REFRIGERACIÓN POR COMPRESIÓN 22

A qualitative or categorical geological classification (such as those described in section 2.5) is not only difficult to integrate into a model but has not intentionally been established for comparisons against mineral processing properties. In order to undertake a comprehensive qquantitative analysis of rock, particle or mineral texture, texture needs to be considered in terms of its individual components: size, shape and mineral constituents. This will allow the impact of individual mineralogical or textural characteristics on different mineral processing behaviours to be established. The research that is presented in this thesis relies heavily on quantified textural data and presented in this section are the methods and relevant previous studies for the quantified analysis of the textural attributes: size (section 2.6.1), shape (section 2.6.2), modal mineralogy (section 2.6.3), mineral associations (section 2.6.4) and mineral distribution (section 2.6.5).

2.6.1 Size

The size of a mineral or rock is the most widely used of all the textural parameters (e.g. Jones, 1987, Higgins, 2006a). In many respects it is the easiest to measure. It is a dimensional parameter that can be expressed as a unit of length, area or volume. The ability to quantify size makes it amenable to comparisons with physical rock properties and forms the basis of many routine physical tests that are used in the design and optimization of mineral processing plants (e.g. Wills and Napier-Munn, 2005). Size parameters are obtained from individual minerals as well as rock particles. These data are typically examined as populations of various products created from one sample. For example, a distribution of particle sizes can be produced from the crushed product of a selected drill-core interval. The distribution of particle sizes is a function of the rock hardness, mineral types, mineral form and hardness as well as the rock texture (e.g. Bojcevski, et al., 1998). These distributions can be used to determine the hardness properties of that interval and the energy that will be required to crush this product in the mineral processing circuit (e.g. Wills and Napier-Munn, 2005).

In this research, size parameters have been measured from the mineral and particle features of particulate rock samples as well as the mineral features of intact rocks. Traditionally, size parameters are measured from the planar surfaces of rocks and minerals (Higgins, 2006a). In this thesis, RGB images of planar surfaces have been produced at various magnifications from different measurement platforms. The use of RGB images means that the size parameters can be measured primarily using pixels as a unit measure. The use of image analysis as a technique for quantifying texture will be described in further detail in section 2.8.

The most commonly used measurements of size are area and perimeter (Higgins, 2006a). These can be applied to rocks, minerals or particles as well as other geological features such as faults, veining, lithological units, alteration zones and bedding. Other measurements of size that are used less commonly are the length, width, smallest enclosing ellipse, largest enclosed ellipse and the Feret diameter (Pirard et al., 2004). These measures and their formulae are described in more detail in Table 2.11.

T

Table 2.11. Formulae and descriptions of the most commonly used measurements of size. Measurement

o of Size

Formula Description References

Area The total region enclosed by an objects perimeter.

Square and rectangle = length x width Circle or Ellipse = r2_{π where r = radius} Triangle = ½ base length x height

The formula for area is dependent on the object shape.

e.g. Wills and Napier-Munn, 2005

Perimeter The sum of all object sides. The perimeter is a measure of the length of an objects boundary.

e.g. Wills and Napier-Munn, 2005

Length The length and width of an object can be calculated using a number of methods:

1. Creating a bounding box around the object and calculating the shortest and longest intercepts

2. Calculating an equivalent ellipse of an object and then calculating the longest and shortest intercepts

3. Calculating the length and width by using the ratio of the eigenvalues of the objects covariance matrix.

Visually, the length and width of an object appears easy to calculate. The length being the longest intercept through the object, and the width being the shortest intercept. In terms of image processing this can become more difficult when processing includes thousands of objects all oriented in varying directs. Russ et al., 2007 Definiens, 2010 Width Smallest Enclosing Ellipse

The radius of the smallest circle that can enclose the object.

These parameters are considered a more robust method than area, perimeter and length and width for measuring the size of particles that have undergone sieving (Pirard et al., 2004). Pirard et al., 2004 Largest Enclosed Ellipse

The radius of the largest circle that can be contained anywhere within the object.

Pirard et al., 2004 Feret

Diameter

The distance between two parallel objects that is at a tangent to the object profile and perpendicular to the ocular scale.

