Biomass granular screw feeding: An experimental investigation

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Biomass granular screw feeding: An experimental investigation Jianjun Dai, John R. Grace* Department of Chemical and Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, BC, V6 T 1Z3, Canada

article info

abstract

Article history:

Successful feeding is critical to biomass utilization processes, but difficult due to the

Received 18 August 2009

heterogeneity, physical properties and moisture content of the particles. The objectives of

Accepted 4 November 2010

the present study were to find the mechanisms of blockage in screw feeding and to

Available online 4 December 2010

determine the effects of particle mean size (0.5e15 mm), size distribution, shape, moisture content (10e60%), density and compressibility on biomass particle feeding at room

Keywords:

temperature. Wood pellets, sawdust, hog fuel and wood shavings were tested in a screw

Biomass

feeder/lock hopper system previously employed to feed sawdust into a pilot-scale circu-

Feeding

lating fluidized-bed gasifier. Experimental results showed that large particles, wide size

Screw feeder

distributions, large bulk densities and high moisture contents generally led to larger torque

Torque

requirements for screw feeding. The “choke section” and seal plug play important roles in

Blockage

determining the torque requirements. ª 2010 Elsevier Ltd. All rights reserved.

Hopper

1.

Introduction

Interest in using biomass feedstocks to produce heat, power, liquid fuels, and hydrogen and to reduce greenhouse gas emissions is increasing worldwide. Biomass feedstocks are potentially available in five categories: mill wastes, urban wastes, forest residues, agricultural residues and energy crops. Approximately 50% of the biomass globally available is woody, whereas 20e40% is grassy [1]. Demolition woods (both pure and mixed with sewage sludge and paper sludge) may also be used for gasification [2]. The chemical composition and physical properties of the feedstocks influence the design of biomass-processing reactors, such as gasifiers, combustors and pyrolysers, as well as the composition of the product gas and downstream cleanup methods. In general, fuels with high energy contents, high carbon-to-nitrogen ratios, relatively little sulfur and ash, regular shapes, small particle size, narrow size distribution, moisture content <55% (wet basis), suitable bulk density, and

low contaminant level are preferred as raw materials. Biomass fuels (such as sawdust, hog fuel, straw, rice hull, sugar cane, bagasse and grass) are unique materials, with particles varying greatly in size and shape. Some are wet, leading to sticking. They also tend to be compressible and pliable. Some may be easily fractured (e.g., wood pellets, walnut shells), while others may be stringy and resilient (e.g., grass, straw, hay, cotton stalk, corn stover, wood chips). Many biomass processes, including combustion, gasification, and pyrolysis, are under development. A critical problem in all cases is how to feed biomass into reactors. Feeding problems often impede smooth operation. Such properties as mean particle size, size distribution, shape, particle surface (e.g., smooth, rough or sharp edges), density, moisture content, compressibility and other fuel properties (e.g., strength of large particles, consolidation over time) can all affect the ability to feed the material. In biomass energy processes, several kinds of feeders and their combinations have been reported, in particular hopper

* Corresponding author. Tel.: þ1 604 822 3121; fax: þ1 604 822 6003. E-mail address: [email protected] (J.R. Grace). 0961-9534/$ e see front matter ª 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.biombioe.2010.11.026

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or lock hopper systems, screw feeders, rotary valves, piston feeders and pneumatic feeders. They can also be combined rather than be separate, especially for continuous operations. These feeders have been developed for a variety of solids, but they have limitations in handling certain types of biomass and/or in feeding to pressurized reactors. Screw or piston operated plug feeders, common in feeding coal, have also been tested with biomass [3e10]. Hopperescrew feeders are common in biomass applications. Lack of flow is a common and serious solids handling problem. Flow stoppage may be caused by a bridge or “rathole” in the hopper, or by blockage or slippage in the screw itself. The flow patterns developed by screw feeders coupled to a hopper have been studied extensively, and mechanics and transport function of screw feeders have been investigated in detail [11e18]. Mixing and transportation of the particles inside screw feeders have also been analyzed [19]. However, biomass fuels have largely been ignored in previous research. The present study focuses on the feeding of biomass particles. The objectives are to define what limits screw feeding in terms of the mechanisms of blockage and to examine the effects of mean particle size (0.5e15 mm), size distribution, shape, moisture content (10e60%), density and compressibility. The work does not emphasize hopper flows, which have been widely studied, but rather the flow of biomass particles through the screw feeder.

2.

Background on screw feeders

Screw feeders are volumetric devices, with delivery depending on the screw’s outside and inside (shaft) diameter, pitch (distance between adjacent flights) and fullness. If the solids are compressible (e.g., sawdust, hog fuel), the mass delivered per unit time varies. The velocity of conveyed solid material is a vector having an angle to the direction of rotation. As the screw rotates, particles move in helical paths of direction opposite to that of the screw. The frictional effects of the solids on the screw flights and on the casing surface, together with the configuration of the screw, determine the efficiency of the feeder. The efficiency decreases as the clearance between the discharge casing surface and screw flight tips increases. The screw feeder design must

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complement the hopper design so that the bulk solids do not arch or “rathole” across the feeder inlet [12,16,18,20e23]. Screw feeders used to feed biomass operate in a manner similar to piston feeders, but have a somewhat lower pressurization range (0.5e1.5 MPa). In a screw feeder, an auger compresses the feedstock into a compact plug, aided by tapering the feed channel, or by gradually reducing the pitch of the screw. The feed plug then forms a barrier, preventing backflow of gases and bed material from the reactor [5,9]. The feeder volumetric flow capacity is calculated based on the screw and casing dimensions at the entrance to the choke section. The volumetric feed rate is given [15] by: V ¼ Avhv

(1)

where A is the cross-sectional area of the screw feeder, and v is the ideal axial feeding velocity of the screw, ¼uP/(2p), P is the pitch, u is the angular velocity, and hv is the volumetric efficiency, i.e., the volumetric flow divided by the flow if the pockets were completely full and particles traveled at the feeder speed without slip or rotation. The corresponding mass flow rate M is obtained by multiplying the bulk density, i.e., M ¼ V  rb. The thickness of the screw flight is usually neglected in predicting the flow rate. The volumetric efficiency, hv, is less than 1 for several reasons: (1) The axial velocity of particles is less than the ideal or optimum velocity owing to the rotary motion imparted by the screw. (2) Slip may occur in the clearance space between the screw and casing. (3) The filling fraction of screw pockets decreases as rotational speed increases because the screw has a capacity greater than what can be filled in practice.

