SciELO - Scientific Electronic Library Online

vol.18 issue3PrefacePerformance of cylindrical-conical cyclones with different geometrical configurations author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand




Related links


Brazilian Journal of Chemical Engineering

Print version ISSN 0104-6632On-line version ISSN 1678-4383

Braz. J. Chem. Eng. vol.18 no.3 São Paulo Sept. 2001 



C.P.Narimatsu1 and M.C.Ferreira2
1Graduate Program of Chemical Engineering, 2 Chemical Engineering Department,
Universidade Federal de São Carlos (UFSCar), PO. Box 676, 13569-265,
Phone 55-16-260-8264, Fax: 55-16-260-8266, São Carlos - SP, Brazil,


(Received: April 19, 2001 ; Accepted: June 9, 2001)



Abstract - In this work, the effects of particle size and density on the fluid dynamic behavior of vertical gas-solid transport of Group D particles in a 53.4 mm diameter transport tube were studied. For the conditions tested, the experimental curves of pressure gradient versus air velocity presented a minimum pressure gradient point, which is associated with a change in the flow regime from dense to dilute phase. The increases in particle size from 1.00 to 3.68 mm and in density from 935 to 2500 kg/m3 caused an increase in pressure gradient for the dense-phase transport region, but were not relevant in dilute transport. The transition velocity between dense and dilute flow (Umin) also increased with increasing particle density and diameter. An empirical equation was fitted for predicting transition air velocity for the transport of glass spheres. Additional experiments, covering a wider range of conditions and particles properties, are still needed to allow the fitting of a generalized equation for prediction of Umin.
Keywords: pneumatic conveying, coarse particles, flow regimes, transition velocity.




Pneumatic conveying is used to transport a wide variety of powders or granular solids in a gas stream. A review by Marcus et al. (1990) provides an extensive list of ca. 300 types of materials suitable for pneumatic conveying with remarkably different particle properties, such as size, size distribution, shape, density and surface hardness. The fluid dynamic behavior of gas-solid suspension plays an important role in defining the performance of a pneumatic transport bed, and aspects such as the transport flow regime, pressure loss and slip velocity are strongly affected by the characteristics of the solids and transport tube and by operational conditions. The prediction of parameters such as the transition velocity between dense and dilute flow, the suspension voidage and the interaction forces acting between the phases is also dependent on empirical correlations, for no author has been successful in proposing general models that take into account all the variables involved. Therefore, experimental research is essential in defining how the fluid dynamic behavior of gas-solid transport is affected by the properties of the solids and by the riser characteristics.

Several aspects of gas-solid suspension behavior in tubes of different sizes and materials under a variety of operational conditions are reported in the literature (Ravi Sankar and Smith, 1986; Laouar and Molodtsof, 1998; Molerus and Heucke, 1999; Costa et al., 2000). However, relatively little work has been conducted concerning the effects of the physical properties of the particles on the fluid dynamics of the system, and contradictory results are often reported. Ravi Sankar and Smith (1986) suggested that the effect of particle density appears to be of little significance in comparison with the effect of particle size on slip velocity for the vertical transport of glass beads, sand and steel shots (for particle sizes varying from 96 to 637 mm).

Jiang et al. (1994) studied the influence of particle size on the fluid dynamic characteristics for the transport of low density polymeric particles (660 kg/m3) and a mean size ranging from 90 to 500 mm. For comparison, experiments with FCC (dp=89 mm) and glass beads (dp=2000 mm) and with mixtures of different particles were also carried out. The results indicated a significantly wider operating range for the fast fluidization regime and enhancement of fine particle holdups in a bed with coarse particles. A mechanistic model considering particle-particle collision was proposed (Jiang et al.; 1994) to explain the enhancement of fine particle holdups observed experimentally.

For the vertical transport of glass spheres with diameters varying from 64 to 210 mm, Rautiainen and Sarkomaa (1998) observed that the solid-wall friction factors attain a constant value at high air velocities, but the parameter varies with particle diameter. With the coarser particles the solids friction factor increases when the solids velocity decreases and for the smallest particles it decreases smoothly with the decreasing solids velocity. The authors could not detect the influence of particle diameter on transition air velocity between dense- and dilute-phase flows, but verified that this velocity increases with increasing solids flow rates.