Typically, 8 or 16 discrete diameters are taken through the object and the minimum or maximum Feret diameter is used.

Howarth and Rowlands, 1987

In mineral processing, the area and the perimeter are used together to quantify the perimeter complexity and are typically applied to particles (Vink, 1997; Pirard et al, 2004). This is referred to as the Phase Specific Surface Area (PSSA) which is calculated by dividing the perimeter of the object by its area. It is considered that if a particle has a complex perimeter (i.e. high PSSA) then it will have a larger exposed surface area, which will increase the particles potential to float if it contains valuable minerals. For particulate samples, where the size and shape of a mineral or particle has been reduced by the comminution process and the texture partially destroyed, the PSSA is an appropriate measurement of size and perimeter complexity. However, research undertaken within this project found that when the PSSA is applied to intact mineral grains, it is only appropriate for smaller mineral grains. Figure 2.4 shows two examples of objects (measured in pixels) that have a PSSA of

1.38. The larger object (left) has a more complex perimeter than the smaller object on the right. As the area of the mineral increases the PSSA becomes less sensitive to perimeter complexities.

F

Figure 2.4. PSSA becomes less sensitive to complex perimeters as size increases. The larger object (left) has a more complex perimeter than the smaller object (right), yet both have a PSSA of 1.38. The pixel size is the same for both objects.

For process mineralogists, who primarily work with particulate samples, the mineral or particle area is typically converted to Equivalent Circle Diameter (D0; Figure 2.5; e.g. Pirard et al.,

2004, Wills and Napier-Munn, 2005. The purpose of this conversion is to produce a distribution of particle sizes that can easily be related to standard sieve sizes (Tyler’s √2 sieve series) that are used in the measurement of comminution and grinding products (Grupta and Yan, 2006). It should be recognised that D0 does not accurately reflect the true diameter of the actual particle that will pass

through a given sieve (Wills and Napier-Munn, 2005). Figure 2.5 shows three examples of particle that have similar D0 values. During actual sieving, it is likely that particles A and B will fall through

a smaller diameter sieve, given the right orientation, than that estimated by D0.

Figure 2.5. Three examples of particles (orange) with similar ECDs. The area has been calculated from the number of pixels.

Traditionally, particles that have been sized into fractions using the sieving process are weighed as a proportion of the total sample. The most common method for plotting this data is as a cumulative frequency curve using a semi-logarithmic plot (Wills and Napier-Munn, 2005). However, there have been a number of methods developed with the aim of avoiding congestion and extremities in these plots. The two most widely accepted are the Gates-Gaudin-Scuhmann (Schumann, 1940; later in Wills and Napier-Munn, 2005) and the Rosin and Rammler (1933). Both methods are derived from equations that contract and expand different areas of the graph in

order to produce as close to a straight line as possible (Wills and Napier-Munn, 2005). A straight line is typically considered to be easier to interpret. However, the use of these methods as well as using a cumulative frequency curve rather than a histogram could potentially mask any bimodality that is present in a sample as a result of rock texture. Further detail regarding the Gates-Gaudin- Schuhmann and Rosin and Rammler methods can be found in Harris (1971) and Wills and Napier- Munn (2005).

2.6.2 Shape

The analysis of grain shapes has been widely explored in the field of sedimentary geology (e.g. Ehrlich and Weinberg, 1970; Oakey et al., 2005) and to a lesser extent, igneous petrology (e.g. Triebold et al., 2006). In ore texture studies, shape is often considered indirectly (e.g. Barton, 1991; McArthur, 1996; Ramdhor, 1980; Craig and Vaughan, 1981). For example, an ore texture described as ‘a quartz vein exhibiting a comb texture’ implies that prismatic crystals are growing in a unidirectional pattern and are perfectly euhedral. To date there are limited examples in the literature regarding ore textures that use quantified shape parameters as part of their textural classification however examples include Donskoi, et al., (2007) and Triffit and Bradshaw, (2008) who examined the effect of mineral shape on the flotation and recovery behaviour at specific sites.

