1.9.1 Grade

The grade, or assay, refers to the content of the marketable commodity in any stream, such as the feed and concentrate. In metallic ores, the percent metal is often quoted, although in the case of very low-grade ores, such as gold, metal content may be expressed as parts per million (ppm), or its equivalent grams per ton (g t⁻¹). Some metals are sold in oxide form, and hence the grade may be quoted in terms of the marketable oxide content: for example, %WO₃, %U₃O₈, etc. In nonmetallic operations, grade usually refers to the mineral content: for example, %CaF₂ in fluorite ores. Diamond ores are usually graded in carats per 100 t, where 1 carat is 0.2 g. Coal is graded according to its ash content, that is, the amount of incombustible mineral present within the coal. Most coal burned in power stations (“steaming coal”) has an ash content between 15% and 20%, whereas “coking coal” used in steel making generally has an ash content of less than 10%.

The metal content of the mineral determines the maximum grade of concentrate that can be produced. Thus processing an ore containing Cu in only chalcopyrite (CuFeS₂) the maximum attainable grade is 34.6%, while processing an ore containing galena (PbS), the maximum Pb grade is 86.6%. (The method of calculation was explained in Example 1.1.)

1.9.2 Recovery

The recovery, in the case of a metallic ore, is the percentage of the total metal contained in the ore that is recovered to the concentrate. For instance, a recovery of 90% means that 90% of the metal in the ore (feed) is recovered in the concentrate and 10% is lost in (“rejected” to) the tailings. The recovery, when dealing with nonmetallic ores, refers to the percentage of the total mineral contained in the ore that is recovered into the concentrate. In terms of the usual symbols recovery R is given by:

$R=\frac{Cc}{Ff}$ (1.1)

(1.1)

where C is weight of concentrate (or more precisely flowrate, e.g., t h⁻¹), F the weight of feed, c the grade (assay) of metal or mineral in the concentrate, and f the grade of metal/mineral in the feed. Provided the metal occurs in only one mineral, metal recovery is the same as the recovery of the associated mineral. (Example 1.2 shows how to deal with situations where an element resides in more than one mineral.) Metal assays are usually given as % but it is often easier to manipulate formulas if the assays are given as fractions (e.g., 10% becomes 0.1).

Related measures to grade and recovery include: the ratio of concentration, the ratio of the weight of the feed (or heads) to the weight of the concentrate (i.e., F/C); weight recovery (or mass or solids recovery) also known as yield is the inverse of the ratio of concentration, that is, the ratio of the weight of concentrate to weight of feed (C/F); enrichment ratio, the ratio of the grade of the concentrate to the grade of the feed (c/f). They are all used as measures of metallurgical efficiency.

1.9.3 Grade–Recovery Relationship

The grade of concentrate and recovery are the most common measures of metallurgical efficiency, and in order to evaluate a given operation it is necessary to know both. For example, it is possible to obtain a very high grade of concentrate (and ratio of concentration) by simply picking a few lumps of pure galena from a lead ore, but the recovery would be very low. On the other hand, a concentrating process might show a recovery of 99% of the metal, but it might also put 60% of the gangue minerals in the concentrate. It is, of course, possible to obtain 100% recovery by not concentrating the ore at all.

Grade of concentrate and recovery are generally inversely related: as recovery increases grade decreases and vice versa. If an attempt is made to attain a very high-grade concentrate, the tailings assays are higher and the recovery is low. If high recovery of metal is aimed for, there will be more gangue in the concentrate and the grade of concentrate and ratio of concentration will decrease. It is impossible to give representative values of recoveries and ratios of concentration. A concentration ratio of 2 to 1 might be satisfactory for certain high-grade nonmetallic ores, but a ratio of 50 to 1 might be considered too low for a low-grade copper ore, and ratios of concentration of several million to one are common with diamond ores. The aim of milling operations is to maintain the values of ratio of concentration and recovery as high as possible, all factors being considered.

Ultimately the separation is limited by the composition of the particles being separated and this underpins the inverse relationship. To illustrate the impact of particle composition, consider the six particle array in Figure 1.10 is separated in an ideal separator, that is, a separator that recovers particles sequentially based on valuable mineral content. The six particles represent three mineral (A) equivalents and three gangue (B) equivalents (all of equal weight), thus the perfect separator would recover the particles in order 1 through 6. The grade of A and the recovery of A after each particle is separated into the concentrate is given in Table 1.3 and plotted in Figure 1.11 (which also shows the conversion from mineral grade to metal grade assuming the valuable mineral in this case is chalcopyrite, CuFeS₂). The inverse relationship is a consequence of the distribution of particle composition. The figure includes reference to other useful features of the grade–recovery relationship: the grade of all mineral A-containing particles, the pure mineral grade approached as recovery goes to zero, and the feed grade, which corresponds to recovery of all particles.

The grade–recovery corresponding to perfect separation is known as the mineralogically-limited or liberation-limited grade–recovery. For simple two component mixtures with well differentiated density, it is possible to approach perfect separation in the laboratory using a sequence of “heavy” liquids (e.g., some organics or concentrated salt solutions) of increasing density (Chapter 11). The liberation-limited curve can be generated from mineralogical data, essentially following the calculations used to generate Figure 1.11. The liberation-limited grade–recovery curve is used to compare against the actual operation and determine how far away it is from the theoretical maximum separation.

The grade–recovery curve is the most common representation of metallurgical performance. When assessing the effect of a process change, the resulting grade–recovery curves should be compared, not individual points, and differences between curves should be subjected to tests of statistical significance. To construct the curve, the data need to be collected in increments, such as increments of density or increments of flotation time, and then assembled into cumulative recovery and cumulative grade. There are other methods of presenting the data, such as recovery versus total solids recovery, and recovery of mineral A versus recovery of mineral B. Together these are sometimes referred to as “separability curves” and examples will be found in various chapters.

