DIRIGIDA A LA ADMINISTRACIÓN PÚBLICA DESCENTRALIZADA “SOBRE LA APERTURA DE DATOS ABIERTOS”

The minimum fluidization velocity, umf, is a fundamental characteristic of a fluid- ized bed. Its accurate prediction is important for the successful design and opera- tion of a fluidized-bed process. At minimum fluidization conditions, the drag force by upward-moving gas equals the weight of particles lifted in the fluidized bed. The following relationship can be shown to hold (see the Nomenclature section for terms): Ar⫽ 1501 ⫺ εmf φ2ε3 mf Remf⫹ 1.75 φε3 mf Re2 mf (1) or Ar⫽2C1 C2 Remf⫹ 1 C2 Re2 mf (2) where Ar⫽d 3 pρg(ρp ⫺ ρg)g µ2 g , Remf⫽ dpumfρg µg C1 ⫽ 42.86(1⫺ εmf) φ (3) C2⫽ φε 3 mf 1.75 (4)

Working on the assumption that the particles constituting the bed can be approxi- mated by a constant value ofφ and that εmfremains constant over the entire range of operating conditions of temperature and pressure, various investigators have proposed values of C1 and C2 on the basis of experimental results to be in the range 18.75–33.7 and 0.0313–0.0651, respectively [3].

The first terms on the right-hand sides of Eqs. (1) and (2) are important if laminar, or viscous, flow predominates in the system, whereas the second terms are important if turbulent, or inertial, flow predominates.

For small particles (Remf⬍ 20), the simplified form of Eqs. (1) and (2) is

umf⫽

冢

冣冢

冣

For large particles (Remf⬎ 1000), the simplified form becomes u2 mf⫽ C2

冢

冣

With gas viscosity,µg, almost independent of pressure and becauseρp⬎⬎ ρgfor

most materials, Eq. (5) indicates that umf is relatively unaffected by changes in pressure for fine particles. On the other hand, according to Eq. (6), umffor larger particles will vary with (1/ρg)0.5, indicating that umfdecreases for increasing pres- sure.

For changes in temperature, Eq. (5) indicates that umfvaries with 1/µg. Because

the gas viscosity,µg, increases with temperature, umf decreases with an increase in temperature for fine-particle systems in which viscous forces dominate. For large particles, Eq. (6) indicates that umf will increase with temperature because an increased temperature results in a decreasedρg.

For systems in the intermediate regime (20 ⬍ Remf⬍ 1000), Eq. (2) can be rearranged and used:

umf⫽

冢

g

dpρg

冣

[(C2

1⫹ C2Ar)0.5⫺ C1] (7)

The trends that umfis relatively unaffected by changes in pressure and decreases for increases in temperature for fine-particle systems and that umf decreases for increases in pressure and increases for increases in temperature for large-particle systems are consistent with those reported experimentally. However, the absolute values of the predictions may be incorrect because of the difficulty in determining a representative value for dpandφ, or estimating εmf.

In the absence of reliable data, use C1⫽ 33.7 and C2⫽ 0.0408 [4] for fine- particle systems and C1⫽ 28.7 and C2⫽ 0.0494 [5] for coarse-particle systems. A recommended method for improving the accuracy of umfis to first determine umfexperimentally at ambient conditions and to back-calculate an effective particle diameter (i.e., deff) from Eq. (5), (6), or (7), using fixed C1 and C2. Using this effective particle diameter, calculate umf at the desired conditions of temperature and pressure. This method substitutes an effective value for dpandφ, which are

independent of temperature and pressure; however, it does not account for any changes inεmf which might occur for changes in temperature and pressure.

The effect of temperature and pressure onεmf has been studied by a number of investigators. Several studies [5,6] have indicated that pressure has essentially no effect onεmf for fine particles and a slight increasing effect onεmf for larger particles. The effect of temperature on εmf has been reported to be much more significant [7–10] and to affect fine-particle systems more than coarse-particle sys- tems. The temperature effect appears to be the result of interparticle forces which affect packing properties [8,10]. The dependence of εmf on temperature can be expressed in linear form as [8]

εmf⫽ εmf(amb)⫹ k(T ⫺ T(amb)) (8)

Although substantial data have been reported in the literature, no reliable correla- tions are available for predictingεmffor a given system. However, it is clear that incorporating an accurate value ofεmfwith an effective particle size, deff, in Eq. (1) will allow an accurate calculation of umf. Without experimental data, the use of Eq. (7) with the recommended values for C1and C2is suggested for calculating umf.

Minimum Bubbling Velocity, umb

and Dense Phase

Voidage,ε

As the gas velocity is increased above that required to incipiently fluidize the bed of particles, gas bubbles eventually form (at u0⫽ umb) and rise through the dense phase. In fine-particle systems at high pressures, it is possible to observe a particu- lately (or homogeneously) fluidized bed without bubbles for intermediate gas ve- locities between umf and minimum bubbling, umb(i.e., for umf ⬍ u0⬍ umb). The minimum gas velocity at which bubbles appear, umb, has been found to equal umf for coarse-particle systems [11]. However, for fine-particle systems, there is a range of velocities between umf and umb over which the bed expands uniformly. The velocity range over which this ‘‘delayed bubbling’’ occurs can be extended with an increase in operating pressure.

Abrahamsen and Geldart [12] observed that umband, hence, the region of partic- ulate expansion is increased by adding fines (increased F, weight fraction of parti- cles⬍45 µm) to a fluidized bed of fine Group A powders:

umb umf ⫽2300ρ0.126g µ0.523g exp(0.716F )umf d0.8 p g0.934(ρp⫺ ρg)0.934 (9)

Equation (9) indicates that umbwill increase for an increase in gas temperature and pressure (via increased ug and ρg) and that the sensitivity to viscosity is more

significant than the sensitivity to pressure. This equation has been shown to be valid over a wide range of pressures for fine-particle systems [13].

For fluidized beds of fine Group A powders that particulately fluidize (i.e., umb ⬎ umf), the voidage of the dense phase, εD, exceeds εmf. This voidage has been shown to be adequately described for high-pressure systems of fine powders [14] by the empirical correlation of Kmiec [15]:

εD⫽

(18Re⫹ 2.7Re1.687₎0.209

Ar0.209 (10)

It is important to note that an increase inεDresults in a decrease in dense phase

viscosity,µD.

The effect of umb⬎ umf andεD⬎ εmf is to increase the interchange between feed gases and solid particles because more feed gas flows directly through the dense phase (i.e.,⬎ qD/qB). Hence, overall reaction rates for catalytic and gas–

increased pressure due to the effect of pressure on fluidization hydrodynamics alone.