Ind. Eng. Chem. Res. 2008, 47, 9517–9526
9517
Distribution of Electrostatic Potential in a Gas-Solid Fluidized Bed and Measurement of Bed Level Wang Fang, Wang Jingdai,* and Yang Yongrong State Key Laboratory of Chemical Engineering and Department of Chemical and Biochemical Engineering, Zhejiang UniVersity, Hangzhou 310027, People’s Republic of China
A theory on the electrostatic charge distribution in gas-solid fluidized beds was proposed. It consists of an interpretation of the causes of bipolar charging, the charging mechanisms in the fluidized bed, and the relationship between charge distribution and particle-size distribution in fluidized beds. Experiments were performed in a three-dimensional column gas-solid fluidized bed to measure the electrostatic charge distribution. It was found that the electric field inside the bed was nonuniform. If there was a distinct interface between the dilute and dense phases, the voltage polarity would reverse near the bed level, resulting in a Z-shaped axial profile of potential. The heights where voltage polarity reversal happened rose with the increase of gas velocity and static bed height. It was also found that the electrostatic voltage rose with increasing radial distances from the axis of the column. To sum up, the voltage at any axial cross section of the bed showed double saddles, with bed level as the interface. Accordingly, three special zones to be emphasized were identified: distributor, stagnant, and bed level zones, of which the latter two have high voltages and are more readily disturbed by particle/wall adhesion and even wall sheets. Based on the characteristics of axial profile of electrostatic potential in the fluidized bed, a new technique that could successfully predict bed level was developed. Good agreement was observed between visual measurements of bed level and predictions by the electrostatic method, with maximum relative error of 4.08% and mean relative error of 2.02%. 1. Introduction The occurrence of electrostatic charges is almost unavoidable in particulates and multiphase systems such as gas-solid fluidization, due to repeated particle contacts and separation, supplemented by the friction of particles rubbing against each other and the vessel wall.1 These charges can be accumulated by dielectric materials (in this case polyethylene powders). The build-up of high equilibrium charges in fluidized systems can interfere with the normal hydrodynamics of the bed, resulting in particle-wall adhesion, interparticle cohesion, electrostatic discharges, and even wall sheetings.2-6 All of the obstacles owing to electrostatics, especially for sheeting in fluidized bed polymerization reactors, may cause serious operational problems and bring production losses. Thus there is significant economic incentive to prevent overaccumulation of charges. Hendrickson5 and Yang and co-workers6 have given detailed reviews on relationship between fluidized bed polymerization reactor wall sheeting and the presence of excess electrostatic charges. The polydispersity of polymer powders and complexity of hydrodynamics in fluidized beds make it difficult to know the nonuniform charge distribution in fluidized beds.2,7-10 Besides, the charging mechanisms of dielectric are not well understood now. Therefore, it is still a rather rough job to achieve static control and relative hazards elimination in the fluidization of polymer powders. Ciborowski and Wlodarski2 measured the electrostatic potential in fluidized beds of polyvinyl acetate, polystyrol, and sand using an electrode immersed in the bed from the top. They found the electrical potential was at its highest value when the electrode was located at the static bed level. Fulks et al.7 indicated that the radial electric field intensity was strongest near the reactor wall and was zero at the axis of the reactor. Gajewski8 constructed a fluidized bed made of glass where the inner surface was covered with rings of copper sheet * To whom correspondence should be addressed. Telephone/fax: +86-571-87951227. E-mail:
[email protected].
isolated from each other but connected to the ground. He measured the current to the ground from each of the copper rings in the different sections of the column with polypropylene spheres fluidized. The current was referred to as “electrification current”. The results showed that the direction of electrification current reversed near the static bed level. Both Fujino et al.9 and Goode10 reported that the polarity of the electrostatic voltage may change from the bottom to the top of the reactor. However, these observations could not lead to a unified conclusion and a generally acceptable explanation on charge distribution in fluidized bed. As a result, further work is critical for development of static control methods used in multiphase flow of fluidization. It is well-known that net charges with one pole on powders will generate during fluidization. However, few people ever think that the net charges may be the result of a bipolar charge distribution because of bipolar charging, which has been explained as contact charging between particles with different sizes where larger particles gain charges of opposite polarity compared to the smaller particles.11,12 Bipolar charging can occur in natural events such as sandstorms13 and dust devils13-16 and in industrial powder-handling processes.11,12,17,18 Interestingly, it appears to be found in different size powders having similar or dissimilar chemical compositions. In particular, it has been observed that the polarity of fine particles and coarse particles is independent of the net charge, within a mixture of particle sizes.18 So it is significant to understand the role of bipolar charging in the distribution of electric field of fluidized beds. However, very few quantitative data exist in the literature concerning this phenomenon, and no generally acceptable explanation currently exists. This paper is focused on the relationship of electrostatic charge distribution with charging mechanisms, especially the bipolar charging of fluidized powders in gas-solid fluidized beds. First, a theory of the electrostatic charge distribution in fluidized beds was proposed, which was based on the interpreta-
10.1021/ie800805t CCC: $40.75 2008 American Chemical Society Published on Web 10/31/2008
9518 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 1. Particle-size Distribution of LLDPE Particles dp, mm wt %
1.700 3.7
1.275 38.5
0.780 19.3
0.568 9.0
0.438 10.1
0.350 12.4
