The influence of paste feed on the minimum spouting velocity

THE INFLUENCE OF PASTE FEED ON THE MINIMUM SPOUTING VELOCITY

P.I.Spitzner Neto¹, F.O.Cunha¹ and J.T.Freire²

¹PPG-EQ/UFSCar, ² DEQ/UFSCar,

Department of Chemical Engineering, São Carlos Federal University (UFSCar),

C.P. 676, CEP 13565-905, Phone [phone],

Fax [phone], São Carlos - SP, Brazil

E-mail: [e-mail]

(Received: April 19, 2001; Accepted: July 12, 2001)

Abstract - Due to the lack of reliable mathematical models for predicting the minimum spouting velocity in spouted bed dryers, in this work a new model is proposed that takes into account the effects of adhesive forces acting on particle agglomerates due to the presence of pastes. The results are compared with experimental data reported by Spitzner and Freire (2001), obtained by the continuous feeding of egg paste into a spouted bed, and with additional data obtained for batch feeding of glycerol into the same bed. The equipment was a conical spouted bed with a 0.05 m inlet diameter, a 60° cone angle, and a 0.21 m cone height. Glass spheres with a diameter of 2.6x10^-3 m were used as inert particles. It was observed that as saturation increases, the minimum spouting velocity increases for egg paste and decreases for glycerol. The results indicate that there are different forces acting on the bed of particles depending on the paste and operating conditions. The mathematical model provided good predictions only for egg paste, although the values for minimum spouting velocity were slightly overestimated.

Keywords: Spouted bed dryer, egg paste, glycerol, minimum spouting velocity, mathematical model.

INTRODUCTION

The spouted bed is a solid-fluid contact device that provides high solid circulation rates throughout the bed. Unlike that in fluidized beds, circulation has a well-defined pattern: solids ascend through a central cavity with high voidage, called the spout, and descend through the region between the spout and the wall of the bed, called the annulus, where the solids come into contact with each other and voidage is close to that of a fixed bed.

The spouted bed with inert particles has been used to dry pastes, such as suspensions and sludges. The paste is sprayed into the bed and covers the particles by forming a film. This film is dried with hot air, becomes fragile and is knocked off the surface of the particles by interparticle collisions.

Several authors have studied the fluid dynamic differences between the dry and the wet spouted bed. Some worked with a liquid, usually glycerol, that did not evaporate appreciably during the experiment. They injected a known volume of liquid into the bed to simulate the paste film effects. Patel et al. (1986), Schneider and Bridgwater (1993) and Passos and Mujumdar (2000) noted a reduction in pressure drop in the spout with an increase in glycerol content. However, they disagree about the behavior of minimum spouting velocity as a function of glycerol content.

Spitzner and Freire (2001) studied the fluid dynamics when a paste was continuously injected at a constant feed rate and dried in the spouted bed. They worked with bovine blood, homogenized egg and xanthan gum suspension and observed that while pressure drop in the spout decreased, the minimum spouting velocity increased as the paste feed rate was increased.

According to these authors, the increase in the interparticle adhesive force, due to the paste film, is the main reason for the variation in spouted bed behavior. The adhesive force is affected by particle properties (diameter, sphericity), the pastes surface tension and paste saturation in the bed. In batch tests paste saturation is easily measured. During continuous feeding, Barret and Fane (1990), who worked with skim milk, and Spitzner and Freire (2001), who worked with homogenized egg, obtained this parameter indirectly by sampling particles from the bed, washing them and measuring the mass of deposited solids. Spitzner and Freire (2001) obtained a function which related paste saturation to the egg feed rate. They also measured the film’s moistures content and observed that the film was formed of dried egg.

Efforts have been made to model the wet spouted bed. Barret and Fane (1990) proposed a qualitative model in which they noted that knowledge of paste saturation is as important as knowledge of the heat transfer coefficient. Schneider and Bridgwater (1993) adjusted an equation for the ratio between air spouting velocity in a wet spouted bed and saturation, using water, glycerol and alumina suspensions of low viscosities as pastes. Passos and Mujumdar (2000) suggested an empirical model for predicting minimum spouting velocity and pressure drop in the spout in terms of film thickness and annulus bed voidage and applied it to beds wetted with glycerol.

