald, T. and Mersmann, A., Determination of Crystallization Kinetics from Batch Experiments, Proc. 11th Symp. Ind. Crystallization, Garmish-Partenkirchen, Sept. 18-20, 331-336 (1990).        [ Links ]

Harnby N., Edwards M.F. and Nienow A.W., Mixing in the Process Industries. 2nd ed.. Butterworth Heinemann (1992).        [ Links ]

Hounslow, M.J., Collier, A.P., Barrick, J.P. and Mumtaz, H.S., Aggregation During Precipitation: Putting the Pieces of the Puzzle Together, Proc. 14th Int. Symp. Ind. Crystallization, Sept. 12-16, Cambridge, UK (1999).        [ Links ]

Hurle, D.T.J. (ed.), Handbook of Crystal Growth, North Holland, Amsterdam (1994).        [ Links ]

Jagadesh, D., Kubota, N., Yokota, M., Sato, A. and Tavare, N., Large and Mono-sized Product Crystals from Natural Cooling Mode Batch Crystallizers, J. Chem. Eng. Japan, 29, 5, 865-873 (1996).        [ Links ]

Jancic, S.J. and Grootscholten, P.A.M., Industrial Crystallization, Delft University Press, Delft (1984).        [ Links ]

Janzon, J. and Theliander, H., On the Suspension of Particles in an Agitated Vessel, Chem. Eng. Sci., 49, 3522-3529 (1994).        [ Links ]

Jones, A.G., Wachi, S. and Hostomský, J., Modeling and Analysis of Particle Formation in Agglomerative Precipitation Systems, Chem. Eng. Comm., 146, 105-30 (1996).        [ Links ]

Leão, V.A., Ciminelli, V.S.T. and Rocha, S.D.F., Organic Additives in Gypsum Precipitation, Wilkormisky, I. et al. (eds.), Chemical Metallurgy, 3, 243-55 (1996).        [ Links ]

Martinez, K.C.L., Seckler, M.M., Derenzo, S., Giulietti, M. and Condotta, R., Intensification of Paraffin Crystallization with Ultrasound, Proc. 14th Int. Symp. Ind. Crystallization, Sept. 12-16, Cambridge, UK (1999).        [ Links ]

McCabe, W.L., Smith, J.C. and Harriot, P., Unit Operations of Chemical Engineering, 5th ed., McGraw-Hill, New York (1993).        [ Links ]

Mersmann, A., Angerhöfer, M. and Franke, J., Controlled Precipitation, Chem. Eng. Techn. 17, 1-9 (1994).        [ Links ]

Mersmann, A., Crystallization Technology Handbook, Marcel Dekker, New York (1994).        [ Links ]

Miranda, E.A. and Berglund, K.A., Development of Precipitant Agents for Precipitation of Proteins Based on Hydrophobic Interaction, Bras. J. Chem. Eng., 12, 1-12 (1995).        [ Links ]

Mullin, J.W., Crystallisation, 2nd ed., Butterworths, London (1972).        [ Links ]

Mullin, J.W., Crystallization, 3rd ed. Rev., Butterworth-Heinemann, Oxford (1997).        [ Links ]

Myerson, A.S. (ed.), Handbook of Industrial Crystallization, Butterworth-Heinemann, London (1993).        [ Links ]

Myerson, A.S. (ed.), Molecular Modeling Applications in Crystallization, Cambridge University Press, New York (1999).        [ Links ]

Neumann, A.M., Bermingham, S.K., Kramer, H.J.M. and van Rosmalen, G.M., Proc. 12th International Conference on Crystal Growth, July 26-31, Jerusalem (1998).        [ Links ]

Nielsen, A.E. and Söhnel, O., Interfacial Tensions, Electrolyte Crystal-Aqueous Solution, from Nucleation Data, J. Crystal Growth, 11, 233-242 (1971).        [ Links ]

Nielsen, A.E., Electrolyte Crystal Growth Mechanisms, J. Crystal Growth, 67, 289-310 (1984).        [ Links ]

Nielsen, A.E., Kinetics of Precipitation, Pergamon Press, New York (1964).        [ Links ]

Nývlt, J. and Ulrich, J., Admixtures in Crystallization, VCH Verlagsgesellshaft, Weinheim (1995).        [ Links ]

Nývlt, J., Design of Crystallizers, CRC Press, Boca Raton (1992).        [ Links ]

Nývlt, J., Industrial Crystallisation from Solutions, Butterworths, London (1971).        [ Links ]

Nývlt, J., Söhnel, O., Matuchova, M. and Broul, M., Kinetics of Industrial Crystallization, Academia Prague (1985).        [ Links ]

Ó Meadhra, R., Kramer, H.J.M. and van Rosmalen, G.M., AIChE J., 42, 973-982 (1996).        [ Links ]

Price, C.J., Take Some Solid Steps to Improve Crystallization, Chem Eng. Prog., 93, 9, 34-43 (1997).        [ Links ]

Randolph, A. and Larson, M., Theory of Particulate Processes, 2nd ed., Academic Press, San Diego (1988).        [ Links ]

Randolph, A. and Larson, M., Theory of Particulate Processes, Academic Press, New York (1971).        [ Links ]

Rao, R. K. M. S., Rewatkar, V. B. and Joshi, J. B., Critical Impeller Speed for Solid Suspension in Mechanically Agitated Contactors, AIChE J., 34, 1332-1340 (1988).        [ Links ]

Ré, M.I. and Biscans, B., Preparation of Micro-Spheres of Ketoprofen with Acrylic Polymers by a Quasi-Emulsion Solvent Diffusion Method, Powder Technology, 101, 120-133 (1999).        [ Links ]

