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Ind. Eng. Chem. Res. 2002, 41, 5316-5320
GENERAL RESEARCH Pressure Drop in a Vertical Pneumatic Conveying of Iron Ore Won Namkung* and Minyoung Cho Smelting Reduction Research Team, Research Institute of Industrial Science & Technology (RIST), Pohang, 790-330 Kyungbuk, Korea
The pneumatic conveying characteristics in a vertical tube have been determined using iron ore particles. A pressure drop decreases as the height increases along the accelerating region, while it remains constant at all heights in the fully developed region. An axial pressure drop increases with increasing solids circulation rate at a constant gas velocity. The model is proposed to calculate the axial pressure drop and accurately predicts the experimental axial pressure drop profile. 1. Introduction A knowledge of pressure drop, particle velocity, and friction factor is needed to understand gas-solid flow characteristics in pneumatic conveying lines. Among them, the information of pressure drop is very important to design the pneumatic conveying system successfully.1 Concerns about the acceleration zone are increasing with the recent application of pneumatic conveying for solids over short distances.2 In the acceleration zone, the rates of heat and mass transfer between gas and particles are very high, so that drying rates per unit length are far higher in this region than in the steadystate zone.3 For short pneumatic conveying lines, the knowledge of acceleration length and pressure drop in the acceleration zone is very important in designing practical equipment for suspension flow because the solids are collected before they reach the steady-state condition. The pressure drop and acceleration length can be calculated using the axial pressure drop profile. Although much work has been carried out to calculate the total pressure drop,4,5 studies to predict the axial pressure drop, including the acceleration zone in vertical pneumatic conveying lines, are rare. In this study, pneumatic conveying characteristics have been determined using iron ore particles, and a model to predict axial pressure drop has been proposed. 2. Experimental Section The experimental apparatus is shown in Figure 1. It consists of a vertical pneumatic conveying line (riser), cyclone, hopper, and loop-seal. The stainless steel riser has a diameter of 0.078 m and a height of 6.0 m. Initially, the bottom section of the riser (from distributor to 2.0 m high) was made of a transparent column to observe gas-solid flow before it was changed into the stainless steel. The solid particles used in this study are iron ore with a mean diameter of 338 µm and an apparent density of 4500 kg/m3. The entrained particles * Corresponding author. Telephone: 82-54-279-6492. Fax: 82-54-279-6669. E-mail:
[email protected] Figure 1. Experimental apparatus: 1, riser; 2, cyclone; 3, hopper; 4, loop-seal; 5, three-way valve; 6, sampling tube; 7, bag filter.
from the riser were collected by the cyclone and stored in the hopper. A bag filter trapped the particles not collected in the cyclone. The solid particles from the hopper were transferred into a loop-seal through a downcomer and were fed to the riser through a loopseal with regulation of solids circulation rate by aeration. The superficial gas velocity and the solids circulation rate (Ws) were varied in the range 8.7-23.3 m/s and 0-1.0 kg/s, respectively. The solids circulation rate was determined by measuring the descending time of particles along the known distance in the transparent measuring column. The pressure transducers were connected to pressure taps along the column height to measure pressure drops between the different locations in the bed. The pressure signals from the pressure transducer were amplified and sent via an A/D converter to a personal computer for recording.
10.1021/ie020178p CCC: $22.00 © 2002 American Chemical Society Published on Web 09/20/2002
Ind. Eng. Chem. Res., Vol. 41, No. 21, 2002 5317
Figure 3. Comparison of pressure drops measured at the fully developed region and the exit region.
can be seen, the increase of the pressure drop due to the reflux of particles at the exit region largely decreases with increasing gas velocity at a similar solid circulation rate. At a relatively low gas velocity, the reflux particles at the exit region go downward near the wall region. However, at certain heights, downward particles are reentrained by the shearing action of the upward flowing gas.7 If the gas velocity is very high, although some particles have reflux flow at the exit region, the refluxed particles may be re-entrained immediately by the shearing action of the high upward flowing gas. In this study, the end effect is not observed at high gas velocity (>Ug ) 17.0 m/s). Pneumatic conveying can be divided into two regions: one is a dense phase conveying or core-annulus flow region where downflow of particles is observed, and the other is a dilute phase conveying or uniform flow region. Bi and Fan8 proposed a correlation to predict the boundary velocity between two regions as
UPT ) 10.1(gdp)0.347 Figure 2. Axial pressure drop profiles with variations of gas velocity and solid circulation rate.
