24-MMP-A3 Mineral Processing · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Professional Examination 09-MMP-A3 Mineral Processing, May 2015. Closed book, 3 hours, approved Casio or Sharp calculator only. Five problems totalling 100 marks plus a 2-mark bonus: Problem 1 (34), Problem 2 (7), Problem 3 (17), Problem 4 (30, answer any five of nine), Problem 5 (12, answer any six of nine). Every question and every option is worked below, because the set is a study resource rather than a timed sitting.
Reference texts.
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 examination asks for any five of the nine, at six marks each. All nine are answered here. Each pair follows the same shape, because that is what the question rewards: what the two have in common, what separates them, and where a mineral processing engineer meets the distinction in practice.
Both are chemical means of aggregating fine particles so that they settle at a usable rate, and both are applied in the same places — thickener feedwells, tailings ponds, process water clarification. Both attack the same problem, which is that a one-micrometre quartz particle settles under Stokes' law at a few millimetres per hour and will never clear in a real thickener.
They differ in mechanism and therefore in reagent, dosage and result. Coagulation is electrical: the mineral surface carries a charge, surrounded by a diffuse double layer of counter-ions, and adding a simple electrolyte such as lime, alum or ferric chloride compresses that layer, lowering the zeta potential until van der Waals attraction can overcome the residual repulsion. The particles then stick on contact, forming small, dense micro-flocs. Dosages are in tens or hundreds of grams per tonne and the reagent is cheap. Flocculation is mechanical bridging: a high molecular weight polymer, usually a polyacrylamide of the appropriate charge, adsorbs at several points along its chain onto several particles at once and physically ties them together. The floc is large and open, settles very fast, but shears apart if the pulp is over-agitated. Dosages are in grams per tonne and the reagent is expensive.
In practice the two are used together and in that order: coagulate first to destabilise, then flocculate to build settling mass. The engineering consequence is the size of the thickener — a well-flocculated tailings pulp will thicken in a unit a fraction of the diameter that unflocculated pulp requires — and, downstream, the water recovered for recycle, which in a dry climate is often the whole justification for the reagent bill.
Both are gravity concentrators: they separate minerals by density difference in water, using no chemistry at all, and both are governed by the same concentration criterion, $(\rho_h - \rho_f)/(\rho_l - \rho_f)$, which must exceed about 1.25 for a clean separation to be possible. Both are old, robust, cheap to run and still standard for tin, tungsten, tantalum, chromite, coal and free gold.
The differences are the direction of the motion, the depth of the bed and the size range served. A jig pulses water vertically through a deep bed on a screen; each pulsation dilates the bed and the particles rearrange during the following suction stroke, with dense particles working downwards through hindered settling, differential initial acceleration and consolidation trickling. It is a high-capacity machine handling coarse material, roughly 25 down to 0.5 mm, and it makes a relatively low-grade concentrate. A shaking table runs a thin film of pulp across a sloping riffled deck that is shaken asymmetrically along its long axis; the differential motion moves dense particles along the riffles while the film washes light particles down the slope, producing a visible fan of products that can be cut precisely. It handles fine material, roughly 2 mm to 75 micrometres, has low capacity per unit, and makes a high-grade concentrate.
The engineering relationship is that they are complementary stages of one gravity circuit, not competitors: jigs rough out a large tonnage coarsely and tables clean the finer fraction to saleable grade.
Both are flotation machines: both create a bubble swarm in a conditioned pulp, both rely on hydrophobic mineral attaching to those bubbles, and both remove a mineralised froth over a lip. Both use the same reagent suite of collectors, frothers, activators and depressants.
The difference is in how the bubbles and the particles are brought together, and in what happens in the froth. A mechanical cell uses a rotating impeller both to keep the solids in suspension and to shear the incoming air into bubbles. The result is a highly turbulent zone that gives excellent particle-bubble collision rates — ideal for recovering coarse and slow-floating particles — but the same turbulence entrains gangue and the froth is shallow, so grade suffers. A column cell has no moving parts: feed enters near the top of a tall vessel, air is sparged in at the base, and the two phases move countercurrently. The collection zone is quiescent and the froth zone is deep and washed with clean water from above, which displaces entrained gangue back downwards. Columns therefore make a markedly higher grade at a given recovery but recover coarse particles poorly.
