The Discharge of Pulverized Coal from a Pressurized Aerated Hopper

Sep 29, 2012 - “Fluidized pressurization”, which effectively fluidized the solid and improved the subsequent hopper discharge, was then developed...
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The Discharge of Pulverized Coal from a Pressurized Aerated Hopper Haifeng Lu, Xiaolei Guo, Xingliang Cong, Kai Liu, Xiaolin Sun, Kai Xie, Xin Gong,* and Jun Lu Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, Institute of Clean Coal Technology, East China University of Science and Technology, Shanghai 200237, PR China ABSTRACT: An aerated discharge system was established in this paper to investigate the discharge of pulverized coal from a pressurized aerated hopper. Two opposite effects of aerated gas on solid were first revealed. “Fluidized pressurization”, which effectively fluidized the solid and improved the subsequent hopper discharge, was then developed. The effect of hopper pressure on the discharge of pulverized coal was studied. Our experimental results showed that the gas volumetric flow rate increased and the gas superficial velocity decreased with the increase of the hopper pressure in the range of 0−1800 kPa. It was confirmed that more energy was needed; the uncertainty and instability was increased to discharge pulverized coal at higher pressures. Gas momentum flux was defined and used to describe the effect of aeration. The optimum gas momentum flux, which was independent of the hopper pressure, was obtained on the basis of the experimental data. The optimum gas volumetric flow rates and the optimum gas superficial velocities corresponding to the maximum solid discharge rates were further predicted, which agreed well with the experimental data. On the other hand, the hopper pressure also showed a positive effect on the solid discharge, as the maximum solid discharge rate increased gradually with the hopper pressure until a limit value of about 8000 kg/ h was reached at 800 kPa. During feeding into the gasifer, any fluctuation of coal mass flow rate will affect the oxygen carbon ratio directly and induce a higher or lower temperature in the gasifier. The higher temperature can damage gasifier linings and nozzles while the low temperature can cause the slag blocking phenomenon. Therefore, it is very necessary to discharge pulverized coal within the prescribed time and feed them in a controlled way to ensure the continuous and smooth operation of the gasifier. On the other hand, the entrained-flow pulverized coal gasification often operates with coal pulverized to a size in the order of 90% < 100 μm diameter to ensure the high efficiency of carbon conversion inside the gasifier. For such fine powders, even discharge under atmospheric pressure is very difficult due to the cohesive interparticle interactions, let alone the high pressures.3,4 It has been proved that it is more difficult to discharge pulverized coal from the pressurized lock hoppers, which costs much more, than from the atmospheric hoppers. Here are two example: (1) for GSP gasification introduced by Shenhua Ningxia Coal Industry Group, it costs about 3−4 min for pulverized coal to discharge at atmospheric pressure, while it takes about 10−15 min at 4.5 MPa; (2) for Shell gasification introduced by Sinopec, it costs about 70 s for pulverized coal to discharge at atmospheric pressure, while it takes about 5 min at 4.7 MPa. Both examples indicate a significant influence of pressure on solid discharge. So far, most studies on hopper discharge have been mainly focused on the condition of atmospheric pressure, while there is little report about solid discharge from pressurized hoppers.5 Jenike6 thought that during the hopper pressurization process, gas pressure gradients added to the consolidating stresses acting

1. INTRODUCTION Entrained-flow pulverized coal gasification is currently under development around the world. Its prominent advantages are the ability to handle practically any coal as feedstock and to produce a clean, tar-free gas.1,2 Figure 1 shows the process of

Figure 1. Schematic diagram of entrained-flow pulverized coal gasification process.

entrained-flow pulverized coal gasification, which can be mainly divided into five parts: coal pulverizing, feeding, gasification, clean up, and slag water treatment. Generally, the feeding system has been regarded as one of the key technologies and presents challenges. As shown in Figure 1, locks hoppers are used to feed solids into higher pressure reactor vessels, which receive pulverized coal at atmospheric pressure and, after suitable pressurization, discharge the pulverized coal under gravity into a lower feed hopper. The feed hopper operates at almost constant pressure, slightly above that of the gasifier to assist feeding and prevent reverse flow of hot gases and bed materials from the gasifier. © 2012 American Chemical Society

Received: Revised: Accepted: Published: 13839

June 18, 2012 September 18, 2012 September 28, 2012 September 29, 2012 dx.doi.org/10.1021/ie301604v | Ind. Eng. Chem. Res. 2012, 51, 13839−13845

