**2.1. Flow obstructions and patterns**

feeding and conversion performance [7]. Thus, even if ideal specifications are achieved, care must be taken so that the subsequent unit operations do not unintentionally modify material

**Table 1.** Noninclusive summary of feedstock performance related to particle physical and mechanical properties

**Performance aspect Governing parameters/mechanisms Impacts**

fungal growth

density, chemical composition, moisture, temperature, and trapped

Can be due to many different effects, such as crystallization, material creep, capillary condensation, and

Particle-particle and particle-slurry interactions through particle shape,

size, and ploy-dispersity

Particle sizes and shapes affect surface area to volume ratios

Pore spaces between particles that allow gases and liquids to flow

through bulk solid

Easily flowing materials

to prevent spoilage

consistent flow

flood equipment

containing structures

version efficiency

large particles

from outlets

and transportation volumes

• tend to be easier to mix and blend • if overly aerated, may flow too freely and

• facilitate emptying and cleaning equipment

• readily fill containers to minimize storage

• feed uniformly for processes that requires

• Loss of live storage space because material adheres to storage container walls • Risk of loss of perishable material • Erratic flow with large dynamic forces on

• Material bridges over outlet preventing flow

• Lower volatility resulting in increased con-

• Acidity of product bio-oil may be reduced

• Small particles have much faster thermochemical reaction kinetics as compared to

• More reactive particles can be substantially larger than less reactive particles. For example, biomass particles can be larger than

coal particles in co-fired gasifiers

• Low permeability restricts chemical access to material's interior, slowing reactions • Low permeability can limit discharge rates

"Bulk flowability" Particle-particle interactions, bulk

gases

The behavior of biomass feedstocks in handling and feeding equipment is affected by many factors beyond traditional rheological properties. These factors include chemical composition of particles, temperature, presence of trapped gases and the unique stress and deformation histories of the bulk solid. The impacts of specific parameters are summarized in **Table 1**. Particle size and moisture content often receive the most attention, and it is important to recognize that in some cases the particle size "specification" is based on the screen size of a laboratory mill, rather than a thorough classification of particle-size distribution. Such a screen size specification is often misleading because in most cases the mean product particle size is

properties.

(adapted from [15]).

Time consolidation or caking (increase in strength after prolonged storage

120 Advances in Biofuels and Bioenergy

Handling properties in a slurry for enzymatic

Permeability of bulk solid to flow of gases or liquids

times)

conversion

processes

Reactivity for thermochemical and biochemical conversion Proper storage and retrieval of biomass is critical to maintain quality in terms of both chemical properties for conversion and physical properties for feeding and handling. Retrieval or reclamation of biomass from storage is one of the most trouble-prone processes of biomass plant operation [5]. Silos are common in the agricultural and grain industries to store large quantities of material in a protective environment and can be large in diameter (4–15 m) and quite tall. Material is usually augured into the top of the silo and removed at the bottom. Very cohesive materials require specialized and expensive sweeping reclaimers to extract material from the entire bottom cross-section of the silo, where compressive pressures and material strengths can be very high. These systems require extensive engineering and are not discussed further here; however, additional information can be found at http://www.laidig.com/ reclaimers.

Less cohesive materials and shorter storage systems in which compressive forces are lower often use less expensive hoppers or chutes to funnel biomass to a small feed discharge mechanism. In the 1960s, Andrew Jenike developed the first complete methodology for the flow of bulk solids within the framework of hoppers, bins, and feeders. His work included test equipment and procedures for measuring the necessary material properties, a theory of bulk solids flow within hoppers and bins, and a procedure to determine the hopper slope and outlet dimensions required for unobstructed gravity flow [6, 16]. The development presented here closely follows the formalism that Jenike advanced.

As described by Jenike [17], the primary issues in the design of hoppers and chutes are: (1) solid flow pattern, (2) slope angle of discharge, and (3) size of the discharge opening. Although there are a number of flow obstructions that may develop in a bin, two primary types are analyzed here: arching or doming as illustrated in **Figure 2(a)** and ratholing or piping as illustrated in **Figure 2(b)**. Most particulate solids are easily flowable when they are well-aerated but become cohesive and strong when compacted. For example, fluidized bulk solids have very low shear strengths and typically flow with carrier gases; however, the same bulk solids can be made into rigid briquettes or pellets by subjecting them to high compressive stresses, especially in the presence of moisture or binders. The increasing strength of bulk solids with increasing compressive stress allows them to form arches and bridge over openings. In the case of large bins and hoppers, the weight of material in upper layers compresses the lower

allow some material to remain at rest while only a portion of the material moves through the hopper. In funnel flow, a moving channel of material is formed within the central region of the hopper, while material outside the channel is at rest. A distinguishing feature of funnel flow is that the material flows primarily on itself, such that the walls of the container do not