3. Experimental set-up, methodology and materials fed Two screws were tested in our study. Except where otherwise specified, the work below refers to screw-1. Schematics of the experimental lower hopper and screw feeder appear in Fig. 1,

Fig. 1 e Schematic of lower hopper and screw feeder.

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Fig. 2 e Schematic of biomass feeding system.

could not be broken, the materials were removed from the hopper manually before the next run. Three initial hopper levels were tested: high (0.6 m), medium (0.45 m) and low (0.3 m). The present study employed wood pellets, sawdust, hog fuel and wood shavings as biomass materials, as well as polyethylene particles to provide a reference case for comparison. The most important physical properties of these materials are listed in Table 3. The compacted density in the choke section, including the extended and tapered sections, were estimated by the measured weight of biomass in a known length of the choke section. The particle mean diameters and size distributions in Table 3 and Fig. 3 were determined by sieve analysis. A Sauter mean particle diameter was employed, defined as X xi =di (2) dm ¼ 1= where xi is the mass fraction of particles of mean diameter di. The wood pellets were approximately cylindrical and almost

1.0

0.8

Cumulative weight (%)

while Fig. 2 shows an overall schematic of the experimental set-up. Biomass fuels (e.g., wood pellets, hog fuel and sawdust) were added to the lower hopper and the surface was flattened. A variable-speed DC motor (0.56 kW, Baldor CDP3440) adjusted the rotational speed of the screw. A weighing scale (B.C. Scale Co. Ltd., Model: Cardinal EF 100, capacity: 50 kg, accuracy: 0.02 kg), connected to a computer was used to record the weight of the delivered material at time intervals of 2 s. A torque meter (S. Himmelstein and Company, Model: MCRT28004 T 5e3, capacity: 565 N.m, accuracy: 0.1% of full scale) with Model 721 Mechanical Power Instrument was installed between the DC motor gear reducer and lower hopper to measure the screw torque and rotational speed at a frequency of 36 Hz during feeding. A 102 (ID)  305 mm long cast acrylic transparent tube was installed between the lower hopper and receiving vessel to allow visualization of the flow through the screw feeder. A video camcorder captured images of particles being transported and interacting with each other and with the inside wall of the transparent tube, as well as with the screw flights. Blockage processes were also recorded by the camcorder. Although blockage is a complex phenomenon during hopperescrew feeding and cannot be explained completely by viewing through the transparent tube, visualization is very helpful to understand the flow of particles and the blockage mechanism. Blockage could also be detected by changes in torque and rotational speed. All data were stored in a data acquisition computer for later analysis. Each experiment was performed two to five times in order to determine the range of flow rates and torque values for a given material and corresponding experimental conditions. All measurements were carried out at room temperature (20  C) and atmospheric pressure. The fill level in the feed hopper declines during each feeder trial unless the feeder is periodically refilled. The flow rate was determined from the average flow rate in the first 2 min after stable feeding was established. Feed rate and torque readings are time-averaged for analysis. When blockage occurred and

Sawdust-1 Hog fuel-1 Ground hog fuel Wood shaving-1 Ground wood pellets-2

0.6

0.4

0.2

0.0

0 .1

1

10

Size (mm)

Fig. 3 e Particle size distributions of biomass fuels.

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4.

Experimental results and discussion

4.1.

Feed rate and variability

Theoretical volumetric flow rate Wood pellets Ground wood pellets-1 Ground wood pellets-2 Sawdust-1 Hog fuel-1 Ground hog fuel Wood shavings-1 Polyethylene particles

1.4

1.2 3

Volumetric flow rate m /h

uniform in size (average dimensions: 46.5 mm  15 mm) after removing a small fraction of finer material by sieving through a 4.75 mm opening screen. Some grinding of the wood pellets by the screw feeder occurred in the experiments. Therefore, wood pellets were only reused after removal of fines by again sieving through the same 4.75 mm screen. When the wood pellets changed significantly, they were replaced by new pellets to ensure consistency. Further details of the experimental set-up, particles and methodology are provided elsewhere [24].

1.0

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 4 indicates that the mass flow rate was linearly proportional to screw rotational speeds (<45 rpm) for all materials. The error bars show the variability of the measurements at the 95% level of confidence. Larger screw speeds generally led to lower coefficients of variation, although higher screw speeds caused lower volumetric efficiencies. For all materials in the present study, volumetric feed rates were lower than the theoretical volumetric capacity of the screw feeder (i.e., hv < 1), as shown in Fig. 5. This was due to reduced filling fraction and unavoidable rotation/slippage of the particles. Due to their greater compressibility, hog fuel-1 (11% moisture) and wood shavings-1 (10% moisture) had somewhat higher volumetric efficiencies than the polyethylene particles, wood pellets and ground wood pellets. While the bulk densities of the compressible materials (e.g., hog fuel, sawdust) did not change much when they passed through the screw feeder, these materials were compressed inside the screw feeder, making their bulk density somewhat larger than in the loose state. This allowed more mass flow to be delivered for compressible materials. Hog fuel-1 and wood shavings-1 also had slightly larger volumetric flow rates than sawdust-1 (14% moisture) at the same screw speed. Their wide size W ood pellets Ground wood pellets-1 Ground wood pellets-2 Sawdust-1 Hog fuel-1 Ground hog fuel W ood shavings-1 Polyethylene particles

400

1.6 1.4

3

Mass flow rate (kg/h)

500

300 200 100 0 0

5

10

15

20

distributions are likely the main reason, since fines can fill the spaces between the large particles increasing the mass and volumetric flow rates. Polyethylene particles provided volumetric flow rates similar to sawdust-1 and ground wood pellets at the same screw speed, despite differences in particle shape and surface roughness. The relatively low volumetric efficiencies for the wood pellets can be attributed to their larger mean size, cylindrical shape, rougher surfaces, and larger densities. The initial hopper level (distance from axis of screw to leveled free surface of bulk solids) affected the flow rate somewhat as shown in Fig. 6. A higher hopper level provided larger feeder load, increasing the vertical stress on the screw feeder, increasing the fullness of the screw pockets and promoting flow. Higher hopper levels can increase the fullness of the screw pockets and increase the feeding efficiency, but beyond a certain level there is no further gain. The active stress field is replaced by the passive stress field in the hopper

Volumetric flow rate m /h

600

Fig. 5 e Relationship between volumetric flow rate and screw speed for screw-1 with different biomass materials and initial hopper level of 0.3 m.

