The bubbling fluidized bed - GAS-SOLID FLUIDIZATION

GAS-SOLID FLUIDIZATION

2.3. The bubbling fluidized bed

2.3.1. General characteristics and macroscopic behavior of the bubbling fluidized bed

Let us consider a bed of loose material lying on a porous plate with high flow resistance, enabling uniform distribution of gas flowing through complex irregular channels among the particles (Fig. 2.10).

Figure 2.9. Relative gas-particle velocity for different gas-particle flow regimes

With a velocity increase, the resistance to gas filtration through interspaces among the particles increases, linearly at the beginning while the gas flow regime is laminar, then as the square of the velocity in the turbulent filtration regime. The particles will remain undisturbed. Only the positions of some particles may change to rearrange their position to present the least resistance to gas flow. The bed height also remains unaltered. Gas flow through the fixed bed can be considered like every other flow through tubes and channels, except that these channels are complex, irregularly shaped and of changing diameter, a system of channels with numerous interconnections.

When gas velocity reaches the critical value at which the pressure drop equals the bed weight per unit of cross section area, fluidization takes place.

Each particle itself and the bed as a whole “float.” For each individual particle, flow resistance is balanced by its weight (taking into account the Archimedes buoyancy force). The particles which have been lying on top of each other start to move chaotically. The collisions among them are numerous and frequent, but brief. With further increase of gas velocity, the mean distance between the particles increases. Voids in the bed increase in comparison to the voids in the fixed bed, and the bed expands. The free surface of the bed, which was originally irregular (or conical in case of free pouring) becomes horizontal. Gas-solid fluidization of most loose materials is also accompanied by bubble generation (that is larger volumes of void space free of particles), simultaneously with the attainment of the minimum fluidization velocity. This state is known as non-homogenous, aggregate or bubbling fluidization. Occurrence of bubbles, however, does not accompany liquid-solid fluidization. There are some loose materials in which bubbles do not occur when the minimum fluidization velocity has been achieved.

Over a narrow velocity range, before minimum velocity at which bubbles do occur, vmb (incipient, minimum bubbling velocity), homogenous fluidization takes place accompanied by substantial bed expansion. With the occurrence of the Figure 2.10. Bed height and pressure drop across the bed in transition from

fixed to fluidized bed

first bubbles the bed height drops abruptly, but, with further velocity increase it continues to rise. Experience in fluidization of different materials has suggested that properties of fluidized beds are significantly influenced by the type of material, size, shape and features of particles. Thus, the behavior of one material in bubbling fluidization cannot be used as a parameter for behavior of any other, even apparently similar material.

Geldart [29, 30] was the first to comprehensively study the behavior of different materials in the course of fluidization, and suggest a classification of particulate solids according to density and size of particles. Geldart’s classification (Fig. 2.11) divides particulate solids into four groups [2, 11, 12, 31]:

- group A comprises materials with particles of small mean size and low density (ρp<1400 kg/m³). During fluidization of these materials homogenous fluidization can be attained with substantial bed expansion before the occurrence of bubbles. Bubble rise velocity exceeds the interstitial gas velocity in the emulsion phase. A maximum bubble size, however, does appear to exist,

- group B includes numerous materials with particles of medium size and medium density. Ordinary river or sea sand is a typical representative of the group. Bubbles occur immediately after the minimum fluidization velocity has been reached. The bubble rising velocity is greater than the interstitial gas velocity in the emulsion phase. There is no evidence of a maximum bubble size,

- group C includes highly cohesive, fine powders which do not fluidize easily. They are prone to bed channeling, and

- group D comprises loose materials with extremely dense and coarse particles. Their important feature is that the bubbles rise slowly, much more slowly than the interstitial gas velocity in the emulsion phase.

FBC boilers utilize loose particulate solids included in groups A, B or D according to Geldart’s classification. Materials used in boilers with bubbling fluidization mainly belong to group B, but in the range bordering with group D, and some even actually belonging to group D. Boilers with circulating fluidized beds also utilize materials from group B, but approaching the group A features.

Bubbling fluidized beds have a series of properties which has encouraged development of different technologies in which physical and chemical processes take place in a fluidized bed. A fluidized bed provides an extremely appropriate environment for numerous reactions and for handling of loose material. The reactions are usually heterogeneous gas-solid particle surface reactions. The following conditions are considered most favorable for these reactions: large total surface of particles and chaotic motion of particles associated with frequent collisions, enabling intense mixing of gas and particles and as a consequence high heat transfer.