Based on a balance of forces, a model to estimate the minimum spouting velocity in wet spouted beds was developed in this work. The results were compared with experimental data obtained from batch tests using glycerol and with data from continuous tests with homogenized egg paste, reported by Spitzner and Freire (2001).

MATHEMATICAL MODELING

In the annulus of the spouted bed the inert particles are in contact with one another. For a wet bed, these particles can be considered as a big agglomerate, whose tensile strength affects the spouted bed dynamic. Consequently, in this model it was assumed that the lowest air velocity able to break the bond between the particles is the air velocity at the minimum spout. Under this condition, the tensile force caused by the air flow against the bed of agglomerated particles is the maximum tensile strength that this agglomerate endures before fracture. It is a function of the binding forces and liquid saturation (S), here defined as the rate between the liquid or paste volume and the pore volume in the spouted bed:

where e is the voidage, V_l the liquid or paste volume and V_p the volume of particles.

The model was developed for a conical spouted bed. The following assumptions are adopted for minimum spouting conditions:

1) the drag force required to spout the particles in a wet spouted bed is the sum of the drag force for the dry bed and the cohesive forces between the wetted inert particles;

2) the system obeys the Ergun equation;

3) the film which covers the inert particles is liquid and the wetted particles are bound by movable liquid bridges;

4) the inert particles are uniformly and completely covered by the liquid;

5) the curvature of the liquid bridge surface is almost circular; and

6) the volume of liquid in the bed is not big enough to change the dimensions and the voidage of the spouted bed.

Assuming that the particles are of a single size and spherical, Rumpf (1970) developed the following general formula for the tensile strength of these agglomerates (s_t):

where F_a is the adhesive force and d_p is the particle diameter.

According to the amount of liquid in the bed or the liquid saturation, the following classification, depicted in Figure 1, can be adopted.

According to Schubert (1977), when the liquid saturation is smaller than 0.3 (S_p) the agglomerate will be in the pendular state and when it is higher than 0.9 (S_c) it will be in the capillary state.

The maximum tensile force that can be transmitted by a movable liquid bridge consists of a boundary force at the solid-liquid-gas contact surface (F_b) and a force caused by the negative capillary pressure at the bridge (F_c). In the pendular state, these forces are expressed respectively by (Pietsch, 1997)

where a is the surface tension of the liquid and p_c is the capillary pressure. As illustrated in Figure 2, b is the particle wetting angle and d is the contact angle.

According to Schneider and Bridgwater (1993), the particle wetting angle can be approximated by

As the particles are completely wetted (assumption 4), d = 0 and the capillary pressure is calculated by

where R₁ and R₂ are the radii of curvature of the liquid bridge, which according to assumption 5, is almost circular. For a liquid bridge with a circular curvature, Passos and Mujumdar (2000) presented the following equation for the radii of curvature:

Adding Equations 3 and 4 and substituting Equations 5, 6 and 7 into the resulting expression the following equation is obtained for the adhesive force in the pendular state (F_ap):

Using Equation 2, the maximum tensile strength in the pendular state (s_tp) is obtained.

In the capillary state, only the capillary force is relevant for the adhesion force in the agglomerate, since the contact forces are negligible. As only the pores filled with liquid contribute to the strength, the maximum tensile strength (s_tc ) is determined by

In the funicular state, both pendular and capillary states coexist in the agglomerate, so Rumpf (1962) considered that both binding mechanisms can be superimposed and each one is independent of the other. Assuming that the fraction of pendular state in the agglomerate is 1 at saturation S_p and 0 at saturation S_c and that it decreases linearly, the maximum tensile strength (s_tf) is calculated by

The Ergun equation can be written as

where P is the pressure, U is the air velocity, h is the distance above the inlet and factors A and B are defined as

where m and r are the air viscosity and density, respectively.