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Mass flow hoppers have many advantages over funnel flow hoppers. Mass flow hoppers preserve the first-in-first-out flow sequence, allow powders to deaerate, minimize segregation, and supply uniformly densified material to the feeder (see **Figure 3(a)** and [22]). Funnel flow hoppers have the opposite characteristics: the flow sequence is first-in-last-out, ratholes may form, powders have a strong tendency to flood, segregation problems are exacerbated, and the compaction of material fed to the hopper is nonuniform (see **Figure 3(b)**). Materials that are suitable for mass flow hoppers and not funnel flow hoppers include cohesive solids, fine powders, degradable materials, and solids which segregate [22]. The primary advantage of funnel flow hoppers is that they can have shallow hopper angles and, consequently, require much less headroom. A third common flow pattern, denoted expanded flow, is illustrated in **Figure 3(c)**. In this flow pattern, the lower portion of the hopper is designed to ensure mass flow and prevent arching while the central and top portions are designed solely to prevent ratholing (funnel-type flow is allowed in the central portion of the hopper). Expanded flow designs are practical for hoppers with large diameters filled with solids that exhibit strong

As a particle moves downward through a bin and hopper, the pressure field around the particle first increases as the height of material above it increases and then in the hopper section, the pressure decreases as the cross-section size decreases toward the outlet. At an open outlet,

**Figure 3.** Schematics showing (a) mass flow, (b) funnel flow, and (c) expanded flow. Note that for funnel flow, the shape

influence the shape of the channel or the velocities of moving particles.

tendencies to rathole in funnel flow bins, but flow well in mass flow bins.

**2.2. Yield locus and effective yield locus**

of the flow channel is independent of the shape of the hopper.

**Figure 2.** Schematics showing (a) arching, (b) ratholing, and (c) flow functions FF for two materials and a representative hopper flow factor.

material, causing it to gain strength and become cohesive. The cohesive strength, typically referred to as unconfined yield strength *f c* , of a solid resulting from its stress history is the cause of the arch shown in **Figure 2(a)**. The strength-pressure curve of a solid is known as its flow-function FF and typically increases rapidly with increased pressure in the low pressure range and then increases more slowly at higher pressures [18]. The strength developed by different bulk solids as a function of consolidation pressure varies from solid to solid as exemplified by the flow-functions of materials (1) and (2) in **Figure 2(c)**. It is evident that material (2) is much stronger and less free flowing than material (1).

Approximating the downward pressure across an arch to be nearly uniform, the total force acting to break the arch scales with the area (π*d*<sup>2</sup> /4 for a circular outlet, where *d* = diameter), while the material's ability to maintain the arch only scales with the perimeter (π*d* for a circular outlet) of the hopper outlet. Thus, if the size of the hopper outlet is steadily increased, eventually the strength of the material becomes insufficient to support the arch and the bulk solid flows. Flow of a bulk solid material can be assured for a hopper with specified geometry and wall material, as long as the strength of the material is maintained below a certain value, giving rise to the concept of a hopper flow-factor, which is also shown in **Figure 2(c)**. The intersection of the material's flow-function with the hopper's specific flow-factor usually determines the minimum outlet size needed to assure consistent gravity flow. Similar reasoning also applies to the formation of ratholes or pipes.

The flow pattern in a hopper affects all aspects of its performance, including not just the outlet size required to assure reliable discharge, but also the order in which the contents are discharged [19] and the loads acting on the structure [20, 21]. Two recent standards identify some flow patterns that have been identified [ISO 11697 (1992) and Eurocode 1 part 4 prEN 1991–4 (2002)]. For most purposes, flow patterns can be classified into two categories, mass flow and funnel or plug flow, as illustrated in **Figure 3(a)** and **(b)**. Perfect mass flow requires that all the material moves downward when material is removed from the outlet. Typically, smooth and steep walls are required to achieve mass flow. In contrast, funnel flow hoppers allow some material to remain at rest while only a portion of the material moves through the hopper. In funnel flow, a moving channel of material is formed within the central region of the hopper, while material outside the channel is at rest. A distinguishing feature of funnel flow is that the material flows primarily on itself, such that the walls of the container do not influence the shape of the channel or the velocities of moving particles.

Mass flow hoppers have many advantages over funnel flow hoppers. Mass flow hoppers preserve the first-in-first-out flow sequence, allow powders to deaerate, minimize segregation, and supply uniformly densified material to the feeder (see **Figure 3(a)** and [22]). Funnel flow hoppers have the opposite characteristics: the flow sequence is first-in-last-out, ratholes may form, powders have a strong tendency to flood, segregation problems are exacerbated, and the compaction of material fed to the hopper is nonuniform (see **Figure 3(b)**). Materials that are suitable for mass flow hoppers and not funnel flow hoppers include cohesive solids, fine powders, degradable materials, and solids which segregate [22]. The primary advantage of funnel flow hoppers is that they can have shallow hopper angles and, consequently, require much less headroom. A third common flow pattern, denoted expanded flow, is illustrated in **Figure 3(c)**. In this flow pattern, the lower portion of the hopper is designed to ensure mass flow and prevent arching while the central and top portions are designed solely to prevent ratholing (funnel-type flow is allowed in the central portion of the hopper). Expanded flow designs are practical for hoppers with large diameters filled with solids that exhibit strong tendencies to rathole in funnel flow bins, but flow well in mass flow bins.

