Humedad Relativa

For understanding solid fuel fluidized bed combustion processes and for their modelling, heat transfer processes between fuel particles and the emulsion phase of the fluidized bed of hot inert material are the most important. After the cold fuel particle gets to the hot fluidized bed, the process of particle heating takes place, and the particle is heated to its ignition temperature. During particle heating, drying and devolatilization processes also take place. These processes depend on the intensity of heat transfer from the fluidized bed to the fuel particle. After particle ignition heat emission from the fuel particle, which is at higher temperature, takes place. Besides the heat transfer process, during combustion the oxygen diffusion process towards the fuel particle is also important, as well as the diffusion of combustion products from the fuel particle to the bed volume.

Because of that, we will discuss in more detail the heat and mass transfer processes between fuel particles and the fluidized bed. There was little interest for research into heat and mass transfer processes of fluidized bed particles and particles of different kinds (mobile and immobile, larger or smaller than the bed particles) until intensive research of solid fuel fluidized bed combustion began.

So experimental data on these process are scarce. In older literature these problems are not addressed at all or it is recommended that for particles much larger than bed particles, formulae for immersed surfaces (tubes, spheres) should be used.

For particles of size comparable to bed particles formulae for heat transfer between gas and bed particles have been recommended [7, 8, 17].

In the last several years there are more and more experimental investigations of these processes [20–24]. In [22, 24] exhaustive reviews of work in this field have been given.

Experimental investigations have been carried out with moving and fixed particles, using naphthalene particles for mass transfer process research [24], and using spherical or cylindrical heaters for heat transfer investigations [25], monitoring cooling and heating of spherical particles with inserted thermocouples [14, 24, 26], and also by monitoring char or graphite particle combustion [20, 21, 23].

3.3.1. Mass transfer between fuel particles and bubbling fluidized beds When discussing the mass transfer process of a fuel particle in the fluidized bed, it is assumed that the fuel particle exists solely in the emulsion phase.

Under these conditions convective mass transfer is very low due to small gas velocities (vmf), especially in beds of small particles of type B according to Geldart. Besides, inert material particles “screen” the fuel particle and slow down the access of oxygen and outflow of CO2. The first attempts to encompass mass transfer in mathematical models of fluidized bed combustion have assumed that mass is transferred by molecular diffusion, i. e., that Sh=2 [27].

The presence of inert material particles has been accounted for by multiply ing with εmf, Sh=2εmf. Later, especially due to the fact that solid fuel combustion mostly takes place in a fluidized bed of large particles where the influence of convection should not be neglected, the correlation analogous to (3.1) for the heat transfer has been used [28]:

(3.14) Table 3.1 gives the correlations that different authors have used to describe mass transfer to the fuel particle in the fluidized bed.

Table 3.1. Empirical correlations for calculating mass transfer from large particles to the fluidized bed

Remark: Characteristic dimension in Sh and Re numbers is the diameter of active particle d

The greatest shortcoming of the above correlations is that they do not take into account the size ratio of fuel and inert material particles. It is obvious that mass transfer conditions, gas flow around fuel particles and their contact with the inert bed material particles, will be different if d<dp or d>dp. In the case where the fuel particle size is close to the size of fluidized bed particle size, formulae for mass transfer between bed particle and gas may be used (see Section 3.2).

The most detailed experimental research of mass transfer to particles of different diameter in the fluidized bed of inert material particles to date has been conducted by W.Prins [24]. Investigations have been carried out in fluidized beds of different density materials (glass beads, alumina, porous alumina, silica sand) with particle diameter ranging between 100 and 740 µm.

The fluidized bed was 12.7 cm in diameter and 15 cm in height. The diameter of spherical naphthalene particles for which mass loss (mass transfer) has been measured, was d=2–20 mm. The ratio of naphthalene and bed material particle diameters ranged from 2 to 300. Fluidization velocity was vf/vmf=1.5–7.2.

Experiments have shown that fluidization velocity has no influence on mass transfer. This fact confirms the statements of many authors who claimed that mass transfer intensity is the same for fixed and fluidized beds [38] and that the same correlations may be used. Measurements of W.Prins [24] in fixed beds have confirmed such opinions.

The greatest influence on mass transfer comes from the size of active (fuel) particles and inert material particles. The influence of inert material particles is surely the consequence of minimum fluidization velocity—increase in particle size yields an increase in mass transfer. With the increase in active (fuel) particle size, mass transfer decreases, most probably because of the increase in boundary layer thickness at the particle surface.

Figure 3.3 [24] shows the influence of both diameters, that of the active (fuel) particle and fluidized bed particle. The influence of active particle diameter stops at:

(3.15) As a result of his experiments, W.Prins [24] has managed to correlate with the following non-dimensional correlation, with scatter of ±15%:

(3.16) where:

(3.17) Figure 3.4 [24] shows this correlation compared with the experimental data based on which it has been obtained.