1.9.4 A Measure of Technical Separation Efficiency

There have been many attempts to combine recovery and concentrate grade into a single index defining the metallurgical efficiency of the separation. These have been reviewed by Schulz (1970), who proposed the following definition:

$\mathrm{Separation}\mathrm{efficiency}(\mathrm{SE})=R_{\mathrm{m}}–R_{\mathrm{g}}$ (1.2)

(1.2)

where R_m is the recovery of the valuable mineral and R_g is the recovery of the gangue into the concentrate.

Calculation of SE will be illustrated using Eq. (1.1). This equation applies equally well to the recovery of gangue, provided we know the gangue assays. To find the gangue assays, we must first convert the metal assay to mineral assay (see Example 1.1). For a concentrate metal grade of c if the metal content in the mineral is m then the mineral content is c/m and thus the gangue assay of the concentrate is given by (assays in fractions):

$g=1-\frac{c}{m}$ (1.3)

(1.3)

This calculation, of course, applies to any stream, not just the concentrate, and thus in the feed if f is the metal assay the mineral assay is f/m. The recovery of gangue (R_g) is therefore

$R_{\mathrm{g}}=\frac{C}{F}\frac{\left(1-\frac{c}{m}\right)}{\left(1-\frac{f}{m}\right)}\to \frac{C}{F}\frac{(m-c)}{(m-f)}$ (1.4)

(1.4)

and thus the separation efficiency is:

$\begin{array}{ll}\mathrm{SE}\hfill & =\frac{Cc}{Ff}-\frac{C}{F}\frac{(m-c)}{(m-f)}\to \frac{C}{F}\left(\frac{c}{f}-\frac{(m-c)}{(m-f)}\right)\hfill \\ \hfill & =\frac{C}{F}\frac{m}{f}\frac{(c-f)}{(m-f)}\hfill \end{array}$ (1.5)

(1.5)

Example 1.3 illustrates the calculations. The concept can be extended to consider separation between any pair of minerals, A and B, such as in the separation of lead from zinc.

Example 1.3

A tin concentrator treats a feed containing 1% tin, and three possible combinations of concentrate grade and recovery are:

High grade	63% tin at 62% recovery
Medium grade	42% tin at 72% recovery
Low grade	21% tin at 78% recovery

Determine which of these combinations of grade and recovery produce the highest separation efficiency.

Solution

Assuming that the tin is totally contained in the mineral cassiterite (SnO₂) then m=78.6% (0.786), and we can complete the calculation:

Case	${\displaystyle \frac{C}{F}}$ (from Eq. (1.1))	SE (Eq. (1.5))
High grade	$\begin{array}{ll}0.62\hfill & =\frac{C}{F}\left(\frac{0.63}{0.01}\right)\hfill \\ \frac{C}{F}\hfill & =9.841E^{-3}\hfill \end{array}$	$\begin{array}{ll}\mathrm{SE}\hfill & =9.841E^{-3}\left(\frac{0.63}{0.01}-\frac{0.786-0.63}{0.786-0.01}\right)\hfill \\ \hfill & =61.8\%\hfill \end{array}$
Medium grade	$\begin{array}{ll}0.72\hfill & =\frac{C}{F}\left(\frac{0.42}{0.01}\right)\hfill \\ \frac{C}{F}\hfill & =1.714E^{-2}\hfill \end{array}$	$\begin{array}{ll}\mathrm{SE}\hfill & =1.714E^{-2}\left(\frac{0.42}{0.01}-\frac{0.786-0.42}{0.786-0.01}\right)\hfill \\ \hfill & =71.2\%\hfill \end{array}$
Low grade	$\begin{array}{ll}0.78\hfill & =\frac{C}{F}\left(\frac{0.21}{0.01}\right)\hfill \\ \frac{C}{F}\hfill & =3.714E^{-2}\hfill \end{array}$	$\begin{array}{ll}\mathrm{SE}\hfill & =3.714E^{-2}\left(\frac{0.21}{0.01}-\frac{0.786-0.21}{0.786-0.01}\right)\hfill \\ \hfill & =75.2\%\hfill \end{array}$

The answer to which gives the highest separation efficiency, therefore, is the low-grade case.

The concept of separation efficiency is examined in Appendix III, based on Jowett (1975) and Jowett and Sutherland (1985), where it is shown that defining separation efficiency as separation achieved relative to perfect separation yields Eq. (1.5).

Although separation efficiency can be useful in comparing the performance of different operating conditions, it takes no account of economic factors, and is sometimes referred to as the “technical separation efficiency.” As will become apparent, a high value of separation efficiency does not necessarily lead to the most economic return. Nevertheless it remains a widely used measure to differentiate alternatives prior to economic assessment.

1.10.1 Contained Value

Every ton of material in the deposit has a certain contained value that is dependent on the metal content and current price of the contained metal. For instance, at a copper price of £2,000 t⁻¹ and a molybdenum price of £18 kg⁻¹, a deposit containing 1% copper and 0.015% molybdenum has a contained value of more than £22 t⁻¹. To be processed economically, the cost of processing an ore must be less than the contained value.

1.10.2 Processing Costs

Mining is a major cost, and this can vary from only a few pence per ton of ore to well over £50 t⁻¹. High-tonnage operations are cheaper in terms of operating costs but have higher initial capital costs. These capital costs are paid off over a number of years, so that high-tonnage operations can only be justified for the treatment of deposits large enough to allow this. Small ore bodies are worked on a smaller scale to reduce overall capital costs, but capital and operating costs per ton are correspondingly higher (Ottley, 1991).