#### **2.2. Yield locus and effective yield locus**

**Figure 2.** Schematics showing (a) arching, (b) ratholing, and (c) flow functions FF for two materials and a representative

material, causing it to gain strength and become cohesive. The cohesive strength, typically

cause of the arch shown in **Figure 2(a)**. The strength-pressure curve of a solid is known as its flow-function FF and typically increases rapidly with increased pressure in the low pressure range and then increases more slowly at higher pressures [18]. The strength developed by different bulk solids as a function of consolidation pressure varies from solid to solid as exemplified by the flow-functions of materials (1) and (2) in **Figure 2(c)**. It is evident that material (2)

Approximating the downward pressure across an arch to be nearly uniform, the total force

while the material's ability to maintain the arch only scales with the perimeter (π*d* for a circular outlet) of the hopper outlet. Thus, if the size of the hopper outlet is steadily increased, eventually the strength of the material becomes insufficient to support the arch and the bulk solid flows. Flow of a bulk solid material can be assured for a hopper with specified geometry and wall material, as long as the strength of the material is maintained below a certain value, giving rise to the concept of a hopper flow-factor, which is also shown in **Figure 2(c)**. The intersection of the material's flow-function with the hopper's specific flow-factor usually determines the minimum outlet size needed to assure consistent gravity flow. Similar reason-

The flow pattern in a hopper affects all aspects of its performance, including not just the outlet size required to assure reliable discharge, but also the order in which the contents are discharged [19] and the loads acting on the structure [20, 21]. Two recent standards identify some flow patterns that have been identified [ISO 11697 (1992) and Eurocode 1 part 4 prEN 1991–4 (2002)]. For most purposes, flow patterns can be classified into two categories, mass flow and funnel or plug flow, as illustrated in **Figure 3(a)** and **(b)**. Perfect mass flow requires that all the material moves downward when material is removed from the outlet. Typically, smooth and steep walls are required to achieve mass flow. In contrast, funnel flow hoppers

, of a solid resulting from its stress history is the

/4 for a circular outlet, where *d* = diameter),

*c*

hopper flow factor.

122 Advances in Biofuels and Bioenergy

referred to as unconfined yield strength *f*

is much stronger and less free flowing than material (1).

acting to break the arch scales with the area (π*d*<sup>2</sup>

ing also applies to the formation of ratholes or pipes.

As a particle moves downward through a bin and hopper, the pressure field around the particle first increases as the height of material above it increases and then in the hopper section, the pressure decreases as the cross-section size decreases toward the outlet. At an open outlet,

**Figure 3.** Schematics showing (a) mass flow, (b) funnel flow, and (c) expanded flow. Note that for funnel flow, the shape of the flow channel is independent of the shape of the hopper.

the stresses perpendicular to the material surface are nearly zero (i.e., the material is unconfined). At some point in this process, the major and minor principal stresses (pressures), *σmajor* and σminor, respectively, experienced by neighboring particles pass through maximum values, labeled as *σ*<sup>1</sup> and *σ*<sup>2</sup> , respectively. For materials with low spring back or elasticity, the final bulk density *ρ*<sup>b</sup> of the material depends only on *σ*<sup>1</sup> and σ<sup>2</sup> , which are the dominant consolidation pressures.

The local cohesion of the material, which is a measure of the inter-particle binding strength in the absence of applied pressure (i.e., the shear strength with zero consolidation pressure) is the intercept of the yield locus with the shear stress axis. A fourth parameter that can be found from the yield locus is the effective angle of internal friction *δ*, which is the angle between the *σ* axis and the tangent to the Mohr's circle passing through point "0." *δ* defines the straight line termed

To measure the yield locus curves of finely divided materials (i.e., powders) at specified values

**Figure 5**. The shear cell is closely modeled after simple direct shear cells used to measure the shear strength of soils (A direct shear tester is one in which the design of the tester controls the location of the shear zone. In an indirect shear tester, the shear zone is allowed to develop according to the applied state of stress). The primary difference between the Jenike shear cell and simple shear cells used in soil analysis is that Jenike's cell is designed to be much more sensitive to small normal loads *N* and provision is made to ensure that the sample experiences

and *σ*<sup>2</sup>

The process to measure a point on a yield locus actually consists of two steps, referred to as (1) "preconsolidation" or "preshear" and (2) "shear." The objective of the first step is to preconsolidate the sample to the point "0" in **Figure 4**. The exact procedure to fill the ring and preconsolidate the sample is described in an ASTM and other standards [ASTM D-6128-06; Institution of Chemical Engineering, UK, 1989]. After uniformly filling the cell with material,

applied to the bracket to move the lid and ring at a slow constant velocity relative to the base. The sample is slowly sheared in this manner until a steady state flow with constant force S is observed, indicating that the sample is preconsolidated to point "0" in **Figure 4**. This short preshearing step helps establish a uniform stress state throughout the sample. The force S is

, Jenike developed a special shear cell test apparatus, shown schematically in

is applied to preconsolidate the sample. A horizontal shear force *S* is then

is replaced with a smaller load *N*<sup>1</sup>

, before different points on the yield locus

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. The second step of

the "effective yield locus" and is a measure of the internal friction at steady flow.