Because the strengths are opposite, plants use both: mechanical cells for roughing and scavenging, where recovery is what matters, and columns for cleaning, where grade is what matters. The Bell flowsheet in Question 1 uses mechanical cells throughout because it predates the widespread adoption of columns; a modern rebuild would put a column in place of the second and third cleaner stages.
Both are surface-active flotation reagents added to the pulp in small doses, both are heteropolar molecules with a polar head and a hydrocarbon tail, and both are indispensable — neither works without the other.
They act at different interfaces and do different jobs. A collector acts at the solid-liquid interface: its polar group chemisorbs or physisorbs onto a specific mineral surface, leaving the hydrocarbon tail pointing into the water, which makes that mineral hydrophobic so a bubble will attach to it. Xanthates for sulphides, fatty acids for oxides and carbonates, and amines for silicates are the classic families. A collector is therefore selective — that is its whole purpose. A frother acts at the air-water interface: it lowers surface tension and, more importantly, retards bubble coalescence, so the cell produces a fine, stable, but not over-persistent bubble population and a froth that survives long enough to be removed but breaks down in the launder. Alcohols such as MIBC and polyglycols are typical. A frother is not selective and does not bond to any mineral.
The practical consequence for an operator is that grade and recovery are tuned by different levers: too little collector loses recovery of the valuable mineral, too much loses selectivity and floats the gangue, while too little frother gives a coarse unstable froth that drops its load and too much gives a persistent froth that carries entrained gangue into the concentrate and can flood the launders.
These are the same machine in principle. Both are compression crushers in which a conical mantle, mounted on an eccentric, gyrates inside a fixed concave, so that the gap closes on one side while it opens on the other; crushing therefore proceeds continuously at some point around the circumference, which is what distinguishes both of them from the intermittent jaw crusher and gives them their high capacity.
They differ in chamber geometry, and every other difference follows from that. The gyratory has a deep, steeply inclined chamber with a large feed opening and a long mantle, so it accepts run-of-mine rock up to a metre or more and reduces it at a ratio of about 6 to 1. It is a primary crusher and is usually the single largest item in a crushing plant. The cone has a flattened chamber with a much shorter, wider mantle and, critically, a parallel zone at the discharge, a short section where the mantle and concave surfaces run parallel so that every particle is squeezed at least once at the closed side setting. It takes a much smaller feed, gives a similar reduction ratio and produces a far better controlled, more cubical product. It is a secondary or tertiary crusher.
On the Bell flowsheet, position A is the secondary crusher and position B the tertiary crusher, and both would in practice have been cone crushers of different chamber configurations — standard head for the secondary duty and short head for the tertiary — while the machine labelled primary crusher would be a gyratory.
Geometrically these are the same device: a cylindrical section with a tangential inlet and a vortex finder, joined to a conical section ending in an apex. In both, the tangential entry generates a strong vortex, a low-pressure air core forms along the axis, and the feed divides into a coarse or dense underflow at the apex and a fine or light overflow at the vortex finder. Neither has any moving part.
The difference is the medium and hence the property being separated. A dense medium cyclone is fed a suspension of finely ground magnetite or ferrosilicon in water, whose effective relative density is set between the densities of the two minerals to be separated, typically 1.3 to 1.5 for coal and 2.7 to 3.3 for ores. Material lighter than the medium reports to the overflow and heavier material to the underflow, so the cut is on density and is very sharp, with probable errors of 0.02 to 0.04 relative density units. It also requires a medium recovery and cleaning circuit with magnetic separators. A classifying cyclone is fed pulp in water only; there is no dense medium, so separation depends on the balance between centrifugal force and drag, which is dominated by particle size. The cut is therefore on size — the d50 of the next part — although density does influence it, which is why a cyclone in a grinding circuit sends fine heavy sulphides to the underflow and returns them to the mill, a real disadvantage.
Position E on the Bell flowsheet is a classifying cyclone closing the grinding circuit; the coal circuit of Question 3, by contrast, uses water-only cyclones which sit between the two ideas, exploiting the fact that a dense enough coal pulp becomes a weak autogenous medium in its own right.
Both are methods of raising a tailings storage facility in stages as the impoundment fills, both begin from a compacted starter dyke of borrow or waste rock, and both use the coarse fraction of the tailings, usually cycloned sand, as the construction material for the raises. Staged construction is used because it spreads the capital cost over the mine life and because the required height is rarely known at the outset.
