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.
Six of the nine are required at two marks each; all nine are answered.
The critical speed is the rotational speed at which a grinding ball or rod at the inside surface of the mill is held against the liner by centrifugal force through the whole revolution, so that it never falls and no grinding takes place. It is found by setting the centrifugal acceleration equal to gravity at the top of the path: $$N_c = \frac{42.3}{\sqrt{D}}\ \text{rev/min},\ \ D\ \text{in metres}$$ A 3.2 m diameter mill therefore has a critical speed of 23.6 rev/min. Mills are operated at 65 to 80 per cent of critical — about 17 rev/min for that mill — because it is the cataracting and cascading charge, not the centrifuged one, that does the work.
Laser diffraction, in which the angular pattern of light scattered by a dilute suspension is inverted to a volume distribution over roughly 0.1 to 2 000 micrometres, and is the standard on-line and laboratory method in modern plants. Sedimentation methods, such as the Andreasen pipette or an X-ray sedimentograph, which infer size from settling velocity through Stokes' law. Other acceptable answers are the electrical sensing zone or Coulter method, optical or automated image analysis, and elutriation or cyclosizing.
In $M = C d^3 / s^2$, d is the nominal top particle size of the material being sampled, conventionally the 95 per cent passing size, in centimetres; and s is the acceptable fundamental sampling error, expressed as the relative standard deviation of the assay of the sample as a fraction, so that a 5 per cent error is 0.05. C is the sampling constant, itself the product of the mineralogical, liberation, shape and size-range factors. The dependence on the cube of the top size is the practical message: crushing the sample finer before splitting reduces the mass required eightfold for every halving of top size.
First, it is valid only in the laminar regime, particle Reynolds number below about 0.2, which for quartz in water means particles finer than roughly 50 micrometres; above that the drag is no longer purely viscous and Newton's law or an intermediate correlation must be used. Second, it assumes an isolated, smooth, rigid sphere falling in an unbounded Newtonian fluid, so it fails for non-spherical or porous particles, for hindered settling in a concentrated pulp, and near container walls. Brownian motion below about one micrometre and flocculation are further limits.
The contact angle is the angle formed at the three-phase contact line between the solid surface and the tangent to the air-water interface, measured conventionally through the water. It is fixed by the balance of the three interfacial tensions, Young's equation $\gamma_{sa} = \gamma_{sw} + \gamma_{wa}\cos\theta$, and it measures how hydrophobic the surface is. A perfectly wetted mineral gives an angle of zero and cannot float; a collector raises the angle to 60 degrees or more, and the work of adhesion holding the particle to the bubble, $W = \gamma_{wa}(1 - \cos\theta)$, rises with it.
Aluminium, at about 8.1 per cent by mass, and iron, at about 5.0 per cent. They are the third and fourth most abundant elements overall, after oxygen at 46 per cent and silicon at 28 per cent, which are not metals. Their abundance is the reason both are bulk commodities whose price is set by processing energy rather than by scarcity.
In $R = R_{\infty}(1 - e^{-kt})$, k is the first-order flotation rate constant, in reciprocal minutes, which measures how fast the floatable mineral is recovered and depends on particle size, degree of liberation, reagent dosage, bubble size and cell hydrodynamics. R-infinity is the ultimate or maximum recovery, the asymptote approached at infinite flotation time; it is always less than 100 per cent because some of the mineral is locked in gangue or too coarse or too fine to float at all, and it therefore measures how much of the mineral is floatable in principle. With $R_{\infty} = 92$ per cent and $k = 0.6\ \text{min}^{-1}$, for instance, five minutes gives 87.4 per cent recovery, and 90 per cent of the ultimate recovery is reached in 3.8 minutes. The pair together is what sets the required cell residence time and hence the number of cells in a bank.
Graphite and molybdenite. Both have layered crystal structures in which the sheets are held together only by van der Waals forces, so a fracture across the weak bonding exposes a non-polar face that water does not wet. Talc, sulphur, coal and, to a lesser degree, stibnite are other acceptable answers. Their natural floatability is a double-edged property: it makes molybdenite easy to recover in a copper-molybdenum plant, but it also means talc and graphite gangue float unbidden and must be depressed with an organic colloid such as carboxymethyl cellulose or dextrin.
Sodium ethyl xanthate is sodium O-ethyl dithiocarbonate. An ethyl group is joined through an oxygen to a carbon that carries one double-bonded sulphur and one single-bonded sulphur, the latter carrying the negative charge balanced by the sodium ion. The dithiocarbonate head chemisorbs on a sulphide mineral surface, forming the metal xanthate and dixanthogen, while the ethyl tail projects into the water and makes the surface hydrophobic. Lengthening that tail to amyl or hexyl raises collecting power but lowers selectivity, which is the whole basis of xanthate choice in a plant.
