Ind. Eng. Chem. Res. 2007, 46, 2877-2884
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Operating Conditions of Conical Spouted Beds with a Draft Tube. Effect of the Diameter of the Draft Tube and of the Height of Entrainment Zone Marı´a J. San Jose´ ,* Sonia Alvarez, Alvaro Ortiz de Salazar, Martin Olazar, and Javier Bilbao Departamento de Ingenierı´a Quı´mica, UniVersidad del Paı´s Vasco, Apartado 644, 48080 Bilbao, Spain
The bed stability of conical spouted beds with a nonporous draft tube located at the bottom of the contactor has been studied, and these results have been compared with those obtained without internal devices, under the same experimental conditions. To design the appropriate geometry of the nonporous draft tube, as well as the height of the entrainment zone without any instability or operating drawbacks in conical spouted beds, the effect of the ratio of the draft tube diameter to the gas inlet diameter, and the height of the entrainment zone on the contactor inlet, on bed stability has been studied. An original correlation for calculation of the minimum spouting velocity in conical spouted beds with a draft tube has been developed, which is also valid for conical spouted beds without internal devices. 1. Introduction Despite the versatility of the conical spouted beds, there are situations in which the gas-solid contact is not fully satisfactory, because of instability of the bed. In previous papers,1-3 the ranges of the geometric factors of the conical contactor and of the contactor-particle system for stable operating conditions have been established1-3 to define the stability. The insertion of a draft tube in a conventional spouted bed overcomes the limitations of the spouted bed for improving gassolid contact. There are several advantages of using a draft tube in a conventional spouted bed:4-7 greater flexibility in the operation, lower gas flow and pressure drop, solids of any size or nature may be treated, narrower residence time distribution, better control of solid circulation, and a maximum spoutable bed height can be avoided. Consequently, solid circulation may be controlled by changing the column diameter, stagnant bed height, or particle diameter independently. Among the disadvantages, the following are worth mentioning: lower degree of mixing, complexity of design, risk of tube blockage, lower contact between gas and solids, lower heat and mass transfer, and longer recirculation time. Applications of conventional spouted beds with a draft tube cover a wide range of operations and chemical processes, including drying,8-20 combustion,6,21-23 pyrolysis of hydrocarbon,7,24,25 ultrapyrolysis of heavy oils,26 pneumatic conveying,27-29 pharmaceuticals,30-35 and mixing.36 In some papers, the results of the effect of a nonporous draft tube in conventional spouted beds, which have mainly focused on flow characteristics,37,38 particle circulation,5,39-45 and hydrodynamics,46-48 as well as spouting of finer particles,49 have been published. To widen the range of the bed stability in conical spouted beds, in this paper, the effect of the diameter of the nonporous draft tube and the height of the entrainment zone on the contactor inlet, as well as geometry factors of the contactor and operating conditions on the bed stability, have been analyzed in these contactors with a central draft tube. 2. Experimental Section The experimental unit design on a pilot scale has been detailed in previous papers.1,50,51 The blower supplies a maximum air * To whom correspondence should be addressed. Tel.: 34-946015362. Fax: 34-94-6013500. E-mail:
[email protected].
Figure 1. Geometric factors of the contactor and the draft tube.