The transport of several types of coarse particles in horizontal tubes was studied by Molerus and Heucke (1999). In order to understand how particle-fluid interactions affect flow regime and pressure loss in pneumatic transport, the authors carried out experiments in which several significant parameters were varied, including diameter of the transport tube, static pressure, particle and fluid densities, particle size and gas and solids flow rates. From all the parameters studied, particle size was found to be the least relevant.

The effect of both particle density and size on the distribution of solids in the riser of a circulating fluidized bed and on the radial profiles of solids mass flux was studied by Mastellone and Arena (1999), who worked with particles from groups A and B of Geldart’s classification (ballotini spheres, sand and FCC) with Sauter mean diameters from 67 to 310 mm. They observed that the influence of particle density and diameter was remarkable only in the entrance region of the transport tube. They also observed that the coarser particles gave flatter radial profiles with no solids flowing downwards at the walls and that under similar operating conditions the transport flow regime could be substantially different for different solids.

The short literature review presented here shows that the lack of experimental data is even more remarkable for the transport of coarse particles. The present study aims to study the effect of operating conditions and of the physical properties of the particle on some the aspects of fluid dynamic behavior in the vertical transport for particles from group D in Geldart’s classification. Five materials were selected in order to study the effects of particle size and density on fluid dynamic behavior separately: glass spheres with four different diameters and low density polypropylene particles with a diameter equal to that of one of the glass particles. Particular attention was paid to the transition velocity between dense- and dilute-phase conveying and also to pressure loss, mean voidage and length of entrance region established in the process.



The apparatus used in the experiments is shown in Figure 1. Particles were conveyed through a 53.4 mm galvanized iron pipe 3.0 m long (1). Air was supplied to the system by a 7.5 HP blower, and its volumetric flow rate was measured with an orifice flow meter. Solids were introduced into the transport tube by means of a 45o angle inclined screw feeder (2). A glass window was placed slightly above the solids entrance region to allow visual observation of the flow and the transport tube was grounded to minimize electrostatic effects.



After being pneumatically transported, the particles return through a standpipe (3), which was kept filled with solids while in operation. The gas flow rates through it were estimated using the Forchheimer equation, with the pressure drop measured between two positions of the standpipe. The gas flow rates in the transport tube were then obtained from a mass balance that considered the difference between the air supplied by the blower and the air deviated to the standpipe, which in most cases was negligible.

The solids flow rates were measured by diverting the flow and collecting the solids in the sample collector (4), which is described in detail in Silva (1997). The static pressures along the transport tube were measured at seven points by pressure taps (5) connected to U-type manometers.

Mean voidage at the transport tube was measured by means of two pneumatically operated traps (6) which closed off a 2.05 m long section of the tube, located above the acceleration region, estimated in preliminary tests. The solids accumulated at the bottom trap were collected and weighed, providing the average voidage. The accuracy of the voidage measurements was estimated as ± 0.15 % (Ferreira, 1996).

Air velocity was initially fixed at a maximum value, and fluid dynamic measurements were carried out. For a fixed air velocity, the solids flow rates were varied by changing the screw rotating velocity over the whole possible range; then the gas velocity was slowly decreased and the experimental procedure repeated until achieving a condition for which transport ceased.

Properties of the materials tested are listed in Table 1. Polypropylene particles (with a sphericity of 0.93) and a spherical glass particle having the same mean diameter but different densities were tested, as were spherical glass particles of three different mean diameters (the glass particles were sifted between two successive sieves and the mean diameter quoted here is the average of the sieve openings). The terminal velocity of the particles was estimated from a correlation proposed by Haider and Levenspiel (1989).



In Table 2 the range of experimental conditions studied is illustrated.




It is known that the performance of the solids feeding system may affect the fluid dynamic characteristics either by introducing instabilities in the entrance region or, particularly in the case of the screw feeder, by affecting particle properties due to attrition effects. Since it was not possible to optimize the screw feeding system for each particle tested, the performance of each was checked. In Figure 2 typical curves of solids flow rate as a function of air velocity, obtained for 1.00 mm spherical glass particles, are shown.



