where g = ore grade; Qm = cumulative mine production (kg); and l=depletion constant.
where EI= energy intensity (J/kg) and e0 SR and e0 MM are the energy requirements (J/kg) for smelting and refining (SR) and mining and milling (MM). A distinction is made in a minimum energy requirement (e0) based on thermodynamics and a part depending on technological development.
where COR = capital-output ratio ($/kg) and a, p, y1, y2, y3 are constants representing the effects of economies of scale and ore grade decline on the capital-output ratio. (Based on de Vries 1989a.)
cos^p = Cenp + COp + Cexp,p = priceen X EIp + CORp X Ann + Cexplp (29A.7)
where costs = costs ($/kg), Cen = energy production costs ($/kg), Ccap = capital production costs ($/kg), Cexpl = exploration costs ($/kg) = 0 except for p = 1, priceen = the average price of energy ($/J) and Ann = annuity factor.
p p pricep)
p whereproducp = production per production category p (primary or secondary) (in kg), IMS = indicated market share, pricep = price of metal produced by production category p (more or less equal to costs) ($/kg) and P = logit parameter). If capacity is insufficient, the real market share of category p can be lower than suggested by IMS. D = demand for metals.
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