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The design process for silos, bins, and hoppers is often thought of as a &#;black art,&#; known by only a chosen few. However, a proven, practical method for storage bin process design has been in use for over 60 years. Just as a pump must be designed specifically for the liquid it will handle, so, too, must a silo be designed for a particular powder or bulk solid. The characteristics of the material being handled will dictate the storage vessel design.
Although design requirements such as storage capacity, throughput, overall height, and other spatial features are important inputs, other critical parameters, including powder cohesion, coefficient of sliding friction, and permeability, can significantly affect the bin&#;s design. Figure 1 illustrates a typical bin installation. A conveyor delivers the bulk material to the bin, which provides storage capacity within the flow path; a feeder (a rotary valve in this case) controls the solids discharge from the bin and feeds the material to the next part of the process. In any industrial application, negative consequences may arise if the bin does not reliably discharge the powder or bulk solids to the downstream process or if the discharging material no longer meets quality specifications.
Figure 1: A typical bulk-solids handling operation includes an inlet feed conveyor, a storage bin, and an outlet feeder that controls solids discharge.This article details a step-by-step process to design bins that will ensure reliable discharge of powders and bulk solids based on their unique flow behaviors and the requirements of the process. The terms bin and silo are used interchangeably throughout the article.
The first step in designing a bin to store a powder or bulk solid is to review key storage requirements and operating conditions. These include:
While bulk-material handling problems can be experienced in a variety of equipment (e.g., feeders, transfer chutes, dust collectors), they most often occur in bins. Common flow problems include:
There are many consequences of flow problems. A bin experiencing ratholing will have limited live (i.e., useable) capacity, as low as only 10&#;20% of the bin&#;s rated storage capacity. Additionally, material stagnation in a poorly designed bin can lead to caking of materials, spoilage of food powders, or other forms of quality degradation. Collapsing arches, ratholes, and nonuniform loading contribute to localized, and at times catastrophic, storage vessel failures.
Many of these flow problems occur in a bin that is discharging material in an undesirable flow pattern. The discussion of Step 5, choosing the type of flow pattern in the bin, explains how the flow pattern can directly influence the type of material flow performance you will experience.
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The flow properties of the material must be measured in order to predict and control how it will behave in a bin. These flow properties can be measured1,2 in a bulk-solids testing laboratory under conditions that accurately simulate how the material is handled or processed in your facility. If the bulk solid&#;s properties change rapidly or if special precautions are required, tests should be conducted onsite. Table 1 lists the most important bulk-solids handling properties that are relevant to predicting flow behavior in bins and hoppers. Each of these parameters can vary with changes in:
The approximate height of the cylinder section needed to store the desired capacity (initially ignoring the capacity in the hopper section) is simply:
\[H = {m \over ρ_{avg} A}\]
where:
The final cylinder height needed to hold the required volume depends on the volume lost at the top of the cylinder due to the bulk solid&#;s angle of repose, as well as the volume of material in the hopper section. Because this design process is iterative, a reasonable estimate for cylinder height is sufficient at this point.
Try to keep the height of a circular or square cylinder between about one and four times the cylinder&#;s diameter or width. Values outside this range often result in designs that are uneconomical.
Note that the bin&#;s calculated storage volume and its live, usable volume are not necessarily identical. Depending on the type of flow pattern in the bin (described in the next section), stagnant regions of material in a bin will reduce the usable capacity.
ParameterMeasured ByRequired ToCohesive strengthDirect shear testerCalculate outlet size to prevent arching and ratholingWall frictionDirect shear testerCalculate hopper angles for mass flow, internal frictionBulk density/compressibilityCompressibility testerCalculate pressures, bin loads; design feederPermeabilityPermeability testerCalculate discharge rates, settling timeSegregation tendencySegregation testerPredict whether or not segregation will occurAbrasivenessAbrasive wear testerPredict the wear life of a bin linerSliding at impact pointsChute testerDetermine minimum angle of chute at impact pointsParticle friabilityAnnular shear testerDetermine effect of flow pattern on particle breakageTable 1. Critical flow properties of bulk solids are required for proper selection of bins, hoppers, feeders, and chutes.Although it is natural to assume that a bulk solid will flow through a storage bin in a first-in/first out sequence (just as liquid moves through a tank), this typically is not the case. Many bins discharge bulk solids in a funnel-flow pattern.