The solid lines in Figure 2 represent the mean values of solids flow rate at each screw rotating velocity, calculated from the individual measurements under each condition. The mean relative deviations (Erm) were calculated by the following equation:

For the 1.0 mm glass particles, Erm was less than 5.1 %, thus indicating that the screw feeder provided an excellent control of the solids flow rate. The performances of the other particles tested were similar, with the greatest relative mean deviations being 5.1 % for the glass spheres and 5.8 % for the polypropylene beads. According to Table 2, the range of solids flow rates provided by the feeder does not change with particle diameter, but it is strongly reduced when the polypropylene particles are used. Even though the glass spheres are subjected to some attrition in the process, their mean diameters were not significantly altered after being transported.

Typical curves of pressure profiles for several air velocities obtained for the transport of glass spheres and polypropylene beads at a fixed solids flow rate are shown in Figures 3 (a) and 3 (b) respectively.





Figure 3 shows that static pressure decreases with decreasing air velocity until reaching a critical value of U, at which point such behavior changes to show a slight increase with increasing air velocity (the changes occur at U=11.86 m/s for polypropylene and at U=16.16 m/s for glass particles). The maximum value of the range of air velocities studied was limited by blower capacity, while the lower values were set by the minimum air velocity required to transport the particles.

In dilute-phase flow, which occurs for high air velocities, pressure loss decreases as air velocity is reduced. The continuous decrease in transport air velocity at a constant solids mass flux causes a simultaneous decrease in pressure loss due to fluid-wall friction and an increase in solids holdup. As a result, the contribution of friction forces to the total pressure loss is reduced, while the contribution of solids weight, a force that acts on the whole volume of particles, is increased. When the increase in weight overcomes the reduction in friction loss, static pressure in the tube begins to increase.

The length of the acceleration region in the transport tube is characterized by the presence of velocity gradients, since solids and fluid are introduced into the transport tube at very different velocities and the momentum transfer requires an entrance length to be stabilized. This acceleration length can be obtained experimentally by identifying the nonlinear region in the curves of P versus z (Ferreira et al., 1996). It can be noted in Figure 3 that a linear behavior is observed for z greater than 0.83 m, and the first and second points show a clear deviation from this linearity. For the conditions studied in this work, no clear dependence on either the solids flow rate or on the particle density and diameter could be detected. In fact, for all the conditions studied a linear behavior was observed for values of z greater than 0.83 m. It must be noted that the dependence of acceleration length on particle properties (particularly particle density) was expected because such variables should affect the gas-solid momentum transfer. Although the discontinuities observed in the transition from the nonlinear to the linear regions seem to be more accentuated for the glass particles when compared to polypropylene, the methodology based on pressure profiles does not seem sufficiently sensitive to detect differences in acceleration length.

The pressure gradient for each run was obtained from a linear fitting of the curves of P versus z, neglecting the first two points. The fittings always provided correlation coefficients greater than 0.99. Typical curves of pressure gradient versus air velocity are shown in Figures 4 (a) to 4 (c) for glass particles with diameters of 1.00; 2.05 and 2.85 mm respectively.

The curves depicted in Figure 4 reproduce the same qualitative behavior. Considering a fixed solids flow rate, the pressure gradient initially decreases with increasing air velocity until a minimum point is reached, which is followed by a region in which the curve behavior changes and the pressure gradient increases with increasing air velocity. The curves of pressure gradient versus air flow rate at constant solids flow rate are adopted by several authors as a criterion for identifying the flow regime (Marcus et al., 1990; Pan, 1999). The region to the right of the minimum point of the pressure gradient is usually referred to as dilute-phase transport and the region to the left is called dense-phase transport. Air velocity at the minimum point is the minimum velocity at which dilute flow can be achieved and is adopted as the transition velocity between these two flow modes. The change in behavior of (-dP/dz) versus U curves is again caused by the increase in solids holdup and the decrease in gas-wall friction, as previously discussed in the analysis of Figure 3. In this work, the occurrence of dilute- and dense-phase flow conditions was observed for all the conditions studied. The change in flow regime could also be qualitatively noted by monitoring the intensity of oscillations in the water columns of U-type manometers connected to the transport tube. For the highest air flow rates no oscillations were detected, but as air velocity was reduced the water columns of the manometers started to increase, and for the lowest air velocities, oscillations reached up to ± 2.0 cm, depending on the operational conditions.