flow rate of 300 Nm3/h at a pressure of 15 kPa. The flow rate is measured by means of two mass-flow meters in the ranges of 50-300 and 0-100 m3/h, with both being controlled by a computer. The blower supplies a constant flow rate, and the first mass-flow meter controls the air flow that enters the contactor (in the range of 50-300 m3/h) by acting on a motor valve that diverts the remaining air to the outside. When the flow required is 0.15 m, the spoutedbed regime is attained. By comparing beds with and without a draft tube, it is observed that, with a draft tube, the unstable spouted-bed state is not reached at any stagnant bed height. Furthermore, minimum spouting velocity is greater without this device and this difference is more pronounced as the stagnant bed height increases. Thereby, the draft tube stabilizes the bed and/or enhances the stable operating conditions. Therefore, spouted beds with draft tubes allow for working with any stagnant bed height under stable operating conditions. 3.3. Effect of the dd/D0 Ratio on the Stable Operation Conditions with a Central Draft Tube. The effect of the geometric factors of the contactor and of the draft tube in conical spouted beds has been observed by studying, separately, the systems in which the draft tube diameter dd is smaller than or equal to the gas inlet diameter D0, and the systems in which dd is bigger than D0. 3.3.1. Spouted Bed with a Draft Tube Diameter Greater than or Equal to the Gas Inlet Diameter (dd/D0 g 1). As an example of the experimental results of stability obtained when D0 is smaller than or equal to dd, in Figure 5, a diagram of H0 vs u has been plotted for an experimental system with a contactor angle of γ ) 33° and a gas inlet diameter of D0 ) 0.04 m, with a bed of glass spheres with a particle diameter of dp ) 4 mm. The draft tube diameter is dd ) 0.04 m, the draft tube length is ld ) H0 - hd, and it is located at a level of hd ) 0.05 m. As observed, the minimum spouting velocity increases as the stagnant bed height increases; nevertheless, this increase is less than that in the contactor without a draft tube, so the stability range increases by inserting a draft tube in the contactor. These results are in agreement with Konduri et al.,21 in a cylindrical
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Ind. Eng. Chem. Res., Vol. 46, No. 9, 2007
Figure 7. Operating maps. System conditions: γ ) 33° and D0 ) 0.03 m, with beds of glass spheres with a particle diameter of dp ) 4 mm; draft tube diameter, dd ) 0.04 m; and height of the entrainment zone, hd ) 0.05 m.
Figure 8. Operating maps. System conditions: γ ) 33° and D0 ) 0.04 m, with beds of glass spheres with a particle diameter of dp ) 4 mm; draft tube diameter, dd ) 0.04 m; and various heights of the entrainment zone ((a) hd ) 0.04 m and (b) hd ) 0.07 m).
Figure 6. Operating maps: (a) γ ) 45°, (b) γ ) 39°, (c) γ ) 36°, and (d) γ ) 28°. System conditions: D0 ) 0.04 m, with beds of glass spheres with a particle diameter of dp ) 4 mm; draft tube diameter, dd ) 0.04 m; and height of the entrainment zone, hd ) 0.05 m.
spouted bed with a conical base of 60°, that a draft tube expands the stable operating regime. On the other hand, as observed, for a draft tube diameter to the gas inlet diameter (dd/D0) ratio greater than or equal to unity, by increasing the gas velocity
over the corresponding to the minimum spouting velocity, the jet spouted-bed regime (dilute spouted-bed regime) is attained. In Figure 6, diagrams of H0 vs u have been plotted for contactor angles of γ ) 45°, 39°, 36°, and 28°, under the same experimental conditions as those described in Figure 5. In addition, at γ ) 33°, as the stagnant bed height increases, the air velocity increases and the spouted-bed regime is attained more easily. As observed, the decreasing contactor angle gives a decrease in air velocity. Figure 7 is a stability diagram of H0 vs u for a gas inlet diameter of D0 ) 0.03 m, under the same experimental conditions as those described in Figure 5. A comparison of Figures 5 and 7 shows that, as D0 decreases, the minimum spouting velocity necessary to reach the stable regime of
Ind. Eng. Chem. Res., Vol. 46, No. 9, 2007 2881
Figure 10. Operating maps. System conditions: γ ) 45° and D0 ) 0.06 m, with beds of glass spheres with a particle diameter of dp ) 4 mm. Draft tube dimensions of dd ) 0.04 m and hd ) 0.05 m. Table 2. Experimental Conditions of the Graphics of Figures 4-10
Figure 9. Operating maps. System conditions: γ ) 33° and D0 ) 0.04 m, with beds of glass spheres with a particle diameter of dp ) 4 mm; height of the entrainment zone hd ) 0.05 m; various draft tube diameters ((a) dd ) 0.05 m and (b) dd ) 0.06 m).
