(a) Describe Sampling. Add a note on common geological sampling methods. (15 marks) (b) Explain the ore reserve estimation…

(a) Sampling and common geological sampling methods (15 marks)

Sampling. Sampling is the collection of a small part of a deposit that represents the whole, so that its grade, mineralogy and physical properties can be estimated. It is the basis of every later calculation, so the sample must be representative: each part of the deposit must have an equal chance of being included, and ore and gangue must be present in the same proportions as in the deposit. Errors from bias, contamination and poor spacing cannot be corrected later.

Sample size. The weight of a sample needed rises with the size of the largest particle and the irregularity of the mineralisation. The Richards–Czeczott relation Q = k d² (Q = minimum weight, d = diameter of the largest fragment, k = a constant that depends on the ore) shows that the weight must be reduced by crushing and splitting (coning and quartering, riffle splitting) in steps, and Gy's theory relates the fundamental error to particle size and sample mass.

Geological sampling methods.

• Grab: random pieces taken from a dump or face. It is cheap but unreliable.
• Chip: chips broken at regular points along a line or grid on the face. It is moderately reliable.
• Channel: a continuous groove of fixed width and depth cut across the face or vein, and the most reliable for surface and underground workings.
• Bulk: several tonnes, for metallurgical tests or for erratic ore.
• Core: cylinders of rock obtained by diamond drilling, reliable when recovery is high, and used for subsurface sampling.
• Sludge or cuttings: powder from percussion or rotary drilling. It is cheap, but the fines may be lost or contaminated from higher levels.

(b) Ore reserve estimation, tonnage and grade (15 marks)

Procedure.

• Collect data from geological mapping, drilling, sampling and assays, and measure the bulk density.
• Plot the data on plans and cross-sections and set the ore boundaries with a cut-off grade and minimum mining thickness.
• Divide the deposit into blocks and estimate the volume, tonnage and average grade of each.
• Sum the blocks, apply losses and dilution, and classify the reserves by confidence into proved (measured), probable (indicated) and possible (inferred), as in the UNFC system.

Tonnage. Tonnage = volume × bulk density, or volume divided by the tonnage factor (m³ per tonne). The volume of a block is the area multiplied by the thickness, from the cross-section, polygon or contour method.

Grade. The average grade is the weighted average G = Σ(gᵢwᵢ)/Σwᵢ, where gᵢ is the assay of a sample and wᵢ is the weight, taken as the sample length, thickness or tonnage. Metal content = tonnage × grade.

Estimation methods.

• Classical: the polygon (nearest-neighbour), triangle, cross-section and contour methods, and inverse-distance weighting.
• Geostatistical: kriging with a variogram, which gives the best unbiased estimate and an estimation variance.

(c) Beneficiation of sulphide ores (20 marks)

Beneficiation raises the metal content by removing gangue without changing the chemistry of the ore minerals. The flowsheet is as follows.

• Comminution and liberation: crushing (jaw, gyratory and cone crushers) and grinding (rod and ball mills) in closed circuit with cyclone classifiers frees the sulphide grains from the gangue. The grind size is set by the grain size of the intergrowth.
• Froth flotation: this is the main method for sulphides. The ground ore is made into a pulp with water, and the mineral surfaces are made hydrophobic by collectors (xanthates), while frothers (pine oil, MIBC) stabilise the air bubbles. Sulphide particles attach to the bubbles and rise into the froth, and the gangue sinks. Activators (copper sulphate for sphalerite), depressants (sodium cyanide, zinc sulphate for pyrite and sphalerite) and pH regulators (lime) give selectivity. Rougher, scavenger and cleaner stages raise recovery and grade.
• Selective (differential) flotation: for complex Cu–Pb–Zn ores, the minerals float in turn: copper and lead first with zinc and pyrite depressed, then sphalerite after activation with copper sulphate. In bulk flotation, a mixed concentrate is made and later separated.
• Dewatering: thickeners, filters and dryers produce a concentrate for smelting.
• Complementary methods: gravity methods (jigs, shaking tables, spirals, heavy-media separation) for coarse, dense galena; magnetic separation for pyrrhotite or magnetite; and hydrometallurgy, in which leaching (including bacterial leaching of low-grade copper sulphides), solvent extraction and electrowinning recover the metal.
• The tailings are thickened and stored safely.