The bubbling fluidized bed has found its place in many chemical technologies and processes: cracking and reforming of hydrocarbons, coal carbonization and gasification, ore roasting, Fischer-Tropsch synthesis, aniline production, polyethylene production, calcination, coking, aluminum anhydride production, powder granulation, vinyl chloride and melamine production, incineration, nuclear fuel processing, combustion of solid, liquid and gas fuels.

The fluidized bed is also used for the following physical processes: drying, adsorption, cooling, freezing, transport, and thermal treatment.

The bubbling fluidized bed (hereinafter simply referred to as fluidized bed), due to mobility of the particles, has numerous features typical of liquids.

The presence of bubbles and their motion, in addition to chaotic particle motion, result also in directed, organized particle circulation. The free surface of the fluidized bed is roughly horizontal (Fig. 2.12a), roughly, since it is irregular due to the presence of bursting bubbles and does not present a very sharp transition. At the transition between the fluidized bed and the space above the bed (freeboard), depending on fluidization velocity, there is a wider or narrower zone in which concentration of particles typical for a fluidized bed falls towards zero far from the bed surface. This transition zone, the splash zone, is the area of abrupt, but not drastic, discontinuous decrease of particle concentration.

Two bodies, one with lower, and the other with higher density than the bed density can lie on the free surface of the fixed bed. If the bed is fluidized, the higher density body will sink to the bottom of the vessel. The less dense body will float on the surface (Fig. 2.12c). If some other loose material is poured on the surface of the particulate solids in a fixed bed, it will remain on the surface. In the fluidized state, however, the two materials will immediately mix and a fluidized bed of the mixture will result. The mixture will be

homogenous over the entire bed volume (Fig. 2.12b). If the lateral walls of the vessel, for an “immobile” fixed bed of particulate solids are heated, it will take a relatively long time for the material located round the vessel axis to become heated. Only after a substantial period of time will a uniform temperature distribution in the bed be established. When a fluidized bed is heated, however, a uniform temperature distribution in the entire bed volume is obtained very quickly (Fig. 2.12d).

Loose materials will pour out of the vessel until an arch is formed, which will eventually prevent further outflow. In the case of free flowing materials, the vessel will effectively empty, but some material will still remain in the corners (Fig. 2.12e). Fluidized material, under the same conditions, will flow out like a liquid. If the opening is located on a lateral wall at the level of the free surface, the surplus will flow out of the vessel. In two linked vessels, a fluidized bed of particulate solids will behave like liquid in linked vessels, that is, the free surface in both vessels will achieve the same level (Fig. 2.12f).

2.3.2. Minimum fluidization velocity

As has already been noted, the minimum fluidization velocity, vmf, of a particulate solid is the velocity at which all particles begin to float^*. When Figure 2.12. Some overall characteristics of the fluidized bed compared

with the behavior of the fixed bed

* It has become customary in engineering practice, although physically not justified, when studying the fluidization process to refer all velocities on the whole cross section, as if no solids were present. These velocities are lower than the true gas velocities in the interspace between the particles. These apparent velocities will be marked as “v,” while the true gas velocities will be marked as “u” in this book

fluidization is established, the pressure drop will remain constant if gas velocity continues to increase (Fig. 2.10). Thus, the minimum fluidization velocity can be simply determined by using a diagram of the measured pressure drop as a function of’ fluidization velocity.

For a bed of ideal monodisperse particulate material with insignificantly small interparticle forces, the line presenting pressure drop across the fixed bed breaks abruptly when the minimum fluidization velocity is achieved (Fig.

2.13a). Determination of the minimum fluidization velocity of a polydisperse material, with irregularly shaped particles and rough particle surface, or with strong cohesive forces, and for the materials of the Geldart’s group C, is somewhat more complex. Intense cohesive forces among the particles will result in significantly higher pressure drop before the minimum fluidization velocity has been attained. When fluidization has been established, the pressure drop will assume a normal value (“b” curve). During velocity decrease hysteresis will occur “c” curve).

When polydisperse materials are fluidized, the transition is gradual.