The drag force, F_d, exerted by the air in an elemental volume of the bed with height dh and diameter D, located at distance h from the air inlet, is

According to Bi et al. (1997), for a conical bed, integration over the entire bed height (H) gives

where D_i is the inlet diameter, D_b is the diameter at the bed surface and U_i is the air velocity through the inlet orifice.

From assumption 1,

where F_d⁰ is the drag force for the dry bed.

Using Equation 2, the cohesive force between two particles in the wet bed is calculated. Multiplying it by the number of particles, the total tensile strength of the agglomerate of particles in the bed, F_t, is obtained.

where N_p is the number of particles.

Substituting Equations 15 and 17 into Equation 16, the following equation is obtained:

where U_mj,i is the minimum spouting velocity and U_mj,i is the minimum spouting velocity for the dry bed.

With the saturation estimated from Equation 1 and the assumed values of S_p and S_c, the distribution of liquid in the agglomerates is determined. The maximum tensile strength is calculated from Equations 2 and 8 for the pendular state, from Equation 9 for the capillary state, or from Equations 2, 8, 9 and 10 for the funicular state. With the minimum spouting velocity for the dry bed, the minimum spouting velocity for the wet bed is calculated.

MATERIALS AND METHODS

Materials and Equipment

The conical-cylindrical spouted bed used in this study is schematically shown in Figure 3. It consists of a cylindrical column 0.30 m in diameter and 0.90 m in height and a conical base with a height of 0.21 m and a 0.05 m air inlet diameter (60° cone angle).

Glycerol is a Newtonian colorless fluid, whose density at 50°C is 1260 kg/m³. Its surface tensions at different temperatures (Weast, 1971) can be seen in Table 1.

The bed of inert particles consisted of glass spheres with a diameter of 2.6x10^-3 m and a density of 2490 kg/m³.

Experimental Procedure

The experiments were performed for a static bed height of 0.21 m, or 9.4 kg of inert particles, using only the conical part to obtain a good particle circulation pattern over the bed. The bed temperature, measured at a height of 0.11 m and a radial position of 0.27 m from the wall of the bed, was 60°C. The inlet air temperature was 62-63°C.

Minimum spouting velocity (U_ms) and pressure drop in the spout (DP_s) were determined from the pressure drop vs. air velocity curve. Glycerol has a low vapor pressure and did not evaporate considerably during the tests. It was fed in batch mode at volumes of (1.8, 3.6, 7.3 and 11.8)x10^-5 m³.

Because the glycerol did not appreciably adhere to the walls of the bed and was not appreciably carried by the air, saturation was determined by Equation 1.

RESULTS AND DISCUSSION

For the dry spouted bed, the pressure drop in the spout (DP_s⁰) and the minimum spouting velocity (U_ms⁰) at a 60°C inlet air temperature were 1600 Pa and 16.1 m/s, respectively.

Figures 4 and 5 show the dimensionless pressure drop in the spout and the minimum spouting velocity as functions of saturation for glycerol and homogenized egg paste.

Saturation at the lowest egg paste feed rate studied by Spitzner and Freire (2001) was 0.07; therefore, the curves for this paste start at this value.

Figure 4 shows that pressure drop in the spout decreases as saturation increases for both egg paste and glycerol, agreeing with results from Patel et al. (1986), Schneider and Bridgwater (1993) and Passos and Mujumdar (2000), although their data were obtained with equipment of different shapes and dimensions and using different inert particles. However, in the present work, as saturation increases pressure drop in the spout first displays a slight increase until reaching a maximum value at S = 0.05 and then decreases. As the difference between the values for the maximum pressure drop in the spout and the pressure drop in the spout for the dry bed is smaller than the accuracy of the experiment, the DP_s/DP_s⁰ ratio was assumed to be constant for saturations ranging from zero to 0.05.

As the volume of residual paste volume increases, particle mobility in the annulus decreases, decreasing the number of particles in the spout and making air passage through it easier. Also, the available area for air flow in the annulus is reduced, thus increasing the proportion of air that passes through the spout. These two facts reduce DP_s/DP_s⁰ as saturation increases for both solid (homogenized egg paste) and liquid (glycerol) films.

