Question 1 of 7: Mineral Processing (20 marks)

Question 1 — Mineral Processing (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The ten terms trace a concentrator from size reduction, through the physical and surface-chemistry methods used to split value from gangue, to the vocabulary that describes what those methods produce.

(a) Comminution. Comminution is the staged size reduction of run-of-mine ore — primary and secondary crushing followed by rod, ball or SAG milling — carried out to liberate the valuable mineral grains from the gangue that encloses them. It is deliberately staged because the specific energy to break rock rises sharply as particle size falls, so a plant grinds only to the liberation size the ore actually needs; comminution is consistently the largest single power draw in a concentrator, typically 35–50 % of site electricity.

(b) Bond work index. The Bond work index $W_i$ is an empirical measure of an ore's resistance to grinding, obtained from a standardized locked-cycle test on a laboratory Bond ball (or rod) mill. It enters Bond's third theory of comminution,

where $W$ is the specific grinding energy (kWh/t) and $F_{80}$, $P_{80}$ are the 80 %-passing sizes ($\mu$m) of the feed and product. A harder ore (higher $W_i$, e.g. a siliceous quartzite) demands more energy for the same size reduction than a soft one (e.g. a weathered oxide ore); $W_i$ is the single number mill designers use to size a comminution circuit's installed power before a plant is ever built.

(c) Dense media separation. Dense media separation (DMS) is a static-density gravity method: crushed feed is immersed in a suspension of finely ground ferrosilicon or magnetite in water, whose bulk density is set between the density of the valuable mineral and that of the gangue. Particles denser than the medium sink and lighter particles float, and the cut is essentially size-independent over a wide range, which is a real advantage over jigs and tables. The medium is recovered magnetically and recirculated; DMS is the standard pre-concentration step for coal and for kimberlite diamond ore.

(d) Direct flotation. Direct flotation is the "normal" mode of froth flotation: a collector is chosen to render the valuable mineral hydrophobic, so it attaches to rising bubbles and reports to the froth (concentrate), while the gangue is left hydrophilic and depressed to the cell underflow (tailing). Floating chalcopyrite away from a silicate gangue with a xanthate collector is the textbook example. Direct flotation is preferred whenever the value mineral is the minority component, because only a small fraction of the feed mass has to cross into the froth product.

(e) Reverse flotation. Reverse flotation inverts the roles: the gangue mineral is made hydrophobic and floated away, while the valuable mineral is depressed and reports to the sink (underflow), where it is recovered as the non-floated product. It is chosen when the gangue is the smaller, more selectively floatable fraction, or when direct flotation of the value mineral would drag too much gangue along with it. The classic case is iron-ore beneficiation: quartz is floated with an amine collector at high pH while haematite/magnetite is depressed with starch, because it is easier to selectively float the small silica fraction than to selectively float the bulk iron oxide.

(f) Tailings. Tailings are the discard, low-value stream leaving a concentration step — the pulp that never attached to a bubble in flotation, or the light fraction rejected by a gravity/DMS circuit. They still carry residual reagent and unrecovered value, so tailings-facility design and closure are now as much a part of mine economics and permitting as the concentrator itself.

(g) Middling. A middling is the intermediate-grade fraction reporting between clean concentrate and true tailing: composite particles in which value and gangue are still physically locked together (incomplete liberation), or particles a separator cannot confidently assign to either product. Middlings are almost always recirculated — reground and re-fed to the head of the stage, or recleaned through a scavenger circuit — rather than discarded or accepted as concentrate.

(h) Concentrate. The concentrate is the enriched product stream of a separation step, in which the valuable mineral has been upgraded from its feed grade $f$ to a higher grade $c$. Concentrate grade is never reported alone: it trades directly against recovery (pushing recovery up by floating longer or coarser always drags in more gangue and lowers $c$), so a metallurgical balance always quotes grade and recovery, and usually the enrichment ratio $c/f$, together.

(i) Selective flocculation. Selective flocculation uses a polymeric flocculant that adsorbs preferentially on the surface chemistry of one fine mineral, bridging those particles into large, fast-settling flocs while a dispersant keeps the other minerals individually suspended. It targets the size range — typically below about 20 $\mu$m — where flotation loses efficiency and gravity settling becomes impractically slow; the classic example is flocculating fine haematite out of a dispersed silica slime in iron-ore fines processing.

(j) Hydrophobicity. Hydrophobicity is the property of a surface not readily wetted by water, expressed as a finite contact angle through Young's equation, $\gamma_{SW}=\gamma_{SA}+\gamma_{AW}\cos\theta$. A handful of minerals (graphite, molybdenite, talc, native sulphur, coal) are naturally hydrophobic; almost every sulphide, oxide and silicate of economic interest is naturally hydrophilic and must be made hydrophobic on purpose by adsorbing a collector. Creating and exploiting hydrophobicity on the target mineral (or, in reverse flotation, on the gangue) is precisely what froth flotation is built to do.