Figure 3.4. Generalization of experimental results for mass transfer from naphthalene spheres in fluidized bed of glass beads.

Comparison with correlation given by W.Prins (3.16) (Reproduced by kind permission of the author Dr. W.Prins from [24])

Figure 3.3. Dependence of mass transfer coefficient for naphthalene spheres in fluidized bed of glass beads on sphere diameter, and for different bed particle sizes. According to the measurements of W.Prins (Reproduced by kind permission of the author Dr. W.Prins from [24])

Expressions (3.16) and (3.17) hold true in the 0.1<Remf< 20 and 1<d/dp<

300 range, but for d/dp→∞ also shows good agreement with other authors’ results for mass transfer from immersed large bodies. Good agreement has also been shown with the results of mass transfer measurements during char particles combustion [36], which have been obtained at much higher temperatures.

This exhaustive experimental research has also shown that the results of mass transfer measurements for fixed particles differ from those obtained with free-moving particles, and are consistently higher by 20–50%, probably for the influence of bubbles and higher relative gas velocity.

The conventional approach to physical description of the mass transfer process between fuel and fluidized bed particles (emulsion phase) is based on molecular diffusion and convective transfer, analogous to mass transfer of single particles in cross flow, taking into account that inert material particles are “in the way” of mass transfer. Formulae from Table 3.1 are based on such a model, except for the La Nause, Jung and Kastl formula (No. 9). La Nause, Jung and Kastl [23] have proposed a different model similar to the “packet”

heat transfer model (which will be discussed in Section 3.5). According to this model mass transfer to the fuel particle is based on two mechanisms:

– particle “packets” carry fresh gas from the bed towards the fuel particle;

movement of these “packets” of particles is caused by the moving of bubbles. This mechanism constitutes the “particle” component of mass transfer, and

– the second component is classical, convective mass transfer with the gas flowing through the emulsion phase.

Both mass transfer mechanisms are depicted in Fig. 3.5.

Figure 3.5.

Different mass transfer processes from a large “active

“particle in a fluidized bed. According to the model of La Nause, Jung and Kastl (Reprinted from [23].

Copyright 1978, with permission from Elsevier Science)

3.3.2. Heat transfer between fuel particles and bubbling fluidized bed During combustion of fuel particles in the fluidized bed heat transfer processes occur in both directions: (1) during particle heating, drying and devolatilization heat is transferred from the fluidized bed to the fuel particle, and (2) after ignition of volatiles, and especially during char combustion, fuel particle temperature is higher than the bed temperature and heat is transferred from the fuel particle to the fluidized bed.

In general, heat is transferred between fuel particle and fluidized bed by three mechanisms: gas convection, particle contact and radiation. Heat transfer by radiation has not been sufficiently researched and so is mostly neglected.

Depending on the fuel particle size mentioned mechanisms may or may not significantly influence heat transfer. For fuel particles equal or smaller than inert material particles, convective heat transfer is most important, while for the large particles heat transfer through particle contact has a major influence.

Exhaustive experimental research of W.Prins [24] enables insight into the influence of the most important parameters on fuel particle to bed heat transfer.

In fluidized beds with different particle density (glass beads, alumina), 130–1011 mm in diameter, heat transfer from large particles has been investigated in the temperature range of 300–900 °C and for fluidization velocities vf<0.8 m/s.

Heat transfer has been measured for silver particles (d=4–8 mm) and graphite particles (d=4–20 mm), having inserted thermocouples. Particles have been virtually free since very thin thermocouples have been used (0.1, 0.5, and 1.5 mm).

Similar to the heat transfer to large immersed surfaces (tubes, tube bundles), the heat transfer coefficient for the fuel particle (in this experiment replaced with silver or graphite sphere) has a maximum at certain, optimal, fluidization velocities.

This maximum increases with the decrease in bed particle size. Figure 3.6 [24]

shows the dependence of heat transfer coefficient for free graphite particle on fluidization velocity and the influence of the inert material particle size.

Figure 3.7 shows the influence of the silver (stationary) and graphite (mobile) particle diameter on the maximum heat transfer coefficient in the fluidized bed of glass beads of variable size.

Comparing these results with the mass transfer measurements, the following differences can be noted:

– fluidization velocity does not influence mass transfer but has major influence on heat transfer,

– with the increase of particle size of inert material, mass transfer increases but the heat transfer decreases, and

– heat transfer coefficients of free particles are some 10% lower than for stationary particles (for mass transfer the difference has been 20–50%).

These differences are the consequence of different heat and mass transfer mechanisms. In the case of mass transfer the basic process is gas convection

and inert material particles disturb the process. In the case of heat transfer inert material particles play a significant role as well as heat transfer by particle contact. Gas convection is less significant, so the fuel particle mobility is less important.

Figure 3.6.

Dependence of heat transfer coefficient for free silver sphere in fluidized bed of glass beads on fluidization velocity and bed particle size. According to the measurements of W.Prins (Reproduced by kind permission of the author Dr. W.Prins from [24])

Figure 3.7.