25

30

35

40

45

Screw speed (rpm)

Initial hopper level: 0.3 m 0.45 m 0.6 m

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

Fig. 4 e Relationship between mass flow rate and screw speed for screw-1 and different biomass materials with initial hopper level of 0.3 m. Error bars correspond to 95% confidence intervals.

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 6 e Effect of hopper level on volumetric flow rate for sawdust-1 and screw-1.

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once feeding has been initiated, inhibiting hopper flow and reducing the effect of hopper level on flow rate [25]. The effects of hopper level on flow rates depended on the biomass properties, packing density inside the hopper, and the hopper and screw configurations. Moisture content also affected the flow rate. Higher moisture content was more likely to cause bridging or rat-holes in the hopper, leading to reduced mass and volumetric feed rates. Sawdust of higher moisture content showed lower volumetric efficiencies than ones of lower moisture contents, as shown in Fig. 7, although the mass flow rates were similar for a given screw speed. Sawdusts of higher moisture content (e.g., 40 or 60%, wet basis), especially after 24 h of consolidation, readily bridged in the hopper due to increased cohesion, while also increasing wall and internal friction, especially for hopper levels > 0.2 m. The arches or bridges in the hopper had to be broken for the sawdust to fall into the screw pockets. While blockage sometimes occurred in the hopper, no blockage could be observed inside the screw feeder itself. However, loud “screeching” could be heard from time to time, indicating that the screw was having difficulty overcoming the pressure and friction of the sawdust on the screw and casing surfaces.

4.2.

Blockage tests and analysis

Higher hopper levels could trigger blockages, depending on the particle properties and equipment configuration. As shown in Fig. 1, the hopper used here was wedge-shaped, a shape generally less likely to bridge than a cone-shaped hopper [26,27]. For wood pellets of uniform size (6.5(D)  15(L) mm), blockage inside the screw feeder tended to occur when the hopper level exceeded 0.35 m. When the feeder load was large enough (e.g., hopper level > 0.4 m), the screw feeder blocked almost immediately after the screw began to rotate. Most of these blockages were irreversible, i.e., they could not be broken by either reversing or restarting the motor. To recover, it was necessary to remove the wood pellets from the hopper. On the other hand, blockages could be dislodged within w6 s or by reversing or restarting the motor for hopper levels < 0.4 m. Compared to polyethylene spheroidal particles,

Theoretical volumetric flow rate

1.2

3

Volumetric flow rate m /h

1.4

1.0

moisture (wet basis): 14 % 40 % 60 %

0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 7 e Effects of moisture content on volumetric flow rate for sawdust and screw-1.

which did not block the screw for hopper levels 0.6 m, wood pellets blocked more easily. This is mainly attributed to their poor flowability caused by larger particle size (9.8 mm mean diameter), more irregular shapes (cylindrical), and rougher particle surfaces. The screeching due to the friction of the pellets on the screw and casing surfaces could often be heard during wood pellet feeding. Wood pellets containing 14% by mass of particles finer than 4.75 mm and 3.2% by mass < 0.5 mm blocked more readily than wood pellets of uniform size (100% > 4.75 mm). However, blockages could be dislodged relatively easily for the former, without major intervention. The time at which the first blockage occurred provides some indication of how readily blockage occurred for each material. This time was determined three times for each screw speed. Higher screw speeds led to quicker blockage after feeding began, but more fuel was delivered to the receiving vessel at higher screw speeds before blockage occurred. The experiments indicated that somewhat higher screw speeds (>30 rpm) reduced the tendency to block inside the screw feeder compared to slower speeds (e.g., 5 rpm) for relatively incompressible particles (e.g., wood pellets and polyethylene particles). However, when a blockage occurred at the higher rotation speeds, it was harder to dislodge. The stress in the hopper directly above the screw is influenced by the screw speed. With increasing speed, and hence increasing flow, the porosity of the bulk material increases slightly near the screw as materials in the vicinity of the screw in the hopper section slightly dilate due to increased screw speed. Even minimal increases of porosity can cause a distinct decrease of stress at the hopper outlet [28], also decreasing the torque requirement. For fine particles inside the bulk material, even slight increases in inter-particle distance cause a drastic decrease of van der Waals forces, contributing to a reduced blockage tendency for higher screw speeds. Furthermore, the screw feeder may shake or vibrate during feeding due to its cantilever structure, minor manufacturing eccentricities and imperfect fabrication tolerances. Shaking or vibrating may cause erratic flow, as well as mechanical wear. The higher the screw speed, the more the screw vibrated, and the more the screw dilated the materials inside the screw feeder. This may be one reason why high screw speeds resulted in fewer blockages and why blockages at high screw speeds were difficult to dislodge. No clear relationship between screw speed and blockage tendency was found for compressible biomass particles. A small favourable pressure drop (0.02 bar) from the hopper to the downstream vessel led to an increase in mass flow rate as indicated in Fig. 8, and a reduction in the tendency to block. When the hopper was at somewhat higher pressure than the receiving vessel, particles in the upper part of the screw pockets were mainly transported by air, reducing the filling fraction and the tendency to block the inside of the screw feeder, whereas particles in the lower part of screw pockets were mainly transported by the screw flights. In the hopper feeding section, bulk solids exert vertical stress on the screw, causing resistance to rotation. The greater the vertical stress, the more the resistance. When particles enter the choke section (see Fig. 1), their movement is controlled by screw rotation and the casing. The screw flights

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400

300

200

100 0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 8 e Effect of screw speed and difference in pressure between hopper and receiver on mass flow rate for wood pellets and screw-1 at initial hopper level of 0.3 m.

