A Recovery Bound for Mixed Circuit Boards: The Separation Stage at Which Marginal Recovery Stops Paying, and a Reagent Bound That Rules Out Small-Scale Hydrometallurgy at Stated Grades

A tonne of mixed printed circuit boards contains more gold than a tonne of most mined gold ores, and it also contains copper, lead solder, and brominated flame-retardant plastics. This paper models mechanical recovery - shredding followed by density and eddy-current separation, with the middlings fraction re-passed - for a stated tonne of boards containing 200 kg of copper, 250 g of gold, 1,000 g of silver, and 100 g of palladium, a gross contained value of $26,000 at stated prices. Each separation pass recovers a stated fraction of the metal remaining, subject to a liberation ceiling of 92% for copper and 80% for the precious metals. Marginal recovery value falls below the stated marginal cost of $310 per pass at the ninth pass; the economic optimum is eight passes, recovering 183.7 kg of copper (91.8%) and 193.6 g of gold (77.5%), for a net value of $17,916 per tonne, while 56.4 g of gold per tonne is lost to residue even at the optimum. The mechanical route leaves 88% of the brominated plastic in a controlled solid residue and 2.4 kg of lead in collected dust per tonne. The small-scale hydrometallurgical alternative is assessed as a bound and does not survive it: stated reagent consumption of 4,000 litres per tonne costs $26,000, more than the $24,610 gross value the leach recovers, a net of -$1,390 per tonne before labour, energy, or treatment of 4,800 litres of effluent carrying 28.5 kg of lead. Hydrometallurgy at this scale breaks even only above a gold grade of 268 g per tonne; the stated feed, at 250 g per tonne, is below the line. All results are SIMULATED, NOT MEASURED.