Metallurgical Calculations

Computations of performance in milling are complicated by the fact that it is continuous rather than a batch operation, that the quantities of solid material handled are large and usually mixed with water, hence difficult or impossible to weigh. Fortunately it is possible to determine many facts concerning performance without knowing weights, if the value of various constituents is known in some common units, e.g., the content of same particular metal or mineral, or of water, or of particles of a particular size or falling between some particular size range, and the like. Metal content may be expressed in percent, by weight or volume, or units of weight as ounces per ton, or even in units of value, as in dollars per ton, provided, in the latter case, that the value is in direct proportion to the metal content and not an artificial value dependent both upon metal cont ent and lack of other content, as in frequently the case in valuation of concentrate.

Definitions and notation:

Feed (F) = weight of feed. This may be expressed in any units. The word Feed applies to the material entering treatment in any machine or operation, e.g. the ore entering a treatment plant, or the material entering an individual machine.

Concentrate (C) = weight of concentrate, expressed in any units, but necessarily in the same units as the feed. Concentrate may be defined, for the purpose of these calculations, as any product of the treatment of a given feed that is richer in content of a given ingredient than the feed.

Tailing (T) = weight of tailing, expressed in any unit, but necessarily in the same units as the feed. Tailing is defined as the product of the treatment of a given feed which is distinctly impoverished in content of a given ingredient as compared to the feed.

Recovery (R) = is the ratio, expressed as percentage, of the weight of the sought-for ingredient, in the finished product of a given operation, to the weight of the same ingredient in the material entering to the operation.

Ratio of Concentration (K) = this term is defined as the ratio of the weight of the feed in a given operation to the weight of concentrate obtained from it; or, stated another way, as the number of tons of feed required to produce one ton of concentrate.

Assays: f = assay of feed, c = assay of concentrate, t = assay of tailings

Formulas: F = C + T

• C = F (f – t)/(c – t)
• K = F/C = (c – t)/(f – t)
• R = 100Cc/Ff = 100c (f – t)/f(c – t)

Example : From a 8 g/t gold ore, milled at the rate of 300 tons per day is produced a concentrate assaying 1850 g/t Au, and a tailing with 0.5 g/t.

Using the formulas: C = 300( 8 – 0.5)/(1850 – 0.5) = 1.217 tons

• K = (1850 – 0.5)/(8 – 0.5) = 246.6
• K = 300/1.217
• R = 100 (1.217)(1850)/(300)(8) = 93.8%
• R = 100(1850)(8 – 0.5)/8(1850 – 0.5) = 93.8%
• T = 300 – 1.217 = 298.783 tons