De los mecanismos de Participación Social

The materials participating in the processes in FBC boilers (sand, coal, limestone, ash) belong to a class of materials called loose (particulate) solids.

The hydrodynamics of fluidized beds, heat transfer in fluidized beds, coal combustion, motion of particles in the bunkers, feeders, cyclones and separators, stand pipes and other pipelines for transport of sand, limestone, coal and ash, all crucially depend on the physical properties of solid particles.

These particulate solids (or loose, disperse) are a mechanical mixture of numerous solid particles. Many solid materials occur in nature and technical practice in the loose form. Inorganic particulate solids in nature result from long-term natural processes: heating, cooling, thermal expansion, crushing, attrition and crumbling under the influence of atmospheric phenomena, river flows and sea waves. Numerous modern technological operations result in loose, particulate solids—crumbling, crushing, grinding, cry stallization, precipitation, spraying, and drying.

In most cases, particulate solids are composed of numerous solid particles of different shapes and very variable sizes. Most inorganic particulate solids appear in nature in a wide spectrum of particle sizes. These substances are called polydisperse materials. Loose materials resulting from technological operations are usually polydisperse. Some technological processes enable the production of particles that are similar in size and shape. Organic loose materials occurring in nature (seeds of various plants) will have similar sizes and shapes.

Particulate solids with uniform particle size and shape are called monodisperse materials.

Loose or powdered materials, not involved in some technological process, usually occur as a “so-called” stagnant or fixed bed. Beds of reposed (fixed) loose material are an important, and characteristic state of particulate solids that are the basis for many subsequent considerations.

Physical and chemical characteristics of loose material and hydrodynamic properties of solid particles are incorporated into formulae for the calculation of numerous processes in FBC boilers. It is, therefore, indispensable to know them in great detail. In the following pages basic definitions of these properties, modes of calculation and determination will be provided. Descriptions of the reposed, fixed bed of loose material and its features will be used for a comparison with substantially different features of fluidized beds.

2.1.1. Physical properties of the particulate solids

Bulk density of particulate solids is the mass of particles per unit of bed volume. Bulk density is always smaller than the true density of a solid particle, since the bed volume includes the volume of voids between the particles. Bulk density depends on the size and shape of the particles, state of particle surface, density of the solid particle and mode of particle “packing.” If mode of particle

“packing” is overlooked, major errors may ensue in determination of bulk density. Bulking of loose material to great depths, vibrations of the container walls etc., may result in settling of the bed, better packing of the particles and an increase of bulk density. The highest and lowest bulk density of particulate solids may differ by as much as 1.5 times.

According to definition, bulk density of a particulate solid may be calculated from the following expression:

(2.1) Rough classification of particulate solids may be accomplished according to their bulk density:

– light materials ρb<600 kg/m³,

– medium heavy materials 600 kg/m³<ρb<2000 kg/m³, and – heavy materials ρb>2000 kg/m³.

Sand, limestone, coal and ash belongs to the medium heavy materials. Bulk densities of those, and some other materials are given in Table 2.1.

Particles of many particulate solids are porous. It is also therefore necessary to differentiate between particle density (including the volume of the pores), ρp and true particle density, ρs (skeletal density). The ρs density is frequently referred to as true, and ρp as apparent density, or even more commonly, particle density. Coal particles are a typical example of porous particles. It should also not be overlooked that the combustion process for some types of coal takes place not only on the external surface of the particle, but inside on the pore surface as well. In that case the data on the skeletal density, ρs, are needed as well as knowledge of how the particle density ρp is changing during the combustion process. Limestone particles are also porous.

The two densities are related in the following way:

(2.2)

The void fraction of a fixed or fluidized bed is expressed as the ratio between the total volume of void space between the particles and the volume of the bed:

(2.3) Void fraction of a fixed, stagnant bed of loose material depends on the size and shape of the particles, and also their size distribution, state of particle surface and mode of packing. Loose materials used in FBC boilers and other apparatuses with fluidized beds have 0.4–0.45 void fraction of the fixed bed.

The definition of the void fraction (2.3) applies to all states and regimes of the mixtures of solid materials and fluids, as well as for all regimes of fluidized bed. Void fraction is smallest in fixed beds of particulate solid material.