Alluvial mining is the cheapest method and, if on a large scale, can be used to mine ores of low contained value due to low grade or low metal price, or both. For instance, in S.E. Asia, tin ores containing as little as 0.01% Sn are mined by alluvial methods. These ores have a contained value of less than £1 t⁻¹, but very low processing costs allow them to be economically worked.

High-tonnage open-pit and underground block-caving methods are used to treat ores of low contained value, such as low-grade copper ores. Where the ore must be mined selectively, however, as is the case with underground vein-type deposits, mining methods become very expensive, and can only be justified on ores of high contained value. An underground selective mining cost of £30 t⁻¹ would obviously be hopelessly uneconomic on a tin ore of alluvial grade, but may be economic on a hard-rock ore containing 1.5% tin, with a contained value of around £50 t⁻¹ ore.

In order to produce metals, the ore minerals must be broken down by the action of heat (pyrometallurgy), solvents (hydrometallurgy), or electricity (electrometallurgy), either alone or in combination. The most common method is the pyrometallurgical process of smelting. These chemical methods consume large quantities of energy. The smelting of 1 t of copper ore, for instance, consumes in the region of 1,500–2,000 kWh of electrical energy, which at a cost of say 5 p kWh⁻¹ is around £85 t⁻¹, well above the contained value of most copper ores. In addition, smelters are often remote from the mine site, and thus the cost of transport to the site must be considered.

The essential economic purpose of mineral processing is to reduce the bulk of the ore which must be transported to and processed by the smelter, by using relatively cheap, low-energy physical methods to separate the valuable minerals from the gangue minerals. This enrichment process considerably increases the contained value of the ore to allow economic transportation and smelting. Mineral processing is usually carried out at the mine site, the plant being referred to as a mill or concentrator.

Compared with chemical methods, the physical methods used in mineral processing consume relatively small amounts of energy. For instance, to upgrade a copper ore from 1% to 25% metal would use in the region of 20–50 kWh t⁻¹. The corresponding reduction in weight of around 25:1 proportionally lowers transport costs and reduces smelter energy consumption to around 60–80 kWh in relation to a ton of mined ore. It is important to realize that, although the physical methods are relatively low energy consumers, the reduction in bulk lowers smelter energy consumption to the order of that used in mineral processing. It is significant that as ore grades decline, the energy used in mineral processing becomes an important factor in deciding whether the deposit is viable to exploit or not.

Mineral processing reduces not only smelter energy costs but also smelter metal losses, due to the production of less metal-bearing slag. (Some smelters include a slag mineral processing stage to recover values and recycle to the smelter.) Although technically feasible, the smelting of low-grade ores, apart from being economically unjustifiable, would be very difficult due to the need to produce high-grade metal products free from deleterious element impurities. These impurities are found in the gangue minerals and it is the purpose of mineral processing to reject them into the discard (tailings), as smelters often impose penalties according to their level. For instance, it is necessary to remove arsenopyrite from tin concentrates, as it is difficult to remove the contained arsenic in smelting and the process produces a low-quality tin metal.

Against the economic advantages of mineral processing, the losses occurred during milling and the cost of milling operations must be charged. The latter can vary over a wide range, depending on the method of treatment used, and especially on the scale of the operation. As with mining, large-scale operations have higher capital but lower operating costs (particularly labor and energy) than small-scale operations.

Losses to tailings are one of the most important factors in deciding whether a deposit is viable or not. Losses will depend on the ore mineralogy and dissemination of the minerals, and on the technology available to achieve efficient concentration. Thus, the development of flotation allowed the exploitation of the vast low-grade porphyry copper deposits which were previously uneconomic to treat (Lynch et al., 2007). Similarly, the introduction of solvent extraction enabled Nchanga Consolidated Copper Mines in Zambia to treat 9 Mt per year of flotation tailings, to produce 80,000 t of finished copper from what was previously regarded as waste (Anon., 1979).

In many cases not only is it necessary to separate valuable from gangue minerals, but also to separate valuable minerals from each other. For instance, complex sulfide ores containing economic amounts of copper, lead, and zinc usually require separate concentrates of the minerals of each of these metals. The provision of clean concentrates, with little contamination with associated metals, is not always economically feasible, and this leads to another source of loss other than direct tailing loss. A metal which reports to the “wrong” concentrate may be difficult, or economically impossible, to recover and never achieves its potential valuation. Lead, for example, is essentially irrecoverable in copper concentrates and is often penalized as an impurity by the copper smelter. The treatment of such polymetallic base metal ores, therefore, presents one of the great challenges to the mineral processor.

Mineral processing operations are often a compromise between improvements in metallurgical efficiency and milling costs. This is particularly true with ores of low contained value, where low milling costs are essential and cheap unit processes are necessary, particularly in the early stages, where the volume of material treated is high. With such low-value ores, improvements in metallurgical efficiency by the use of more expensive methods or reagents cannot always be justified. Conversely, high metallurgical efficiency is usually of most importance with ores of high contained value and expensive high-efficiency processes can often be justified on these ores.

Apart from processing costs and losses, other costs which must be taken into account are indirect costs such as ancillary services—power supply, water, roads, tailings disposal—which will depend much on the size and location of the deposit, as well as taxes, royalty payments, investment requirements, research and development, medical and safety costs, etc.

1.10.3 Milling Costs

As discussed, the balance between milling costs and metal losses is crucial, particularly with low-grade ores, and because of this most mills keep detailed accounts of operating and maintenance costs, broken down into various subdivisions, such as labor, supplies, energy, etc. for the various areas of the plant. This type of analysis is used to identify high-cost areas where improvements in performance would be most beneficial. It is impossible to give typical operating costs for milling operations, as these vary considerably from mine to mine, and particularly from country to country, depending on local costs of energy, labor, water, supplies, etc.