3. Results and Discussion The axial pressure drop profiles with variations of gas velocity (Ug) and solid circulation rate (Ws) are shown in Figure 2. As can be seen, the pressure drop increases with increasing Ws at constant Ug. Because of the particle acceleration, the pressure drop at the bottom region of the riser decreases with increasing height to a fully developed region where it has a constant value irrespective of increasing height. As shown in Figure 2A and B, at relatively lower gas velocities, the pressure drops in the top part of the riser increase along with the riser height because of the end effect as observed in circulating fluidized bed (CFB) studies.6,7 With an abrupt exit structure, the entrained particles are separated when the particle laden gas impacts the top dead end of the riser. This results in a considerable internal particle reflux along the riser walls and a consequent increase in the pressure drop in the top section of the riser. The pressure drops measured at the fully developed region and the exit region are shown in Figure 3. As
() () Gs Fg
0.310
dp D
-0.139
Ar-0.021 (1)
Equation 1 covers the range of variables 31 e dp (µm) e 1910, 660 e Fs (kg/m3) e 4510, 0.02 e Dt (m) e 0.2, and 1.35 e Gs (kg/m2‚s) e 225. In this study, the calculated transition velocity is in the range 7.0-10.0 m/s depending on the Ws. Also, particle reflux near the wall at the bottom region of the riser is not observed by the naked eye at above Ug ) 11.5 m/s. Therefore, the data obtained at higher than 11.5 m/s are used in the model because the model is developed for the dilute pneumatic conveying region. Pressure drops measured in a pneumatic conveying line are the sum of acceleration, static head, and friction loss terms as
-
[
]
dUp dUg dP + [Fs(1 - ) + ) (1 - )FpUp + FgUg dz dz dz 2 2fsFs(1 - )Up2 2fgFgUg + (2) Fg]g + D D
where fg is the gas friction factor and fs is the particle friction factor. In eq 2, the gas momentum term can be
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neglected in dilute phase flow because its value is lower than that of the solid momentum term.9 In the fully developed region, the acceleration term can be neglected
-
2fgFgUg2 dP ) [Fs(1 - ) + Fg]g + + dz D 2fsFs(1 - )Up2 (3) D
The gas holdup is defined as10,11
)1-
4Ws
(4)
(Fp - Fg)πD2Up
It is important to predict the particle velocity for estimating the pressure drop and for performing mathematical modeling.12 Particle velocity in the fully developed region can be expressed as the slip velocity, which is the relative velocity between the gas velocity and the terminal velocity of particles.1,5
Up∞ ) Ug - Ut
(5)
In the acceleration zone, the particle velocity can be predicted using the momentum balance on the particle as
(
Fg U g dUp 3 ) CD - Up dt 4 dpFs
)
2
-g-
2fsUp2 D
(6)
Figure 4. Comparison between measured and calculated values of fg as a function of Re. Table 1. Summary of Correlations Proposed by Various Researchers ref
friction factor
Koo10 Stemerding20 Reddy and Pei21 Konno and Saito8 Van Swaaij et al.19 Capes and Nakamura17
fg ) 0.3164/Re-0.25 fg ) 0.0014 + 0.125(1/Re0.32) fs ) 0.003 fs ) 0.046Up-1 fs ) 0.0285xgDUp-1 fs ) 0.080Up-1 fs ) 0.048Up-1.22
Yang18
0.00315
Blasius15
[
]
1 - (1 - )Ut 3 Ug - Up U 1- t 1- 0.0017 us/Ut 3 Ug/
Garic et al.14
-0.979
[ ]
-1.5
where Up is the cross-sectional average upward particle velocity. The drag coefficient CD in the range 0.3 < Rep < 1000 is written in general form as13
CD )
with the initial condition
K Rep0.6
(7) z ) 0, Up f 0
In the acceleration regime, K can be obtained by applying the following limiting condition
dUp ) 0 at z ) Lacc dz
Up ) Up∞, ) ∞,
(8)
where Up∞ is the particle velocity and ∞ is the voidage in the fully developed region.
2fsUp∞2 g+ D K) F Ug 1 3 g - Up 0.6 4 Re dpFs ∞
( )(
p∞
)
(9)
By replacing K, the momentum eq 6 can be written as follows
Up
(
)
2fsUp∞2 dUp ) g+ × dz D Ug - Up 4Ws 1(Fs - Fg)πD2Up 1.4 Ug - Up∞ ∞
[
[
]
]
1.4
-g-
2fsUp2 (10) D
(11)
Equation 10 is then solved numerically using a Runge-Kutta method from the given value of the particle friction factor. Therefore, if fg and fs are known for a given gas-solid flow, the pressure drop in the fully developed region can be calculated using eq 3 from the calculated particle velocity (eq 5) and gas holdup (eq 4). And the axial pressure drop can be predicted by eq 2 using voidage and Up(z) calculated by eqs 4 and 10, respectively. As shown in Table 1, many researchers proposed the correlations to calculate the gas and solids friction factor. The proper correlation must be selected to predict a friction pressure drop because the friction term is dependent on gas and particle characteristics and is system specific.14 Figure 4 shows the comparison between experimental and calculated values of fg as a function of Re. The gas-alone pressure drop measured varying gas velocities without particle injection in the riser. As can be seen in Figure 4, the calculated values using the correlation proposed by Koo10 and Blasius15 accurately predict the experimental ones. The Koo’s10 correlation is used in this model to calculate the gas friction pressure drop. The comparison between experimental and calculated values of dPs/dz is shown in Figure 5. The pressure drop
Ind. Eng. Chem. Res., Vol. 41, No. 21, 2002 5319
Figure 5. Comparison between measured and calculated values of dPs/dz.