**2.3. Jenike shear tester and test method**

similar maximum consolidation pressures, *σ*<sup>1</sup>

then removed, and the normal load *N*<sup>0</sup>

**Figure 5.** Schematic of Jenike's shear cell showing base, ring, lid and bracket.

of bulk density *ρ<sup>b</sup>*

are measured.

a vertical force *N*<sup>0</sup>

Importantly, the shear strength of a static mass of material depends not only on the instantaneous principal stresses, *σmajor* and σminor, but also on their maximum values, σ<sup>1</sup> and σ<sup>2</sup> , that are attained within the "memory" of the material (i.e., the shear strength is a function of *σmajor*, σminor, and *ρ<sup>b</sup>* ). This relationship is depicted in **Figure 4** as a yield locus curve, which represents the collection of points in consolidation-shear stress space that results in failure of the material at a specified bulk density *ρ<sup>b</sup>* (*σ*1 , *σ*<sup>2</sup> ). This follows the well-known flow-no flow criteria, which is that flow in a bulk solid occurs if the applied stress at a location exceeds the material's yield strength. If the stress in the material is below the yield locus (i.e., the stress is less than material shear strength), then flow does not occur. The point marked "0" denotes the end of the yield locus. If a neighborhood of particles is subjected a pressure greater than that at point "0," then the consolidation pressures, *σ*<sup>1</sup> and *σ*<sup>2</sup> , necessarily increase, which also increases the bulk density, and a new yield locus is formed that is typically higher on the τ axis. Another important point to note in **Figure 4** is that a Mohr stress semi-circle through the point "0" and tangent to the yield locus determines the maximum major and minor consolidation pressures, *σ*<sup>1</sup> and *σ*<sup>2</sup> , (as described in nearly any strength of materials text book). The unconfined yield stress *f c* (*σ*1 , *σ*<sup>2</sup> ) can also be determined using the yield locus because it is the major consolidation pressure that corresponds to zero minor consolidation pressure (corresponding to an unconfined surface). Thus, the Mohr-stress semi-circle that defines *f c* is also tangent to the yield locus but is subject to the additional constraint that it pass through the origin (i.e., the minor stress is zero), as depicted in **Figure 4**.

**Figure 4.** Schematic showing typical yield locus and effective yield locus for a material that has been subjected to maximum consolidation pressures *σ*<sup>1</sup> and *σ*<sup>2</sup> (resulting in a steady bulk density *ρ<sup>b</sup>* , assuming that spring back is negligible).

The local cohesion of the material, which is a measure of the inter-particle binding strength in the absence of applied pressure (i.e., the shear strength with zero consolidation pressure) is the intercept of the yield locus with the shear stress axis. A fourth parameter that can be found from the yield locus is the effective angle of internal friction *δ*, which is the angle between the *σ* axis and the tangent to the Mohr's circle passing through point "0." *δ* defines the straight line termed the "effective yield locus" and is a measure of the internal friction at steady flow.

#### **2.3. Jenike shear tester and test method**

To measure the yield locus curves of finely divided materials (i.e., powders) at specified values of bulk density *ρ<sup>b</sup>* , Jenike developed a special shear cell test apparatus, shown schematically in **Figure 5**. The shear cell is closely modeled after simple direct shear cells used to measure the shear strength of soils (A direct shear tester is one in which the design of the tester controls the location of the shear zone. In an indirect shear tester, the shear zone is allowed to develop according to the applied state of stress). The primary difference between the Jenike shear cell and simple shear cells used in soil analysis is that Jenike's cell is designed to be much more sensitive to small normal loads *N* and provision is made to ensure that the sample experiences similar maximum consolidation pressures, *σ*<sup>1</sup> and *σ*<sup>2</sup> , before different points on the yield locus are measured.

The process to measure a point on a yield locus actually consists of two steps, referred to as (1) "preconsolidation" or "preshear" and (2) "shear." The objective of the first step is to preconsolidate the sample to the point "0" in **Figure 4**. The exact procedure to fill the ring and preconsolidate the sample is described in an ASTM and other standards [ASTM D-6128-06; Institution of Chemical Engineering, UK, 1989]. After uniformly filling the cell with material, a vertical force *N*<sup>0</sup> is applied to preconsolidate the sample. A horizontal shear force *S* is then applied to the bracket to move the lid and ring at a slow constant velocity relative to the base. The sample is slowly sheared in this manner until a steady state flow with constant force S is observed, indicating that the sample is preconsolidated to point "0" in **Figure 4**. This short preshearing step helps establish a uniform stress state throughout the sample. The force S is then removed, and the normal load *N*<sup>0</sup> is replaced with a smaller load *N*<sup>1</sup> . The second step of