press and shear the particles, propelling them forward in spiral trajectories. There are significant normal pressure and shear stresses on the wall surfaces, including the casing and screw flight surfaces. If the flowability of the particles is adequate for screw feeding (e.g., smooth spherical particles of low bulk density), the pressure and friction can be accommodated. However, for materials that do not flow readily (e.g., those with large bulk density, irregular particle shapes and rough particle surfaces), the screw flights must overcome the normal pressure and friction resistance, or the particles will remain stationary. When the power and torque delivered by the motor are large enough, the materials can be transported relatively smoothly by the screw feeder. However, if the power and torque are too small, the particles cannot gain enough energy and momentum from the screw surfaces to advance. In such a case, blockage, possibly irreversible, may occur. If the power and torque provided by the motor are approximately equal to those needed to push particles forward, blockage may occur. This may be momentary, breaking up without intervention, or be resolved by reversing or restarting the motor. For the conditions studied here, a relatively smooth screw finish and a relatively rough trough or casing surface can reduce particle rotation and increase feeding efficiency. If the mass flow decreases, while the screw rotation is nearly constant, bridging or rat-holing may be occurring in the hopper. When the screw slows down and the torque increases due to high resistance, blockage inside the screw feeder is likely to be imminent. Particles at the front of the hopper (end closer to feeder discharge as indicated in Fig. 2) cannot enter the screw pockets because they are already filled by particles which entered at the back of the hopper. Hence particles pile against the front wall of the hopper, forming a relatively stagnant region. If the stagnant region cannot be broken up and the hopper is refilled, particles from the back of the hopper are transported first, as before, and the strength of the stagnant region at the front of the hopper increases, especially when the materials are cohesive and adhesive. This creates

4.3.

Torque

Increases in torque and power requirements during feeding were found to signify a larger blockage tendency for a given biomass and feeder configuration. Starting torque and operating torque are important for screw feeders [29]. The maximum, average and starting torques were all determined in the present study. The average torque was determined after relatively steady state conditions had been achieved. Maximum torque is the largest torque recorded during feeding. It is a critical parameter for biomass feeding, since if the screw feeder is unable to provide this much torque, blockage may occur at any time. Starting torque is the largest torque experienced during the onset of feeding (see Fig. 9). For 40

100

Max. torque: 29.3 N.m, 7.0 min after initiation

35

90 80

30

70 25 60 20 50 15

Ave. torque: 24.9 N.m Standard deviation: 1.77

40

10

30

Starting torque: 10.5 N.m, 3.7 s after initiation

5

Screw speed (rpm)

Mass flow rate (kg/h)

500

a “funnel” flow or “first in, last out” pattern which should be avoided in hopperescrew feeder systems [26]. The stagnant region is a potential contributor to screw feeder blockage. The interface between the hopper feeding section and choke section (see Fig. 1) is important, as it corresponds to the location from which particles are transported into limited casing space. Some particles build up on the outside, since not all particles can enter the casing smoothly. Observations suggested that wood pellets accumulated at the front of the hopper as a result of the screw motion, making the screw expend increasing torque and requiring increasing power to continue the feeding. The stagnant region limits screw feeding. Furthermore, if the material in the stagnant region should collapse, e.g., due to external forces, the screw may shear and compress the materials from the stagnant region, which may already be compact and hard due to consolidation. In general, non-uniform drawdown in the hopper leads to greater torque and power requirement for screw feeding than for uniform draw-down. Different screw configurations (e.g., variable pitch, screw diameter and core shaft diameter) and various mechanical aids may assist in achieving uniform draw-down. However, uniform draw-down and smooth feeding are even harder to achieve for biomass than for other particulate materials due to the unique properties of biomass, discussed above.

Torque (N.m)

No pressure difference 0.02 bar pressure difference (hopper pressure > receiver pressure)

600

20 10

0

speed range: 10.2-11.9 rpm 0

240

480

720

960

1200

1440

0 1680

Time (s)

Fig. 9 e Torque vs. time for screw feeder operating at 10 rpm for sawdust-1 and screw-1 with an initial hopper level of 0.45 m.

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8 7 6

Standard deviation

all materials tested in the present study, the screw speed increased from zero to a final speed of 5e40 rpm within 1 s after commencement of feeding. The time corresponding to the last zero screw speed is chosen as time 0. Table 4 shows that compressible materials spend more time than incompressible materials after feeding commences to reach the starting torque for a given screw speed. Torque was found to be related to the blockage tendency. The larger the torque, the more difficult it is to transport biomass particles. With small loads inside the hopper, the screw feeder ran smoothly, with minor torque spikes, depending on the screw speed. There was direct correspondence between the screw speed and the frequency of torque fluctuations, showing that fluctuations are due to cyclic characteristics of screw feeding and inherent drawbacks of the screw systems (e.g., slight eccentricities). When biomass entered the choke section, the required torque increased. The choke section plays a critical role in biomass feeding. Generally, its length should be at least one to two times the standard pitch [12,17,30]. For biomass feeding, the choke section may be longer, e.g., 6-e10 times the pitch, to promote plug formation and prevent backflow of hot gases and bed materials from the reactor [10]. This causes the torque to increase gradually after initiating feeding. When the biomass was distributed relatively evenly in the hopper and choke section, the torque became relatively stable, and average torque requirements could then be maintained. Since the screw in the present study had a constant pitch, constant core shaft diameter and constant screw diameter in the hopper section, the draw-down pattern was not uniform. Instead a stagnant region formed at the front of the hopper, whereas the back of the hopper tended to become empty after some time. The total feeder load also decreased as feeding proceeded. Furthermore, the passive stress field became important after feeding commenced. All of these factors led to a decrease in torque after a relatively stable series of torque readings. The torque reading fluctuated significantly during feeding, probably because of intermittent momentary bridging in the hopper, and complex dilation and compression inside the choke section. Screw speeds also fluctuated, decreasing

4 3 2 1

0

Starting

0.5

Ground wood pellets-1 Ground wood pellets-2 Sawdust-1 Hog fuel-1 Ground hog fuel Wood shaving-1 Polyethylene particles

0.3 0.2 0.1 0

5

10

15

20

25

40

50

60

70

80

60 50 40 30 20 10 60 50 40 30 20

Wood pellets; Ground wood pellets-1 Ground wood pellets-2

c

b

80 Maximum

0.4

30

when the torque reading increased and increasing as the torque decreased. Stopping and restarting the screw feeder did not affect the torque reading significantly (see Fig. 9). Ratios of average-to-maximum torque and starting-tomaximum torque are plotted in Fig. 10. This ratio is in the range of 0.25e0.70 for hog fuel, ground hog fuel and wood shavings or 0.75e0.90 for the other materials tested. The smaller values are mainly attributed to the wider size distributions and more irregular shapes of hog fuel, ground hog fuel and wood shavings relative to the other materials. The ground hog fuel consists of cylindrical fibrous particles with a relatively narrow size distribution, leading to poor flowability and relatively large torque fluctuations. The ratio of starting-tomaximum torque represents the percentage of starting torque in the actual torque requirement during feeding (i.e., maximum torque). The smaller this ratio, the less important the starting torque and the more significant the choke section

Average

0.6

20

Fig. 11 e Variability of torque, expressed as standard deviation vs. maximum torque for different materials and screw-1 with initial hopper level of 0.3 m.