Smaller particles begin to float at lower velocities. The pressure drop curve is similar to “c” curve (“d” curve). Minimum fluidization velocity is generally determined in these cases at the crossing point of the extrapolated left and right branches of the pressure drop curve. During fluidization of polydisperse materials at velocities substantially above the minimum fluidization velocity, the pressure drop diminishes (“e” curve), due to elutriation of fine particles. In case of nonuniform fluidization, or if bed channeling takes place, the pressure drop plot will be similar to the “c” and “d” curves.

Figure 2.13. Some characteristic curves of the bed pressure drop dependence on the fluidization velocity

The shape of the fluidization diagram (pressure drop versus fluidization velocity) provides a great deal of information on the nature and character of the fluidized bed and features of loose material in the fluidized state. Therefore, it is quite useful if FBC boilers are equipped with pressure drop measurement across the bed of inert material. Monitoring of the pressure drop is particularly important during the boiler start-up period.

The minimum fluidization velocity of a wide range of diverse materials has been determined since the inception of fluidization studies, and the literature offers a wide range of correlations for determination of the minimum fluidization velocity (e.g., references [2, 11, 31, 33]). Originally, all such correlations were empirical, but the functional form proposed by Wen and Yu [34] is now widely accepted. These workers obtained this form by equating the correlations for the pressure drop of fixed and fluidized bed.

If we assume that the pressure drop through complex, irregular interspaces among the particles of a fixed bed can be expressed using the commonly employed Darcy formula:

(2.24) which applies for a streamline flow through a pipe with circular (or almost circular) cross section, the Carman-Kozeny equation is obtained for the pressure drop across a fixed bed (see references [2, 7, 35]):

(2.25)

where the following relations have been used:

- the total volume of interspaces between the particles

(2.26) - the mean hydraulic diameter

(2.27)

and

- the total surface of particles in the bed

(2.28) The numeric coefficient in the Carman-Kozeny equation (2.25) was obtained mainly based on experiments carried on with fine powders, Geldart’s group A, for

laminar flow. Therefore, it does not provide a satisfactory result when used for pressure drop measurements across a bed of particles with size >150 µm.

Here, Ergun’s equation is used (see references [2, 35]) to cover practically all materials, since the second term accounts for inertia forces that become important in the turbulent flow regime:

(2.29) In these equations, the mean equivalent diameter of polydisperse particulate material is calculated according to definition 7, Table 2.4. Gas velocity vf is based on the total cross section of the vessel (or a tube), as if there were no particles in it, as it has become customary in fluidization practice.

The pressure drop across a fluidized bed of particulate solids equals the weight of the bed material, reduced by the buoyancy forces, per unit of bed surface:

(2.30) Following the assumptions of Wen and Yu [34], at incipient fluidization, that is at the minimum fluidization velocity vmf, the values of the pressure drop calculated according to (2.29) and (2.30) must be equal:

(2.31) Wen and Yu [34] have shown that for widely different loose materials the following holds:

(2.32) according to which, with slight rearrangements, eq. (2.31) can be written as:

(2.33) The expression (2.33) can be used for calculation of the minimum fluidization velocities when the characteristics of particles and gas are known. The correlation (2.33) is obtained on the basis of 284 experimental points over the range of Re=0.001–4000, and the minimum fluidization velocity can be calculated with a SD=±34%. In recent times, this expression is frequently used in practice. The general form of this expression is also used for presentation of results of experimentally determined minimum fluidization velocity of

different materials, where the constants specific for each given material are determined.

If it is necessary to know more accurately the correct minimum fluidization velocity, measurements are still inevitable. Numerous formulae for the calculation of the minimum fluidization velocity proposed in literature so far, illustrate the attempts to obtain more precise formulae for actual materials and actual working conditions for pertinent technologies in which fluidized beds are used. At the same time, it has also become obvious that generalized formulae do not give satisfactory accuracy. Table 2.8 gives some of the best known correlations listed in literature. Most of these correlations are obtained for fine particles and powders, mostly Geldart’s group A, since most processes in industry use this kind of material, that is they employ fluidized beds of these materials. Only recently with development of fluidized bed combustion technology has it become necessary to know the minimum fluidization velocity for coarse particle beds. Figure 2.14 [32] gives a comparison of some of the formulae given in Table 2.8. The significant disagreement in the results is obvious, especially for particles greater than 0.5 mm.