0.185 7.0
tion of bipolar charging, theoretical analysis of charging mechanisms in fluidization, and the relationship between charge distribution and particle segregation. Second, efforts were made to systematically investigate the profiles of electrostatic potential in gas-solid fluidized beds under various operating conditions. The theory presented in this article can provide convincing interpretations of the experimental results. Finally, a new electrostatic technique that can monitor electrostatic potential and bed level simultaneously was established. 2. Theory Gajewski8 has presented an interpretation that the reversal of direction of electrification current was based on zones of charge generation and dissipation. He thought that most of the electrostatic charge generation occurred at the grid plate in the lower portion of the fluidized bed and the maximum charge dissipation occurred near the upper part of the bed, which resulted in the reversal of current flow direction along the axial height. However, a bipolar electric field dependent on altitudes still occurs in the sandstorm, although there is only friction among sand particles but no friction between particle and column wall or grid, just like in the fluidized bed. The phenomenon mentioned above cannot get a reasonable explanation from Gajewski’s theory.8 In this section, a theory describing the electrostatic charge distribution in fluidized beds will be proposed. This theory consists of an interpretation of causes of bipolar charging, analysis of charging mechanisms in the fluidized bed, and the relationship between charge distribution and particle-size distribution in the fluidized beds. The theory will provide convincing interpretations fo the experimental results in section 4. 2.1. Causes of Bipolar Charging. As mentioned earlier, there appears to be no generally accepted theory to explain why bipolar charging occurs in a polydisperse mixture. Since bipolar charging is the result of contact charging among particles, it implies that there are differences in effective work functions of the surfaces in contact. There are at least four possible reasons that could explain this phenomenon.19 (1) Effective work function is inherently size-dependent. The effective work function of a polymer material is defined as the minimum energy required to extracting a charge carrier from the surface of a particle. In general, the effective work function is inversely proportional to particle size.20 Consequently, it is more difficult to extract a charge carrier from a small particle than from a larger one. Depending on the type of most charge carriers (electrons, positive ions, or negative ions) in particles, different polarity charges will be carried by large and small particles, respectively. A small particle in contact with a large one will preferentially charge negatively if electrons or negative ions are the charge carriers.11,12,17-19 On the other hand, if the charge carrier is a positive ion, small particles will charge positively.11 (2) Microscopic structure in the surface of small and large particles is different. In the polymerization of olefins in gas-solid fluidized beds, polymer powders generally have a very wide particle-size distribution (dp )100∼5000 µm). Furthermore, it has been shown that some properties of polymer particles are dependent on particle sizes. For example, polyethylene particles with different size have distinctions in molecular weight, copolymer content, surface roughness, and
Figure 1. Schematic representation of charging mechanisms in gas-solid fluidized beds.
residue catalyst content. Clearly, this could influence the effective work function and charging of the materials. (3) Capacity to selectively attract /absorb to intermediate species is size-dependent. It is well-known that small particles have a much higher specific surface (square meters per kilogram) than larger ones. As a result, submicrometer-sized contaminants or additives are more likely to be attracted to and adhere to, the surfaces of the fine particles. Therefore, in the production of polymers, the third-body gaseous or liquid materials in the gas feed are more easily adsorbed at the surface of fine particles, and change the physical/chemical structure of the surfaces of the fines relative to the coarser particles. (4) There are differences in surface energy. The surface energy of a material is the work done to separate two surfaces to infinity. For the same materials there is evidence that the surface energy increases as size decreases. This will give rise to surface energy differences between small and large particles, possibly leading to charge transfer. There is no doubt that other possible explanations for this phenomenon also exist. 2.2. Charging Mechanisms in Gas-Solid Fluidized Beds. 2.2.1. Theory Analysis. Due to the wide size distribution of polymer powders (Table 1), collision, friction, and contact occur between large particles (L) and column wall, between small particles (S) and column wall, and among large and small particles in dense phase of the gas-solid fluidized bed. Therefore, charging mechanisms in fluidized beds can be summarized as three different categories as Figure 1 shows. In the experiments, collisions between particles and neutral column wall will result in particles being negatively charged and the wall being positively charged due to charge separation,21 no matter whether the particle is large or small (case A). As mentioned in section 2.1, collisions among particles with different sizes will induce bipolar charging (case B), which is also the result of charge separation.21 Case C is the contact and separation between particles and positively charged wall. Mehrani et al.21 has shown that electrostatic charge polarity on the large polyethylene particles is almost independent of initial charges on the plate when they are in contact. Therefore, they concluded that there was negligible transfer of charges between the polyethylene particles and the plate. Besides, charge separation was the dominant charging mechanism. In the gas-solid fluidized bed, the column wall can be regarded as a plate in view of the much smaller size of polymer powders. As a result, positive charges in the wall could not be transferred to
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9519 Table 2. Charge Mass Ratios of LLDPE Particles with Different Sizes after Friction with PMMA Flask particle type
dp, mm
Q/m, µC · kg-1
P1 P2 P3 P4 P5