Table 1.4 is an approximate breakdown of costs for a 100,000 t d⁻¹ copper concentrator. Note the dominance of grinding, due mainly to power requirements.

1.10.4 Tailings Reprocessing and Recycling

Mill tailings which still contain valuable components constitute a potential future resource. New or improved technologies can allow the value contained in tailings, which was lost in earlier processing, to be recovered, or commodities considered waste in the past to become valuable in a new economic order. Reducing or eliminating tailings dumps by retreating them also reduces the environmental impact of the waste.

The cost of tailings retreatment is sometimes lower than that of processing the original ore, because much of the expense has already been met, particularly in mining and comminution. There are many tailings retreatment plants in a variety of applications around the world. The East Rand Gold and Uranium Company closed its operations in 2005 after 28 years having retreated over 870 Mt of the iconic gold dumps of Johannesburg, significantly modifying the skyline of the Golden City and producing 250 t of gold in the process. Also in 2005, underground mining in Kimberley closed, leaving a tailings dump retreatment operation as the only source of diamond production in the Diamond City. Some platinum producers in South Africa now operate tailings retreatment plants for the recovery of platinum group metals (PGMs), and also chromite as a by-product from the chrome-rich UG2 Reef. The tailings of the historic Timmins gold mining area of Canada are likewise being reprocessed.

Although these products, particularly gold, tend to dominate the list of tailings retreatment operations because of the value of the product, there are others, both operating and being considered as potential major sources of particular commodities. For example: coal has been recovered from tailings in Australia (Clark, 1997), uranium is recovered from copper tailings by the Uranium Corporation of India, and copper has been recovered from the Bwana Mkubwa tailings in Zambia, using solvent extraction and electrowinning. The Kolwezi Tailings project in the DRC (Democratic Republic of Congo) that recovered oxide copper and cobalt from the tailings of 50 years of copper mining ran from 2004 to 2009. Phytomining, the use of plants to accumulate metals, could be a low-cost way to detoxify tailings (and other sites) and recover metals. Methods of resource recovery from metallurgical wastes are described by Rao (2006).

Recovery from tailings is a form of recycling. The reprocessing of industrial scrap and domestic waste for metal recycling is a growing economic, and environmental, activity. “Urban ore” is a reference to forgotten supplies of metals that lie in and under city streets. Recovery of metals from electronic scrap is one example; another is recovery of PGMs that accumulate in road dust as car catalytic converters wear (Ravilious, 2013). Many mineral separation techniques are applicable to processing urban ores but tapping them is held back by their being so widely spread in the urban environment. The principles of recycling are comprehensively reviewed by Reuter et al. (2005).

1.10.5 Net Smelter Return and Economic Efficiency

Since the purpose of mineral processing is to increase the economic value of the ore, the importance of the grade–recovery relationship is in determining the most economic combination of grade and recovery that will produce the greatest financial return per ton of ore treated in the plant. This will depend primarily on the current price of the valuable product, transportation costs to the smelter, refinery, or other further treatment plant, and the cost of such further treatment, the latter being very dependent on the grade of concentrate supplied. A high-grade concentrate will incur lower smelting costs, but the associated lower recovery means lower returns of final product. A low-grade concentrate may achieve greater recovery of the values, but incur greater smelting and transportation costs due to the included gangue minerals. Also of importance are impurities in the concentrate which may be penalized by the smelter, although precious metals may produce a bonus.

The net return from the smelter (NSR) can be calculated for any grade–recovery combination from:

$\mathrm{NSR}=\mathrm{Payment}\mathrm{for}\mathrm{contained}\mathrm{metal}-(\mathrm{Smelter}\mathrm{charges}+\mathrm{Transport}\mathrm{costs})$ (1.6)

(1.6)

This is summarized in Figure 1.14, which shows that the highest value of NSR is produced at an optimum concentrate grade. It is essential that the mill achieves a concentrate grade that is as close as possible to this target grade. Although the effect of moving slightly away from the optimum may only be of the order of a few pence per ton treated, this can amount to very large financial losses, particularly on high-capacity plants treating thousands of tons per day. Changes in metal price, smelter terms, etc. obviously affect the NSR versus concentrate grade relationship and the value of the optimum concentrate grade. For instance, if the metal price increases, then the optimum grade will be lower, allowing higher recoveries to be attained (Figure 1.15).

It is evident that the terms agreed between the concentrator and the smelter are of paramount importance in the economics of mining and milling operations. Such smelter contracts are usually fairly complex. Concentrates are sold under contract to “custom smelters” at prices based on quotations on metal markets such as the London Metal Exchange (LME). The smelter, having processed the concentrates, disposes of the finished metal to the consumers. The proportion of the “free market” price of the metal received by the mine is determined by the terms of the contract negotiated between mine and smelter, and these terms can vary widely. Table 1.5 summarizes a typical low-grade smelter contract for the purchase of tin concentrates. As is usual in many contracts, one assay unit (1%) is deducted from the concentrate assay in assessing the value of the concentrates, and arsenic present in the concentrate (in this case) is penalized. The concentrate assay is of prime importance in determining the valuation, and the value of the assay is usually agreed on the result of independent sampling and assaying performed by the mine and smelter. The assays are compared, and if the difference is no more than an agreed value, the mean of the two results may be taken as the agreed assay. In the case of a greater difference, an “umpire” sample is assayed at an independent laboratory. This umpire assay may be used as the agreed assay, or the mean of this assay and that of the party which is nearer to the umpire assay may be chosen.

The use of smelter contracts, and the importance of the by-products and changing metal prices, can be seen by briefly examining the economics of processing two base metals—tin and copper—whose fortunes have fluctuated over the years for markedly different reasons.