Investigations of minimum fluidization velocity at elevated temperatures pertinent to fluidized bed combustion are rare. Figure 2.14 shows the results of experimental determination of the minimum fluidization velocity of silica sand with particles 0.3–1.2 mm in size, and in the 20–500°C temperature

Figure 2.14. Experimental data for minimum fluidization velocity for silica sand in the temperature range 20–500°C [32], compared with the formula (2.34) and some correlations given in Table 2.8

Chapter 2 Table 2.8 Various experimental correlations for minimum fluidization velocity

range [32]. The results from these experiments are best presented by correlation in the form (2.33), but with different coefficients:

(2.34) Specific values of the coefficients are influenced by particle shape.

Minimum fluidization velocity of large particles (Geldart’s group D) necessitates further investigations especially at high temperatures (500–1000°C).

Numerous processes in the chemical and process industries that take place in fluidized beds and, to a somewhat lesser degree fluidized bed combustion technology itself, require knowledge of maximum fluidization velocity at which fluidization can be maintained. Conditionally, this upper limit for monodisperse material can be approximated by the free fall velocity of a single isolated particle, or, for polydisperse materials, by free fall velocity of the tiniest particle. Comparison of the physical essence of the minimum fluidization velocity to the free fall velocity of a single isolated particle reveals that these physical properties share the same nature. In both cases, these are velocities at which, though in different conditions, a balance of forces acting on a particle exposed to the vertical gas flow is realized. Therefore, quite logically very early investigators tried to find out the relation between the minimum fluidization velocity and the free fall velocity. Thus, P.H. Pinchbeck and F.Popper [37] carried out series of experiments and established the following ratios of these velocities:

- for fine particles, i.e., Ret<4

(2.35) and- for coarse particles, i.e., Ret>1000

(2.36) Further studies of Wen and Yu [34] and Godard and Richardson [38] confirmed these relationships suggesting their dependence on the bed porosity at incipient fluidization (that is porosity of a fixed bed). The above relations can be generalized, starting from equation (2.31) if the free fall velocity is appropriately introduced (see [2, 31]):

(2.37)

Figure 2.15 [31] illustrates this correlation for spherical particles compared with experimental results of several authors.

If the analysis of Wen and Yu is used, given by expression (2.32) and appropriate expressions for the free fall velocity given in Table 2.6, the correlation (2.37) can be reduced to a general form applicable to materials composed of nonspherical particles:

(2.38)

where constants a and c have values given in the following table:

The results given in Fig. 2.15 show that for fluidized beds of coarse particles, most commonly used in bubbling FBC boilers, the range of practically feasible velocities is relatively narrow, about 10 vmf, which should be kept in mind during selection of working parameters of the furnace, especially in the light of the polydisperse nature of actual inert materials used in practice.

Figure 2.15. Ratio of terminal velocity to minimum fluidization velocity versus Galileo number (Reproduced by kind permission of the author prof. J.F.Davidson from [31])

Minimum bubbling velocity is present only in fluidized beds of fine powders (Geldart’s group A) and for fluidized bed combustion is of no practical relevance, because bed materials belong to groups B or D, and working conditions are far from the vmb-vmf velocity range. Determination of the minimum bubbling velocity is connected with large experimental errors and is usually performed visually, so that the few studies do not yield reliable data [2, 11, 31]. Only one of the recently recommended formulae will be given here (according to Abrahamsen and Geldart, [11]):

(2.39)

where Φ is the mass content of particles smaller than 45 µm.

2.3.3. Bed expansion

It has become customary to point out that a bubbling fluidized bed has a sharply marked horizontal free surface. In practice, this surface cannot be described as either horizontal or clearly marked. Rising through the bed, bubbles grow up to substantial sizes and burst in an intense manner profoundly perturbing the bed surface, and ejecting all particles from their upper surface out into the freeboard. Larger particles fall back into the bed, and numerous small particles are elutriated and removed from the furnace. Therefore, the free surface of the bed is very turbulent and irregularly shaped, similar to the surface of boiling liquid. At the same time, the assumption of an abrupt, discontinuous change of particle concentration cannot be justified. At the free surface zone there is an area called the splash zone. In the splash zone the particle concentration gradually changes from the values characteristic for a bubbling fluidized bed

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