Particulate solids are characterized also with the following physical properties: moisture content, abrasion, stickiness, tendency of particles to aggregate. Magnitudes of some of these can only be described qualitatively.

2.1.2. Geometrical characteristics of the particulate solids

Individual particles of particulate solids can take various shapes: regular spheres, approximate spheres, sharp-edged crystals, squamous, fibrous, etc.

Size of particles is, therefore, quite a general and vague term that can hardly be defined and quantitatively determined.

Materials composed of uniform spherical particles have a single, easily recognizable geometrical feature—the sphere diameter. The geometrical characteristics of irregularly shaped particles are not so simple to define.

Irregular particles may also have numerous characteristic dimensions.

It has generally been accepted that the particle size should be defined by a mean equivalent diameter, and that irregular particles should be considered spheres with the diameter equal to the mean equivalent particle diameter.

Table 2.1. Bulk density of some particulate solids

Numerous definitions of the mean equivalent particle diameter exist and these are given in Table 2.2.

Table 2.2. Different definitions of the mean equivalent particle diameter

The different definitions for the geometric characteristic of a particle are appropriate for description of different processes. It is usually more convenient to define a particle size according to its surface area, volume or mass, than according to purely geometric dimensions—d1, d2, d3, width, length and height of a particle. Irrespective of the definition used, it is also important to know what kind of mean equivalent diameter was used for processing of experimental results and derivation of formulae. One should be consistent in selection and application of geometric characteristics.

In practice, the sieve analysis is most commonly used for determination of the particle size of particulate solids used in FBC boilers. The mean equivalent particle diameter is calculated then as the geometrical mean of the size of orifices on adjacent sieves:

(2.4) where di is the smallest opening size of the sieve through which the particle has passed, while dl+1 is the largest opening size through which the particle fails to pass in the course of the sieving process.

The assumption that irregular particles can be considered as spherical, with the diameter corresponding to the mean equivalent diameter, does not imply that irregularity of the particles can always be disregarded. The hydrodynamic properties of irregularly shaped particles differ from those of spherical particles. When processes involving the particle external surface are considered, the fact that the surface area of irregular particles is larger than for spherical ones with the same volume must not be overlooked. The particle shape factor, sphericity, has been introduced to take into account aberration from the ideal sphere. It is customary to define the particle shape factor as the ratio of surface area of a sphere and surface of the particle having identical volumes [1, 2]:

(2.5)

Table 2.3 gives particle shape factors for some materials [3].

Table 2.3. Particle shape factor of some loose materials

Defining geometrical features of polydisperse materials is more complex.

In principle, it is impossible to describe such a material with a single geometrical

characteristic, even if it is composed of uniform, regular spheres. The mean equivalent diameter of polydisperse particulate solids has to take into account the particle size distribution, that is the contribution of each class of particle size.

Table 2.4 gives different definitions of the mean equivalent diameter of polydisperse materials.

The mean equivalent diameters for a given polydisperse material calculated according to definitions given in Table 2.4 can vary a great deal. Different listed definitions originate from an effort to find the most appropriate geometric characteristic of polydisperse material for descriptions of different processes taking place in fluid-solid mixtures in different states and regimes. To describe the heat and mass transfer processes, definitions 3 and 7 are the most appropriate.

Definition 8, however, is more appropriate for studying processes involving volume forces. In [2], definition 7 is consistently applied for description of all processes. When the experimental formulae are used, it is necessary to know which of the definitions of the mean equivalent diameter has been incorporated.

The mean equivalent diameter cannot accurately describe the geometrical properties of a polydisperse material. Loose materials with quite different particle size distribution may have the same mean equivalent diameter. For example, analyses of numerous processes necessitate knowledge of the exact proportion of the smallest particles known to be present, although they do not contribute substantially to the magnitude of the mean equivalent diameter.

Analyses of combustion processes of solid fuels in a fluidized bed necessitate knowledge of the content of particles <1 mm in the total mass of burning coal. The odds that these particles will be elutriated from the bed unburned are high. Knowing the mean equivalent diameter of coal is, therefore, not sufficient for the analysis of its behavior in the furnace. For more detailed analysis of the processes in which poly disperse particles take place, knowledge of the mean equivalent diameter, and the so called granulometric composition is necessary.