1.275∼1.700 0.780∼1.275 0.438∼0.780 0.350∼0.438 0.185∼0.350
-0.03 -1.29 -15.56 -23.40 -25.00
the large particles. So the large particles are still negatively charged after they collide with positively charged wall. On the contrary, charge transfer will occur between small particles and positively charged plate,21 which means that positive charges can be transferred to the fines and make them positively charged. Because charges on the wall are all derived from particles, the positive charges obtained by fines due to contact with the wall can be regarded as indirectly from large powders. In conclusion, charge polarity on large particles is dependent on the total amount of charges from collisions with the neutral wall and fine particles. Moreover, the net charges on fines are the sum of charges transferred from the neutral wall, positively charged wall, and large particles. Which of the charging mechanisms is predominant depends on the size of the fluidized column. In large vessels, the ratio of the area of column wall to bed volume is low, so the charging mechanism among particles is likely to be dominant. Therefore, the polarity of charges on entrained fines is opposite to that of the larger particles staying behind in the bed. For small vessels, charge transfer and separation between particles and vessel wall are likely to play a more important role. 2.2.2. Bench-Scale Shaking Experiments. To distinguish between particle/wall and particle/particle charging mechanisms, bench-scale shaking experiments were conducted. A small 100 mL cylindrical flask made of Plexiglas (PMMA, εr ) 3.6) was chosen to shake the particles, since the fluidization experiments were performed in a Plexiglas column. The diameter of the flask is 5 mm, which is small enough to consider the collisions between particle and wall as the main charging mechanism in the shaking experiments. A Burrell Wrisk-Action Model 75 shaker (with a shaking radius of 0.133 ( 0.004 m and an arc travel of 10° at a frequency of 300 ( 30 oscillations/ min) was used to agitate the samples in the PMMA flask for a predetermined time. Solid particles used in the experiments are sieved from linear low-density polyethylene (LLDPE, with size distribution shown in Table 1; 0.833 mm mean diameter). The LLDPE particles were provided by Sinopec in their original resin form, directly from the fluidized bed reactor. Five kinds of sieved particles used in the bench-scale shaking experiments have narrower size distributions: these are 1.275∼1.7 mm (P1), 0.78∼1.275 mm (P2), 0.438∼0.568 mm (P3), 0.350∼0.438 mm (P4), and 0.185∼0.350 mm (P5) in size, respectively. The polyethylene particles with coarse surface have low sphericity and crystallinity. Particle density is 920 kg · m-3, melt index (MI) is 2.0 g · (10 min)-1, and relative dielectric constant εr is 2.3. Before each sample was shaken, it was dried at a temperature of about 70 °C for 24 h in a vacuum dryer and then cooled for 12 h in vacuum, to eliminate influences of the moisture adsorbed by the dielectric particles on triboelectrification behavior. Furthermore, the initial charges on the walls of the empty flask and the samples were measured by the Faraday cup to ensure near zero. Subsequently, five kinds of particles (P1-P5) were shaken in the PMMA flask for 10 min, and then the charges on particles were measured by the Faraday cup. The charge/mass ratios (Q/m) of LLDPE particles are given in Table 2. The results
Figure 2. Schematic diagram of experimental apparatus: (1) fan; (2) dryer; (3) flow meter; (4) mixing room; (5) distributor; (6) fluidized bed; (7) expanding section; (8) static probe; (9) signal transmitter; (10) computer and data acquisition system. Table 3. Axial Heights of Measurement Points above the Distributor point He, mm
1 80
2 160
3 245
4 380
5 515
6 650
7 780
8 910
show that all the particles were all negatively charged. Therefore, it can confirm that bipolar charging is mainly due to the interaction between large and small particles. 2.3. Charge Distribution in Gas-Solid Fluidized Beds. During fluidization, bubbles carry the charged particles as they rise. At the top of the fluidized bed, the bubbles burst and the charged particles are transferred to the space above the bed level. Most of the large particles would be back to the bed due to gravity, and fine particles would move upward with gas flow and would not fall back any more. In the space above the bed level, which is called free space or dilute phase, gas turns to continuous-phase but particles become dispersion-phase, while in the dense phase below bed level, powders are continuousphase and gas is dispersion-phase. Due to particle segregation in the bed, there will be an axial particle-size distribution for the polydisperse polymer powders in the fluidized bed. As a result, particles in dilute phase are mainly fines, but most of large particles concentrate in the dense phase, especially at the bottom of the bed. Then one could imagine the polarity at the top of the fluidized bed to be largely determined by the charge polarity of small particles. Conversely, the polarity at the bottom of the bed would depend on the polarity of charges on large particles. This observation would be the result of particle-size segregation in the fluidized bed and would be shown in the following experimental results. 3. Fluidization Experiments 3.1. Experimental Apparatus. A schematic diagram of the experimental apparatus is shown in Figure 2. It consists of a three-dimensional Plexiglas fluidized bed (150 mm in inner diameter and 1000 mm high) and a static online detection (SOD) system. The gas distributor at the bottom is a stainless steel perforated plate with an opening of 2.0 mm and 2.6% open area. Furthermore, the plate should be kept well-grounded during fluidization experiments. Eight electrostatic monitoring points were located at various heights along the fluidized bed, as shown in Table 3, and connected to the SOD system to measure the axial distribution of electrostatic potential. To prevent any contamination that might affect the generation of charges inside the fluidized bed, pure dry nitrogen is served as the fluidizing gas. All experiments were performed at room temperature. Solid particles used in the experiments are LLDPE with the wide size
9520 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Table 4. Radial Distances of Measurement Points from the Axis of the Column point r, mm
Figure 3. Calculation of steady-state potential (He ) 160 mm, H0 ) 300 mm, u ) 0.7 m · s-1).