1.10.6 Case Study: Economics of Tin Processing

Tin constitutes an interesting case study in the vagaries of commodity prices and how they impact the mineral industry and its technologies. Almost half the world’s supply of tin in the mid-nineteenth century was mined in south-west England, but by the end of the 1870s Britain’s premium position was lost, with the emergence of Malaysia as the leading producer and the discovery of rich deposits in Australia. By the end of the century, only nine mines of any consequence remained in Britain, where 300 had flourished 30 years earlier. From alluvial or secondary deposits, principally from South-East Asia, comes 80% of mined tin. Unlike copper, zinc, and lead, production of tin has not risen dramatically over the years and has rarely exceeded 250,000 t per annum.

The real price of tin spent most of the first half of the twentieth century in a relatively narrow band between US$10,000 and US$15,000 t⁻¹ (1998$), with some excursions (Figure 1.16). From 1956 its price was regulated by a series of international agreements between producers and consumers under the auspices of the International Tin Council (ITC), which mirrored the highly successful policy of De Beers in controlling the gem diamond trade. Price stability was sought through selling from the ITC’s huge stockpiles when the price rose and buying into the stockpile when the price fell.

From the mid-1970s, however, the price of tin was driven artificially higher at a time of world recession, a toxic combination of expanding production and falling consumption, the latter due mainly to the increasing use of aluminum in making cans, rather than tin-plated steel. Although the ITC imposed restrictions on the amount of tin that could be produced by its member countries, the reason for the inflating tin price was that the price of tin was fixed by the Malaysian dollar, while the buffer stock manager’s dealings on the LME were financed in sterling. The Malaysian dollar was tied to the American dollar, which strengthened markedly between 1982 and 1984, having the effect of increasing the price of tin in London simply because of the exchange rate. However, the American dollar began to weaken in early 1985, taking the Malaysian dollar with it, and effectively reducing the LME tin price from its historic peak. In October 1985, the buffer stock manager announced that the ITC could no longer finance the purchase of tin to prop up the price, as it had run out of funds, owing millions of pounds to the LME traders. This announcement caused near panic, the tin price fell to £8,140 t⁻¹ and the LME halted all further dealings. In 1986, many of the world’s tin mines were forced to close due to the depressed tin price, and prices continued to fall in subsequent years, rising again in concert with other metals during the “super-cycle.” While the following discussion relates to tin processing prior to the collapse, including prices and costs, the same principles can be applied to producing any metal-bearing mineral commodity at any particular period including the present day.

It is fairly easy to produce concentrates containing over 70% tin (i.e., over 90% cassiterite) from alluvial ores, such as those worked in South-East Asia. Such concentrates present little problem in smelting and hence treatment charges are relatively low. Production of high-grade concentrates also incurs relatively low freight charges, which is important if the smelter is remote. For these reasons it has been traditional in the past for hard-rock, lode tin concentrators to produce high-grade concentrates, but high tin prices and the development of profitable low-grade smelting processes changed the policy of many mines toward the production of lower-grade concentrates. The advantage of this is that the recovery of tin into the concentrate is increased, thus increasing smelter payments. However, the treatment of low-grade concentrates produces much greater problems for the smelter, and hence the treatment charges at “low-grade smelters” are normally much higher than those at the high-grade smelters. Freight charges are also correspondingly higher. Example 1.4 illustrates the identification of the economic optimum grade–recovery combination.

Example 1.4

Suppose that a tin concentrator treats a feed containing 1% tin, and that three possible combinations of concentrate grade and recovery are those in Example 1.3:

High grade	63% tin at 62% recovery
Medium grade	42% tin at 72% recovery
Low grade	21% tin at 78% recovery

Using the low-grade smelter terms set out in the contract in Table 1.5, and assuming that the concentrates are free of arsenic, and that the cost of transportation to the smelter is £20 t⁻¹ of dry concentrate, what is the combination giving the economic optimum, that is, maximum NSR?

Solution

As a common basis we use 1 t of ore (feed). For each condition it is possible to calculate the amount of concentrate that can be made from 1 t of ore and from this, the smelter payment and charges for each combination of grade and recovery can be calculated.

The calculation of the amount of concentrate follows from the definition of recovery (Eq. (1.1)):

$R=\frac{Cc}{Ff};F=1\to C=\frac{(1\times f)\times R}{c}$

For a tin price of £8,500 t⁻¹ (of tin), and a treatment charge of £385 t⁻¹ (of concentrate) the NSR for the three cases is calculated in the table below:

Case	Weight of Concentrate (kg t−1)	Smelter Paymenta	Charge		NSR
			Treatment	Transport
High grade	$\frac{(1t\times 1\%)\times 62\%}{63\%}=9.84\mathrm{k}\mathrm{g}$	$\frac{P\times 9.84\times (63-1)}{100,000}=\pounds 51.86$	$\frac{9.84\times 385}{1,000}=\pounds 3.79$	£0.20	£47.88
Medium grade	$\frac{(1t\times 1\%)\times 72\%}{42\%}=17.14\mathrm{k}\mathrm{g}$	$\frac{P\times 17.14\times (42-1)}{100,000}=\pounds 59.73$	$\frac{17.14\times 385}{1,000}=\pounds 6.59$	£0.34	£52.80
Low grade	$\frac{(1t\times 1\%)\times 78\%}{21\%}=37.14\mathrm{k}\mathrm{g}$	$\frac{P\times 37.14\times (21-1)}{100,000}=\pounds 63.14$	$\frac{37.14\times 385}{1,000}=\pounds 14.30$	£0.74	£48.10

The optimum combination is thus the second case

^aNote: units of 10 are to convert from %.