Granulometric composition provides information on distribution of particle sizes, and it is usually described in one of the following ways:

– differentially, as a probability density distribution of the particle sizes, – integrally, i.e., cumulatively, as a resting curve, showing the distribution

of the total mass that rests on the sieve with openings of size dpi—for each class of the particle size. The total share of particles larger than this class is entered in the graph, and

– integrally, i.e., as a passing through curve, showing the distribution of the total mass that passes through the sieve with openings of size dpi—for each class of the particle size. The total share of particles smaller than this class is entered the graph.

The three ways for presentation of particle size distribution are illustrated on Fig. 2.1.

Table 2.4. Common definitions of the mean equivalent diameters of polydisperse, loose, materials

The terms “passing through curve” and “resting curve” originate from the most common mode of determination of granulometric composition—

sieving through standard sieves. The “passing through” or “resting” curve, provide information on the share of the material that passes through or rests on the sieve with the di opening size in the total mass of the material.

The probability density size distribution, passing through and resting curves are interrelated as follows:

(2.6) In the course of granulometric analyses, particles are divided into classes according to their sizes. According to generally accepted recommendations, the number of classes should neither go below 5 nor exceed 20 [2]. A small number of classes cannot correctly represent granulometric composition of the material. A large number of classes may introduce into consideration particle sizes that are not representative of the material (e. g., a few extremely large particles which occur only exceptionally).

Materials obtained by grinding or crushing, usually have granulometric composition which can be represented by the well-known Rosin-Rammler distribution:

(2.7) where R is expressed in [%]. The constants b and n depend on the type of material, its internal structure and coarseness of grinding. The d=1/b constant

Figure 2.1. Three possible presentations of the particle size distribution of the loose materials:

p—probability density distribution of the particle size, R—distribution of the total mass that rests on the sieve with openings of size d_pi, D—distribution of the total mass that passes through the sieve with openings of size d_pi

is also called the Rosin-Rammler mean diameter and represents particle size corresponding to R=36.8%.

If we know what has remained on a certain sieve after sieving (e.g., a 90 µm sieve, usually used for pulverized coal combustion analyses), the formula (2.7) can be represented as:

(2.8)

where R90 is the remaining material on a 90 µm sieve.

Granulometric composition of many materials obtained with different technological processes (e.g., spray driers) can be described by their Gauss probability density distribution.

The median diameter, d50, is also often used for estimation of size of particulate solids. It marks the particle size at which 50% of the total number of particles, or the total mass or surface area, is due to particles smaller than d₅₀ [2].

In addition to the already mentioned conditional representation of the size of particulate solids (d50), the values of d30 or d40 are also used to describe the features of hydraulic transport. Measurements carried out on actual plants [4, 5] have shown that the actual values of the pressure drop, closest to the calculated ones, are those obtained when the particle sizes, below which lie 30–40% of material, are used in the calculation formulae. For evaluation of fineness of the coal grind in the thermal power plant mills, the R90 is used, i.e., what remains on a 90 µm sieve.

Estimation of polydisperse composition of particulate solids, i.e., the range of the particle size distribution, can be performed according to the ratio of the particle size corresponding to the share at 90% on the “passing through”

curve, and the size of particles accounting for only 10% in the studied material:

(2.9)

The material is conditionally considered as monodisperse if 1<j<3 [5].

According to [6], a material can be described as monodisperse if dp max/dpminⱕ 5–10. If granulometric composition is determined by sieving, the strictest condition of monodisperseness is, obviously, when all material remains between two adjoining standard sieves:

(2.10)

where δ is the ratio of the opening sizes of the two adjoining sieves in the standard sieve range. A wide range of particle sizes of different particulate solids, the differences in the shape and properties of the material, as well as a spectrum of acceptable definitions of the mean equivalent diameter, makes it impossible to adopt a single method for determination of particle size distribution by measurements.

The following methods have been used: sieving, air classification, centrifugation, elutriation, precipitation, impaction techniques, microscopic analysis, image analysis and light scattering [2, 4]. For materials with particles ⱖ40 µm, sieve analysis is most commonly used in engineering practice.