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in the solid under its own weight, resulting in an increasing of the bulk density and the solid strength. The higher the strength, the more difficult the solid discharge. Powder consolidation, arching phenomena, and discontinuous flow may occur at high pressures, which affect the continuous, stable, and long period operations of gasification and require urgent resolution. This paper mainly focuses on the discharge of pulverized coal from a pressurized aerated hopper. It is a further research of our previous work.7 An aerated discharge system was established to carry out the experiments. Especially, the hopper in this work reaches the pilot-scale, which makes the research more valuable for scale-up. In the paper, the pressurization process considered as the key factor to affect the hopper discharge was first discussed. The hopper pressure was then arranged from atmospheric pressure to 1800 kPa to investigate its effect on the discharge of pulverized coal.

2. EXPERIMENTAL SETUP Pulverized coal from Yangchangwan coal mine (Ningxia Province, China) was used for this work. The particle size distribution, measured by a laser diffraction particle size analyzer (Malvern Mastersizer 2000), particle density, determined by the pycnometer method, and bulk density, measured by a powder characteristics tester (Type BT-1000), are reported in Table 1. According to the Geldart classification,

Figure 2. Schematic diagram of the pressurized aerated hopper.

Table 1. Properties of the Pulverized Coal size distribution [μm]

powder pulverized coal

10%

50%

90%

particle density [kg/m3]

4

24

73

1532

bulk density [kg/m3]

Geldart’s group

469

C

this powder belongs to the Group C or, in other words, it is a “cohesive powder”, which is characterized as a small size, strong interparticle cohesive force, easy to form agglomerates and extremely hard to be fluidized and discharged.8 The hopper used for this work is illustrated in Figure 2. Top of the hopper is a bin with a diameter of 600 mm and a height of 1000 mm. The conical section, with an outlet diameter of 50 mm and a hopper half angle (α) of 15°, consists of two parts, the lower of which is a porous cone with a height of 340 mm. The surface of the porous cone is completely covered by small air vents as shown in Figure 2. At the bottom, a standpipe (50 mm ID) is attached to the hopper to channel the powder into the receiving vessel. The complete setup for the experiments is illustrated in Figure 3, the aerated discharge system. The experimental facility consists of gas feeding system, vessels, pipeline, filter, instruments, and data acquisition system. It is a closed system for the powder so that the dust emission problem is minimized. The core facility is the pressurized aerated hopper, which is made of carbon steel. The whole system can be operated under a maximum pressure of 2.5 MPa. Before starting the experiment, the hopper was first loaded with about 120 kg of pulverized coal, showing an initial solid height of about 1.5 m. The aeration gas was then introduced. As shown in Figure 3, gas supplied by the N2 cylinders, first flowed into the buffer tank and then entered the hopper. It was aerated through the air vents into the porous cone in the form of “Distributed case” described by Altiner.9 Assuming that the gas

Figure 3. Experimental setup of the aerated discharge system.

velocity is distributed uniformly over the whole aeration area, the gas superficial velocity is therefore the gas volumetric flow rate divided by the aerated surface area, as defined in eq 110 Ug =

Qg 2

p0 2

π sin α(ri − rj ) p0 + p

(1)

where Qg is the gas volumetric flow rate, P0 is the atmospheric pressure, P is the hopper pressure, and ri and rj are radial distance of apex to upper and lower boundary aeration section, respectively. In the experiments, the gas flow rate was regulated 13840

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by a valve and measured with a gas flow meter. The hopper pressure was gradually increased until the desired value was reached. In the experiment, this pressure was adjusted and remained stable by the pressure control system, which included a pressure transducer at the top of the hopper and a pressure regulator in the venting channel. The valve in the equalizing pipe was opened at the beginning of pressurization process and lasted until the end of hopper discharge to ensure the “no pressure differential” discharge process. Weighing cells were installed in the hopper to monitor the mass variation of the pulverized coal. To eliminate the effect of storage time, the pulverized coal was aerated at the desired aeration conditions before each measurement. The outlet valve was then opened after a period of time long enough for the bed to reach stationary aeration conditions. During the discharge, time series of pressure signals and mass of residual solid were acquired by the data acquisition system at the frequency of 1 Hz. The solid discharge rate was determined from the weight-versus-time curve. After being discharged, the pulverized coal was transported back to the hopper by dense phase pneumatic conveying technology. The experiment was repeated with different hopper pressures and aeration rates.