Dependence of maximum heat transfer coefficients for free large particles in fluidized bed of glass beads on large particle diameter and bed particle size. According to the measurements of W.Prins (Reproduced by kind permission of the author Dr. W.Prins from [24])

The different nature of heat and mass transfer processes shows that it is not justified to speak of the analogy between them with respect to immersed fuel particles (bodies) and the fluidized bed.

W.Prins has presented his experimental results by the following non-dimensional expressions, for a bed temperature of 300 °C:

(a) maximum heat transfer coefficients for fixed spherical particles (Fig. 3.8):

(3.18) where:

(3.19)

(b) maximum heat transfer coefficient of a free spherical particle (Fig. 3.9):

Figure 3.8. Dependence of Nu_max for fixed spherical particle in fluidized bed on sphere to bed particle diameter. Experimental data of W.

Prins compared with correlation (3.18)(Reproduced by kind permission of the author Dr. W.Prins from [24])

Figure 3.9. Dependence of Nu_max for free spherical particle in fluidized bed on sphere to bed particle diameter. Experimental data of W. Prins [24] compared with correlation (3.20) (Reproduced by kind permission of the author Dr. W.Prins from [24])

(3.20) where:

(3.21) Results of experiments carried out at fluidized bed temperatures 300, 600 and 900 °C have been correlated with the same expressions by dividing the left hand side of correlations (3.18) and (3.20) with the factor:

(3.22) By comparing the results for silver and graphite particles, which have very different emissivities, W.Prins has concluded that radiation has no influence up to a fluidized bed temperature of 900 °C.

The suitability of using the obtained results—described by correlations (3.18) and (3.20)—together with (3.22) may be judged from Fig. 3.10 where these results are compared to the results of heat transfer coefficient measurements based on the experiments during graphite particle combustion [20, 24, 25, 41, 42].

Results obtained by W.Prins [24] obtained from the combustion experiments are in good agreement with the proposed formula obtained by measuring the heat transfer coefficient, while the results of other authors are some 30% above the line defined by eq. (3.20) and factor (3.22). According to the analysis by W.Prins, the main reason lies in the use of the wrong heat release for carbon combustion, because it is usually assumed that the combustion is complete, i. e., that only CO2 is formed. In experiments of W.Prins the concentration of both CO and CO2 has been measured and so good agreement has been obtained with the measured heat transfer coefficient.

Figure 3.10. Comparison of maximum heat transfer coefficients for large particles in fluidized bed determined in combustion experiments and correlation (3.20)(Reproduced by kind permission of the author Dr W.Prins from [24])

In literature, for small bodies and particles comparable to the bed particle size, it is recommended to calculate heat transfer by the formulae given in Section 3.2 for heat transfer between gas and bed particles [3, 4, 7, 8]. If the active particle diameter is close to the fluidized bed particle diameter, in Soviet literature [4] for fluidized beds of small particles (group B according to Geldart) it is recommended to calculate heat transfer using the Nusselt number values Nup=10, and for beds of large particles according to the interpolation formula:

(3.23) In mathematical modelling of particle heating and devolatilization for large coal particles (>1 mm) Agarwall et al. [39] have used, for Re<100, formula (3.2) and for Re>100 the following formula:

(3.24) In [40], for mathematical modelling of devolatilization processes in large coal particles (3–11 mm), Botterill’s recommendation [7] has been used, that heat transfer coefficient may be calculated using formulae for bodies (tubes) immersed in the fluidized bed.

Based on the assumption of Tamarin and Galerstein [20, 21] about the analogy of heat and mass transfer between fuel particles and fluidized bed, La Nause and Jung [22] have, using expression No. 10 from Table 3.1, proposed the following formula for calculating heat transfer coefficient:

(3.25) In deducing this expression they have used their own experimentally determined correlation for the temperature difference of coke particles and the fluidized bed during combustion:

(3.26) where the diameters are in centimetres (0.07<dp<0.2 cm, and for coke particles 0.4<d<1.2 cm).

Tamarin and Galerstein [20, 21] recommend a simple formula (for d=dp):

(3.27) These data and the exhaustive review of experimental research of heat transfer between small bodies and the fluidized bed (e. g., [25]) or measurements of burning particle temperature (e. g., [20, 21]) given in W.Prins’ work [24], show that this problem is still not investigated thoroughly enough. It is not

possible to, reliably, recommend the formula for heat transfer coefficient between fuel particles and the fluidized bed.

Heat and mass transfer to the fuel particles is now more often the subject of research due to intensive development of fluidized bed combustion mathematical modelling. Presented results of W.Prins are a major advance in research of these mechanisms and form a firm basis for developing mathematical models of combustion. However, new experimental research is required, especially combustion experiments, in order to enable more reliable calculation of heating rate, fuel particle temperature, devolatilization rate and fuel particle burning rate.

3.4. Apparent conductive heat transfer in