Sieve analysis is conducted in such a way to pour a measured quantity of solids collected on a series of standard sieves, each sieve having smaller openings that the one above. Selection of the size of sieves is made according to estimation of the range of particle sizes and the desired fineness of granulometric composition determination. A standard set of sieves is used for sieve analysis. The Soviet Standards GOST-3584–53 [4] require the ratio of the opening sizes of adjoining sieves to be 20.5 for fine sieves and 20.25 for coarser ones. Table 2.5 gives the values of opening sizes or sets of standard sieves according to some international standards [2].

Sieving analysis has several disadvantages that should be kept in mind in order to achieve the necessary reproducibility. Some materials tend to agglomerate, and it is also common for attrition and crumbling of particles to take place during sieving. Thus, the particle size distribution obtained may not accurately correspond to the actual situation. If particles <40 µm are found, some of the additional methods mentioned above have to be applied for determination of the detailed granulometric composition. In spite of these shortcomings, sieve analysis is used for investigations and calculations related to fluidized bed combustion as the most appropriate and convenient method.

Analysis of the experimental results obtained in measurements on FBC boilers in operation require knowledge of granulometric composition for the following materials: coal as received, coal at the furnace feeding point, fly ash at different locations along the fuel gas duct to the flue gas exhaust, inert material in the bed, inert material removed from the bed, limestone used for desulphurization. Determination of granulometric composition of these materials provides important information needed for designing the boiler, calculation of boiler parameters and analysis of the processes in the boiler.

Therefore, the methods of granulometric analysis must be applied carefully and carried out in a consistent manner.

In the literature, different classifications of particulate materials are provided, according to the particle size [2, 7]. One of the most commonly used classifications is the following: lumps (dmax>10 mm), coarse grained (dmax=2–10 mm), fine grained (dmax=0.5–2 mm), powders (dmax=0.05–0.5 mm) and pulverized material (dust) (dmax<0.05 mm).

Table 2.5. Sets of standard sieves

Table 2.5. Continued

2.1.3. Hydrodynam ic properties of solid particles

The fluidized bed (fluidization state) is one of the possible states of a mixture of solid particles and fluid. According to its definition, it is a state, i.e., a process of interaction of numerous particles and fluid. In different modes of fluidization, particles move randomly and chaotically, either alone or in smaller or larger groups (clusters). The clusters disintegrate and reintegrate alternately, and/or randomly. The presence and motion of the surrounding particles significantly affect the interaction of particles and fluid.

For investigation of fluidization and for description of the phenomenon, it is important to know one of the basic hydrodynamic properties of a single particle– the free fall (or terminal) velocity. Knowing the free fall velocity and its physical implications is of utmost importance in understanding the fluidization process. The physical interpretation of the free fall velocity and fluidization is practically identical. In both cases it is a question of achieving a balance of the forces acting on a particle-gravity, buoyancy force and hydrodynamic resistance of a particle during motion. Free fall velocity of a particle and the minimum velocity for the fluidized state share the same physical essence, although the pertinent values for the same particles are quite different.

The free fall velocity, as a characteristic magnitude, is incorporated into many formulae which describe fluidized state and other possible states of a mixture of solid particles and fluids (for example, pneumatic transport). When the upward velocity of a fluid passing through the fluidized bed of particulate material (fluidization velocity) reaches the free fall velocity of a single, isolated particle, further increase of velocity will result in removal of that particle from the fluidized bed, followed by the larger ones, as well. Therefore, the free fall velocity determines the upper limit of the velocity range in which it is possible to maintain a fluidized state of a bed of particulate solids. Elaboration of the processes in FBC boilers and furnaces necessitates knowing the free fall (transport) velocity, especially for analysis of energy losses associated with unburned particles that are removed from the furnace. Analysis of ash behavior

The free fall velocity, as a characteristic magnitude, is incorporated into many formulae which describe fluidized state and other possible states of a mixture of solid particles and fluids (for example, pneumatic transport). When the upward velocity of a fluid passing through the fluidized bed of particulate material (fluidization velocity) reaches the free fall velocity of a single, isolated particle, further increase of velocity will result in removal of that particle from the fluidized bed, followed by the larger ones, as well. Therefore, the free fall velocity determines the upper limit of the velocity range in which it is possible to maintain a fluidized state of a bed of particulate solids. Elaboration of the processes in FBC boilers and furnaces necessitates knowing the free fall (transport) velocity, especially for analysis of energy losses associated with unburned particles that are removed from the furnace. Analysis of ash behavior