With funnel flow, some of the material moves in the center of the hopper while the rest remains stationary along the hopper walls (Figure 4). This first-in/last-out sequence is acceptable if the bulk solid is relatively coarse, free-flowing, and non-degradable, and if segregation during silo discharge is not an issue. Provided that the bulk material meets all four of these criteria, a funnel-flow bin may be the most economical storage choice.
Unfortunately, with many bulk materials, funnel flow can create serious product quality and process reliability problems. Arches and ratholes may form, and flow may be erratic. Fluidized powders often have no chance to deaerate, so they remain fluidized in the flow channel and flood when exiting the bin. Some materials cake, segregate, or spoil. In extreme cases, unexpected structural loading results in equipment failure.
These problems can be prevented by designing storage vessels to move materials in a mass flow pattern. With mass flow, all the material moves whenever any is withdrawn (Figure 5). Flow is uniform and reliable; feed density is independent of the head of solids in the bin; there are no stagnant regions, so material will not cake or spoil, and level indicators work reliably; sifting segregation of the discharge stream is minimized by a first-in/first-out flow sequence; and residence time is uniform, so fine powders deaerate. Mass-flow bins are suitable for cohesive materials, powders, materials that degrade with time, and whenever sifting segregation must be minimized.
Figure 4. Funnel-flow discharge results in material stagnation along the hopper walls. Many undesirable flow effects can occur with a funnelflow pattern. Figure 5. Mass-flow discharge occurs when material flow is achieved against the sloping hopper walls. A massflow pattern prevents ratholing, allows first-in/first-out flow, and minimizes segregation.Use the flowchart in Figure 6 and the requirements identified in Step 1 to determine which flow pattern your bin needs. As indicated in the diagram, if segregation, caking, spoilage, flooding, or ratholing are likely to occur, then a mass-flow discharge pattern should be selected. If a mass-flow bin is required based on the flow characteristics of the powder or bulk solids, the next step is to determine an appropriate outlet size and feeder. Keep in mind that the mass-flow bin design process is iterative. The actual outlet size will depend on the required discharge rate from the bin and the feeder selected. These factors, in turn, affect the slope and shape of the mass-flow hopper wall, as discussed in the next section.
Figure 6. Use this flow pattern selection diagram to determine the most-effective bin design for your powder or bulk solid storage application.Designing for mass flow. With this flow pattern, it is essential that the converging hopper section is steep enough and the wall-surface friction low enough to facilitate solids flow without stagnant regions whenever any solids are withdrawn. In addition, the outlet must be large enough to prevent arching and achieve the required discharge rate.
Andrew Jenike, renown as the founding father in the field of bulk solids handling, developed hopper design charts showing the limits of mass flow for conical and wedge-shaped hoppers1. In these charts, the hopper angle (measured from vertical) is on the abscissa, and wall friction angle is on the ordinate, as shown in Figure 7 for conical hoppers and Figure 8 for wedge-shaped hoppers. The wall friction angle is determined through powder testing with various wall surfaces, such as carbon steel, stainless steel, plastic, abrasion-resistant liners, etc. The coefficient of sliding friction for the powder against a wall surface can be calculated from the tangent of the wall friction angle. Tests are conducted using a direct shear tester according to ASTM standard test method D-.