Rewatkar, V. B. and Joshi, J. B., Critical Impeller Speed for Solid Suspension in Mechanically Agitated Three-Phase Reactors. 2. Mathematical Model, Ind. Eng. Chem. Res., 30, 1784-1787 (1991).        [ Links ]

Seckler, M.M., Bragatto, C., Derenzo, S. and Giulietti, M., 7th Intern. Workshop on Indust. Crystallization, September 6 and 7, Halle-Wittenberg, Germany (1999b).        [ Links ]

Seckler, M.M., Bruinsma, O.S.L. and van Rosmalen, G.M., Calcium Phosphate Precipitation in a Fluidized Bed in Relation to Process Conditions: A Black Box Approach, Wat. Res., 30, 7, 1677-1685 (1996a).        [ Links ]

Seckler, M.M., Bruinsma, O.S.L. and van Rosmalen, G.M., Influence of Hydrodynamics on Precipitation: A Computational Study, Chem. Eng. Comm., 135, 113-131 (1995).        [ Links ]

Seckler, M.M., Bruinsma, O.S.L. and van Rosmalen, G.M., Phosphate Removal in a Fluidized Bed. Part I: Identification of Physical Processes, Wat. Res., 30, 7, 1585-1588 (1996b).        [ Links ]

Seckler, M.M., Bruinsma, O.S.L. and van Rosmalen, G.M., Phosphate Removal in a Fluidized Bed. Part II: Process Optimization, Wat. Res., 30, 7, 1589-1596 (1996c).        [ Links ]

Seckler, M.M., Bruinsma, O.S.L. and van Rosmalen, G.M., Phosphate Removal from Wastewater. in: Calcium Phosphates in Biological and Industrial Systems, Zahid Amjad (ed.), Kluwer Academic Publisher, Boston (1997).        [ Links ]

Seckler, M.M., Calcium Phosphate Precipitation in a Fluidized Bed, Ph.D. Thesis, Delft University of Technology, Delft University Press, Holland (1994).        [ Links ]

Seckler, M.M., Danese, M., Derenzo, S., Valarelli, J.V., Giulietti, M. and Rodríguez-Clemente, R., Influence of Process Conditions on Hydroxyapatite Crystallinity Obtained by Direct Crystallization, Materials Research, 2 (2), 59-62 (1999a).        [ Links ]

Seckler, M.M. (ed.), Tecnologia da Cristalização, Instituto de Pesquisas Tecnológicas, São Paulo, 2000.        [ Links ]

Seidell, A. and Linke, W.F., Solubilities of Inorganic and Metal Organic Compounds, Van Rostrand, New York (1958).        [ Links ]

Söhnel, O. and Garside, J., Precipitation: Basic Principles and Industrial Applications, Butterworth-Heinemann, Oxford (1992).        [ Links ]

Strickland-Constable, R.F., Kinetics and Mechanisms of Crystallization, Academic Press, London (1968).        [ Links ]

Tavare, N., Industrial Crystallization: Process Simulation Analysis and Design, Plenum Press, New York (1995).        [ Links ]

Thompson, L.H. and Doraiswamy, L.K., Sonochemistry: Science and Engineering, Ind. Eng. Chem. Res., 38, 1215-1249 (1999).        [ Links ]

Thring, R. W. and Edwards, M. F. An Experimental Investigation into the Complete Suspension of Floating Solids in an Agitated Tank, Ind. Eng. Chem. Res., 29, 676-680 (1990).        [ Links ]

Tosun, G., An Experimental Study of the Effect of Mixing on the Particle Size Distribution in BaSO4 Precipitation Reaction, 6th European Conf. on Mixing, Pavia, Italy, May 24-26, 161-170 (1988).        [ Links ]

Toyokura, K., Matsuda, F., Uike, Y., Sonoda, H. and Wakabayashi, Y., The Design of Crystallizers, in Industrial Crystallization, Mullin, J.W. (ed.), Plenum Press, New York, 303-310 (1976).        [ Links ]

van Leeuwen, M.L.J., Bruinsma, O.S.L. and van Rosmalen, G.M., Precipitation and Mixing: Influence of Hydrodynamics on the Precipitate, Proc. 13th Symp. Ind. Crystallization, Sept. 16-19, Toulouse (1996).        [ Links ]

van Rosmalen, G.M. (ed.), Industrial Crystallization and Precipitation Course, Delft University of Technology, Delft (1999).        [ Links ]

van Rosmalen, G.M. and Kramer, H.J.M., personal communication (1999).        [ Links ]

Veiga, A.R., Calmanovici, C.E. and Giulietti, M., Operational Conditions Evaluation in Ammonium Bicarbonate Crystallization, Proc. 14th Int. Symp. Ind. Crystallization, Sept. 12-16, Cambridge, UK (1999).        [ Links ]

Volmer, M., Kinetik der Phasebildung, Steinkopf, Dresden (1939).        [ Links ]

Walker, W.H., Lewis W.K. and McAdams, W.H., Principles of Chemical Engineering, McGraw-Hill, New York (1923).        [ Links ]

Wichterle, K., Conditions for Suspension of Solids in Agitated Vessels, Chem. Eng. Sci., 43, 467-471 (1988).        [ Links ]

Winn, D. and Doherty, M.F., Predicting the Shape of Organic Crystals from Polar Solvents, Proc. 14th Int. Symp. Ind. Crystallization, Sept. 12-16, Cambridge, UK (1999).        [ Links ]

Zwietering, T.N., Suspension of Solid Particles in Liquids by Agitators, Chem. Eng. Sci., 8, 244-253 (1958).        [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License