This result in Example 1.4 is in contrast to the maximum separation efficiency which was for the low-grade case (Example 1.3). Lowering the concentrate grade to 21% tin, in order to increase recovery, increased the separation efficiency, but adversely affected the economic return from the smelter, the increased charges being greater than the increase in revenue from the metal.

In terms of contained value, the ore, at free market price, has £85 worth of tin per ton ((1%/100)×£8,500 t⁻¹ (of tin)); thus even at the economic optimum combination, the mine realizes only 62% of the ore value in payments received (£52.80/£85).

The situation may alter, however, if the metal price changes appreciably. If the tin price falls and the terms of the smelter contract remain the same, then the mine profits will suffer due to the reduction in payments. Rarely does a smelter share the risks of changing metal price, as it performs a service role, changes in smelter terms being made more on the basis of changing smelter costs rather than metal price. The mine does, however, reap the benefits of increasing metal price.

At a tin price of £6,500 t⁻¹, the NSR per ton of ore from the low-grade smelter treating the 42% tin concentrate is £38.75, while the return from the high-grade smelter, treating a 63% Sn concentrate, is £38.96. Although this is a difference of only £0.21 t⁻¹ of ore, to a small 500 t d⁻¹ tin concentrator this change in policy from relatively low- to high-grade concentrate, together with the subsequent change in concentrate market, would expect to increase the revenue by £0.21×500×365=£38,325 per annum. The concentrator management must always be prepared to change its policies, both metallurgical and marketing, if maximum returns are to be made, although generation of a reliable grade–recovery relationship is often difficult due to the complexity of operation of lode tin concentrators and variations in feed characteristics.

It is, of course, necessary to deduct the costs of mining and processing from the NSR in order to deduce the profit achieved by the mine. Some of these costs will be indirect, such as salaries, administration, research and development, medical and safety, as well as direct costs, such as operating and maintenance, supplies and energy. The breakdown of milling costs varies significantly from mine to mine, depending on the size and complexity of the operations (Table 1.4 is one example breakdown). Mines with large ore reserves tend to have high throughputs, and so although the capital outlay is higher, the operating and labor costs tend to be much lower than those on smaller plants, such as those treating lode tin ores. Mining costs also vary considerably and are much higher for underground than for open-pit operations.

If mining and milling costs of £40 and £8, respectively, per ton of ore are typical of underground tin operations, then it can be seen that at a tin price of £8,500, the mine producing a concentrate of 42% tin, which is sold to a low-grade smelter, makes a profit of £52.80−48=£4.80 t⁻¹ of ore. It is also clear that if the tin price falls to £6,500 t⁻¹, the mine loses £48−38.96=£9.04 for every ton of ore treated.

The mine profit per ton of ore treated can be illustrated by considering “contained values.” For the 72% recovery case (medium-grade case in Example 1.4) the contained value in the concentrate is £85×0.72=£61.20, and thus the contained value lost in the tailings is $23.80 (£85−£61.20). Since the smelter payment is £52.80 the effective cost of transport and smelting is £61.20−52.80=£8.40. Thus the mine profit can be summarized as follows:

$\mathrm{Contained}\mathrm{value}\mathrm{of}\mathrm{ore}–(\mathrm{costs}+\mathrm{losses})$

which for the 72% recovery case is:

$\pounds (85–(8.4+40+8+23.8)=\pounds 4.80{\mathrm{t}}^{-1}.$

The breakdown of revenue and costs in this manner is summarized in Figure 1.17.

In terms of effective cost of production, since 1 t of ore produces 0.0072 t of tin in concentrates, and the free market value of this contained metal is £61.20 and the profit is £4.80, the total effective cost of producing 1 t of tin in concentrates is £(61.20−4.80)/0.0072=£7,833.

The importance of metal losses in tailings is shown clearly in Figure 1.17. With ore of relatively high contained value, the recovery is often more important than the cost of promoting that recovery. Hence relatively high-cost unit processes can be justified if significant improvements in recovery are possible, and efforts to improve recoveries should always be made. For instance, suppose the concentrator, maintaining a concentrate grade of 42% tin, improves the recovery by 1%, i.e., to 73%, with no change in actual operating costs. The NSR will be £53.53 t⁻¹ of ore and after deducting mining and milling costs, the profit realized by the mine will be £5.53 t⁻¹ of ore. Since 1 t of ore now produces 0.0073 t of tin, having a contained value of £62.05, the cost of producing 1 t of tin in concentrates is thereby reduced to £(62.05−5.53)/0.0073=£7,742.

Due to the high processing costs and losses, hard-rock tin mines, such as those in Cornwall and Bolivia, had the highest production costs, being above £7,500 t⁻¹ of ore in 1985 (for example). Alluvial operations, such as those in Malaysia, Thailand, and Indonesia, have lower production costs (around £6,000 t⁻¹ in 1985). Although these ores have much lower contained values (only about £1–2 t⁻¹), mining and processing costs, particularly on the large dredging operations, are low, as are smelting costs and losses, due to the high concentrate grades and recoveries produced. In 1985, the alluvial mines in Brazil produced the world’s cheapest tin, having production costs of only about £2,200 t⁻¹ of ore (Anon., 1985a).

1.10.7 Case Study: Economics of Copper Processing

In 1835, the United Kingdom was the world’s largest copper producer, mining around 15,000 t per annum, just below half the world production. This leading position was held until the mid-1860s when the copper mines of Devon and Cornwall became exhausted and the great flood of American copper began to make itself felt. The United States produced about 10,000 t in 1867, but by 1900 was producing over 250,000 t per annum. This output had increased to 1,000,000 t per annum in the mid-1950s, by which time Chile and Zambia had also become major producers. World annual production now exceeds 15,000,000 t (Figure 1.12).