Torque (N.m)

0.7

10

Maximum torque (N.m)

0.9 0.8

Empty condition Wood pellets Ground wood pellets-1 Ground wood pellets-2 Sawdust-1 Hog fuel-1 Ground hog fuel Wood shaving-1 Polyethylene particles

0

1.0

Ratio of average to maximum torque

5

30

35

40

45

Screw speed (rpm) Fig. 10 e Ratio of average-to-maximum torque for various materials and screw-1 at different screw speeds (initial hopper level of 0.45 m).

60 40 20 0

a 5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 12 e Effects of screw speed and particle size for screw-1 for wood pellets and ground wood pellets with initial hopper level of 0.3 m. (a) Maximum torque; (b) average torque; (c) starting torque.

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Average torque (N.m)

60

and higher bulk densities lead to higher torque. Larger mean particle size and wider particle size distribution cause the maximum torque and starting torque for hog fuel-1 to be larger than for sawdust-1. The larger bulk density of sawdust1 may contribute to its somewhat higher average torque relative to hog fuel-1. For wood shavings-1, the size distribution and particle strength cover wide ranges. Some particles in wood shavings are harder and have larger strengths due to the manufacturing process, leading to more variability (relatively high standard deviation and relatively wide confidence interval) (in Fig. 11). The smaller torque requirement for the polyethylene particles is mainly attributed to their regular shape and smooth particle surfaces. Biomass feeders differ significantly from the feeders used for other materials (e.g., in their screw configurations and choke section length), so that the torque measurements in the present study cannot be readily compared with previous results from other facilities using non-biomass materials.

Ground wood pellets: mean size: 4 mm, shape: cylindrical, conical and discal Polyethylene particles mean size: 4 mm, shape: spheroidal

50

40

30

20

10 0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 13 e Effects of particle shape and screw speed on average torque for screw-1 for polyethylene particles and ground wood pellets-1 with initial hopper level of 0.3 m.

4.3.1. in determining the total torque. In this work, all biomass materials were found to have ratios in the 0.25e0.5 range, whereas polyethylene particles gave ratios of 0.55e0.65. These values indicate that the starting torques of all fuels were manageable relative to the overall torque requirements. Smaller ratios were mostly found for low bulk density materials, and for the long choke section. The longer the choke section, the greater influence it had in determining the total torque requirements for biomass screw feeding. Average torques and corresponding 95% confidence intervals for a rotation speed of 5 rpm appear in Table 5. Examination of these data together with the particle properties in Table 3 indicates that larger particles, more irregular shapes

Maximum torque (N.m)

60

Effect of particle size

Wood pellets, ground wood pellets-1 (3.35e4.75 mm) and ground wood pellets-2 (<3.35 mm) were all irregular in shape with similar bulk density, particle strength and particle surface roughness. The wood pellets had relatively smooth surfaces compared to ground wood pellets. Their differences in torque requirements are mainly attributable to different mean sizes. Fig. 12 (a), (b) and (c) show that larger particles require larger average, maximum, and starting torques. Ground wood pellets-2 (containing more fines, see Table 3) have relatively low torque requirements compared to ground wood pellets-1, indicating an insignificant effect of fines, which generally increase the fullness of screw pockets and cohesive strength, requiring somewhat larger torque. Maximum torque is related to instantaneous blockage

3

Moisture=14 % (wet basis), bulk density=210 kg/m 3 Moisture=60 % (wet basis), bulk density=440 kg/m

50

40

30

20 0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 14 e Effects of moisture content and screw speed on maximum torque for screw-1 for sawdust-1 and sawdust-3 with initial hopper level of 0.3 m.

950

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4.3.2.

Effect of particle shape

Since ground wood pellets-1 and polyethylene particles have similar mean sizes and size ranges, particle shape and surface roughness are the main reasons for their different torque requirements. Fig. 13 shows that particles of more irregular shape (e.g., cylindrical, conical) need much more torque to be fed. The maximum torque for ground wood pellets-1 was almost independent of screw speed, whereas that of the polyethylene particles is seen to have been somewhat dependent on screw speed. For the wood pellets, the faster the screw rotates, the less the maximum torque. Interlocking of ground wood pellets appears to have been much more intense than for wood pellets and polyethylene particles due to their relatively small size, rough surfaces and high compressibility. Vibration of the screw and dilation of ground wood pellets inside the screw feeder are offset by intense interlocking of particles (even at relatively high screw speeds). As a result, high speeds cannot significantly reduce the maximum torque for ground wood pellets-1.

4.3.3.

Effect of moisture content

Sawdust-1 (14% moisture) and sawdust-3 (60% moisture) can be compared to investigate the effect of moisture content. Bridging of the wetter sawdust in the hopper was severe, whereas blockage inside the screw casing decreased since the screw pockets were nearly empty. Any bridge in the hopper needs to be broken to allow the wet sawdust to enter the screw casing. Sawdust-3 had a lower average torque than sawdust-1, but sawdust-3 had higher maximum and starting torques (see Fig. 14), indicating that wet sawdust is more likely to block the screw feeder if no bridging occurs in the hopper. Both maximum and average torques decreased as the screw speed increased for wet sawdust (60%moisture) due to increased

50

Hopper level=0.30 m

45

Average torque (N.m)

potential, since, if the screw feeder cannot provide the maximum torque, the screw stalls, at least temporarily. Fig. 12 (a) shows that the maximum torque decreased as the screw speed increased for wood pellets. Hence blockage was found to be less likely as the screw speed increased. This may be partly because of more dilation of bulk materials at relatively high screw speeds and intense interlocking of particles at relatively low screw speeds, as well as blockage break-up due to vibration at higher speeds.