**Figure 5.** Schematic of Jenike's shear cell showing base, ring, lid and bracket.

**Figure 4.** Schematic showing typical yield locus and effective yield locus for a material that has been subjected

the stresses perpendicular to the material surface are nearly zero (i.e., the material is unconfined). At some point in this process, the major and minor principal stresses (pressures), *σmajor* and σminor, respectively, experienced by neighboring particles pass through maximum values,

Importantly, the shear strength of a static mass of material depends not only on the instan-

are attained within the "memory" of the material (i.e., the shear strength is a function of

represents the collection of points in consolidation-shear stress space that results in failure

flow criteria, which is that flow in a bulk solid occurs if the applied stress at a location exceeds the material's yield strength. If the stress in the material is below the yield locus (i.e., the stress is less than material shear strength), then flow does not occur. The point marked "0" denotes the end of the yield locus. If a neighborhood of particles is subjected

essarily increase, which also increases the bulk density, and a new yield locus is formed that is typically higher on the τ axis. Another important point to note in **Figure 4** is that a Mohr stress semi-circle through the point "0" and tangent to the yield locus determines

mined using the yield locus because it is the major consolidation pressure that corresponds to zero minor consolidation pressure (corresponding to an unconfined surface). Thus, the

the additional constraint that it pass through the origin (i.e., the minor stress is zero), as

(*σ*1 , *σ*<sup>2</sup>

taneous principal stresses, *σmajor* and σminor, but also on their maximum values, σ<sup>1</sup>

a pressure greater than that at point "0," then the consolidation pressures, *σ*<sup>1</sup>

*c*

the maximum major and minor consolidation pressures, *σ*<sup>1</sup>

any strength of materials text book). The unconfined yield stress *f*

of the material depends only on *σ*<sup>1</sup>

, respectively. For materials with low spring back or elasticity, the final

). This relationship is depicted in **Figure 4** as a yield locus curve, which

, which are the dominant consolida-

). This follows the well-known flow-no

and *σ*<sup>2</sup>

*c* (*σ*1 , *σ*<sup>2</sup>

is also tangent to the yield locus but is subject to

and σ<sup>2</sup>

and *σ*<sup>2</sup>

, (as described in nearly

) can also be deter-

, that

, nec-

and σ<sup>2</sup>

(resulting in a steady bulk density *ρ<sup>b</sup>*

, assuming that spring back is

and *σ*<sup>2</sup>

to maximum consolidation pressures *σ*<sup>1</sup>

negligible).

labeled as *σ*<sup>1</sup>

bulk density *ρ*<sup>b</sup>

124 Advances in Biofuels and Bioenergy

tion pressures.

*σmajor*, σminor, and *ρ<sup>b</sup>*

and *σ*<sup>2</sup>

of the material at a specified bulk density *ρ<sup>b</sup>*

Mohr-stress semi-circle that defines *f*

depicted in **Figure 4**.

the shear process, referred to as "shear," is accomplished by again applying a force *S* on the bracket and recording the maximum force required to shear the sample. The normal load *N*<sup>1</sup> and the maximum recorded shear force S are then converted to a consolidating pressure and yield shear stress, respectively by dividing each value by the horizontal area of the shear cell. The two values obtained in this manner define a single point on the desired yield locus. To obtain additional points on the yield locus, the two steps "preshear" and "shear" are repeated with different normal loads *N*<sup>2</sup> , *N*<sup>3</sup> , etc. The entire process is shown schematically in **Figure 6**.

This classification scheme is most useful for materials for which the flow-function is approximately a straight line. If the slope of the flow function of a material is not approximately

from very cohesive to free-flowing depending on the consolidation pressure it is exposed to. Classification of such a material requires choosing a point on the flow function that is repre-

Although Jenike's approach offers proven principles for designing systems to handle bulk solids, it also has drawbacks, which have greatly hindered its widespread adoption by industry [20, 23]. First, ensuring that the preconsolidation stresses at the point "0" in **Figure 4** are consistently and properly attained before measuring each point on the yield locus is not trivial and requires a high level of skill and training. Second, the tests are very time-consuming and expensive. It has been estimated that obtaining a flow-function curve for a material requires approximately 15 h for a skilled technician. The time cost is further exacerbated if multiple flow functions are required to understand a material's flow behavior at different moisture contents, temperatures, or after prolonged periods of consolidation (the shear strength of many materials increases with temperature, moisture, and after prolonged consolidation times). A third drawback is that measurements are not possible at small normal stresses, so that it is necessary to extrapolate the yield locus to find its intersection with the τ axis (cohesion). A fourth drawback is that the Jenike tester has very limited travel (approximately 7 mm) to minimize the reduction of the shear cross-sectional area during the test. The small amount of travel is sometimes insufficient to ensure that a consistent stress state is attained during the preshear step. Materials that are particularly problematic are those with large particles, high moisture content, and/or a high elastic limit (large spring back). The final drawback to the Jenike tester is that substantial variability often exists in the measured values, increasing the error in the extrapolation of the yield locus to find its intersection with the τ axis (cohesion) and making it necessary to employ conservative designs for hoppers to

is not constant and the material can exhibit behavior ranging

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constant, then the ratio *σ*<sup>1</sup>

promote flow.