spouting decreases slightly; therefore, the range of operating conditions in the spouting regime is slightly greater. The effect of increasing the height of the entrainment zone is shown in Figures 5, 8a, and 8b, in diagrams of H0 vs u for a contactor angle of γ ) 33° and a gas inlet diameter of D0 ) 0.04 m, with a bed of glass spheres with a particle diameter of dp ) 4 mm; the draft tube diameter is dd ) 0.04 m, and the values for the height of the entrainment zone are hd ) 0.05, 0.04, and 0.07 m, respectively. A comparison of these figures shows that the extent of the length of the entrainment zone of the central draft tube of varying length increases the minimum spouting velocity, and, therefore, the stable spouted-bed zone is smaller. This result is consistent with the effect reported by Ishikura et al.7 for cylindrical spouted beds with an angle base of 60° with a porous draft tube. However, it is not consistent with the experimental results of Konduri et al.,21 because they reported that the height of the entrainment region did not have an important effect on the stable spouted-bed regime. The stability diagrams of H0 vs u for a conical contactor angle of γ ) 33° and a gas inlet diameter of D0 ) 0.04 m, with a bed of glass spheres with a particle diameter of dp ) 4 mm with central draft tubes set at a level of hd ) 0.05 m, with draft tube diameters of dd ) 0.04, 0.05, and 0.06 m, are shown in Figures 4, 9a, and 9b. The increasing central draft tube diameter gives way to a slight decrease in the range of operating conditions in the stable spouted-bed regime. This result agrees with the effect reported by Ishikura et al.7 for cylindrical spouted beds with an angle base of 60° with a porous draft tube. 3.3.2. Spouted Bed with the Draft Tube Diameter Smaller than the Gas Inlet Diameter (dd/D0 < 1). Figure 10 corresponds to the results obtained with a contactor angle of γ ) 45°, with a bed of glass spheres with a particle diameter of dp
figure
γ (deg)
D0 (m)
H0 (m)
dp (m)
dd (m)
hd (m)
4a 4b 5 6a 6b 6c 6d 7 8a 8b 9a 9b 10
45 45 33 45 39 36 28 33 33 33 33 33 45
0.05 0.05 0.04 0.04 0.04 0.04 0.04 0.03 0.04 0.04 0.04 0.04 0.06
0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20
0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004
0 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.05 0.06 0.04
0 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.04 0.07 0.05 0.05 0.05
) 4 mm and a gas inlet diameter of D0 ) 0.06 m (D0 ) Di); the draft tube diameter is dd ) 0.04 m and it is positioned at a level of hd ) 0.05 m, relative to the gas inlet. This figure proves that the use of the draft tube stabilizes the bed, because, under these conditions (for D0 ) Di), without this device, the spouting is unstable under all operating conditions used. On the other hand, comparing the spouted-bed regime zone of the systems of Figure 10 with those of Figure 4b, under the same experimental conditions (except the gas inlet diameter), it is observed that when the gas inlet diameter is greater than the central tube diameter, the increasing gas inlet diameter gives way to a decrease in the operating zone of the spouted-bed regime. In addition, for dd/D0 < 1, by increasing the gas velocity above that corresponding to the minimum spouting velocity, the diluted spouted-bed regime (the jet spouted-bed regime) is not attained, because, in this experimental system, the unstable spouted-bed regime is attained for gas velocities greater than that shown in the graphics of these figures. Table 2 summarizes the experimental conditions of Figures 4-10. The operating values of the draft tube diameter dd, relative to dp, which do not hinder particle flow in any form, have been determined experimentally. The ratio of the draft tube diameter to the particle diameter (dd/dp) must be within the range of 5-50, which also allows bed stability to be attained in the spoutingbed regime. The lower limit of the height of the entrainment zone hd has also been determined experimentally, and it is imposed by the minimum value of the ratio, hd/dp ) 10, to avoid hindrance in the particle flow. 3.4. Minimum Spouting Velocity of Conical Spouted Beds with a Central Draft Tube. The experimental values of the minimum spouting velocity for the spouting-bed regime, which
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Figure 11. Values of the (Re0)ms/Ar0.5 modulus calculated using eq 1 versus the stagnant bed height (H0). System conditions: γ ) 33°, D0 ) 0.03 and 0.05 m, with beds of glass spheres with a particle diameter of dp ) 4 mm. Central draft tube with dimensions of dd ) 0.04 m and hd ) 0.04, 0.05, and 0.07 m.