distribution shown in Table 1 and five sieved particles (P1-P5) introduced in section 2.2.2. The SOD system is composed of a data collection system and a computer. The data collection system consists of a static probe, a 4 × 1011 Ω resistor, a voltage to current transmitter, a DC power supply, and a data acquisition card. The static probe used in this case is a copper bar, 1 mm in diameter and 10 mm immersed in the fluidized bed. To ensure the precision of samples of static signal, a sampling frequency of 100 Hz and a sampling time of 300 s are adopted. 3.2. Experimental Method. Before each run of the experiments, the fluidized materials should be dried in the same way as illustrated in section 2.2.2 to ensure the reproducibility of the experimental results. During the triboelectrification of the bed, the variation of bed voltage with time observed in Figure 3 can be regarded as the sum of two processes: pure charge generation and charge dissipation. While a state of equilibrium of the two processes is attained, the bed voltage reaches a steady value. If charge generation rate is faster than the charge dissipation, |Us| will exponentially increase with time (Figure 3); otherwise it will exponentially decrease with time. The observed variation of voltage in experiments can be written as22 dU ) kg(Umax - U) - kdU (1) dt where Umax is the voltage corresponding to the maximum allowable bed charge level without simultaneous charge dissipation, kg is the kinetic constant of pure generation, and kd is the kinetic constant of charge dissipation. Integration of eq 1, when it is assumed that U ) 0 for t ) 0 and U ) U for t ) t, gives U ) Us[1 - exp(-Kt)]
1 5
2 15
3 25
4 35
5 45
6 55
7 65
voltage data to eq 2. An example is shown in Figure 3. In the fluidization experiment for LLDPE particles shown in Table 1, with 300 mm of static bed height (i.e., height when there was no gas flow) and 0.7 m · s-1of superficial gas velocity, Us ) -1603 V (0) have been obtained by fitting the data from the probe located at 300 mm height above the distributor. The results show that the total charge on particles in the bed was negative and the absolute value of the bed voltage (|Us|) exponentially increases with time. The level of bed electrification can be compared by calculating the stationary voltage (Us) at different fluidization conditions. First, with the fluidization condition fixed, a time series of static potential at various axial and radial positions in the fluidized bed can be obtained through the SOD system. Second, Us can be calculated by fitting the time and voltage data to eq 2. Finally, the axial and radial profiles of electrostatic potential are obtained. The radial distances of measurement points from the axis are shown in Table 4. 4. Results and Analysis 4.1. Axial Profiles of Electrostatic Potential in the Fluidized Bed. 4.1.1. Effect of Superficial Gas Velocity. Experiments were performed in the Plexiglas column shown in Figure 2. Dry nitrogen (RH ) 0%, at room temperature of 25 °C) was used as the fluidizing medium, at five different superficial gas velocities of 0.3, 0.4, 0.5, 0.6, and 0.7 m · s-1. The axial heights of eight measurement points are as shown in Table 3, with radial distance 65 mm from the axis of the column. Solid particles used in the experiments were LLDPE powder with a wide size distribution shown in Table 1. The amount of fluidized powder was fixed in each run, with static bed height of 300 mm. Figure 4 illustrates that |Us| at different axial heights rises with increasing gas velocity, as expected. It is believed that greater gas velocity enhances the turbulence of bubbles and particles inside the bed, thereby increases the frequency and velocity of particle/wall and particle/particle impacts. As a result, charging of particles will be intensified, and thus the voltage rises with more charge accumulation in the bed. As shown in Figure 5, electric field inside the bed is nonuniform at a constant gas velocity. It is mainly due to differences in particle-size distribution, bubble size, and void fraction at different axial
(2)
where Us )
kg U kg + kd max
(3)
and K ) kg + kd
(4)
Us is the bed potential for steady-state generation, which can be called the steady-state potential, and K is the kinetic constant for the observed charge generation, that is, the kinetic constant for charge accumulation in the bed. The values of Us and K for each experiment can be obtained by fitting the of time and
Figure 4. Variation of static potential at different axial heights with superficial gas velocity. He ) (9) 80, (b) 160, (2) 245, (4) 380, and (0) 515 mm.
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9521
Figure 5. Effect of superficial gas velocity on the axial profile of static potential in the bed. u ) (9) 0.3, (b) 0.4, (2) 0.5, (4) 0.6, and (0) 0.7 m · s-1.
heights. Except for 0.3 m · s-1, the bed voltage polarity all reverses near the bed level (about 400 mm above the distributor) at the other four gas velocities. The reversal results in a Z-shaped axial profile of potential, which is negative below the bed level and positive above the bed level. In addition, the greater the flow velocity of the gas, the higher the position where reversal of voltage polarity occurs, the greater positive values of potential above the bed level become, and more distinct the Z-shape of potential distribution will be. Based on the bipolar charging theory on fluidized particles proposed in section 2, feasible explanations of the observations illustrated in Figures 4 and 5 can be given. First, it can be inferred that the coarse particles at the bottom of the bed are negatively charged but fines in the dilute space are positively charged. The results show that charge carriers on the surface of polyethylene particles are probably positive ions, which were possibly derived from the residual catalyst in particles and polar impurities adsorbed on the surface of particles. Positive ions in larger particles are more easily extracted and transferred, so they will charge negatively, but small ones will be positively charged after they contact each other. If the gas velocity is too low (u < 0.3 m · s-1), turbulence inside the bed is not so vigorous that the dissipation rate of charges is almost equal to the charge generation rate. So little charge accumulates and potential in the bed is low. On the other hand, there is not a distinct interface between the dense and dilute phases at 0.3 m · s-1. Accordingly, we cannot observe the reversal of voltage polarity when gas velocity is less than 0.3 m · s-1. Higher gas velocities cause more turbulent agitation, mixing, and motion of solids, and considerable amounts of fine particles are thrown into the free space. Consequently, the charge accumulation and bed voltage increase. At the same time, a more distinct interface between dilute and dense phases forms, which causes the polarity reversal of potential near the bed level. Both the height of the bed level and the position where polarity reversal occurs become higher with increasing gas velocity. Furthermore, the increased gas velocity will arouse greater elutriation amount of particles. The higher concentration of fines in dilute phase leads to the rise of positive voltage. According to the charge conservation law, there are more negative charges left in the dense phase below bed level. Apart from the bed level, concentration of fines in free space will reduce gradually, and static potential will accordingly decrease until near-zero. 4.1.2. Effect of Static Bed Height. To further investigate and verify why polarity of bed voltage reverses along axial heights of the fluidized bed, experiments with varied static bed
Figure 6. Variation of static potential at axial heights with static bed level. He ) (9) 80, (b) 160, (2) 245, (4) 380, (0) 515, and (O) 650 mm.