effect, characterized by arching or unstable discharge; when introduced at the bottom, it has a positive effect and improves discharge to mass flow. For the former (Qgtop), it is thought that the direction of gas flow is downward and the gas pressure gradient adds directly to the weight of the solid with resultant significant densification as discussed by Jenike. Therefore, the higher the hopper pressure, the harder the hopper discharge. On the contrary, for the latter (Qgbottom), the gas stream tends to lift the mass of solid, improves the flow properties of pulverized coal to liquid-like, and benefits the discharge. These two effects of aerated gas on solid are similar with those proposed by Liu:11 (1) gas shows a compaction effect and can be regarded as a mechanical thrust on the powder surface; (2) gas penetrates into the material and reduces its shear stress. Our previous study12 showed that, for aerated discharge, fluidization in the hopper was the initial state of the discharge process; the state of gas−solid fluidization affected the subsequent hopper discharge significantly. It is therefore considered that the gas supplement method affects the gas−solid fluidized state inside the hopper and is responsible for the hopper discharge. On the basis of the discussion above, pulverized coal is almost consolidated and fluidized at the same time during pressurization of the hopper. The conception of “fluidized pressurization” was proposed in this work so as to improve the fluidization quality and the hopper discharge. However, there is also a price to pay. On one hand, the hopper must have a void space at the top to accommodate the expanding solid. On the other hand, gas must be injected uniformly over a large area. In this case, gas velocity is considered to be distributed uniformly over the whole conical aeration area, which will minimize the consolidation effects. Both these requirements are satisfied for the pressurized hopper in our aerated discharge system. The “fluidized pressurization” process has been proved to be effective to promote the solid discharge even under high pressures. It should be noted that, in the operating cycle, the time of depressurization, filling the hopper, and pressurization cannot exceed the time of discharge. Thus, in order to shorten the pressurization time, sometimes the two kinds of gas supplement methods above are adopted. Our patent13 has pointed out that, to avoid the consolidation effects, the gas from the top should be no more than 30% of the total gas flow rate. 3.2. Effect of Hopper Pressure on Discharge. The discharge experiments (with “fluidized pressurization”) were carried out by changing the aeration rate at the hopper pressure ranged from atmospheric pressure to 1800 kPa. Some features can be summarized as follows: Figure 5 shows the relationship between the gas volumetric flow rate (Qg) and the solid discharge rate (WS) at five different pressure levels, including atmospheric pressure, 200, 400, 1000, and 1800 kPa. It can be seen clearly that, the solid discharge rate first increases and then decreases with the increasing gas volumetric flow rate at each fixed hopper pressure. Our previous study14 carried out at the atmospheric pressure demonstrated that the solid discharge rate increased with the gas volumetric flow rate until a maximum value was reached, beyond this point additional gas flow was either ineffective or actually retarded flow. Figure 5 indicates that the relationship is maintained in the experimental range even though the hopper pressure varies a lot. There is always a region of gas volumetric flow rate [Qglow,Qghigh] available to discharge pulverized coal, and

3. RESULTS AND DISCUSSION Generally, the operating cycle of a lock hopper can be divided into four steps: filling, pressurization, discharge and depressurization. For a given solid, the time needed to fill a hopper from the atmospheric bin above is governed by the design of the bin and by the size of the inlet valve. The shorter the available time the larger the required inlet valve. On the other hand, depressurization can be always accomplished rapidly and causes no problem. However, the process of pressurization is less well understood and discharge from the pressurized hopper can be often problematic.6 In this section, processes of depressurization and discharge will be discussed, respectively. 3.1. Process of Pressurization. Gas can be generally aerated either at the top (Qgtop) or at the bottom (Qgbottom) of the vessel, as shown in Figure 4. The experimental results shown in

Figure 4. Methods of injecting air into a vessel.

Table 2 present the opposite effects of these two aerated methods: when introduced at the top, it always has a negative Table 2. Effect of Gas Supplement Method gas supplement method