Figure 4 shows that in the transport of glass particles, the pressure gradient increases as the solids flow rate is increased as a result of the increase in solids holdup and weight force. For comparison, curves of (-dP/dz) versus U obtained for the flow of air without particles are also shown.

Air velocity at the minimum pressure gradient (Umin) was obtained from the minimum point on each curve (-dP/dz) versus U. Identification of the minimum point depends partly on individual judgement, and for some conditions it could not be clearly done. In such cases a polynomial equation was fitted for those data and the value of Umin was obtained by differentiating the equation and making it equal to zero. The minimum pressure conditions are indicated by the + symbol on the curves in Figure 4. Values of Umin varied from 12.60 to 14.00 m/s for glass spheres with dp=1.00 mm, from 16.47 to 17.20 m/s for dp=2.05 mm and from 19.15 to 20.00 m/s for dp=2.85 mm. Since the solids flow rate varies within similar ranges, the results indicate that the range of air velocities that allow transport in dilute-flow conditions is reduced when particle diameter is increased. This finding may be explained by the pressure loss caused by the slip between the phases, which tends to increase as the particle areas are increased.

Authors such as Rautiainen and Sarkomaa (1998) and Marcus et al. (1990) report that an increase in the solids flow rates results in higher values of Umin. In most cases this was also observed in the present experimental data, and the uncertainties involved in determination of Umin probably justify the discrepancies observed for some conditions.

The values of mean voidage in the transport tube as a function of air velocity at constant solids flow rate are depicted in Figures 5(a) to 5(c) for the transport of spheres with diameters of 1.00, 2.05 and 2.85 mm respectively.

For all the conditions studied, the mean voidage was larger than 0.980 and reached values up to 0.999. Although such a range is considered typical of a dilute-phase transport (Leung, 1980), the pressure gradient versus air velocity curves depicted in Figure 4 clearly show the presence of two different transport flow regimes, thus indicating that mean voidage cannot be used alone to define the flow regime. The qualitative dependence of voidage on air velocity supports the assumption of changes in the transport flow regimes. Analysis of Figure 5(a) for instance shows that voidage displays an initial steep increase with air velocity between 8.9 and 13.0 m/s, but for air velocity greater than 14.0 m/s its variation is very small. Similar behaviors are observed for the 2.05 and 2.85 mm glass spheres (Figures 5(b) and 5(c)). The change in regime patterns can be attributed to the increase in resistive forces caused by increasing solids concentration in the transport tube when air velocity is reduced at constant solids flow rates. A comparison between Figures 4 and 5 for any given particle diameter shows that the range of air velocities at which voidage displays a steep increase is located on the left of the minimum pressure point (dense-phase flow), while the region of nearly constant voidage is located to the right (dilute-phase flow). The transition point on these curves, however, is not well defined and also depends on individual judgment.

In order to compare particles of different densities, Figure 6 shows data on pressure gradient versus air velocity for glass and polypropylene particles with the same mean diameter.



It can be noted that due to their low density, pressure gradient for polypropylene particles is only slightly dependent on solids flow rate. By comparing data obtained at identical solids flow rates (ws=0.037 kg/s), one notes that in the dilute-phase flow the pressure gradients are practically the same, i.e., particle density does not affect the dilute-phase flow transport. Such results are consistent with those reported by Ravi Sankar and Smith (1986), who found that the effect of particle density appears to be of little significance in comparison with the effect of particle size for the whole range of solids concentrations studied by them, which includes dilute- and dense-phase flows.

The positions of minimum pressure gradient points (indicated by the + symbol in Figure 6) are affected by particle density, with Umin values for polypropylene particles varying from 11.24 to 16.46 m/s, which are much lower than those obtained for glass spheres (from 19.28 to 22.23 m/s). As the terminal velocity of polypropylene particles is about 70% of the value of the terminal velocity of the glass sphere with the same diameter (see Table 2), transport under dilute-flow conditions is expected to occur within a wider range of air flow rates for such particles. This can also be observed by a comparison between the curves of voidage versus air velocity for glass and polypropylene particles shown in Figure 7. It can be seen that voidage varies within the same range for both particles, but the region in which voidage remains constant begins at a lower air velocity for polypropylene and the curves are shifted to the left.