due to solid in a fully developed region can be predicted as
-
dPs 2fsFs(1 - )Up∞2 ) Fs(1 - )g + dz D
(12)
The solid holdup and particle velocity in the fully developed region can be calculated using eqs 4 and 5, respectively. In this study, voidage is in the range 0.994-0.999 depending on gas velocity and Ws. The solid pressure drop can be calculated by eq 12 using the solid friction factors proposed in Table 1. For fine particles, Boothroyd16 found that the frictional pressure drop of suspension flow was less than that of the gas flow only at the identical gas velocity because the solid particles suppressed the turbulence of the flow. However, this phenomenon did not occur with coarse particles.16 Shimizu et al.15 and Capes and Nakamura17 reported that an additional pressure drop due to the addition of particles to the gas stream increased monotonically with the solid loading ratio, as demonstrated in this experimental result. As shown in Figure 5, the calculated values using Konno and Saito5 and Yang’s18 correlation underestimated the experimental ones. Instead, in this study using iron ore, van Swaaij et al.’s19 correlation accurately predicts the experimental values, although they worked with cracking catalyst. Therefore, the application of van Swaaij et al.’s19 correlation to the other model has to be cautious. Van Swaaij et al.’s correlation is used to calculate solid friction pressure drops in this model. The particle velocity calculated by eq 10 is shown in Figure 6. When the particles were injected into the riser, their velocities were nearly zero and they had to be accelerated in the bottom region of the riser17 so the particle velocity increased with increasing height at the bottom region of the riser. Thus, the variation of fs is also considered in the acceleration zone because Up decreases largely along the height. As can be seen in Figure 6A, the particle velocity increases with increasing gas velocity at a constant solid circulation rate, while it is not largely changed with a solid circulation rate at identical gas velocity. The comparison between calculated values and experimental ones of the axial pressure drop is shown in Figure 7. As can be seen, the calculated values of the axial pressure drop using the model (eqs 2 and 10) compare well with experimental ones except in the exit
Figure 6. Particle velocity as a function of position.
Figure 7. Comparison between measured and calculated values of the axial pressure drop.
region at relatively low gas velocity where an end effect is observed. If the gas velocity is high (Figure 2C and Figure 7B) and the exit structure is changed into a smooth structure,7 the end effect is not observed. Using the model, one can expect an axial pressure drop profile in a vertical pneumatic conveying line. The calculated pressure drop of each component at Ug ) 15.0 m/s and Ws ) 0.35 kg/s is indicated in Figure
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Ind. Eng. Chem. Res., Vol. 41, No. 21, 2002 Subscripts g ) gas s ) particle
Literature Cited
Figure 8. Calculated pressure drop of each component at Ug ) 15.0 m/s and Ws ) 0.25 kg/s.