results

at the top, Qtop at the bottom, Qbottom

negative effect, hinder discharge positive effect, improve discharge 13841

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superficial velocities, aeration can be effective on a local level; increasing gas flow increases the volume of powder affected and the solids discharge rate; when gas flow increases beyond a certain degree, excess energy would produce the bubble motion and restrain the discharge instead. Contrary to gas volumetric flow rate, Figure 6 shows that the region of gas superficial velocity [Uglow,Ughigh] available for the solid discharge moves left with the increasing hopper pressure. Although the gas superficial velocity decreases as the hopper pressure increases, it is actually more difficult to discharge pulverized coal from the pressurized hopper, because the discharge region becomes narrower as the hopper pressure increases which increases the uncertainty and instability of the hopper discharge. At high hopper pressures, the optimum gas superficial velocities (Ugopt, corresponding to the maximum solid discharge rate) is harder to obtain; even a small fluctuation of the gas superficial velocity can lead to a significant change in the solid discharge rate or even in the arching phenomena. Furthermore, Figure 6 shows that the range of the discharge rate [Uglow,Ughigh] decreases gradually with the increase of the hopper pressure. Specifically, when the hopper pressure increases from atmospheric pressure to 200 kPa, Ugopt decreases about 20 mm/s; when the hopper pressure increases from 200 to 400 kPa, Ugopt decreases about 10 mm/s; when the hopper pressure increases from 400 to 1000 kPa, Ugopt decreases about 8 mm/s; when the hopper pressure increases from 1000 to 1800 kPa, Ugopt decreases about 4 mm/s. This is led to a speculation that, Ugopt would be a relatively stable value when the hopper pressure varies in a certain range. This is important and can provide a valuable reference point for solid discharge at high pressures as well as industrial applications, for the entrainedflow gasifiers are always operating at pressure of about 4.0 MPa and there is always a requirement for discharging pulverized coal from lock hoppers at pressure of about 5.0 MPa. As mentioned, the gas volumetric flow rate and the gas superficial velocity show an opposite trend with the increase of the hopper pressure. Therefore, the relationship between their products and the hopper pressure is of concern. First of all, gas momentum flux (Ig) is defined in eq 2,

Figure 5. Relationship between gas volumetric flow rate and solid discharge rate.

there is always an optimum gas volumetric flow rate (Qgopt) corresponding to the maximum solid discharge rate (WSmax) at each hopper pressure. In other words, the hopper pressure shows little effect on the basic discharge law. However, Figure 5 shows that the range of the discharge rate moves right gradually with the increase of the hopper pressure, which indicates more energy input is needed to discharge solid from the pressurized hopper. On one hand, in order to mobilize the solids effectively, the gas volumetric flow rate should be remained in a certain range under a fixed hopper pressure. On the other hand, when the hopper pressure increases, the gas volume is nearly compressed proportionally, and thus the gas velocity decreases sharply accordingly. Therefore, our experimental result shows that the larger gas volumetric flow rate is needed to discharge pulverized coal from the pressurized hopper. As shown in Figure 5, the gas volumetric flow rate increases with the hopper pressure; the higher the hopper pressure, the larger the gas volumetric flow rate is needed to support the solid discharge. On the other hand, Figure 6 shows the solid discharge rate as a function of the gas superficial velocity (Ug). At low gas

Ig = Q gUgρg

(2)

where ρg is gas density. Figure 7 shows the relationship between the gas momentum flux and the solid discharge rate. It can be seen clearly that the solid discharge rate first increases then decreases with the increase of the gas momentum flux at each hopper pressure. On one hand, the observation of the discharge rate as a function of the gas momentum is somewhat in agreement with other more precise theories on the prediction of the solids flow rate.15,16 For example, there is a quadratic term in the gas rate of eq 18 in Barletta et al.,16 which is proportional to the square root of the gas velocity and the gas density as the Ig term of eq 2 in this paper. It is considered that the quadratic term accounts for turbulent friction between the aeration gas exiting through the hopper outlet and the discharging solids. This term is predominant for aggregates of the order of the millimeter. In our work, the pulverized coal used shows small size and strong interparticle cohesive force, which is discharged in the form of aggregates rather than single particles.8 This justifies the observed trend of the discharge rate with the gas momentum also in light of eq (18) in Barletta et al.

Figure 6. Relationship between gas superficial velocity and solid discharge rate. 13842

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Table 3. Effect of Hopper Pressure on Pulverized Coal Discharge