/*f c*

sentative of conditions that exist when the material is required to flow.

**2.4. Other shear testers capable of determining the flow function**

*c*

capable of measuring the unconfined yield stress *f*

very simple, and underestimate *f*

Despite the drawbacks of the Jenike shear tester, it remains one of the very few testers that is

rial without additional uncertain assumptions. Other instruments that can also measure *f*

include biaxial shear testers, uniaxial shear testers, and ring shear testers. Biaxial shear testers are uncommon due to their complexity, and are not practical for the measurement of flow properties for routine design of bulk solids handling systems. So-called "uniaxial" testers are

direction as the shear stress [23]. A further disadvantage of uniaxial testers is that they can only be used to test bulk solids that are sufficiently cohesive that they retain their consolidated shape when lateral support is removed. A result of the last observation is that uniaxial testers cannot perform tests at low consolidation pressures. The primary advantage of uniaxial testers is their simplicity-tests can be performed quickly. It is worth noting that a simpler and quicker procedure can be followed with the Jenike shear tester to obtain approximate results

*c*

(and hence the flow function) of a mate-

because the consolidation pressure is applied in the same

*c*

It is critical that the first step ("preshear") be performed in as nearly as identical a manner as possible before each point on the yield locus is measured to ensure that the preconsolidation stresses are the same for each measurement (i.e., each measurement shares the same maximum principal stresses σ<sup>1</sup> and σ<sup>2</sup> ). After a sufficient number of points are obtained to define a yield locus, the unconfined yield stress *f c* for the specific maximum principal stress σ<sup>1</sup> is found as described above. A plot of several values of *f c* versus corresponding values of σ<sup>1</sup> yields the material flow function featured in **Figure 2(c)**. The measured flow-function FF is used with design charts developed by Jenike to quantitatively design systems to handle flowing bulk solids, such as determining the minimum outlet of a hopper that is required to ensure that an arch or rathole cannot form.

The flow-function is also used to classify the flowability of bulk solids. Jenike warns that several numbers and curves are required to precisely define the flowability of a bulk solid [20]; yet, for the sake of convenience, Jenike offered a simple flowability scale based on the flow function. The classification is accomplished by picking a point on the flow-function and determining the ratio of the major principal stress σ<sup>1</sup> to the unconfined yield strength *f c* , denoted as *ff<sup>c</sup>* = *σ*<sup>1</sup> /*f c* . The flowability of the material is then defined by the following scale:

0 < *ff<sup>c</sup>* < 2—Very cohesive and non-flowing

2 < *ff<sup>c</sup>* < 4—Cohesive


**Figure 6.** Procedure to measure three points on a yield locus using the Jenike shear tester.

This classification scheme is most useful for materials for which the flow-function is approximately a straight line. If the slope of the flow function of a material is not approximately constant, then the ratio *σ*<sup>1</sup> /*f c* is not constant and the material can exhibit behavior ranging from very cohesive to free-flowing depending on the consolidation pressure it is exposed to. Classification of such a material requires choosing a point on the flow function that is representative of conditions that exist when the material is required to flow.

Although Jenike's approach offers proven principles for designing systems to handle bulk solids, it also has drawbacks, which have greatly hindered its widespread adoption by industry [20, 23]. First, ensuring that the preconsolidation stresses at the point "0" in **Figure 4** are consistently and properly attained before measuring each point on the yield locus is not trivial and requires a high level of skill and training. Second, the tests are very time-consuming and expensive. It has been estimated that obtaining a flow-function curve for a material requires approximately 15 h for a skilled technician. The time cost is further exacerbated if multiple flow functions are required to understand a material's flow behavior at different moisture contents, temperatures, or after prolonged periods of consolidation (the shear strength of many materials increases with temperature, moisture, and after prolonged consolidation times). A third drawback is that measurements are not possible at small normal stresses, so that it is necessary to extrapolate the yield locus to find its intersection with the τ axis (cohesion). A fourth drawback is that the Jenike tester has very limited travel (approximately 7 mm) to minimize the reduction of the shear cross-sectional area during the test. The small amount of travel is sometimes insufficient to ensure that a consistent stress state is attained during the preshear step. Materials that are particularly problematic are those with large particles, high moisture content, and/or a high elastic limit (large spring back). The final drawback to the Jenike tester is that substantial variability often exists in the measured values, increasing the error in the extrapolation of the yield locus to find its intersection with the τ axis (cohesion) and making it necessary to employ conservative designs for hoppers to promote flow.