Figure 7. Effect of static bed level on the axial profile of static potential in the fluidized bed. H0 ) (9) 200, (b) 300, (2) 350, (4) 400, and (0) 450 mm.
levels of 200, 300, 350, 400, and 450 mm, at constant gas velocity of 0.6 m · s-1, were performed. The bed level varies significantly with different static bed heights but constant gas velocity. At 0.6 m · s-1, the fluidization regime in all experiments is free bubbling fluidization or turbulent fluidization, which means that there is a distinct interface between dense and dilute phases of the bed. The experimental results are illustrated in Figures 6 and 7. Figure 6 shows the variation of static potential at different measurement points with static bed height. It can be seen that values of potential at three measurement heights (He ) 80, 160, and 245 mm) are negative all the time. It was observed that the three measurement points were always below the bed level with any static bed height, where the polarity of static potential is determined by the negative charges carried by large particles, as mentioned in section 4.1.1. That is why voltages at the three bottom measurement points are all negative. Similarly, voltages at He ) 650 mm, which is always in the free space, are kept positive. The reason is that the electric field in free space is mainly dependent on net charges on fine particles, which mostly charge positively. However, with the increase of static bed height, values of potential at the other two measurement heights (He ) 380 and 515 mm) changes oppositely. This phenomenon can be explained by the theory proposed in section 2. When static bed heights are 200 and 300 mm, the point at 380 mm above the distributor is located in free space. While static bed height is higher than 300 mm, it sinks into the dense phase of the bed. Similarly, with static bed height H0 lower than 350
9522 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008
Figure 8. Variation of static potential at different axial heights with particle size. He ) (9) 80, (0) 160, (4) 245, (2) 380, (b) 515, and (O) 650 mm.
mm, the measurement point at 515 mm is in the free space. When H0 is higher than 350 mm, the point of He ) 515 mm is lower than the bed level. According to the bipolar charging theory of fluidized particles, it is different in voltage polarities of the dense phase and the dilute phase. As a result, changes in voltage polarity of the two positions mentioned above occur. As Figure 7 shows, the axial electric fields in the bed with different static bed heights are all nonuniform, with the voltage polarity reversal along the axial heights. With the increase of static bed level, axial height where the potential polarity reverses rises distinctly. Electrostatic potentials are positive in dilute phase and negative below the bed level in all the experiments of this section. The results further verify that bipolar charging theory of fluidized particles can provide feasible explanations to why axial profile of electrostatic potential in fluidized beds is Z-shaped. 4.1.3. Effect of Particle Size. Polyethylene particles applied in this case include five kinds of sieved particles: P1 (1.275∼1.700 mm), P2 (0.780∼1.275 mm), P3 (0.438∼0.568 mm), P4 (0.350∼0.438 mm), and P5 (0.185∼0.350 mm). Use of polyethylene particles with narrower size distributions in the experiments allows us to define the dependence of electrostatic potential distribution in the fluidized bed on the particle size. The number of particles contributing to triboelectrification and contact area between particle and wall depends on the size of fluidized particles. In theory, it might be expected that smaller particles would have greater numbers in a unit volume. Thereby, it would induce more intensive electrification of the fluidized bed. The bulk volume of particles in each run is maintained constant, with static bed height 300 mm. The gas velocity in all experiments is 0.6 m · s-1. Experimental results are shown in Figures 8 and 9. As illustrated in Figure 8, in the case of particles with dp > 0.2685 mm (including P1, P2, P3, and P4), the intensity of the electrostatic potential increases with decreasing particle diameter and reaches its maximum for particles P4 with dp ) 0.394 mm (0.350∼0.438 mm). For particles P5 with dp ) 0.2685 mm (0.185∼0.350 mm), the intensity of electrostatic potential begins to drop, although the electrification of this kind of particles is the most intensive (see Table 2). This unexpected phenomenon of reduction of electrification with increasing number of particles in a unit volume has two main reasons. The first one is the formation of a particle layer adhering to the inside wall of the column. It is a known fact that in such a case the friction between particle and wall would be hindered and there appears to be a tendency for symmetrical electrification among particlessthe particles acquire both posi-
Figure 9. Effect of particle size on the axial profile of static potential in the fluidized bed. dp ) (9) 1.275∼1.700, (b) 0.780∼1.275, (f) 0.438∼0.568, (4) 0.350∼0.438, and (O) 0.185∼0.350 mm.
tive and negative charges. Moreover, small particles tend to accumulate and form agglomerates. Such agglomerates consisting of a number of particles cannot “retain” the charge, which is a sum of charges of the individual particles. Dissipation of the charge during particle agglomeration follows. Second, this behavior can be explained if the type of bed fluidization is taken into account. For bubbling fluidization, as the bubbles rise, their velocity and size both increase, leading to the more vigorous motion of particles and the more intensive friction charging. If the particles are small enough, they tend to form aggregative states. Agglomeration will result in the interparticle force being more than the drag force imposed on particles by gas flow. Consequently, fine particles are fluidized with difficulty, and slugging fluidization more easily happens. In the experiments, the fluidized pattern for particles P1, P2, P3, and P4 at gas velocity of 0.6 m · s-1 is bubbling fluidization, while for particles P5, it is slugging fluidization. In slugging fluidization, the slugs have lower rise velocity than free bubbles so that less motion is produced and charge generation decreases. From the axial profiles in Figure 9, when particles P2, P3, and P4 were fluidized, the reversal of voltage polarity near the bed level also occurred, although their size distribution is narrower. But for the largest particles P1 and the smallest particles P5, |Us| was much lower than the other three particles and no polarity reversal occurred. The main reason is that particles P1 are formed through sufficient growing-up during polymerization; thus the similarity among them is higher because of the print effect of catalyst powders. Furthermore, larger particles have weaker capacity to selectively attract/absorb to intermediate species. So the amount of polar impurities serving as charge carriers on the surface of particles P1 is less than the other particles. Charges transferred during contact and separation among particles or between particles and wall are less, as shown by a low electrostatic potential voltage. Meanwhile, when particles P1 were fluidized, the concentration of fine particles in the free space was near zero, so potential there is unmeasurable. Causes of low electrification degree of particles P5 have been given in the preceding paragraph. Since the pattern of particles P5 at 0.6 m · s-1 is slugging fluidization, there is no apparent bed surface. Therefore the reversal of voltage polarity was not observed. In the experiments with particles P2, P3, and P4, the fluidization patterns are free bubbling fluidization or approximate to turbulent fluidization with relatively distinct phase interfaces. Therefore, these three kinds of polyethylene powders have similar axial profiles of potential, which are Z-shaped.