Depending on the combination of hopper angle and wall friction angle, either mass-flow or funnel-flow discharge with the particular bulk material will result. Simply speaking, a highly frictional bulk solid, such as sand, will require a steep hopper angle to achieve mass flow, whereas a low-friction bulk solid, such as smooth catalyst beads, can achieve mass flow at a relatively shallow hopper angle.
Figure 7. This chart for conical hopper design determines wall slope based on the wall friction angle. Mass flow results from a combination of sufficiently low wall friction and steep enough hopper angle.Note that a 60-deg. (from horizontal) hopper angle for a cone is usually not sufficient to provide mass flow for most bulk solids. This angle is optimum for manufacturing the hopper with minimal waste &#; it will not guarantee mass flow as is sometimes promised.
Calculating the outlet size needed to overcome arching is more challenging. Arching can be analyzed by measuring the cohesive strength of the material. First, the flow function of the material (i.e., the cohesive strength vs. consolidating pressure) is measured through laboratory testing. This test is also conducted according to ASTM D- using a direct shear tester2. As in the wall friction test, consolidating forces are applied to material in a test cell, and the force required to shear the material is measured. This information directly relates to a material&#;s ability to form a cohesive arch or a rathole. Once the flow function is determined, minimum outlet sizes required to prevent arching can be calculated using the design charts published by Jenike1. Reference 3 provides the step-by-step Jenike method for hopper outlet calculation based on a material&#;s cohesive strength.
Sizing the outlet for the required discharge rate is straightforward, provided the bulk material is both coarse and free-flowing4. A material is considered coarse if the majority of its particles are larger than 1/8 in. or 3 mm. A free-flowing material is one that does not experience arching or ratholing flow problems. Assuming that the bulk material is both coarse and free-flowing, such as plastic pellets, the following equation can be used to approximate the maximum discharge rate from a converging hopper:
\[M = {&#;A \sqrt{Bg \over 2(1 + m) tan \theta}}\]
where:
Equation 2 will not accurately estimate the flowrate of a fine powder (e.g., fumed silica, terephthalic acid). Because it does not account for the material&#;s resistance to airflow (or permeability), it will grossly overestimate the hopper&#;s discharge flowrate capability. A more accurate estimation of powder discharge rate can be made using the powder&#;s permeability5,6, but the analysis is complex and beyond the scope of this article.
Designing for funnel flow. The key requirements for funnel flow are sizing the hopper outlet large enough to overcome arching and ratholing, and making the hopper slope steep enough to be self-cleaning.
Determining the minimum dimensions to overcome arching and ratholing requires knowledge of the material&#;s cohesive strength and internal friction. References 1 and 3 provide the relevant design procedures. It is important to note that with funnel-flow bins, overall size matters, whereas the design of mass-flow bins is essentially independent of scale. Ratholing is affected by consolidating pressure; thus, large funnel-flow bins have a higher ratholing tendency. In mass flow, there is no chance of ratholing, so the size of the bin is not important.
The requirement that the funnel-flow bin be capable of self-cleaning can usually be met by making the hopper slope 15 deg. to 20 deg. steeper than the wall friction angle. This assumes that a stable rathole has not formed.
Figure 8. This chart for planar (wedge) hopper design determines wall slope based on wall friction angle. Wedge shaped hoppers are typically 10-deg. less steep than cones for mass flow.A square or rectangular straight-sided section at the top of a bin is preferable to a circular cross-section, because it is easier to fabricate and it provides a larger cross-sectional area per unit of height. However, material flow or structural issues often outweigh these advantages. Flat walls are susceptible to bending, whereas a cylinder is able to resist internal pressure through hoop tension. Therefore, thinner walls and less external reinforcement are needed for circular cross-sections. In addition, there are no corners in which material can build up, which is particularly important at the interface between the bin and the hopper.
Hoppers come in a variety of geometries. Figure 9 shows some of the more common hopper shapes. When choosing a hopper, consider these factors:
The feeder is just as important as the hopper above it. To be effective, the feeder must uniformly draw material through the entire cross-section of the bin&#;s discharge outlet7. An obstructed outlet, due, for example, to a poorly designed feeder or partially opened gate, will result in funnel flow regardless of the hopper design.