Figure 12. Values of (Re0)ms/Ar0.5 modulus calculated using eq 1 versus the stagnant bed height (H0). System conditions: γ ) 33°, 36°, and 45° and D0 ) 0.05 m, with beds of glass spheres with a particle diameter of dp ) 4 mm. Central draft tube with dimensions of hd ) 0.05 m and dd ) 0.04 and 0.06 m.
is expressed as the Reynolds number of minimum spouting, obtained in conical spouted beds with central draft tubes, have been fitted by the complex method for nonlinear regression to the following equation:
spouted beds and this improvement enlarges the range of operating conditions. The increase in bed stability that is attained with a draft tube is greater for systems in which the gas inlet diameter (D0) is smaller than or equal to the central tube diameter. For D0 bigger than the central tube diameter, the dilute spouted-bed regime (the jet spouted-bed regime) is not attained. The stability of conical spouted beds with a draft tube is dependent on the diameter of the draft tube (dd), as well as the height of the entrainment zone on the contactor inlet (hd). The length of the draft tube (ld) has been calculated as ld ) H0 hd. The ratio of the draft tube diameter to the particle diameter (dd/dp) must be between 5 and 50, so that particle flow in any form is not hindered and bed stability may be attained in the spouting-bed regime. The increase in the distance between the contactor base and the bottom of the draft tube, and in dd, gives way to an increase in the minimum spouting velocity, therefore decreasing in the range of operating conditions in the spoutingbed regime. It has been proven that, using an appropriate value of hd, the range of stable operating conditions in conical spouted beds with a draft tube is wider than that without a draft tube without any instability or operation drawbacks. The minimum value of the ratio ht/dp would be 10, to avoid hindrance of the particle flow. For a ratio of the draft tube diameter to the gas inlet diameter (dd/D0) of greater than or equal to unity, by increasing the gas velocity, the spouted-bed regime and the jet spouted-bed regime (dilute spouted-bed regime) are attained; however, for dd/D0 < 1, only the spouted-bed regime is attained. An original correlation for calculation of the minimum spouting velocity in conical spouted beds with central draft tubes, which takes into account the geometric design ratios of the draft tube (hd/H0, and dd/Di), a dimensionless modulus, which is valid for these contactors, as well as those without a draft tube, has been proposed. The importance of this correlation lies in the fact that it allows the calculation of the minimum spouting velocity in conical spouted beds with a central draft tube, because literature is scarce on this topic.
(Re0)ms ) 0.126Ar0.5
() [ Db D0
1.68
(γ2)]
tan
-0.57
(
) (
H0 - ld H0
0.45
)
Di Di - dd
0.17
(1)
where
dd e Ds D0 e Ds < Di ld ) H0 - hd and
hd g 10dp This equation includes not only the dimensionless modulus of the equation proposed by Olazar et al.1 for conical spouted beds without draft tubes, but also the dimensionless modulus the ratio of the height of the entrainment zone to the height of the conical section (hd/H0) and the ratio of the diameter of the draft tube to the contactor base diameter (dd/Di). This equation is valid for calculation of the minimum spouting velocity of stable beds in conical spouted beds not only with a draft tube but also without a draft tube. The regression coefficient of all the experimental data is r2 ) 0.97, and the maximum relative error is