Analysis of Figure 5 shows that the presence of paste makes the flow pattern in the spout unstable, so a higher air velocity should be necessary to sustain it. On the other hand, as reported previously, it decreases the number of particles in the spout, thus reducing the air velocity required to achieve a stable spout. The increase in air spout velocity is probably high enough to compensate for the flow instabilities if the film that covers the particles is liquid (glycerol), but not if it is solid (egg paste), justifying the different degrees of dependence of U_ms/U_ms⁰ curves on saturation, as observed in Figure 5.

As previously mentioned, Patel et al. (1986), Schneider and Bridgwater (1993) and Passos and Mujumdar (2000) worked with equipment and inert particles different from those used in this work. The data from Passos and Mujundar (2000) were obtained using particles similar to the ones used here (3.0x10^-3 m glass spheres), but they worked with a bidimensional spouted bed. Data from Patel et al. (1986) and Schneider and Bridgwater (1993) were obtained in a conical-cylindrical spouted bed with a diameter of half the size of the one used here, but while the data from Patel et al. (1986) were obtained using 4.1x10^-3 m PVC cylinders, the data from Schneider and Bridgwater (1993) were obtained using 5.0x10^-3 m glass spheres (almost two times the diameter of the glass spheres used here). Only the behavior reported by Patel et al. (1986) agrees with

that obtained in this work, probably because this behavior depends on the equipment and the inert particles. More studies with glycerol are necessary to reach a conclusion.

The variation in minimum spouting velocity with egg paste feed rate, calculated by the mathematical model, is presented in Figure 6 for the data reported by Spitzner and Freire (2001). As stated in assumption 3, in the model the egg paste film was supposed to behave like a liquid film and the surface tension of the apparent liquid bridge was assumed to be equal to the surface tension of the homogenized egg paste.

Qualitatively, the experimental curve is quite similar to that estimated by the model, but the calculated values are 10 to 17% higher than the experimental values. This could be occurring because the model overestimates the forces for the egg paste, either because, as the film is in fact solid, the dimensions of the apparent liquid bridges are underestimated resulting in overestimated capillary pressures or because Equations 5 and 7 are not accurate enough for this paste. More accurate equations could probably improve the estimates of minimum spouting velocity.

Figure 7 shows the comparison between the minimum spouting velocities calculated using the model and those obtained experimentally for glycerol.

The experimental data is not in agreement with that predicted by the model. It must be mentioned that the assumptions greatly simplify the physical process by assuming that the agglomerate of particles fractures uniformly throughout the bed when the spout arises; however, there are differences between the fracture mechanisms in the annulus and those in the spout. The model needs to be improved to consider these differences.

CONCLUSIONS

The results indicate that there are different forces acting on the inert particles depending on whether the film that covers the inert particles is liquid or solid. While for a solid film the minimum spouting velocity increases as saturation increases, for a liquid film this parameter decreases. However, due to the disagreement observed between the results obtained by other authors who worked with liquid films, it can be concluded that more careful experiments must be carried out. In contrast, the behavior of the pressure drop in the spout does not depend on the film, equipment or inert particle characteristics: it always decreases as bed saturation increases.

The assumptions of the model greatly simplify the complex processes involved in the drying of pastes; therefore, the mathematical model does not provide a good description of the process. For the liquid film tested, the behavior of the calculated minimum spouting velocity does not agree with the experimental results, and for the solid film the calculated parameters are overestimated. Additional theoretical studies must be developed to improve the model.

ACKNOWLEDGMENTS

The authors are grateful to CAPES, CNPq and PRONEX/ CNPq for their financial support.