#### **2.4. Other shear testers capable of determining the flow function**

**Figure 6.** Procedure to measure three points on a yield locus using the Jenike shear tester.

the shear process, referred to as "shear," is accomplished by again applying a force *S* on the bracket and recording the maximum force required to shear the sample. The normal load *N*<sup>1</sup> and the maximum recorded shear force S are then converted to a consolidating pressure and yield shear stress, respectively by dividing each value by the horizontal area of the shear cell. The two values obtained in this manner define a single point on the desired yield locus. To obtain additional points on the yield locus, the two steps "preshear" and "shear" are repeated

It is critical that the first step ("preshear") be performed in as nearly as identical a manner as possible before each point on the yield locus is measured to ensure that the preconsolidation stresses are the same for each measurement (i.e., each measurement shares the same maxi-

*c*

material flow function featured in **Figure 2(c)**. The measured flow-function FF is used with design charts developed by Jenike to quantitatively design systems to handle flowing bulk solids, such as determining the minimum outlet of a hopper that is required to ensure that an

The flow-function is also used to classify the flowability of bulk solids. Jenike warns that several numbers and curves are required to precisely define the flowability of a bulk solid [20]; yet, for the sake of convenience, Jenike offered a simple flowability scale based on the flow function. The classification is accomplished by picking a point on the flow-function and deter-

. The flowability of the material is then defined by the following scale:

*c*

, etc. The entire process is shown schematically in **Figure 6**.

). After a sufficient number of points are obtained to define a

versus corresponding values of σ<sup>1</sup>

to the unconfined yield strength *f*

is found

yields the

, denoted as

*c*

for the specific maximum principal stress σ<sup>1</sup>

with different normal loads *N*<sup>2</sup>

126 Advances in Biofuels and Bioenergy

mum principal stresses σ<sup>1</sup>

arch or rathole cannot form.

*ff<sup>c</sup>* = *σ*<sup>1</sup> /*f c*

10 < *ff<sup>c</sup>*

2 < *ff<sup>c</sup>* < 4—Cohesive

4 < f *ff<sup>c</sup>* < 10—Easy-flowing

—Free-flowing

yield locus, the unconfined yield stress *f*

as described above. A plot of several values of *f*

mining the ratio of the major principal stress σ<sup>1</sup>

0 < *ff<sup>c</sup>* < 2—Very cohesive and non-flowing

, *N*<sup>3</sup>

and σ<sup>2</sup>

Despite the drawbacks of the Jenike shear tester, it remains one of the very few testers that is capable of measuring the unconfined yield stress *f c* (and hence the flow function) of a material without additional uncertain assumptions. Other instruments that can also measure *f c* include biaxial shear testers, uniaxial shear testers, and ring shear testers. Biaxial shear testers are uncommon due to their complexity, and are not practical for the measurement of flow properties for routine design of bulk solids handling systems. So-called "uniaxial" testers are very simple, and underestimate *f c* because the consolidation pressure is applied in the same direction as the shear stress [23]. A further disadvantage of uniaxial testers is that they can only be used to test bulk solids that are sufficiently cohesive that they retain their consolidated shape when lateral support is removed. A result of the last observation is that uniaxial testers cannot perform tests at low consolidation pressures. The primary advantage of uniaxial testers is their simplicity-tests can be performed quickly. It is worth noting that a simpler and quicker procedure can be followed with the Jenike shear tester to obtain approximate results for quality control or product development. This method employs only a single test (preshear and shear) and a repetition test to determine an estimate for the yield locus and a single point on the flow-function [20].

**2.5. Conveying and feeding**

ing wood chips.

Silos and bins serve to store material, which is then discharged through reclaimers or hoppers as explained above. After material is reclaimed from storage, it is subjected to final evaluation for suitability, including excessive moisture or unacceptable sizes of particles. Foreign materials, such as rocks and metals are also removed. The material is then conveyed using belt, chain, or pneumatic conveyors to the conversion reactor and is fed into the reactor. There are six primary types of biomass feeders: (1) gravity chute, (2) screw conveyor, (3) pneumatic injection, (4) rotary spreader, (5) moving-hole feeder, and (6) belt feeder. Proper design of the reclaiming, conveying, and feeding equipment is essential to ensure uninterrupted flow from storage to feeder. The design principles are based upon the material properties discussed above and, overall, share similar considerations with the design of silos, bins and hoppers summarized above. For detailed analyses of the various options, the reader is referred to specialized texts, such as those by [5–7, 23]. One topic that is of note here is the cost of biomass handling systems. Material handling represents a significant portion of the capital and operating costs of a biomass conversion facility even if all of the components operate exactly as intended. **Table 2** shows an example of relative costs of handling equipment for two biomass pelleting facilities, one for herbaceous feedstocks and one for woody feedstocks. The herbaceous facility is designed to handle baled material while the woody facility is designed to handle wood chips. For both feedstocks, the drying operation is the single largest cost with grinding and densification being the next most expensive. Overall, handling and processing bales incurs approximately \$1.2 million more in total direct costs than handling and process-

Biomass Handling and Feeding

129

http://dx.doi.org/10.5772/intechopen.74606

**System type Herb. Woody** Material receiving 5% 4% Separator/screener 2% 1% Primary grinder 16% — Dryer 31% 41% Secondary grinder 10% 13% Densification 13% 16% Dust collection 6% 7% Buffer storage 2% 2% Controls 2% 2% Equipment installation and electrical 4% 4% Civil/structural work 9% 9% Total direct cost \$5.4 M \$4.2 M

**Table 2.** Relative estimated costs in 2011 USD (\$) of herbaceous and woody biomass handling and preprocessing

systems, each operating at 9 tons/h (adapted from [27]).

