Jens Plinke, Consulting Engineer, and Priscilla Freire, Business Development Engineer at TUNRA Bulk Solids explain important considerations when determining bulk density, the difference between bulk density and compressibility, the development of improved testing methods and application to stockpile mass estimation for inventory purposes.

Stockpiles are some of the most common means of storing large quantities of bulk materials in industry sectors including mining and steelmaking plants, as well as in the fertiliser industry, ports and others. They are normally used for surge capacity either to store material that will be processed later or to account for differences in throughputs along the handling chain.

**Bulk density: definition, characterisation and applications**

Bulk density is the relationship between mass and the volume occupied by the mass of all constituents: bulk solid particles, moisture and air, as illustrated in Figure 1.

In simple terms, bulk density can be determined as:

Compressibility, on the other hand, concerns the consolidation states of the bulk material. Consolidating the material might affect the air voids and the volume occupied by the particles depending on how compressible the solid is. Therefore, a bulk material may exhibit different bulk densities depending on the consolidation load.

Compressibility characterises the change in bulk density with increasing consolidation stress. Measuring the bulk density at increasing consolidation allows for this relationship to be established (Figure 3). Some applications require explicit knowledge of the compressibility, others, including mass estimation, require knowledge of the relationship between bulk density and consolidation load. The graph in Figure 3 highlights that moisture content might greatly influence compressibility depending on the material.

**Characterising bulk density and compressibility:**

There are several methods for measuring bulk density and compressibility, and it is important to understand the differences to ensure that the most appropriate method will be used for each application. One of the most common methods is described in detail in ASTM D6683-19 and typically uses a small cell of 21-millimetre height by 64-millimetre diameter (approximately a 1:3 aspect ratio). Due to its small size, this cell limits the maximum testable particle diameter, which may not exceed one fifth of the cell height. Bulk materials with particles exceeding this diameter are commonly scalped at 4 millimetres before testing. This method is used for the design of storage and handling equipment such as bins and hoppers. However, for applications like mass reconciliation of materials with a large top size, this method may not yield satisfactory results. However, for applications like mass reconciliation of materials with a large top size this method may not yield satisfactory results.

A large compressibility test available at TUNRA Bulk Solids uses a cell with 100-millimetre height and 300-millimetre diameter (maintaining the 1:3 aspect ratio described in ASTM D6683-19). This cell permits testing of materials of up to 20-millimetre top size. With consolidation pressures reaching up to 200 kPa and larger particle sizes, this tester represents conditions more similar to those experienced in full size applications.

In terms of loose-poured bulk density, the blast furnace feedstock vessel described in ISO 3852 has been typically used in industry for stockpile mass reconciliation, and it uses a 400-millimetre height by 400-millimetre diameter cell (aspect ratio of 1:1). According to the recommendations of D6683 these cell dimensions would permit a top size of up to 40 millimetres.

Figure 4 shows the bulk density measurements for six samples of iron ore, all materials with full size under 10 millimetres. The bulk density was measured both with the -4-millimetre cell and with the large loose-poured cell, which are also shown in the picture. As it becomes clear from the test results, the same material may exhibit very different values when tested with different methods or under different consolidating pressures; this highlights the importance of choosing a suitable method based on the application of test results.

In order to indicate possible effects of scalping on compressibility, Figure 5 shows the results for a sample of bauxite tested both with the small cell in the -4mm size fraction and the large bulk density tester with the full-size material for two moisture contents. The finer fraction of this material is significantly more compressible than the material tested in its full size.

**Towards the development of improved bulk density and compressibility characterisation:**

These analyses of bulk density and compressibility with different testers/vessels and the differences observed in measurements have led to the development of a concept for a new tester able to test materials with larger top-sizes. The requirements for this new tester were:

It must be able to perform loose-poured bulk density tests in conformity with ISO 3852 and AS 1141, which are commonly used for mass reconciliation purposes

It must be able to also perform compressibility tests through the application of loads onto the bulk sample.

This new tester, with commissioning forecast for early 2021, will be able to test materials of full size up to 40 millimetres and a maximum consolidation load of 300 kPa. It consists of a cylindrical cell of 400-millimetre height by 400-millimetre diameter, matching the dimensions specified in ISO 3852.

With such characteristics, this new tester will be able to generate test results closer to the conditions experienced on site for improving stockpile mass estimation procedures.

**Mass reconciliation and stockpile modelling **

One of the main uses for the large bulk density tester is in mass reconciliation for inventory purposes. Determining the volume of a stockpile is a fairly straightforward task using methods such as laser scanning. Nevertheless, determining the actual mass of material within the stockpile relies on an accurate determination of the bulk density – consolidation relationship and on an understanding of the consolidation states within the stockpile.

Common practice reconciliation models may fall short of the best possible accuracy by applying a constant bulk density to the measured volume. Such models do not account for changes in consolidation throughout the height of a stockpile and also discount the variations of the material’s bulk density driven by the changing consolidation.

The stockpile mass estimation method proposed by TUNRA Bulk Solids accounts for both the stockpiled material’s compressibility as well as the consolidation states throughout the stockpile. As shown in Figure 6, a surface scan and a compressibility function similar to that shown in Figure 3 are used to compute the stockpile mass. It is important to consider that possible disturbances may arise from variations in moisture content or consolidation states caused by dozer operation on the surface for example.

The numeric model discretises the stockpile geometry into a number of vertical columns, which, in turn, consist of vertically stacked cubes, as shown in Figure 8. The mass within each column is computed individually, where the mass in the upper-most cube of any column may be computed from the cube’s volume and the material’s loose-poured bulk density. The consolidation state of the next cube below is determined from the mass of the cube(s) above and the appropriate density value can then be applied to determine the cube’s mass. Summing all cubes yields the mass within one column, and summing all columns yields the total mass of the stockpile. By way of example, Figure 8 shows the consolidation states of a 30-metre-tall vertical column comprised of 30 cube elements with a volume of 1m3 each. Also shown are the bulk density and corresponding mass associated with each volume element.

The graph shown in Figure 9 illustrates that consolidation is nonlinear with stockpile depth and that the less consolidated upper cube elements contain less material than the highly consolidated elements at the bottom of the column. Accounting for all these effects yields a more robust method for stockpile mass estimation than applying a constant ‘blanket’ bulk density value to the whole volume.

*This article is based on the presentation “Towards Higher Standard Bulk Density Testing” by Dr Jens Plinke, presented to the Australian Society of Bulk Solids Handling (ASBSH) in 2020. The full presentation can be found on TUNRA Bulk Solids’ YouTube channel. *