Hopper level=0.45 m

40

Hopper level= 0.60 m

35 30 25 20 15 10 0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 15 e Effects of hopper level and screw speed on average torque for sawdust-1 and screw-1. bridging in the hopper and reduced feeder fullness as the screw speed increased. There was no obvious relationship between the starting torque and screw speed for sawdust-3. For drier sawdust-1, none of the recorded torques (maximum, average or starting) changed significantly as the screw speed changed. The same was approximately true also for other dry biomass (hog fuel, ground wood pellets and wood shavings). For wet biomass (e.g., 40 and 60% moisture content sawdust), the flow rates and torque requirements varied considerably, depending on the bridging conditions inside the hopper. Wood shavings-1 (10% moisture), wood shavings-2 (40% moisture) and wood shavings-3 (60% moisture) can also be compared. The torque requirements of wood shavings do not seem to have depended significantly on the moisture content, probably due to their wide size distribution, wide range of particle strengths and low bulk densities.

4.3.4.

Effect of hopper level

Hopper level affects feeder load through the passive stress field after hopper flow begins. In this work, the hopper level was found to play an important role on the torque requirements for hard and heavy particles. For compressible light bulk materials (e.g., sawdust, hog fuel and wood shavings), especially for higher moisture contents, an increase in hopper

Table 1 e Dimensions of the two test screws (all dimensions are in mm). Section

Length(1)

Screw diameter

Shaft

Pitch

Screw-1 (variable-diameter)

a b c

800 300 420

100 90 80

30.5 30.5 30.5

100 100 100

Screw-2 (variable pitch)

a b c d e

100 310 310 495 305

80 80 80 80 80

56.0 43.0 30.5 20.3 20.3

40 56 71 80 70

Note: (1) The total length of both screws is 1520 mm. Of this total, 910 mm are in the hopper, and the remaining 610 mm constitute the choke section. The inside diameter of the screw feeder casing is 102 mm in both cases. Sections aec for Screw-1 and aee for Screw-2 proceed from the rear of the hopper to the choke region.

951

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Table 2 e Hopper and screw dimensions. Screw-1(1) Screw

Clearance, c Flight thickness, g Average helix angle of screw with vertical Material

Screw-2(2)

1, 6 and 11 mm 6.35 mm 14

11 mm 6.35 mm Variable

316 SS

Carbon steel

Trough

Inside diameter, Dti Material Transparent test section

102 mm Carbon steel Cast acrylic tube

Hopper

Type Length Height Angle of hopper wall with horizontal Material

Wedge-shaped 910 mm 910 mm 70 Carbon steel

Notes: (1) screw diameter 100 mm for length of 800 mm, then 90 mm for length of 300 mm, and finally 80 mm for length of 420 mm. (2) P ¼ 40 mm, Dc ¼ 56 mm for first 100 mm length; P ¼ 56 mm, Dc ¼ 43 mm for next 310 mm length; then P ¼ 71 mm, Dc ¼ 30.5 mm for 310 mm length; then P ¼ 80 mm, Dc ¼ 20.3 mm for length of 495 mm; and P ¼ 70 mm, Dc ¼ 20.3 mm for final 305 mm length.

level could increase the feeder load, as well as increasing bridging in the hopper. From Fig. 15, a higher hopper level led to larger average torques. The starting torque seems to have been independent of screw speed and hopper level for sawdust-1 (14% moisture) and hog fuel-1 (11% moisture), indicating again that the choke section plays an important role in torque requirements. For hopper levels of 0.3 and 0.45 m, the average and maximum torque were both independent of screw speed, but when the depth in the hopper increased to 0.6 m, the torque increased somewhat as the screw speed increased. This may be partly because higher

hopper levels increased the degree of fill of the screw pockets, leading to more compression and dilation inside the pockets, with compaction dominant due to compressibility and intense interlocking of particles as the screw speed increased. Incompressible particles (e.g., polyethylene and wood pellets) generally needed less torque to be fed at relatively high screw speeds.

4.3.5.

Effect of choke section length

Due to the need to form a plug seal to prevent backflow of hot gases and bed materials from the reactor, the choke section tends to be longer for biomass than for non-biomass particles (e.g., 6e10 times pitch) [10]. Hence the choke section plays an important role in screw feeding, as well as in determining torque and power. Five different choke section lengths were tested, 0.30, 0.46, 0.61, 0.76 and 0.91 m, with 0.61 m as the base value (Tables 1 and 2). From Fig. 16, it is clear that a longer choke section resulted in more torque. For wood shavings-3 (60% moisture), 0.76 and 0.91 m long choke sections (i.e., extending 0.15 and 0.3 m beyond the screw) tended to cause stoppage of the screw feeding due to formation of a plug inside the extended section, with the plug density in the range of 220e420 kg/m3, whereas the plug density in the screw region was 190e220 kg/m3 for wet wood shavings (60% moisture). For ground hog fuel, the plug density inside the extended section ranged from 200 to 280 kg/m3, whereas it was 180e260 kg/m3 in the screw region of the choke section. To obtain a mechanically stable plug with a suitable gas permeability, plugs should have a bulk density from 1300 to 1500 kg/m3, depending on the texture of biomass and the operation requirements [31]. Plug formation inside the extended section appears to play a significant role in blocking the screw feeder. For extended sections, sawdust-1 (14% moisture) was much more likely to block the screw feeder than hog fuel-1 or ground hog fuel. Larger mean size and wider size distribution of the hog fuel (compared to sawdust-1) appeared to make plug formation inside the extended section more difficult, especially for the

Table 3 e Hydrodynamic properties of materials in the present study. Name of specimen Polyethylene particles Wood pellets Ground wood pellets-1 Ground wood pellets-2 Sawdust-1 Sawdust-2 Sawdust-3 Hog fuel-1 Hog fuel-2 Hog fuel-3 Ground hog fuel Wood shavings-1 Wood shavings-2 Wood shavings-3

Mean diameter (1) (mm)

Size range (mm)

Bulk density (kg/m3)

Particle density (kg/m3)

Moisture (wet basis)(2)

4 9.8 4.05 0.55 0.45 0.45 0.45 0.72 0.72 0.72 0.18 0.67 0.67 0.67

3.0e5.0 8.0e11.6 3.35e4.75 100% < 3.35, 98.5% > 0.09 100% < 6.73, 96% (0.09e2.8) 100% < 6.73, 96% (0.09e2.8) 100% < 6.73, 96% (0.09e2.8) 100% < 25, 90% (0.09e9.5) 100% < 25, 90% (0.09e9.5) 100% < 25, 90% (0.09e9.5) 100% < 4.75, 98.7% (0.09e2.8) 100% < 12.5, 91% (0.09e6.73) 100% < 12.5, 91% (0.09e6.73) 100% < 12.5, 91% (0.09e6.73)

610 630 485 423 210 330 440 200 310 322 150 110 156 188

908 1200 1200 1200 370 550 688 360 490 510 330 300 380 430

dry 8% 8% 8% 14% 40% 60% 11% 40% 60% 14% 10% 40% 60%

Notes: (1) sauter mean particle diameters except for first two which are volume-equivalent diameters; and (2) measured by drying at 105  C for 5 h in an oven.