On the other hand, the relationship in Figure 7 can be also confirmed by Ferrari and Bell,17 who considered that the effect of aeration did not depend on fluidization velocity, but on gas momentum. They further demonstrated that the solid discharge rate was increased even with gas superficial velocities that were considerably lower than the minimum fluidization velocity. These support our results and help to explain why aeration can even obtain higher solid discharge rates at high pressures, though the gas superficial velocities are far smaller than those at atmospheric pressure. In addition, in the report of Ferrari and Bell, there was no observable step effect which corresponded to the gas momentum suddenly reaching a level sufficient to overcome interparticle forces. However, in our work, based on abundant experiments, the optimum gas momentum flux (Igopt) can be obtained from Figure 7, about 0.5 × 10 −3 kg·m/s 2 corresponding the maximum solid discharge rate (WSmax). This value is closely related to powder properties, hopper structure, and aeration method, etc. On one hand, the optimum gas momentum flux keeps constant with the increase of the hopper pressure in the experimental range. This further corroborates the conclusion that the effect of aeration depends on the gas momentum. On the other hand, the maximum solid discharge rate increases to some extent with the hopper pressure, which indicates that pressure can take a positive effect on the hopper discharge. Further, more experiments were carried out to obtain the maximum solid discharge rates at atmospheric pressure, 200, 400, 600, 800,1000, 1200, 1400, 1600 and 1800 kPa. The optimum gas volumetric flow rates, the optimum gas superficial velocities, the optimum gas momentum fluxes and the maximum solid discharge rates at each hopper pressure are reported in Table 3. Meanwhile, the optimum gas volumetric flow rate and the optimum gas superficial velocity can also be calculated from eqs 3 and 4 by substituting eq 1 into eq 2 Qg = opt

Ug = opt

Ig

P0 π sin α(ri − rj )ρg P0 + P

optimum gas volumetric flow rate [Nm3/h]

optimum gas superficial velocity [mm/s]

optimum gas momentum flux [×10−3 kg·m /s2]

maximum solid discharge rate [kg/h]

0 200 400 600 800 1000 1200 1400 1600 1800

26 44 57 68 77 86 93 100 107 112

55 31 25 21 18 17 15 14 14 13

0.51 0.49 0.51 0.51 0.51 0.51 0.51 0.52 0.52 0.51

4419 6066 6735 7607 7943 8659 8265 8206 7994 8262

Figures 8 and 9 show the comparison between experimental data (from Table 3) and model predictions (from eqs 3 and 4).

Figure 7. Effect of gas momentum flux on solid discharge rate.

π sin α(ri 2 − rj 2)Ig P + P opt 0 ρg P0

hopper pressure [kPa]

Figure 8. Comparison between experimental optimum gas volumetric flow rate and those predicted with eq 3: (□) experimental data; () eq 3.

Figure 9. Comparison between experimental optimum gas superficial velocity and those predicted with eq 4: (□) experimental data; () eq 4.

(3)

opt

2

2

(4) 13843

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fluidization quality of a bed of fine powders improves with a pressure increase.20 Rietama21 proposed the concept of elasticity of the bed structure to explain the effect of pressure. Pipers22 confirmed that the amount of N2 adsorption increased considerably at elevated pressure, which increased the elasticity modulus and improved the fluidization quality. It is therefore considered that increasing the hopper pressure can improve the fluidization quality and consequently promote the solid discharge with the precondition of proper pressurization, such as fluidized pressurization process.

It can be seen clearly that eqs 3 and 4 fit the experimental results well. With the increase of the hopper pressure, the optimum gas volumetric flow rate increases and the optimum gas superficial velocity decreases, respectively. Just as discussed above, the reduced magnitude of the optimum gas superficial velocity decreases gradually, and will approach a relatively stable value at a range of high pressures. To make this work meaningful, the value of the optimum gas superficial velocity at pressures of 4.5−5.0 MPa is estimated, which is the common pressure of industrial operations (4.5 MPa for GSP gasification and 4.7 MPa for Shell gasification as shown in the Introduction). It shows that the optimum gas superficial velocity varies in the range of 7.3−7.8 mm/s calculated by eq 4. This value would be very valuable for industrial operation, for which it is always hard to estimate the optimum gas superficial velocities under high pressures. Even though the value might be limited for other system, the analysis method is however effective to push the experimental data to the industrial applications. Furthermore, Figure 10 shows the effect of hopper pressure on the maximum solid discharge rate directly. It can be seen

4. CONCLUSIONS (1) Solids can be consolidated and fluidized at the same time during pressurization of the hopper. The conception of “fluidized pressurization” was proposed on the basis of analyzing the effect of aerated gas on the solid, which improved the fluidization quality and the hopper discharge, effectively. (2) The experimental results showed that the gas volumetric flow rate increased and the gas superficial velocity decreased when the hopper pressure increased gradually from atmospheric pressure to 1800 kPa. With the increase of the hopper pressure, more energy was needed and the discharge uncertainty and instability was increased. (3) At each hopper pressure, there always existed an optimum gas volumetric flow rate and an optimum gas superficial velocity corresponding to the maximum solid discharge rate. The expression of gas momentum flux was defined to describe the effect of aeration, and the optimum gas momentum flux was obtained which was related closely with powder properties, hopper structure, and aerated method but independent of the hopper pressure. The optimum gas volumetric flow rates and the optimum gas superficial velocities were predicted and agreed well with the experimental data, which were valuable for industrial operation (4) With the increase of the hopper pressure, the gas−solid fluidization quality inside the hopper was improved so as to promote the hopper discharge. In the experiments, the maximum solid discharge rate increased with the hopper pressure until it finally reached a limit value of about 8000 kg/h at 800 kPa.