They differ in where the crest of each successive raise sits. In the upstream method the raise is built back over the beach of previously deposited slimes, so the centreline of the dam migrates towards the pond. It is by far the cheapest method and uses the least fill, but each raise is founded on loose, saturated, contractive tailings, and the phreatic surface sits close to the downstream face. The method is highly vulnerable to static and seismic liquefaction, and the failures at Mount Polley in British Columbia in 2014, at Fundao in 2015 and at Brumadinho in 2019 have led Brazil and Chile to ban it outright and made it very difficult to permit in Canada. In the downstream method each raise is placed on the downstream slope of the previous one, so the centreline migrates away from the pond and every raise is founded on compacted engineered fill. Internal drainage can be built in, the phreatic surface is kept low, and the structure can be designed to resist the maximum credible earthquake. It uses several times the fill volume and is correspondingly expensive.
The Canadian engineer's obligation here is explicit: the Mining Association of Canada Towards Sustainable Mining tailings protocol and the Canadian Dam Association guidelines both require a designated Engineer of Record, an independent review board and a documented dam classification, and British Columbia's Health, Safety and Reclamation Code was amended after Mount Polley to require the best available technology to be considered for any new facility. In practice this means upstream construction now has to be argued for rather than assumed.
Both are physical separators that exploit a bulk electrical or magnetic property of a mineral rather than its surface chemistry; both are usually built as a rotating drum or roll onto which a thin, ideally single-particle layer of feed is fed; and in both the separation happens because one class of particle is held onto the surface while the other is thrown off by centrifugal force, so the products are collected simply by placing splitters at different distances. Both are standard in the finishing circuits of beach-sand and other heavy-mineral plants, and the two are almost always used in sequence.
The property exploited is different. A magnetic separator responds to magnetic susceptibility. Low-intensity units, wet or dry, recover strongly magnetic magnetite and pyrrhotite and are also the workhorses that recover magnetite medium in dense-medium plants. High-intensity and high-gradient units recover paramagnetic minerals such as ilmenite, hematite, garnet, monazite and wolframite. A high-tension or electrostatic separator responds to electrical conductivity. The feed passes an ionising electrode and every particle picks up a surface charge; conductors such as ilmenite, rutile and cassiterite bleed that charge away to the earthed roll almost instantly and are thrown clear, whereas non-conductors such as zircon, quartz and monazite retain it and are pinned to the roll by image forces until brushed off.
Two practical distinctions follow. High-tension separation only works on a dry, dust-free, closely sized feed, because surface moisture short-circuits the charge, whereas magnetic separation can be done wet. And because the two properties are independent, a mineral pair that cannot be split magnetically can often be split electrostatically: the classic example is zircon from rutile, both non-magnetic, but one a conductor and one not.
Both are cut sizes read from the partition or Tromp curve of a classifier, and both are defined the same way: the particle size that has an equal chance of reporting to either product. Both are quoted in micrometres, both are used to specify a cyclone and to compare one classifier with another, and both are read at the 50 per cent ordinate.
The difference is which curve they are read from. The actual partition curve does not start at zero at the fine end. In a hydrocyclone a fixed fraction of the feed water short-circuits directly to the underflow through the apex, and it carries its solids with it regardless of size, so the curve begins at some bypass value Rf, typically 15 to 30 per cent, equal to the fraction of feed water reporting to the underflow. The size at which this actual curve crosses 50 per cent is the d50. The corrected curve removes that bypass by rescaling every ordinate as $$Y_c = \frac{Y - R_f}{1 - R_f}$$ so that it starts at zero, and the size at which the corrected curve crosses 50 per cent is the d50c. Because the correction lowers every ordinate, the corrected curve crosses 50 per cent at a coarser size, so d50c is always coarser than d50; for the curve sketched above, with a bypass of 28 per cent, the actual d50 is about 23 micrometres against a corrected d50c of 30 micrometres, a difference of some 22 per cent.
The distinction matters because the two numbers answer different questions. The d50c describes the true classifying action of the cyclone and is the quantity that all the design correlations, from Plitt's and Lynch's equations onward, actually predict; it is also what should be compared between machines. The d50 describes what the machine is actually doing to the plant, bypass included, and is what determines the circulating load in a grinding circuit. Quoting a d50c to a mill operator who needs the d50 will understate the amount of fine material being recycled to the mill.