952

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Table 4 e Time (s) corresponding to starting torque for different materials and rotation speeds.

Wood pellets Ground wood pellets-1 Ground wood pellets-2 Sawdust-1 Hog fuel-1 Ground hog fuel Wood shavings-1 Polyethylene particles

5 rpm

10 rpm

20 rpm

30 rpm

40 rpm

2.1e3.2 3.2e3.9 5.9e6.1 7.1e7.9 2.7e5.3 3.3e7.3 2.3e6 2.3e2.5

1.4e1.6 2.4e3.7 3.4e4.7 3.7e4.8 2.1e2.7 3.2e3.8 1.8e2 1.5e1.9

0.8e1.8 1.3e1.7 1.8e2.1 2e2.4 1.3e1.6 1.5e2 1.4e1.6 0.8e1

0.6e1 1e1.3 1.2e2.1 1.9e2.2 1.2e1.4 1.4e1.9 1.2e1.3 0.5e0.6

0.8e0.9 0.8e1.1 0.9e1.1 1.5e1.6 1.1e1.2 1.3e1.6 1e1.1 0.6e0.8

0.15 m long extension. This is likely because the larger particles led to a larger void fraction, providing more room for particle motion and readjustment inside the extended section, thereby reducing particle interlocking and decreasing the probability of blockage. This indicates that uniform particle size and small voidages are preferred for forming plugs inside the extended section. Blockage occurred for both 0.15 and 0.3 m extended sections for sawdust-1, whereas only the 0.3 m extension caused blockage for hog fuel-1. Experiments with ground hog fuel indicated that the 0.15 m extended section may or may not lead to blockage and stoppage of the screw feeder, depending on the conditions inside the hopper and screw feeder, whereas the 0.3 m extension made ground hog fuel form a tight plug inside the extended section, promoting blockage and stoppage. Ground hog fuel bridged relatively easily in the hopper due to its fibrous cylindrical shape and low bulk density, reducing the fullness of the screw pockets. This was likely the main reason why ground hog fuel passed through the 0.15 m extended section more easily than sawdust-1. The effect of the choke section on torque depended not only on the casing length, but also on its configuration and the length of the screw.

4.3.6.

Effect of casing configuration

Different casing sections were tested, with a straight cast acrylic test section, and 0.15 and 0.30 m long tapered carbon steel sections with 2.6 and 1.2 half-taper angles, respectively. Experimental results are plotted in Fig. 17. The 0.3 m tapered section was the most difficult of the three, needing

more torque for the biomass fuels tested. On the other hand, the resulting plug seals were better than for the other two configurations. Large mean particle size and wide size distribution of hog fuel-1 caused it to be more prone to block in the tapered section. Large hog fuel particles played an important role in setting the torque requirements and in triggering blockage inside the tapered sections. For ground hog fuel, the fibrous cylindrical shape caused more frequent blockages to occur in the tapered sections than for sawdust-1. Relatively uniform particle size, regular shapes and large compressibility of sawdust-1 (14% moisture) are likely the main factors explaining why it passed through the tapered sections more easily than hog fuel-1 and ground hog fuel. For the ground hog fuel (14% moisture) and wood shavings (10, 40 and 60% moisture), the plug densities were in the range 150e300 kg/m3, depending on the compression conditions, in the tapered section.

4.3.7.

Refilling

Refilling is essential for industrial continuous processes. In order to investigate the effect of refilling, 3.5 kg ground hog fuel (14% moisture) was added to the hopper, with the top surface flat (0.15 m hopper level), and then the screw feeder was started. When the hopper was empty, the material was returned to the middle of the hopper (not leveled) while the screw was still turning. These experiments did not show much difference in torque requirements due to refilling. Although there were some torque peaks during refilling, especially for the heavier materials (e.g., wood pellets and 18

Average Wood pellets Ground wood pellets-1 Ground wood pellets-2 Sawdust-1 Hog fuel-1 Ground hog fuel Wood shavings-1 Polyethylene particles

Maximum (N.m)

Starting (N.m)

51.8  3.0 30.6  7.0

80.3  3.0 36.6  5.1

28.1  3.8 14.4  5.1

26.9  6.5

32.2  6.5

12.6  2.4

16.4  4.0 12.0  4.1 9.7  4.6 6.1  3.0 10.3  2.1

20.8  4.2 25.5  5.5 20.9  4.9 19.0  5.1 15.6  2.6

7.7  3.3 11.6  3.6 5.8  2.8 2.7  1.4 7.1  2.0

0.30 m long choke section

16

0.46 m long choke section Average torque (N.m)

Table 5 e Average, maximum and starting torques (N.m) and 95% confidence intervals for 8 different materials for screw-1, an initial hopper level of 0.3 m, and a screw speed of 5 rpm.

14

0.61 m long choke section

12 10 8 6 4

0

5

10

15

20

25

30

35

40

45

Screw speed (rpm)

Fig. 16 e Effects of choke section length and screw speed on average torque for screw-1 and wood shavings-3 with initial hopper level of 0.45 m.

953

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700

120

Pressure difference: 3 2000 Pa, air flow: 0.01 m /s 3 1450 Pa, air flow: 0.008 m /s 3 500 Pa, air flow: 0.004 m /s No pressurization

110

90

Mass flow rate (Kg/h)

100

Average torque (N.m)

600

Straight test section (cast acrylic) o 0.15 m taper section with 2.6 half taper angle (carbon steel) o 0.30 m taper section with 1.2 half taper angle (carbon steel)

80 70 60 50 40 30

500 400 300 200 100

20 10

0

0

5

10

15

20

25

30

35

40

0

45

5

10

Screw speed (rpm) Fig. 17 e Effects of casing configuration on average torque for sawdust-1 and screw-1 with initial hopper level of 0.45 m.

polyethylene particles), it was not clear whether these peaks were caused by the refilling. For heavy particles and a large steep hopper, a large refilling “dump” can cause larger fluctuations in torque and feed rates.