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9523
Figure 10. Radial profile of static potential at different axial heights (LLDPE). He ) (9) 80, (b) 160, (2) 245, (4) 380, (O) 515, and (0) 650 mm.
With different size distributions and mean diameters, LLDPE particles present different triboelectrification behaviors. The size dependence of effective work function, microscopic structure in the surface, capacity to selectively attract/absorb to intermediate species, and surface energy play an important role for the behavior. Therefore, for particles with a narrow size distribution, high build-up of electrostatic charges and bipolar charging will also arise during continual contact and friction. 4.2. Radial Profile of Electrostatic Potential in the Fluidized Bed. The radial profiles of electrostatic potentials were investigated in the same apparatus shown in Figure 1, with dry nitrogen at 0.6 m · s-1 as the fluidized gas. Radial positions of measurement points are shown in Table 4. Solid particles used in the experiments were still LLDPE powder produced by Sinopec, with the same trademarks as the particles shown in Table 1 but belonging to different batches. Therefore, experimental results for the same conditions and positions were not totally consistent with those in section 4.1. The results are shown in Figure 10, with static bed height of 300 mm. The electrostatic potential rises with increasing radial distances from the axis of the column and reaches its maximum absolute value near the wall and the minimum value at the axis. The main reason is that void fraction in the bed decreases with increasing radial distance, resulting in the maximum density of particles and charges near the column wall. Therefore, when the axial profile of the voltage is studied, the radial position of all measurement points should be kept constantsthat is, 10 mm from the wall in this casesto eliminate the influences of radial profile on axial profile of the voltage. Axial profiles of the voltage at different radial distances are illustrated in Figure 11; these are also Z-shaped, as discussed in section 4.1. 4.3. Profile of Electrostatic Potential in the Whole Bed. By combination of the axial and radial profiles of the electrostatic voltage, a three-dimensional graph can be obtained as in Figure 12. The projection in the Us-He plane of the graph is Z-shaped, reflecting the axial profile of electrostatic potential in the fluidized bed, while the projection in the Us-r plane is U-shaped, representing the radial profile of the voltage. Figure 13 shows the equipotential lines in the fluidized bed. It can be seen that the voltage at any axial cross section of the bed showed approximately double saddles with bed level as the interface. In detail, the polarities of voltage in dense and dilute phases are opposite, and the electrostatic potential at the same axial height increases with increasing radial distance. According to the characteristics of voltage profile in the whole bed, there are three special zones that should be emphasized. The first one is the zone near the distributor, where the flow
Figure 11. Axial profile of static potential at different radial heights (LLDPE). r ) (9) 5, (0) 15, (b) 25, (O) 35, (2) 45, (4) 55, and ([) 65 mm.
Figure 12. Distribution of electrostatic potential in the fluidized bed.
Figure 13. Distribution of equipotential line in the fluidized bed.
behavior of gas and solid phases is influenced much by the distributor and has significant differences with the bulk of the bed. As Figure 13 shows, voltages in the “distributor zone” near the axis were lower than -200 V. This might be due to the presence of jet above the distributor. The length of jet can be calculated by formulas23,24 as approximately 60∼80 mm under the experimental conditions in this work. The cushion of gas in the jet might increase the void fraction there, resulting in low particle density, charge amount, and electrostatic potential. The second one is a “stagnant zone” locating near an elevation from 1 /4 to 3/4 of the column diameter above the fluidization gas
9524 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008
Figure 14. Real-time static potential at different measurement points (LLDPE, H0 ) 300 mm, V ) 0.7 m · s-1). Labels 1-8 in the graph are the serial numbers of measurement points; see also Table 1).