NOMENCLATURE

a Distance between two particles (m) A Factor in Equation 12 (kg/m³s) B Factor in Equation 12 (kg/m⁴) d_p Particle diameter (m) D Diameter (m) D_b Diameter at the bed surface (m) D_i Inlet diameter (m) F_a Adhesive force (N) F_ap Adhesive force in the pendular state (N) F_d Drag force (N) F_d⁰ Drag force in the dry bed (N) F_b Component of the adhesive force caused by solid-liquid-gas contact (N) F_c Component of the adhesive force caused by negative capillary pressure (N) h Distance above the inlet (cm) H Bed height (cm) N_p Number of particles in the bed (-) p_c Capillary pressure (N/m²) R₁, R₂ Radii of curvature of the liquid bridge (m) S Saturation (-) S_c Minimum saturation for the capillary state (-) S_p Maximum saturation for the pendular state (-) U Air velocity (m/s) U_i Air velocity at the air inlet (m/s) U_mj,i Minimum spouting velocity at the air inlet (m/s) U_mj,i⁰ Minimum spouting velocity at the air inlet for the dry bed (m/s) V_l Liquid or paste volume in the spouted bed (m³) V_p Inert particles volume in the spouted bed (m³) W Paste feed rate (l/h) a Surface tension (N/m) b Particle wetting angle (-) d Contact angle (-) DP_s Pressure drop in the spout (Pa) DP_s⁰ Pressure drop in the spout for the dry bed (Pa) e Voidage (-) m Air viscosity (kg/m.s) r Air density (kg/m³) r_pt Paste density (kg/m³) s_t Tensile strength (N/m²) s_tc Maximum tensile strength in the capillary state (N/m²) s_tf Maximum tensile strength in the funicular state (N/m²) s_tp Maximum tensile strength in the pendular state (N/m²)

REFERENCES

Barret, N. and Fane, A., Drying Liquid Materials in a Spouted Bed. Drying’ 89, A.S. Mujumdar and M.A. Roques (Eds.), Hemisphere Publishing Corporation, New York (1990).

Bi, H.T., Macchi, A., Chaouki, J and Legros, R., Minimum Spouting Velocity of Conical Beds. The Canadian Journal of Chemical Engineering, 75 (1997).

Passos, M.L. and Mujumdar, A.S., Effect of Cohesive Forces on Fluidized and Spouted Beds of Wet Particles. Powder Technology, 110(3), 222-238 (2000).

Patel, K., Bridgwater, J., Baker, C.G.J. and Schneider, T., Spouting Behavior of Wet Solids. Drying`86, A.S. Mujumdar (Ed.), Hemisphere Publishing Corporation, New York (1986).

Pietsch, W.B., Size Enlargement by Agglomeration. Handbook of Powder Science and Technology, 2^nd edition, M.E. Fayed and L. Otten (Eds.), International Thomson Publishing, New York (1997).

Rumpf, H., The Strength of Granules and Agglomerates. John Wiley, New York (1962). In: Pietsch, W.B., Size Enlargement by Agglomeration. Handbook of Powder Science and Technology, 2^nd edition, M.E. Fayed and L. Otten (Eds.), International Thomson Publishing, New York (1997).

Rumpf, H., Zur Theorie der Zugfestigkeit von

Agglomerate bei Kraftübertragung an Kontaktpunkten. (1970). In: Pietsch, W.B., Size Enlargement by Agglomeration. Handbook of Powder Science and Technology, 2

^nd edition, M.E. Fayed and L. Otten (Eds.), International Thomson Publishing, New York (1997).

Schneider, T. and Bridgwater, J., The Stability of Wet Spouted Beds. Drying Technology, 11(2) (1993).

Schubert, H., Tensile Strength and Capillary Pressure of Moist Agglomerates. Agglomeration 77, K.V.S. Sastry (Ed.), Port City Press, Inc, Baltimore (1977).

Spitzner, P. I. and Freire, J. T., Effect of the Presence of Paste in a Conical Spouted Bed Dryer With Continuous Feeding. Drying Technology, in press (2001).

Windholz, M., The Merck Index – An Encyclopedia of Chemicals and Drugs. 12^nd edition, Merck & Co., Inc (1996).

Weast, R., Handbook of Chemistry and Physics. 52^nd edition, The Chemical Rubber Co., Cleveland (1971).

Publication Dates

• Publication in this collection
  10 Oct 2001
• Date of issue
  Sept 2001

History

• Received
  19 Apr 2001
• Accepted
  12 July 2001