4.3.8.

Pressurization

Pressurization of the hopper relative to the receiving vessel reduced the torque requirements (see Fig. 18) and increased the feeding rate (see Fig. 19). The larger the permeability and the more non-uniform the flow in the hopper and screw casing, the easier it is for air to pass through the screw casing to the reactor. Ground wood pellets were better than wood pellets from a pressure-seal point of view. Ground wood pellets were also more amenable to plug seal formation than wood pellets. Pressurization and airflow in the hopper can help disrupt bridges inside the hopper, especially for light feedstocks (e.g., wood shavings and ground hog fuel). In the present study, the air inlet to the hopper is located at the front of the hopper lid.

20

25

30

35

40

45

Fig. 19 e Effects of pressure difference between hopper and receiving vessel on mass flow rate of wood pellets for screw-1 with initial hopper level of 0.3 m.

Airflow can help break up the stagnant region at the front of the hopper. Observations indicated that small pressurization and airflow did not affect screw feeding significantly when there was an effective pressure seal. Hence, little or no pressurization is needed for biomass feeding when the plug seal inside the screw casing works well. A pressure drop of 0.5e20 kPa has been recommended from the feed hopper to the reactor [32], whereas a pressure drop of 0.3e10 kPa and an air flux < 0.7 m/s (based on cross-sectional area between shaft and casing surface at the entrance of the choke section) were optimal in the present study. Higher pressure differentials and larger airflows not only lead to increased energy consumption, but may also interrupt feeding.

4.3.9.

Effect of screw configurations

Two different screw geometries summarized in Table 1, were compared. Fig. 20 indicates that screw-2 reduced the torque requirements. This is believed to be because screw-2 provides 160

80

Pressure difference: 3 2000 Pa, air flow: 0.01 m /s 3 1450 Pa, air flow:0.008 m /s 3 500 Pa, air flow: 0.004 m /s No pressurization

70 65 60

Max. torque for screw-1

140

Max. torque for screw-2 120

Torque (N.m)

75

Average torque (N.m)

15

Screw speed (rpm)

55 50 45

Ave. torque for screw-1 Ave. torque for screw-2

100 80 60 40

40 35

20

30 0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 18 e Effects of pressure difference between hopper and receiving vessel on average torque for wood pellets and screw-1 with initial hopper level of 0.3 m.

0

5

10

15

20

25

30

35

40

45

Screw speed (rpm) Fig. 20 e Effects of screw configurations on torque requirements for wood pellets with initial hopper level of 0.3 m.

954

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a relatively uniform flow in the hopper due to its increased capacity along the length of the screw, as well as a larger clearance between the flight tips and the casing surface, due to the reduced screw diameter compared to screw-1. The reduced torque requirements were, however, accompanied by a decrease in efficiency.

5.

Conclusions

 Hopper level affected blockage inside the screw feeder. Blockage was more likely to occur as the depth of particles increased inside the hopper.  Larger particles, more irregular shapes, rougher particle surfaces and larger bulk densities increased the likelihood of blockage. Broader particle size distributions required greater torque and were more likely to block.  High moisture contents caused increased cohesion and adhesion, making biomass fuels more likely to bridge in the hopper. Intermittent bridging in the hopper reduced the volumetric flow rate for wet biomass fuels. Wet biomass generally needed much more torque to achieve blockage-free feeding than dry biomass. More compact materials and nonuniform moisture content increased torque requirements.  Compressibility led to higher mass flow rates for screw feeding. Compressible biomass fuels passed through tapered sections more readily than incompressible materials. Plug formation inside the screw casing was also facilitated by compressibility, especially inside the extended “choke” section beyond the screw.  The choke section length and casing taper were closely related to plug formation and sealing, as well as affecting the torque requirements.  Pressurizing the hopper relative to the receiving vessel increased the feed rate and decreased the torque requirements, while also preventing gas and particle backflow.  Careful refilling did not disrupt feeding, especially for biomass of low bulk density.  Torque requirements were nearly independent of screw speeds for both compressible and incompressible materials.

Acknowledgement The authors are grateful for funding from the interdepartmental Program of Energy Research and Development (PERD) of Natural Resources Canada, and for advice from Dr. M. Sayed of the Canadian Hydraulics Centre of the National Research Council of Canada.

Nomenclature

A c Dc dm di Ds

Cross-sectional area of screw feeder, ¼ pðD2s  D2c Þ=4, m2 Clearance, m Core shaft diameter, m Mean diameter of particles, m Arithmetic mean sieve aperture, m Screw flight diameter, m

Dti M P V VTM

v xi

Inside diameter of trough, m Mass flow rate, kg/s. Pitch of screw, m. Volumetric flow rate, m3/s Maximum theoretical throughput with screw feeder completely full and particles moving at feeder speed without slip and/or rotation, m3/s Ideal axial feeding velocity of screw, ¼uP/2p, m/s Mass fraction of particles of size i, e

Greek letters g Screw flight thickness, m. Volumetric efficiency, ¼V/VTM, e hv Bulk density, kg/m3 rb u Angular velocity of screw, 1/s

references

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[17] Yu Y, Arnold PC. Theoretical modeling of torque requirements for single screw feeders. Powder Technol 1997; 93:151e62. [18] Bates L. Guide to the design, selection and application of screw feeders. London: Professional Engineering Publishing; 2000. [19] Tanida K-I, Honda K, Kawano N, Kawaguchi T, Tanaka T, Tsuji Y. Particle motion in screw feeder simulated by discrete element method. Int Conf Digital Print Technol; 1998:429e31. [20] Jenike AW. Storage and flow of solids. Bulletin 123. Utah University; 1964. [21] Bates L. Interfacing hoppers with screw feeders. Bulk Solid Handling 1986;6:66e78. [22] Carson JW. Designing efficient screw feeders. Powder Bulk Eng 1987;12:32e42. [23] Bell TA, Couch SW, Krieger TL, Feise HJ. Screw feeders: a guide to selection and use. Chem Eng Prog 2003;99:44e51. [24] Dai JJ. Biomass granular feeding for gasification and combustion. PhD thesis. University of British Columbia, 2007. [25] Arnold PC, Mclean AG, Roberts AW. Bulk solids: storage, flow and handling. 2nd ed. New South Wales, Australia:

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