Three common types of bulk solids feeders, along with key features required to ensure uniform withdrawal of material from the entire outlet of the hopper, are discussed in the following paragraphs.
Screw feeders. These are well suited for use with hoppers that have elongated outlets. Since a screw feeder is totally enclosed, it is good for use with fine, dusty materials. In addition, it has few moving parts, so it requires less maintenance than a belt feeder.
The key to a proper screw-feeder design is to provide an increase in capacity in the direction of feed. This is critical when the screw is used under a hopper with a slot-shaped outlet. One common way to accomplish this is by using a mass-flow screw feeder design as shown in Figure 108. Each of the screws shown in this figure has a decreasing diameter (tapered) conical shaft followed by a section of increasing pitch.
Belt feeders. Like screws, belt feeders can be a good choice for an elongated hopper outlet. Belt feeders are useful for handling cohesive or coarse bulk solids that require a high discharge rate. Since the idlers of a belt feeder can be mounted on load cells, a belt feeder can also be used to weigh the solids being fed (i.e., gravimetric operation).
Belt feeders are not as good as screws and rotary valves for handling fine or dusty materials. Therefore, if your plant is handling combustible or toxic dusts, belt feeders are not recommended, unless the entire feeder is enclosed, sealed, and incorporates proper dust collection measures.
The key to a proper belt-feeder design is to provide increasing capacity along the direction of feed. An effective way to increase capacity is to install a belt-feeder interface (Figure 11). Rotary valves.
Rotary valves (Figure 12) are a common feeder, especially for discharging bulk materials into a pneumatic conveying system. The use of rotary valves is generally limited to hoppers with circular or square outlets. They should not be used for handling highly cohesive solids, because such materials have a high propensity for bridging that requires large hopper outlets.
A properly designed interface must be provided above the rotary valve to ensure that solids are withdrawn uniformly across the entire hopper outlet cross-section. Typically, a short vertical section, with a height of about 1 to 2 outlet diameters, should be placed between the hopper outlet and rotary valve inlet, as shown in Figure 1. Without such an interface, a preferential flow channel develops on the side of the hopper outlet where the solids are first exposed to the empty pockets, which results in nonuniform discharge. Material then stagnates over the remaining portion of the hopper outlet, thereby increasing the tendency for bridging and other flow problems.
Shallow sloping internal walls located at the inlet of many rotary valves can reduce the active hopper opening, causing material to remain stagnant and obstructing the solids discharge from the hopper above, as well as upsetting the mass flow in the hopper.
Figure 10. Mass-flow screws use a combination of a tapered shaft section followed by an increasing pitch section. Figure 11. A mass-flow belt-feeder interface is required to enforce uniform withdrawal of bulk material from the hopper outlet, thereby maintaining mass-flow discharge.Bin design also involves making decisions about other system components, including:
Storage bins and silos for handling powders and bulk solids come in a variety of materials, although they are typically constructed from metal or reinforced concrete.
Structural design considerations. The bin must be designed to resist the loads applied to it by both the bulk solid and external forces, such as seismic, wind, or ancillary equipment loads. This is particularly important when designing for, or converting an existing bin to, mass flow, because unusually high localized loads may develop at the transition between the vertical section and the mass-flow hopper. Qualified structural engineers should calculate the complex loads that may be induced in the silo, bin, or storage vessel.
This step-by-step bin design approach has been effectively used for over 60 years in thousands of installations handling bulk solids, including fine chemical powders, granular resins, cohesive centrifuged wet cake, biomass, fragile cereal flakes, and abrasive ores (among others). Although it may be appealing to select a standard hopper design with a 45-deg. or 60 deg. angle, if it is not suitable for your bulk material, you will likely incur costs far beyond replacing the original equipment.
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