A comparison between the pressure gradients obtained for glass particles of different diameters is shown in Figures 8(a) to 8(c) . To allow a comparison, each plot was drawn by picking data with solids flow rates which were as close as possible. It must be noted that the accuracy of solids flow rate measurements in this case is about ± 5.0%.

For the conditions studied here, no effect of particle diameter on pressure gradient in the region of dilute-phase flow was detected, in agreement with the results reported by Mastellone and Arena (1999) and Molerus and Heucke (1999) but in contrast to the observations of Ravi Sankar and Smith (1986). It should be mentioned that the latter authors employed particle diameters that are very different from those in this work.. Most of their particles are from group B in Geldart's diagram or are in the limiting region between groups B and D (particle diameters varying from 96 to 644 mm).

In the dense-phase region, pressure gradient increases significantly with increasing particle diameter. Due to the reduction in air flow rate, in this flow regime the solids concentrations are higher than they are in dilute-phase flow, and percolation of the solids by the air flow becomes more difficult. The fluid dynamics therefore tends to be more sensitive to variations in the properties of the solids. As particle diameter is increased, the terminal velocity and the superficial area of the particle increase, so the slip force between the gas and solid phases and the energy required to transport the solids also increase. Such factors also justify the higher values of Umin observed in Figure 6 as particle diameter is increased.

The prediction of minimum air velocity is important to define the range of velocities that allows transport in dilute- or dense-phase flows. Rizk (1986) suggested an empirical equation to estimate Umin that takes into account the influence of geometric parameters (such as particle diameter and transport tube diameter) and operational conditions (such as solids and air flow rates), given by

where d and c are parameters that vary linearly with particle diameter, with coefficients fitted from experimental data.

When equation (2) was applied to experimental data from this work, the estimates of Umin showed high discrepancies when compared to experimental values. This probably occurred because the operational conditions and geometric properties studied by Rizk (1986) are very different from those employed here. So data obtained for glass particles in this work were used to fit new coefficients to estimate parameters d and c . The following equations were obtained:

A comparison between the predicted and experimental values of Umin is shown in Table 3. The deviations between predicted and experimental values varied from 0.21 to 8.22 %.



The qualitative dependence of Umin on the operational conditions and geometric parameters is well described by the equations, i.e., minimum velocity increases with increasing solids flow rate and particle diameter. However, they did not provide good predictions when applied to polypropylene particles, probably because particle density was not considered in the equations. Besides particle density, other variables, such as the shape of particles and the presence of electrostatic effects (Jiang et al., 1994), may affect Umin. Therefore additional experiments, for a wider range of conditions and particles properties, are still needed to allow the fitting of a generalized equation for prediction of Umin.



The effects of particle size and density on the fluid dynamic behavior of vertical gas-solid transport of Group D particles in a 53.4 mm diameter transport tube were studied for five types of solids. For the conditions studied, no influence of the physical properties of the particles on the length of entrance region was detected. The mean voidage measured in the transport tube varied from 0.986 to 0.999 under the whole range of operational conditions and did not depend on particle density or diameter. The high voidage values even for dense phase transport indicate that this variable cannot be used alone to characterize a flow regime. All the curves of pressure gradient versus air velocity, however, presented a minimum pressure gradient point, which is associated with a change in the flow regime from dense to dilute phase. Particle size and density affected pressure gradient only for the dense-phase transport region, where pressure gradient increased with increasing particle diameter from 1.00 to 3.68 mm and density from 935 to 2500 kg/m3. In this range particle properties did not seem to be relevant under dilute-phase flow conditions. The transition velocities between dense- and dilute-phase flow increase with increasing particle density and diameter as a result of the greater slip force required to transport heavier and larger particles. The fitted equation for predicting minimum velocities is limited to transport of glass particles in the range of diameters studied. A more generalized empirical equation should include additional parameters such as particle density and shape, which could not be taken into account with the data available up to now.



dp Particle diameter mm
Dt Transport tube diameter m
-dp/dz Total pressure gradient in transport tube Pa/m
Erm Relative mean deviation (-)
Fr Froude number, U/(gDt)0.5 (-)
g Gravitational acceleration m/s2
p Static pressure N/m2
U Superficial air velocity m/s
Umin Superficial air velocity at minimum pressure drop m/s
Ut Terminal velocity of a falling particle m/s
wf Air flow rate kg/s
ws Solids flow rate kg/s
z Axial distance in the transport tube M
Greek Symbols
e Mean voidage (-)
rf Air density kg/m3
rp Particle density kg/m3
c Coefficient defined by Equation (3) (-)
d Coefficient defined by Equation (4) (-)



The authors thank the Brazilian funding agencies CAPES, PRONEX/CNPq (proc. no 66.418080/1996-5) and FAPESP (proc. no 2000/05920) for their financial support.



