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 the path an ore takes from run-of-mine rock to a settled, dewatered concentrate: comminution (a), classification (b), flotation (c–f), and the aggregation and dewatering operations that recover water and thicken the product (g–j).

(a) Bond work index. The Bond work index, $W_i$, is the specific energy (kWh per short ton) that Bond's third theory of comminution assigns to a material for reducing it from a theoretically infinite particle size down to 80 % passing 100 µm. It is measured in a standard laboratory ball- or rod-mill grindability test and is used through the Bond equation $$W = 10\,W_i\left(\frac{1}{\sqrt{P_{80}}}-\frac{1}{\sqrt{F_{80}}}\right)$$ to size industrial mills, where $F_{80}$ and $P_{80}$ are the 80 % passing sizes of the feed and product (µm) and $W$ is the specific grinding energy (kWh/t). A hard, tough ore (e.g. taconite, $W_i\approx14$–16) demands far more grinding power per tonne than a soft one (e.g. limestone, $W_i\approx11$).

(b) Classifying. Classifying is size (or size-and-density) separation by differential settling rate in a fluid, almost always water, rather than by mechanical screening through an aperture. Coarse, fast-settling particles report to an underflow and fine, slow-settling particles report to an overflow. Hydrocyclones, spiral classifiers and rake classifiers are the common industrial units; classification is the operation that closes a grinding circuit, since screening becomes impractical much below about 100 µm while a cyclone continues to separate efficiently down into the tens of microns.

(c) Direct flotation. Direct flotation is the arrangement in which the valuable mineral is rendered hydrophobic and reports to the froth, while the gangue stays wetted and leaves as tailings from the cell bottom. It is the default configuration because the valuable species is usually the minor component of the feed — floating the smaller stream means less air, less reagent and a smaller froth-handling duty per tonne. Sulphide flotation (chalcopyrite, galena, sphalerite floated from a silicate gangue) is the classic example.

(d) Reverse flotation. Reverse flotation inverts that logic: the gangue is floated into the froth and the valuable mineral is recovered from the cell underflow. It is used when the gangue is more amenable to selective collection, or when the value is too abundant to float economically. Iron ore, where silica is floated off a magnetite/haematite concentrate with an amine collector, is the standard industrial example.

(e) Work of adhesion. The work of adhesion, $W_a$, is the reversible work per unit area required to strip an attached air bubble from a mineral surface and restore separate solid–water and air–water interfaces. Combining the interfacial-energy balance with Young's equation for the contact angle $\theta$ gives the Dupré–Young result $$W_a=\gamma_{AW}\left(1-\cos\theta\right)$$ where $\gamma_{AW}$ is the air–water surface tension. $W_a$ vanishes at $\theta=0$ (fully wetted, no attachment possible) and grows with $\theta$, so it is the quantitative measure of how firmly a bubble holds a floating particle.

(f) Hydrophobicity. Hydrophobicity is the property of a surface that water does not readily wet — equivalently, a surface presenting a finite contact angle and hence a non-zero work of adhesion to air. Graphite, molybdenite, talc and native sulphur are naturally hydrophobic and float with a frother alone; almost every other economic mineral is naturally hydrophilic and must be made hydrophobic deliberately by adsorbing a collector.

(g) Coagulation. Coagulation is the aggregation of fine, negatively charged colloidal particles that occurs when an electrolyte (a coagulant such as lime or alum) compresses the diffuse electrical double layer surrounding each particle, suppressing the electrostatic repulsion that normally keeps them apart. Once the repulsive barrier is reduced, short-range van der Waals attraction pulls particles into small, dense, tightly bound aggregates called coagula. It is a purely physicochemical, charge-driven effect and needs no bridging polymer.

(h) Flocculation. Flocculation is the aggregation of particles by a long-chain polymer (a flocculant) that adsorbs simultaneously on several particles at once and bridges them together into large, open, fast-settling aggregates called flocs. Flocs are much larger and more loosely bound than coagula, and flocculation is often run as a second step after coagulation, which first neutralises the surface charge that would otherwise keep the polymer's target particles apart.

(i) Selective flocculation. Selective flocculation uses a flocculant that adsorbs, through surface-specific chemistry, on only one mineral species present in a mixed fine slurry, so that species aggregates and settles (or is separated by size/density after aggregation) while the other minerals remain dispersed. Starch-based flocculants used to separate haematite from silica in very fine (sub-10 µm) iron-ore slimes are the standard example; the technique is a wet-chemistry alternative to flotation where particles are too fine for froth flotation to work efficiently.

(j) Thickening. Thickening is gravity sedimentation of a dilute slurry in a large-diameter, shallow tank (a thickener), producing a concentrated underflow of solids and a clarified overflow of water for recycle. A flocculant is usually dosed at the feed well to accelerate settling. Thickening is the standard first dewatering stage ahead of filtration for both concentrates and tailings, and it is also the water-recovery step that lets a concentrator recycle the bulk of its process water rather than draw fresh makeup water continuously.