The last type of instrument capable of measuring unconfined yield stress *f c* is a rotational ring shear tester. Early ring tester models were only partly successful in accurately measuring the unconfined yield stress *f c* of materials, and it was not until an improved unit was developed by Schulze in 1994 that the superiority of ring testers over the Jenike shear tester became apparent [23]. The test procedure with a ring shear tester is equivalent to that described above—the sample is still sheared in two steps including "preshear" and "shear." The primary advantage of ring shear testers is the unlimited rotary travel that they offer, making it possible to measure a complete yield locus without changing the sample or refilling the shear cell. Unfortunately, however, ring shear testers do not overcome all of the limitations of linear shear testers. In particular, ring shear testers have difficulty evaluating the flow performance of compressible materials because the stress fields of those materials are highly non-uniform during the test [24, 25]. An automated commercial version of the Schulze ring shear tester is now available that increases the speed of the test process and reduces the dependence of measured flowability properties on the skill level of the operator [6]. Of course, these improvements come at a substantial cost: the base price of a commercial Schulze ring tester is greater than \$70,000 USD. However, even with these features, ring shear tests are not always reliable for biomass as shown in **Figure 7**, which compares predicted minimum hopper opening sizes to ensure consistent flow based on shear test results of various ground pine materials to experimentally measured values [26].

**Figure 7.** Predicted minimum hopper outlet widths versus the values measured using the hopper tests. Symbol size indicates moisture content with larger symbols representing higher moisture content (10–40% wet basis).

#### **2.5. Conveying and feeding**

**Figure 7.** Predicted minimum hopper outlet widths versus the values measured using the hopper tests. Symbol size

for quality control or product development. This method employs only a single test (preshear and shear) and a repetition test to determine an estimate for the yield locus and a single point

ring shear tester. Early ring tester models were only partly successful in accurately measur-

developed by Schulze in 1994 that the superiority of ring testers over the Jenike shear tester became apparent [23]. The test procedure with a ring shear tester is equivalent to that described above—the sample is still sheared in two steps including "preshear" and "shear." The primary advantage of ring shear testers is the unlimited rotary travel that they offer, making it possible to measure a complete yield locus without changing the sample or refilling the shear cell. Unfortunately, however, ring shear testers do not overcome all of the limitations of linear shear testers. In particular, ring shear testers have difficulty evaluating the flow performance of compressible materials because the stress fields of those materials are highly non-uniform during the test [24, 25]. An automated commercial version of the Schulze ring shear tester is now available that increases the speed of the test process and reduces the dependence of measured flowability properties on the skill level of the operator [6]. Of course, these improvements come at a substantial cost: the base price of a commercial Schulze ring tester is greater than \$70,000 USD. However, even with these features, ring shear tests are not always reliable for biomass as shown in **Figure 7**, which compares predicted minimum hopper opening sizes to ensure consistent flow based on shear test results of various ground pine

*c*

of materials, and it was not until an improved unit was

is a rotational

The last type of instrument capable of measuring unconfined yield stress *f*

*c*

on the flow-function [20].

128 Advances in Biofuels and Bioenergy

ing the unconfined yield stress *f*

materials to experimentally measured values [26].

indicates moisture content with larger symbols representing higher moisture content (10–40% wet basis).

Silos and bins serve to store material, which is then discharged through reclaimers or hoppers as explained above. After material is reclaimed from storage, it is subjected to final evaluation for suitability, including excessive moisture or unacceptable sizes of particles. Foreign materials, such as rocks and metals are also removed. The material is then conveyed using belt, chain, or pneumatic conveyors to the conversion reactor and is fed into the reactor. There are six primary types of biomass feeders: (1) gravity chute, (2) screw conveyor, (3) pneumatic injection, (4) rotary spreader, (5) moving-hole feeder, and (6) belt feeder. Proper design of the reclaiming, conveying, and feeding equipment is essential to ensure uninterrupted flow from storage to feeder. The design principles are based upon the material properties discussed above and, overall, share similar considerations with the design of silos, bins and hoppers summarized above. For detailed analyses of the various options, the reader is referred to specialized texts, such as those by [5–7, 23]. One topic that is of note here is the cost of biomass handling systems. Material handling represents a significant portion of the capital and operating costs of a biomass conversion facility even if all of the components operate exactly as intended. **Table 2** shows an example of relative costs of handling equipment for two biomass pelleting facilities, one for herbaceous feedstocks and one for woody feedstocks. The herbaceous facility is designed to handle baled material while the woody facility is designed to handle wood chips. For both feedstocks, the drying operation is the single largest cost with grinding and densification being the next most expensive. Overall, handling and processing bales incurs approximately \$1.2 million more in total direct costs than handling and processing wood chips.


**Table 2.** Relative estimated costs in 2011 USD (\$) of herbaceous and woody biomass handling and preprocessing systems, each operating at 9 tons/h (adapted from [27]).