distributor plate,5 which is around 100∼200 mm in this case. The density of charged polymer particles in the stagnant zone is very high, and the electric field there is intensive, with electrostatic potential near the wall higher than -800 V. At the same time, the drag force imposed on the particles by gas flow in this zone is minimal. Therefore, polymer powders, especially fines, are more readily attracted to the column wall by the electric force. If there was active catalyst in the polymer particles, polymerization reaction would continue at the wall. The heat of reaction cannot be removed due to lack of effective gas flow. So the polymer powders adhering to the wall are likely fused and even form wall sheets. The third zone is located in the dilute phase just above the bed level, called the “bed level zone” here, where large amounts of fine particles charged positively are ejected and elutriated. It was observed the phenomenon of particles adhering to the wall was serious here. As a result, the potential near the wall is higher than 400 V. Therefore, the voltages in the stagnant and bed level zones should be particularly monitored, which will contribute to preventing overaccumulation of charges and wall sheets. 5. Measurement of Bed Level From the results obtained by the experiments in section 4.1, it can be concluded that the polarity of bed voltage will reverse near the interface between dense and dilute phases (i.e., the bed level), whatever the gas velocity, static bed height, or particle size is. It was also found that the closer the distance between the measurement point and the bed level, the closer to zero was the value of |Us|. This phenomenon can be explained by the particle concentration distribution along axial heights of the bed. Large amounts of bubbles near the top of the dense phase reach its maximum size and burst. The burst of bubbles delivers particles nearby to the free space, which results in a very low particle concentration and a very small amount of charges at the zone near the bed level. Due to bipolar charging of particles with different sizes, net charges is negative below bed level and positive above bed level. The bed level can be defined as the horizontal alignment of the center of bursting bubbles at the phase interface. Particle concentration in bubbles can be considered nearly zero. Furthermore, the bed level is located in the interface between positive and negative electric fields, so electric flux lines opposite in direction counterbalance. Therefore, it can be inferred that the voltage at the bed level is zero. Based on the relationship between characteristic of electrostatic potential axial distribution and the height of bed level in fluidized beds (as shown in Figures 14 and 15), a novel method
Figure 15. Static potential axial distribution in fluidized bed and the bed level (LLDPE, H0 ) 300 mm, V ) 0.7 m · s-1).
Figure 16. Comparison of predicted and measured bed levels with different superficial gas velocities.
to measure bed level in free bubbling and turbulent beds is proposed. The detailed procedure is as follows: (1) Define the scale function of electrostatic potential at measurement point i and i + 1 as ξ(i, i + 1) )
Us(i) Us(i + 1)
(5)
(2) Calculate all the scale functions. When ξ (i, i + 1) < 0, it can be considered that the bed level lies between measurement points i and i + 1. (3) Calculate the height of bed level by eq 6, with the assumption of zero voltage at the bed level: Hf ) H(i) + ∆H(i, i + 1)
|Us(i)| |Us(i)| + |Us(i + 1)|
(6)
The bed levels in all experiments with distinct phase interfaces have been predicted through the electrostatic method presented above. The comparisons between the bed levels measured with visual means and calculated by the electrostatic method are illustrated in Figures 16, 17, and 18. Very good agreement can be observed between the visual measurements and calculated values, with a maximum relative error of 4.08% and mean relative error of 2.02%. The results show that the electrostatic technique for measuring bed level proposed here has high
Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 9525
Figure 17. Comparison of predicted and measured bed levels with different static bed heights.
Figure 18. Comparison of predicted and measured bed levels with different particle-size distributions.
precision and can be used to monitor the bed level in industrial fluidized beds. The filling operation of a powder container reveals some similarities with the bubbling/turbulent gas-solid fluidization. It is the presence of dense phase full of coarse particles and dilute phase with fines due to the difference in gravity of the particles. Inculet et al.19 found that as the container is being filled, the electric field generated by particles in the lower part has opposite direction to that generated in the unfilled, upper space of the container. At the level of the powder filling the container, the electric field was approximately zero. As the container fills, the zero electric field level moves upward. Therefore, the phenomenon that the polarity of the electric field reverses may not be the only intrinsic feature for gas-solid fluidized beds. It can also happen in other industrial occasions involving polydispersity powders, such as the filling of containers and the separation and drying of powders. Accordingly, it is promising to extend the electrostatic method for measuring bed level proposed in this work to other dynamic processes handling powders. 6. Conclusion In this work, a theory was proposed to describe the electrostatic charge distribution in fluidized beds. First, the theory provides an interpretation of the causes of bipolar charging of particles. Second, the charging mechanisms in the gas-solid fluidized bed are theoretically analyzed. Third, the bench-scale shaking experimental results help confirm the dependence of