Figure 1.18 shows that the price of copper in real terms grew steadily from about 1930 until the period of the oil shocks of the mid-1970s and then declined steeply until the early twenty-first century, the average real price in 2002 being lower than that at any time in the twentieth century. The pressure on costs was correspondingly high, and the lower cost operators such as those in Chile had more capacity to survive than the high-cost producers such as some of those in the United States. However, world demand, particularly from emerging economies such as China, drove the price strongly after 2002 and by 2010 it had recovered to about US$9000 t⁻¹ (in dollars of the day) before now sliding back along with oil and other commodities.

The move to large-scale operations (Chile’s Minerara Escondida’s two concentrators had a total capacity of 230,000 t d⁻¹ in 2003), along with improvements in technology and operating efficiencies, have kept the major companies in the copper-producing business. In some cases by-products are important revenue earners. BHP Billiton’s Olympic Dam produces gold and silver as well as its main products of copper and uranium, and Rio Tinto’s Kennecott Utah Copper is also a significant molybdenum producer.

A typical smelter contract for copper concentrates is summarized in Table 1.6. As in the case of the tin example, the principles illustrated can be applied to current prices and costs.

Consider a porphyry copper mine treating an ore containing 0.6% Cu to produce a concentrate containing 25% Cu, at 85% recovery. This represents a concentrate production of 20.4 kg t⁻¹ of ore treated. Therefore, at a copper price of £980 t⁻¹:

$\mathrm{Payment}\mathrm{for}\mathrm{copper}=\pounds 980\times \frac{20.4}{1000}\times 0.24=\pounds 4.80$

$\mathrm{Treatment}\mathrm{charge}=\pounds 30\times \frac{20.4}{1,000}=\pounds 0.61$

$\mathrm{Refining}\mathrm{charge}=\pounds 115\times \frac{20.4}{1,000}\times 0.24=\pounds 0.56$

Assuming a transport cost of £20 t⁻¹ of concentrate, the total deductions are £(0.61+0.56+0.41)=£1.58, and the NSR per ton of ore treated is thus £(4.80−1.58)=£3.22.

As mining, milling and other costs must be deducted from this figure, it is apparent that only those mines with very low operating costs can have any hope of profiting from such low-grade operations at the quoted copper price. Assuming a typical large open-pit mining cost of £1.25 t⁻¹ of ore, a milling cost of £2 t⁻¹ and indirect costs of £2 t⁻¹, the mine will lose £2.03 for every ton of ore treated. The breakdown of costs and revenues, following the example for tin (Figure 1.17), is given in Figure 1.19.

As each ton of ore produces 0.0051 t of copper in concentrates, with a free market value of £5.00, the total effective production costs are £(5.00+2.03)/0.0051 t=£1,378 t⁻¹ of copper in concentrates. However, if the ore contains appreciable by-products, the effective production costs are reduced. Assuming the concentrate contains 25 g t⁻¹ of gold and 70 g t⁻¹ of silver, then the payment for gold, at a LME price of £230/troy oz (1 troy oz=31.1035 g) is:

$\frac{20.4}{1000}\times \frac{25}{31.1035}\times 0.95\times 230=\pounds 3.58$

and the payment for silver at a LME price of £4.5 per troy oz

$\frac{20.4}{1000}\times \frac{70}{31.1035}\times 0.95\times 4.5=\pounds 0.19$

The net smelter return is thus increased to £6.99 t⁻¹ of ore, and the mine makes a profit of £1.7 t⁻¹ of ore treated. The effective cost of producing 1 t of copper is thus reduced to £(5.00−1.74)/0.0051=£639.22.

By-products are thus extremely important in the economics of copper production, particularly for very low-grade operations. In this example, 42% of the mine’s revenue is from gold. This compares with the contributions to revenue realized at Bougainville Copper Ltd (Sassos, 1983).

Table 1.7 lists estimated effective costs per ton of copper processed in 1985 at some of the world’s major copper mines, at a copper price of £980 t⁻¹ (Anon., 1985b).

It is evident that, apart from Bougainville (now closed), which had a high gold content, and Palabora, a large open-pit operation with numerous heavy mineral by-products, the only economic copper mines in 1985 were the large South American porphyries. Those mines profited due to relatively low actual operating costs, by-product molybdenum production, and higher average grades (1.2% Cu) than the North American porphyries, which averaged only 0.6% Cu. Relatively high-grade deposits such as at Nchanga failed to profit due partly to high operating costs, but mainly due to the lack of by-products. It is evident that if a large copper mine is to be brought into production in such an economic climate, then initial capitalization on high-grade secondary ore and by-products must be made, as at Ok Tedi in Papua New Guinea, which commenced production in 1984, initially mining and processing the high-grade gold ore in the leached capping ore.

Since the profit margin involved in the processing of modern copper ores is usually small, continual efforts must be made to try to reduce milling costs and metal losses. This need has driven the increase in processing rates, many over 100,000 t ore per day, and the corresponding increase in size of unit operations, especially grinding and flotation equipment. Even relatively small increases in return per ton can have a significant effect, due to the very large tonnages that are often treated. There is, therefore, a constant search for improved flowsheets and flotation reagents.

Figure 1.19 shows that in the example quoted, the contained value in the flotation tailings is £0.88 t⁻¹ treated ore. The concentrate contains copper to the value of £5.00, but the smelter payment is £3.22. Therefore, the mine realizes only 64.4% of the free market value of copper in the concentrate. On this basis, the actual metal loss into the tailings is only about £0.57 t⁻¹ of ore. This is relatively small compared with milling costs, and an increase in recovery of 0.5% would raise the net smelter return by only £0.01. Nevertheless, this can be significant; to a mine treating 50,000 t d⁻¹, this is an increase in revenue of £500 d⁻¹, which is extra profit, providing that it is not offset by any increased milling costs. For example, improved recovery in flotation may be possible by the use of a more effective reagent or by increasing the dosage of an existing reagent, but if the increased reagent cost is greater than the increase in smelter return, then the action is not justified.

