Rules of Thumb: Solids Transfer - Bins & Silos

Stephen Hall discusses the golden rules for design

SOLID materials are stored and dispensed from bins. For the purpose of this article that means bins, hoppers, and silos interchangeably. Bins are vessels that contain solids and discharge them through feeders beneath their tapered, often conical, bottoms.

We expect the bins to preserve critical attributes and successfully discharge the material on demand. Proper bin design will deliver those expectations. However, due to large differences in the physical properties of different solid materials, the selection of the best bin design is far from straightforward. This article gives guidance that will improve the chances for designing and specifying bins that meet the challenge successfully.

A critical safety consideration is explosion prevention and control. Nearly any finely-divided powder (<500 µm particle diameter) can form an explosive cloud if dispersed in air inside the bin, such as during loading. Static electricity, tramp metal or hot embers will spark the explosion. Similarly, over and under pressure of the bin can occur, especially during upset conditions. The design of features to mitigate these hazards is beyond the scope of this article, but you must be acutely aware of the potential dangers and seek expert advice if you are unsure how to proceed.

Throughput

Start by determining the required throughput. How much material must the bin store and at what rate must it deliver? You should know the average, maximum, and minimum values for storage and delivery rate at each step in the process. Storage silos that are refilled from trucks or rail cars are normally sized large enough to accept a full load. There is usually material still in the silo when the delivery is made and that means the minimum size of the silo will be more than 1.5 times the size of the delivery vehicle. The plant may be operating on a “just-in-time” basis to minimise inventory, or perhaps it wants to maintain a certain reserve of materials that could last weeks or months in the event that the material is suddenly unavailable. Material delivery (or shipment) may be restricted to certain days of the week. All of these factors should be considered in the analysis.

The material may have an expiration date or a “best if used by” date that will dictate the overall residence time from receipt until use. This dating probably relates to spoilage, such as microbial growth. But there may be other degradations that occur in the material during storage (and handling) that are not tied to a specific date. These include moisture absorption, particle agglomeration, particle breakage, odour retention, or colour changes. To mitigate these problems, the retention time may need to be controlled either on an overall basis or in individual bins along the material transport pathway in the plant. I will return to this point later when discussing how material moves through a bin.

Constraints and properties

Next, define constraints to the physical size and location. What will restrict the bin sizes? Restrictions will help define the design space for your project. These may include the maximum allowed height of outdoor silos, ceiling heights, floor or yard area, door sizes, and the allowable floor or ground loading.

Determine the material’s physical properties. This is not a straightforward determination, and published information is generally unreliable. Therefore, it may be necessary to contract with a laboratory to test your materials. Note that important properties can change over time as the material is subjected to pressure (material at the bottom of a filled bin is pressed down by the material above it) or subtle chemical or physical bonds form due to, for example, water absorption or water evaporation.

The material’s cohesive strength is used to determine the minimum size of the opening into the bottom feeder. If the opening is too small the material will bridge and prevent free flow. Think of sugar. Normally free-flowing, if it absorbs moisture the sugar granules cake. The cake can form an arch over the opening but there is a limit to the length of the arch that is measured as cohesive strength. Some designers incorporate features that promote flow, such as live (vibrating) bottoms or fluidising air nozzles. A good bin design should not require these features, however; they are band aids that masquerade as good design.

The material’s wall friction parameter is a measure of how steep the hopper wall must be to ensure the material flows freely toward the bottom outlet. This parameter is affected by particle size, size uniformity, chemical purity, moisture content, compression, and more.

The combination of wall angle and size of the bottom opening determine if the material flows through the bin in plug flow (also called mass flow), or instead forms a funnel (also called core flow) which leaves a static tube of the material around the periphery of the bin (see Figure 1). If the wall angle is too shallow, funnel flow will form.

The material’s angle of repose, typically 30-45°, measures the natural slope of a pile at the top of the bin. There is no direct relationship between the angle of repose and the hopper slope that is necessary to achieve mass flow; the hopper angle must be greater than the angle of repose but testing is required to determine the exact value. The bulk density, which can vary with pressure, measures the volume occupied by a certain mass of material.

You can estimate the overall size of a bin and evaluate the practicality of your hopeful design by using the data that I’ve described. Every bin has a top section where material is added and a discharge section where it is removed. The top section may require an empty headroom height as small as 0.5 m or as large as 2–3 m depending on how the material is conveyed into the bin. Filling from a screw conveyor requires very little space, but pneumatic transfer needs a separator such as a cyclone or baghouse. The discharge may be through a rotary valve into a pneumatic line, or directly to a belt conveyor. You should assume at least 1 m beneath the bin for discharge.

Assume a hopper angle, θ_WALL <40°, and angle of repose, θ_REPOSE >35°, plus any assumed bin diameter, D (R=D/2), and bin volume, V, to calculate the height of the material. Add your allowances for the top section and discharge space to get the overall height of the bin assembly. The equations here are for a round bin with centered bottom opening; you can do the math for other shapes. Trig functions in Excel work with radians, so the Excel formula for the top pile height is “=R*TAN(RADIANS(Theta2))”, where the cells for bin radius and angle of repose are named “R” and “Theta2”. See Figure 2 for nomenclature.

Note that some materials (especially powders) can be highly compressible. Consequently, the mass that can be stored in a bin of a certain volume is likely to be more than would suggested by the loose bulk density of the material. Exact determination of the storage capacity in these cases requires lab data and more detailed calculations.

The aspect ratio of sidewall divided by diameter of the bin is typically from 1:1 to 4:1 (based on economics). Keep the diameter below 4 m if the bin will be delivered to the site by truck. Larger diameters will require that the bin be field-fabricated. Rectangular bins store more material in a given area, but the slope of the vertices on a rectangular hopper is less than the adjacent wall slope. Therefore, funnel flow is more likely to occur, which leaves stagnant material in the corners. If the bottom outlet is off center, the bin is taller compared to a bin with centered outlet for a given working volume.

Although it may seem that bins should all be designed to provide mass flow, there are certain situations where funnel flow is preferred. In particular, with funnel flow the sides of the bin (especially the hopper section) are protected from constant sliding of the material. With abrasive materials, funnel flow results in less wear. Also, the shallower angle of the hopper walls provides more volume in a given height. But mass flow is needed if the material can change over time as described earlier in this article or if the material tends to segregate with flow. Mass flow is also needed if there is a need for inventory control for things such as tracking the quality of ingredients or batch identity.

The Rational Design Method (after Jenike, 1964) is a widely-accepted analytical procedure that yields the wall slope and outlet size that will give reliable mass flow through a bin. This method requires accurate determination of several material properties. The resulting bin design may not match a fabricator’s standard line of bins; constructing to the method’s specifications may add cost. Therefore, many fabricators, as many as 80% in the UK according to one analysis, shun using the method, to be more cost competitive. But the result may be a suboptimal design that does not flow properly.

You should consider making the effort, affording the time, and spending the money to apply the rational design method if one of the following statements applies.

• The material can segregate, and this is not acceptable. If the material is free-flowing and has no tendency to consolidate over time or cake, the only measurement needed is the wall friction test to get the hopper slope parameter. This is a simple and cheap test.
• The material is cohesive or becomes cohesive over time. The minimum tests required are flow function, wall friction, and bulk density. Most powders are cohesive enough to cause trouble; you should exercise caution before declaring that the material is always free flowing.

---

This is the seventh in a series that provides practical insights into on-the-job problems. To read more, visit the series hub at https://www.thechemicalengineer.com/tags/rules-of-thumb.

---

Disclaimer: This article is provided for guidance alone. Expert engineering advice should be sought before application.