predominant charging mechanism on the vessel size. For large vessels, bipolar charging due to contact among particles is the dominant mechanism. In small vessels, monopolar charging between particle and wall is predominant. Finally, the relationship between charge distribution and particle-size distribution in fluidized beds is described. It presents the polarity at the top of the bed as largely determined by the net charges on small particles, while the electric field at the bottom of the bed is determined largely by net charges on large particles. An online measurement technique, which consists of the electrostatic probe, signal transmitter, and data acquisition systems, was developed to study the electrostatic characteristics in gas-solid fluidized beds. By measuring the electrostatic potential at different bed axial heights, it was found that the electric field inside the bed was nonuniform. The voltage polarity would reverse near the interface between dense and dilute phases and result in a Z-shaped axial profile of potential. The axial heights where voltage polarity reversal happened would increase with increasing gas velocity and static bed level. Even when the particle-size distribution in the fluidization experiments was narrowed, there was still a significant reversal in potential polarity as long as the distinct interface between dense and dilute spaces existed. It was also found that the electrostatic voltage would rise with increasing radial distances from the axis of the column. As a whole, the voltage at any axial cross section of the bed showed double saddles with bed level as the interface. Accordingly, three special zones to be emphasized were identified, the distributor, stagnant, and bed level zones, of which the latter two have high voltages and are more readily disturbed by particle/wall adhesion and even wall sheets. Based on the characteristics of axial distribution of electrostatic potential in gas-solid fluidized bed, a new technique that could successfully predict bed level was developed. A good agreement of bed level was observed between visual measurements and predictions by the electrostatic method, with a maximum relative error of 4.08% and mean relative error of 2.02%. The novel electrostatic technique for measuring the bed level could monitor electrostatic potential in the bed and bed level simultaneously. Furthermore, it is promising to extend the method to measure bed levels in other dynamic powder handling processes, such as the filling of containers and the separation and drying of powders. Acknowledgment We acknowledge the support and encouragement of the National Natural Science Foundation of China (through Grant 20490205) and the National High Technology Research and Development Program of China (2007AA04Z182). Nomenclature dp ) diameter of particles, mm H0 ) static bed height, mm He ) height of measurement points, mm Hf ) height of bed level, mm H(i) ) height of measurement point i, mm K ) kinetic constant for observed charge generation process, s-1 kg ) kinetic constant for pure charge generation process, s-1 kd ) kinetic constant for charge dissipation process, s-1 r ) radial distance of measurement point from the axis of the bed, mm t ) time, s Umax ) electric potential for maximum allowable charge generation, V
9526 Ind. Eng. Chem. Res., Vol. 47, No. 23, 2008 Us ) electrostatic potential for steady-state generation in the fluidized bed, V Us(i) ) electrostatic potential at the height of measurement point i for steady-state generation, V u ) superficial gas velocity, m · s-1 ξ(i, i + 1) ) ratio of Us(i) to Us(i + 1) ∆H(i, i + 1) ) distance between measurement points i and i + 1, mm
Literature Cited (1) Cross, J. A. Electrostatics: Principles, Problems and Applications, Adam Higler: Bristol, U.K., 1987. (2) Ciborowski, J.; Wlodarski, A. On electrostatic effects in fluidized beds. Chem. Eng. Sci. 1962, 17, 23–32. (3) Boland, D.; Geldart, D. Electrostatic charging in gas fluidized beds. Powder Technol. 1971/1972, 5, 289–297. (4) Wolny, A.; Kazmierczak, W. The influence of static electrification on dynamics and rheology of fluidized bed. Chem. Eng. Sci. 1993, 48, 3529– 3534. (5) Hendrickson, G. Electrostatics and gas phase fluidized bed polymerization reactor wall sheeting. Chem. Eng. Sci. 2006, 61, 1041–1064. (6) Yu, H. X.; Wang, F.; Wang, J. D.; Yang, Y. R. Progress in study of electrostatics and wall sheeting in gas phase polymerization fluidized bed reactor. Petrochem. Technol. 2007, 36, 206–211. (7) Fulks, D. B.; Sawin, S. P.; Aikman, C. D.; Jenkins, J. M. Process for reducing sheeting during polymerization of alpha-olefins. U.S. Patent 4,876,320, 1989. (8) Gajewski, A. Investigation of the electrification of polypropylene particles during the fluidization process. J. Electrostatics 1985, 17, 289– 298. (9) Fujino, M.; Ogata, S; Shinohara, H. The electric potential distribution profile in a naturally charged fluidized bed and its effects. Int. Chem. Eng. 1985, 25, 149–159. (10) Goode, M. G.; Williams, C. C.; Hussein, F. D.; McNeil, T. J.; Lee, K. H. Static control in olefin polymerization. U.S. Patent 61,110,344, 2000. (11) Ali, F. S.; Ali, M. A.; Ali, R. A.; Inclulet, I. I. Minority charge separation in falling particles with bipolar charge. J. Electrostatics. 1998, 45, 139–155.
(12) Zhao, H.; Castle, G. S. P.; Inculet, I. I.; Bailey, A. G. Bipolar charging of poly-disperse polymer powders in fluidized beds. IEEE Trans. Ind. Appl. 2003, 39, 612–618. (13) Stow, C. D. Atmospheric electricity. Rep. Prog. Phys. 1969, 32, 1–67. (14) Crozier, W. D. The electric field of a New Mexico dust devil. J. Geophys. Res. 1964, 69, 5427. (15) Ette, A. I. I. The effect of the Harmattan dust on atmospheric electric parameters. J. Atmos. Terr. Phys. 1971, 33, 295–300. (16) Melnik, O.; Parrot, M. Electrostatic discharge in Martian dust storms. J. Geophys. Res. 1998, 103, 29107–29118. (17) Trigwell, S.; Grable, N.; Yurteri, C. U.; Sharma, R.; Mazumder, M. K. Effects of surface properties on the tribocharging characteristics of polymer powder as applied to industrial processes. IEEE Trans. Ind. Appl. 2003, 39, 79–86. (18) Zhao, H.; Castle, G. S. P.; Inculet, I. I. The measurement of bipolar charge in polydisperse powders using a vertical array of Faraday pail sensors. J. Electrostatics. 2002, 55, 261–278. (19) Inculet, I. I.; Castle, G. S. P.; Aartsen, G. Generation of bipolar electric fields during industrial handling of powders. Chem. Eng. Sci. 2006, 61, 2249–2253. (20) Gallo, C. F.; Lama, W. L. Classical electrostatic description of the work function and ionization energy of insulators. IEEE Trans. Ind. Appl. 1976, IA-12, 7–11. (21) Mehrani, P.; Bi, H. T.; Grace, J. R. Bench-scale tests to determine mechanisms of charge generation due to particle-particle and particlewall contact in binary systems of fine and coarse particles. Powder Technol. 2007, 173, 73–81. (22) Rojo, V.; Guardiola, J.; Vian, A. A capacitor model to interpret the electric behavior of fluidized beds. Influence of apparatus geometry. Chem. Eng. Sci. 1986, 41, 2171–2181. (23) Yang, W. C.; Keairns, D. L. Momentum dissipation of and gas entrainment into a gas-solid two-phase jet in a fluidized bed. In Fluidization; Proceedings of the Second Engineering Foundation Conference, Cambridge, England, 2-6 April 1978;Davidson, D. J., Keairns, D. L., Eds.; Cambridge University Press: Cambridge, England, 1978. (24) Yang, W. C.; Keairns, D. L. Estimation the jet penetration depth of multiple vertical grid jets. Ind. Eng.Chem.: Fundam. 1979, 18, 317.
ReceiVed for reView May 20, 2008 ReVised manuscript receiVed September 18, 2008 Accepted September 23, 2008 IE800805T