8. In the acceleration zone, the total pressure drop is largely affected by the acceleration pressure drop that decreases largely with increasing height at the bottom region of the riser. This value is most affected by a frictional pressure drop in the fully developed region because the static pressure is low due to the very low solid holdup. The static pressure drop is constant along the height except at the bottom region, where it decreases slightly with increasing height. 4. Conclusions The pressure drop decreases largely along the height in the acceleration zone, while it is constant irrespective of increasing height at the fully developed region. The axial pressure drop increases with an increasing solid circulation rate at a constant gas velocity. With the iron ore particles, the correlations of Koo10 and van Swaaij et al.19 accurately predict the measured gas and solid friction pressure drops, respectively. The pressure drop model is proposed to predict the axial pressure drop in a vertical pneumatic conveying line. The proposed model accurately predicts the experimental axial pressure drop profiles. Nomenclature CD ) drag coefficient dp ) particle diameter, m D ) riser diameter, m f ) friction factor g ) acceleration of gravity, m/s2 Gs ) solids flux, kg/m2‚s K ) constant in calculation of drag coefficient Rep ) particle Reynolds number, [Fgdp(Ug/ - Up)]/µ Ug ) superficial gas velocity, m/s Up ) particle velocity, m/s UPT ) transition velocity between the dilute phase pneumatic conveying and the dense phase pneumatic conveying, m/s Ws ) solid circulation rate, kg/s z ) axial position in the riser, m Greek Letters ∆P ) pressure drop, Pa ) voidage F ) density, kg/m3
(1) Plasynski, S. I.; Klinzing, G. E.; Mathur, M. P. Highpressure Vertical Pneumatic Transport Investigation. Powder Technol. 1994, 79, 95. (2) Dhodapkar, C. A.; Zaltash, A.; Myler, C. A.; Klinzing, G. E. Acceleration Zone Studies in Pneumatic Conveying Systems at Various Inclinations. AIChE Symp. Ser. 1989, 85 (270), 1. (3) Kemp, I. C.; Oakley, D. E.; Bahu, R. E. Computational Fluid Dynamics Modeling of Vertical Pneumatic Conveying Dryers. Powder Technol. 1991, 65, 477. (4) Arastoopour, H.; Gidaspow, D. Vertical Pneumatic Conveying Using Four Hydrodynamic Models. Ind. Eng. Chem. Fundam. 1979, 18 (2), 123. (5) Konno, H.; Saito, S. Pneumatic Conveying of Solids through Straight Pipes. J. Chem. Eng. Jpn. 1969, 2 (2), 211. (6) Namkung, W.; Kim, S. W.; Kim, S. D. Flow Regimes and Axial Pressure Profiles in a Circulating Fluidized Bed. Chem. Eng. J. 1999, 72, 245. (7) Pugsley, T.; Lapointe, D.; Hirschberg, B.; Werther, J. Exit Effects in Circulating Fluidized Bed Risers. Can. J. Chem. Eng. 1997, 75, 1001. (8) Bi, H. T.; Fan, L. S. Regime Transition in Gas-Solid Circulating Fluidized Beds. AIChE Annual Meeting, Los Angeles, November, 1991; p 17. (9) Littman, H.; Morgan, M. H., III; Paccione, J. D.; Jovanovic, S. Dj.; Grbavcic, Z. B. Modeling and Measurement of the Effective Drag Coefficient in Decelerating and Nonaccelerating Turbulent Gas-Solids Dilute Phase Flow of Large Particles in a Vertical Transport Pipe. Powder Technol. 1993, 77, 267. (10) Klinzing, G. E. Gas-Solid Transport; McGraw-Hill Book Company: New York, 1981. (11) Yang, W. C. Estimating the Solid Particle Velocity in Vertical Pneumatic Conveying Lines. Ind. Eng. Chem. Fundam. 1973, 12, 349. (12) Lodes, A.; Mierka, D. Particle Velocities in Two-phase Solid-gas Flow. Powder Technol. 1989, 58, 163. (13) Pugsley, T. S.; Berruti, F. A Predictive Hydrodynamic Model for Circulatig Fluidized Bed Risers. Powder Technol. 1996, 89, 57. (14) Garic, R. V.; Grbavcic, Z. B.; Jovanovic, S. Dj. Hydrodynamic Modeling of Vertical Nonaccelerating Gas-solids Flow. Powder Technol. 1995, 84, 65. (15) Shimizu, A.; Echigo, R.; Hasegawa, S. Experimental Study on the Pressure Drop and the Entry Length of the Gas-solid Suspension Flow in a Circular Tube. Int. J. Multiphase Flow 1978, 4, 53. (16) Boothroyd, R. G. Pressure Drop in Duct Flow of Gaseous Suspensions of Fine Particles. Trans. Inst. Chem. Eng. 1966, 44, T306. (17) Capes, C. E.; Nakamura, K. Vertical Pneumatic Conveying: An Experimental Study with Particles in the Intermediate and Turbulent Flow Regimes. Can. J. Chem. Eng. 1973, 51, 31. (18) Yang, W. C. A Correlation for Solid Friction Factor in Vertical Pneumatic Conveying Lines. AIChE J. 1978, 24, 548. (19) van Swaaij, W. P. M.; Burman, C.; van Breugel, J. W. Shear Stresses on the Wall of a Dense Gas-solids Riser. Chem. Eng. Sci. 1970, 25, 1818. (20) Stemerding, S. The Pneumatic Transport of Cracking Catalyst in Vertical Risers. Chem. Eng. Sci. 1962, 17, 599. (21) Reddy, K. V. S.; Pei, D. C. T. Particle Dynamics in Solidsgas Flow in a Vertical Pipe. Ind. Eng. Chem. Fundam. 1969, 8, 490. (22) Hariu, O. H.; Molstad, M. C. Pressure Drop in Vertical Tube in Transport of Solids by Gases. Ind. Eng. Chem. 1949, 41 (6), 1148.
Received for review March 7, 2002 Revised manuscript received August 6, 2002 Accepted August 6, 2002 IE020178P