Costa, I.A.; Ferreira, M.C. and Freire, J.T., Analysis of the Performance of a Spouted Bed Used as Solid Feeding System in a Pneumatic Dryer. Proceedings of 12th International Drying Symposium, edited on CD-ROM (paper no. 105), Noordwijkerhout - Netherlands (2000).        [ Links ]

Ferreira, M.C., Desenvolvimento de um Leito Pneumático com Alimentador Tipo Jorro. Ph. D. diss., Federal University of São Carlos, São Carlos, Brazil (1996).        [ Links ]

Ferreira, M.C., Silva, E.M.V. and Freire, J.T., Mean Voidage Measurements and Fluid Dynamics Analysis in a Pneumatic Bed with a Spouted Bed Type Solid Feeding System. Braz. J. Chem. Eng., vol. 13, no 1, pp. 29-39 (1996).        [ Links ]

Haider, A. and Levenspiel, O., Drag Coefficient and Terminal Velocity of Spherical and Non-Spherical Particles. Powder Technology, vol. 58, pp. 63-70 (1989).        [ Links ]

Jiang, P, Bi, H, Liang, S.C. and Fan, L.S., Hydrodynamic Behavior of Circulating Fluidized Bed with Polymeric Particles. AIChE Journal, vol. 40, no 2, pp. 193-205 (1994).        [ Links ]

Laouar, S. and Molodtsof, Y., Experimental Characterization of the Pressure Drop in Dense Phase Pneumatic Transport at Very Low Velocity. Powder Technology, vol. 93, pp. 165-173 (1998).        [ Links ]

Leung, L.S., The Ups and Downs of Gas-Solid Flow – A Review. In: Fluidization (Eds. Grace, J.R., Matsen, J.M.), New York, Plenum Press, pp. 25-68 (1980).        [ Links ]

Marcus, R.D., Leung, L.S., Klinzing, G.E. and Rizk, F., Pneumatic Conveying of Solids: a Theoretical and Practical Approach. 1st ed. Great Britain, St Edmundsbury Press (Powder Technology Series) (1990).        [ Links ]

Mastellone, M.L. and Arena, U., The Effect of Particle Size and Density on Solids Distribution Along the Riser of a Circulating Fluidized Bed. Chemical Engineering Science, vol. 54, pp. 5383-5391 (1999).        [ Links ]

Molerus, O. and Heucke, U., Pneumatic Transport of Coarse Grained Particles in Horizontal Pipes. Powder Technology, vol. 102, pp. 135-150 (1999).        [ Links ]

Pan, R., Materials Properties and Flow Modes in Pneumatic Conveying. Powder Technology, vol. 104, pp. 157-163 (1999).        [ Links ]

Rautiainen. A. and Sarkomaa, P., Solids Friction Factors in Upward, Lean Gas-Solids Flows. Powder Technology, vol. 95, pp. 25-35 (1998).        [ Links ]

Ravi Sankar, S. and Smith, T.N., Slip Velocities in Pneumatic Transport, part I. Powder Technology, vol. 47, pp. 167-177 (1986).        [ Links ]

Rizk, F., Principles of Pneumatic Conveying. Encyclopedia of Fluid Mechanics, Gulf Publishing Company, Houston, Texas, vol. 1, pp. 311-348 (1986).        [ Links ]

Silva, E.M.V., Desenvolvimento e Análise Fluidodinâmica de um Sistema de Transporte Pneumático Vertical com Alimentadores Tipo Jorro e Parafuso de Rosca Sem Fim. Ph. D. diss., Federal University of São Carlos, São Carlos, Brazil (1997).        [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License