There have been a number of key publications that summarise shape factors and measurements (Serra, 1982; Higgins, 2006a; Pirard and Dislaire, 2005; Pirard, 2005). However, the application of these parameters to real minerals, rather than simulated images of rock particles or mineral grains is limited. Many authors demonstrate the differences in shape descriptors by using a series of manufactured shapes (Rosin, 2003) with only a few showing a practical application of shape analysis using worked examples (Lastra, 2007; Triffett and Bradshaw, 2008). A widely used approach to shape analysis is to use shape descriptors that represent, or are sensitive to, various aspects of simple shapes, e.g. circle, square etc. There are a number of papers that summarise commonly used shape descriptors such as sphericity, rectangularity and elongation and assess the shape measures that are most useful (e.g. Rosin, 1999; 2003, Pirard and Dislaire, 2005). The automatic identification of these shapes can be referred to as ‘pattern recognition’ and is typically used in the field of ‘computer vision’ (Rosin, 2003).

The recent increase in the use of automated mineralogy systems has seen the implementation of shape factors into image analysis software (e.g. Higgins, 2006, Russ, 2007). This has been perceived as a huge advantage for the field of mineral processing in terms of the ability to quantify aspects of texture that have traditionally been considered qualitative and descriptive. However, there is a poor understanding of which shape factors are appropriate to use and which other quantifiable parameters they should be compared to or measured against without creating circular arguments. An extensive review of shape factors found in new image analysis systems (which are described later in this chapter) and their interpretations is given by Pourhahramani and Forssberg (2005).

2.6.3 Modal mineralogy

Modal mineralogy is an important factor in determining the ease with which a rock can be crushed and ground in the mineral processing circuit. Traditionally, modal mineralogy was calculated by point counting using optical microscopy methods (e.g. McArthur, 1996) or estimated from hand- specimens samples. The development of Quantitative X-Ray Diffraction (QXRD) analysis has allowed mineral abundances to be determined for powdered materials (Klug and Alexander, 1954;

Copeland and Bragg, 1958). Newer methods in the imaging of planar rock surfaces, and the identification of minerals allows the modal mineralogy to be calculated using a quantitative and unbiased approach.

2.6.4 Mineral associations

The minerals that are associated with a target mineral will have a direct impact on that minerals liberation potential and ultimately flotation and recovery (Petruk, 2005; Bojcevski, 2004; Goodall and Scales, 2007; Becker et al., 2008). There have been a number of studies that have attempted to quantify mineral associations through visual observations using optical microscopy. In particular, a study undertaken by Arif and Baker (2004) characterizes the gold mineralogy based on the mineral associations of 699 native gold grains observed using optical microscopy. These data were used to draw conclusions regarding the source of the gold and select samples for further laser ablation analysis. Like many geological studies, the minerals that have been analysed or included in the study are those that are easily recognized or within the detection limits of optical microscopy analysis. A more automated approach to mineral identification and classification would mean that user error and bias in grain selection could be reduced.

Another study undertaken by Vaughan and Kyin (2004) characterizes mildly refractive ores based on a pyrite, arsenic or antimony association which has implications for the cyanidation of the ores. Vink (1997) and later Bojcevski (2004) created ore texture classifications based on the modal mineralogy and texture of particles and drill core. While the mineral association was recognized as important and considered in their classifications, the ability to routinely quantify this parameter was difficult. It is still time consuming despite improvements in automated microscopy, computer technology and software developments since those studies took place.

2.6.5 Mineral distribution

There are a number of textural terms that are used to describe the distribution of minerals within a rock e.g. disseminated, seriate, aggregate (e.g. Gifkins et al., 2005). Like many other aspects of texture there have been a number of attempts to measure the distribution of minerals in a rock, namely by mathematicians. For example, the proximity of various objects can be measured using co- occurrence matrices (Gay and Latti, 2006). These studies often use simulated images of artificial objects and are restricted by the size of the surface being analysed.

In liberation studies, proximity functions are potentially a useful measure of mineral clustering. For example, if the grain size of the valuable mineral is small, but there are a large number of grains clustered together, then sufficient surface area is still likely to be exposed in order for that mineral to be recovered, for example by flotation. To this author’s knowledge there are no examples in the literature of proximity functions that have been used on intact rock samples for the purpose of characterizing liberation potential.