21-Mat-A3 Structure and Characterization of Materials · December 2019
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, December 2019 — 10-Met-A3, Metal Extraction Processes. Three hours, closed book, one approved calculator (Casio or Sharp). Seven problems of 20 marks each; the rubric asks for any five, and only the first five in the answer book are marked. All seven are solved here, because this set is a study resource rather than an exam script.
Note on the exam title. The printed exam header reads 10-Met-A3, Metal Extraction Processes. The content is extractive metallurgy — mineral processing, mass and heat balances, pyrometallurgical roasting, refining, magnesium production and electrometallurgy — and is answered as such.
Note on the data. The Question 6 iron heat-balance data set (Cp expressions and transformation enthalpies for α/β/γ/δ-Fe) uses a mass of 55.85 kg (chosen so it equals exactly 1000 mol) and temperature endpoints of 160–1735 °C, crossing the 1535 °C melting point into the liquid.
Reference texts. The answers below are keyed to the works normally recommended for this syllabus code:
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 span the mineral-processing flowsheet, from the physical (density, conductivity) and chemical (surface) methods used to split value from gangue, through the two ways flotation can be run, to the vocabulary used to describe what leaves each stage. They are taken in flowsheet order rather than alphabetically.
(a) Gravity concentration. Gravity concentration separates particles by the difference between their densities, using a fluid (normally water) as the separating medium and no chemical reagent. Jigs, shaking tables, spirals and Reichert cones exploit differential settling velocity or differential response to pulsation and flowing-film motion; separability is summarised by the concentration criterion $CC=(\rho_h-\rho_f)/(\rho_l-\rho_f)$, where $\rho_h$, $\rho_l$ and $\rho_f$ are the heavy-mineral, light-mineral and fluid densities. A value above about 2.5 (gold in quartz) makes gravity separation easy at almost any size; below about 1.25 it becomes impractical below a few hundred microns.
(b) Dense media separation. Dense media separation (DMS, or heavy-media separation) 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 valuable mineral and the gangue. Particles denser than the medium sink, lighter particles float, and the cut is a sharp sink–float split that is essentially independent of particle size over a wide range — an advantage over jigs and tables, whose efficiency is size-dependent. The medium is recovered magnetically and recirculated; DMS is the standard pre-concentration step for coal and for kimberlite diamond ore.
(c) High tension (electrostatic) separation. High tension separation sorts particles by electrical conductivity. A thin monolayer of dry, charged feed is fed onto a grounded, rotating drum electrode inside a high-voltage field (20–30 kV); conductive particles acquire and lose an induced charge quickly, are held only weakly, and are thrown off ballistically, while non-conducting particles retain their charge and cling to the drum until brushed off further round. It is the workhorse of heavy-mineral-sand processing, separating conductive rutile and ilmenite from non-conductive zircon and silica, and requires a dry, closely sized feed since moisture and coarse fines defeat the charge transfer.
(d) Direct flotation. Direct flotation is the normal mode: the collector renders the valuable mineral hydrophobic so it attaches to bubbles and reports to the froth (the concentrate), while the bulk gangue stays wetted and sinks to the tailing. It is the default configuration for sulphide base-metal ores (Cu, Pb, Zn, Ni sulphides), because the value mineral is normally the minority component and floating the minority stream is the lower-reagent-cost route.
(e) Reverse flotation. Reverse flotation inverts that logic: the collector is chosen to float the gangue, leaving the value mineral depressed and reporting to the sink product. It is used when the gangue is the minority phase or when the value mineral does not float cleanly — the classic case is iron ore, where an amine collector floats quartz gangue away from depressed hematite/magnetite, and potash, where flotation removes NaCl from the KCl product. Reverse flotation typically needs less reagent than trying to float a majority value mineral directly.
(f) Froth flotation. Froth flotation is the surface-chemistry separation common to both (d) and (e): finely ground pulp is aerated in a cell, a collector reagent renders the target mineral's surface hydrophobic, and those particles attach to rising air bubbles and are carried into a froth layer that overflows into a launder, while the hydrophilic fraction stays wetted and reports to the cell underflow. Because it discriminates by surface chemistry rather than density or conductivity, it reaches particle sizes and mineral pairs the physical methods cannot, and it is the dominant concentration method for sulphide ores worldwide.
(g) 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 µm — where flotation loses efficiency and gravity methods fail outright because Stokes settling becomes too slow; the classic case is flocculating fine haematite out of a dispersed silica slime in iron-ore fines processing.
(h) Concentrate. The concentrate is the enriched product stream leaving a separation stage, carrying most of the valuable component at a grade well above the feed. Its quality is judged jointly by recovery $R=cC/(fF)\times100\ \%$ (the fraction of feed value captured) and grade $c$ (its purity); the two trade against each other, and a concentrate is never described by one number alone.
(i) Middlings. Middlings are the intermediate-grade fraction reporting between clean concentrate and true tailing — composite particles in which value mineral and gangue are still physically locked together (incomplete liberation), or borderline particles a separator cannot confidently assign to either product. Rather than being discarded or accepted, middlings are almost always recirculated: reground to improve liberation and re-fed to the head of the stage, or recleaned through a scavenger circuit.
(j) Tailings. Tailings are the discard, low-value stream leaving a concentration step — what remains after the wanted mineral has been removed. In direct flotation it is the pulp that never attached to a bubble; in reverse flotation it is (unusually) the product stream, since the value mineral is depressed. Tailings are normally thickened and pumped to an impoundment; because they still carry residual value and reagent, tailings-facility design and closure are now as much a part of mine economics and permitting as the plant itself.
| Term | One-line meaning |
|---|---|
| (a) Gravity concentration | Density-based separation in a fluid (jigs, tables, spirals) |
| (b) Dense media separation | Sink/float in a ferrosilicon or magnetite suspension of intermediate density |
| (c) High tension separation | Conductivity-based sorting in a high-voltage field (mineral sands) |
| (d) Direct flotation | Value mineral floated to the froth (concentrate); default for sulphide ores |
| (e) Reverse flotation | Gangue floated instead; value mineral depressed and sinks (iron ore, potash) |
| (f) Froth flotation | Surface-chemistry separation via bubble attachment (direct or reverse) |
| (g) Selective flocculation | Polymer selectively aggregates one fine mineral for settling, below ~20 µm |
| (h) Concentrate | Enriched product stream; judged by recovery AND grade together |
| (i) Middlings | Intermediate-grade, incompletely liberated fraction, usually recirculated |
| (j) Tailings | Discard stream left after concentration |