Figure 10. Effect of hopper pressure on maximum solid discharge rate.

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clearly that the maximum solid discharge rate increases gradually with the hopper pressure until it finally reaches a stable value of about 8000 kg/h. A positive effect of pressure on hopper discharge is shown for the hopper pressure smaller than 800 kPa. Similarly in Du and Liu’s report,18 the increase of the maximum solid discharge rate exceeded 20% when the hopper pressure increased from 290 to 360 kPa. Jianjun19 also considered that pressurizing the hopper by injecting air could be effective in promoting hopper flow. On the other hand, the maximum solid discharge rate seems independent of the hopper pressure for those bigger than 800 kPa. It is thought that 8000 kg/h is the maximum discharge ability expected of the hopper in our aerated discharge system. Therefore, a continually increase of the hopper pressure is much less efficient on the solid discharge. There is little reported about solid discharge from pressurized hoppers. Thus, the effect of hopper pressure on discharge can tried to be explained based on an analysis of gas− solid fluidization behaviors inside the hopper. As discussed above and proved by Barletta et al,16 the better fluidization state always favors the discharge which always corresponds to the higher discharge rate. Scholars have already found that the

AUTHOR INFORMATION

Corresponding Author

*Tel: +86 21 6425 2521. Fax: +86 21 6425 1312. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (21006027), and “Chen Guang” project supported by Shanghai Municipal Education Commission and Shanghai Educational Development Foundation. Especially, the authors thank the anonymous reviewers for their helpful suggestions on the quality improvement of this article.

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NOMENCLATURE Ig = gas momentum flux, kg·m/s2 Igopt = optimum gas momentum flux, kg·m/s2 P0 = atmospheric pressure, kPa P = hopper pressure (gauge pressure), kPa Qg = gas volumetric flow rate, Nm3/h dx.doi.org/10.1021/ie301604v | Ind. Eng. Chem. Res. 2012, 51, 13839−13845

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(17) Ferrari, G.; Bell, T. A. Effect of aeration on the discharge behaviour of powder. Powder Hand. Process. 1998, 10, 269−274. (18) Du, S. W.; Liu, T. C. A rate model for the discharge of pulverized coal from a pressurized aerated-tank. Powder Technol. 1989, 57, 69−75. (19) Dai, J.; Cui, H. P.; Grace, J. R. Biomass feeding for thermochemical reactors: Review. Prog. Energy Combust. Sci. 2012, 38, 716−736. (20) Barreto, G. F.; Yates, J. G.; Rowe., P. N. The effect of pressure on the flow of gas in fluidized beds of fine particles. Chem. Eng. Sci. 1983, 38, 1935−1945. (21) Rietama, K.; Piepers., H. W. Effect of interparticle force on the stability of gas-fluidized beds. I. Experimental evidence. Chem. Eng. Sci. 1990, 45, 1627−1639. (22) Piepers., H. W.; Cottaar, E. J. E.; Verkooijen, A. H. M.; Rietema, K. Effects of pressure and type of gas on particle-particle interaction and the consequences for gas−solid fluidization behavior. Powder Technol. 1984, 37, 55−70.

Qgtop = aeration at the top of the vessel Qgbottom = aeration at the bottom of the vessel Qglow = lower limit of gas volumetric flow rate for hopper discharge, Nm3/h Qghigh = upper limit of gas volumetric flow rate for hopper discharge, Nm3/h Qgopt = optimum gas volumetric flow rate, Nm3/h ri, rj = radial distance of apex to upper and lower boundary aeration section, m Ug = gas superficial velocity, mm/s Uglow = lower limit of gas superficial velocity for hopper discharge, mm/s Ughigh = upper limit of gas superficial velocity for hopper discharge, mm/s Ugopt = optimum gas superficial velocity, mm/s WS = solid discharge rate, kg/h WSmax = maximum solid discharge rate, kg/h α = hopper half angle, (deg) ρg = gas density, 1.293 kg/m3 at standard state

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