This balance between milling cost and metallurgical efficiency is critical on a concentrator treating an ore of low contained value, where it is crucial that milling costs be as low as possible. Reagent costs are typically around 10% of the milling costs on a large copper mine, but energy costs may contribute well over 25% of these costs. Grinding is by far the greatest energy consumer and this process undoubtedly has the greatest influence on metallurgical efficiency. Grinding is essential for the liberation of the minerals in the ore, but it should not be carried out any finer than is justified economically. Not only is fine grinding energy intensive, but it also leads to increased media (grinding steel) consumption costs. Grinding steel often contributes as much as, if not more than, the total mill energy cost, and the quality of grinding medium used often warrants special study. Figure 1.20 shows the effect of fineness of grind on NSR and grinding costs for a typical low-grade copper ore. Although flotation recovery, and hence NSR, increases with fineness of grind, it is evident that there is no economic benefit in grinding finer than a certain grind size (80% passing size). Even this fineness may be beyond the economic limit because of the additional capital cost of the grinding equipment required to achieve it.

1.10.8 Economic Efficiency

It is apparent that a certain combination of grade and recovery produces the highest economic return under certain conditions of metal price, smelter terms, etc. Economic efficiency compares the actual NSR per ton of ore milled with the theoretical return, thus taking into account all the financial implications. The theoretical return is the maximum possible return that could be achieved, assuming “perfect milling,” that is, complete separation of the valuable mineral into the concentrate, with all the gangue reporting to tailings. Using economic efficiency, plant efficiencies can be compared even during periods of fluctuating market conditions (Example 1.5).

In recent years, attempts have been made to optimize the performance of some concentrators by controlling plant conditions to achieve maximum economic efficiency (see Chapters 3 and 12). A dilemma often facing the metallurgist on a complex flotation circuit producing more than one concentrate is: how much contamination of one concentrate by the mineral that should report to the other concentrate can be tolerated? For instance, on a plant producing separate copper and zinc concentrates, copper is always present in the zinc concentrate, as is zinc in the copper concentrate. Metals misplaced into the wrong concentrate are rarely paid for by the specialist smelter and are sometimes penalized. There is, therefore, an optimum “degree of contamination” that can be tolerated. The most important reagent controlling this factor is often the depressant (Chapter 12), which, in this example, inhibits flotation of the zinc minerals. Increase in the addition of this reagent not only produces a cleaner copper concentrate but also tends to reduce copper recovery into this concentrate, as it also has some depressing effect on the copper minerals. The depressed copper minerals are likely to report to the zinc concentrate, so the addition rate of depressant needs to be carefully monitored and controlled to produce an optimum compromise. This should occur when the economic efficiency is maximized (Example 1.6).

Example 1.6

The following assay data were collected from a copper–zinc concentrator:

		Feed	Cu concentrate	Zn concentrate
Assay	Cu (%)	0.7	24.6	0.4
	Zn (%)	1.94	3.40	49.7

Mass balance calculation (Chapter 3) showed that 2.6% of the feed reported to the copper concentrate and 3.5% to the zinc concentrate.

Calculate the overall economic efficiency under the following simplified smelter terms:

Copper:

Copper price: £1,000 t⁻¹

Smelter payment: 90% of Cu content

Smelter treatment charge: £30 t⁻¹ of concentrate

Transport cost: £20 t⁻¹ of concentrate

Zinc:

Zinc price: £400 t⁻¹

Smelter payment: 85% of zinc content

Smelter treatment charge: £100 t⁻¹ of concentrate

Transport cost: £20 t⁻¹ of concentrate

Solution

1. Assuming perfect milling

a. Copper
Assuming that all the copper is contained in the mineral chalcopyrite, then maximum copper grade is 34.6% Cu (pure chalcopyrite, CuFeS₂).
If C is weight of copper concentrate per 1,000 kg of feed, then for 100% recovery of copper into this concentrate:

$100=\frac{34.6\times C\times 100}{0.7\times 1,000},C=20.2(\mathrm{kg})$

Transport cost=£20×20.2/1,000=£0.40

Treatment cost=£30×20.2/1,000=£0.61

Revenue=£20.2×0.346×1,000×0.9/1,000=£6.29

Therefore, NSR for copper concentrate=£5.28 t⁻¹ of ore.

b. Zinc
Assuming that all the zinc is contained in the mineral sphalerite, maximum zinc grade is 67.1% (assuming sphalerite is ZnS).
If Z is weight of zinc concentrate per 1,000 kg of feed, then for 100% recovery of zinc into this concentrate:

$100=\frac{67.1\times Z\times 100}{1,000\times 1.94},Z=28.9(\mathrm{kg})$

Transport cost=£20×28.9/1,000=£0.58

Treatment cost=£100×28.9/1,000=£2.89

Revenue=£28.9×0.671×0.85×400/1,000=£6.59

Therefore, NSR for zinc concentrate=£3.12 t⁻¹ of ore.

Total NSR for perfect milling=£(5.28+3.12)=£8.40 t⁻¹

2. Actual milling
Similar calculations give:

Net copper smelter return=£4.46 t⁻¹ ore

Net zinc smelter return=£1.71 t⁻¹ ore

Total net smelter return=£6.17 t⁻¹ ore

Therefore, overall economic efficiency=100×6.17/8.40=73.5%.