Coal washery operating point under a tightening ash contract
A coal washery treats 100 t/h of raw coal at 30% ash. Plant trials give three steady operating points: A, a 15% ash product at 55% yield; B, an 18% ash product at 65% yield; C, a 22% ash product at 75% yield. The sales contract allows product ash up to 20%. Prices are $80/t for 15% ash, $70/t for 18% ash, and $58/t for 22% ash; coal at 22% ash cannot be sold under the contract. Washing costs $8/t raw feed, and reject disposal costs $3/t reject. The plant is currently operating at point B. The contract is expected to be tightened to a maximum of 17% ash next year, with a price of $75/t for 17% ash. The washery manager must choose an operating strategy that maximizes net revenue while meeting the contract and leaving room for raw-coal ash variability.
1. Calculate net revenue per hour for A, B and C. Which operating point should be chosen under the current contract?
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For 100 t/h raw feed, A gives 55 t product and 45 t reject. Revenue = 55 x 80 = $4,400; washing cost = $800; reject disposal = 45 x 3 = $135; net = $3,465/h.
B gives 65 t product and 35 t reject. Revenue = 65 x 70 = $4,550; cost = $800; disposal = 35 x 3 = $105; net = $3,645/h.
C gives 75 t product and 25 t reject. Revenue = 75 x 58 = $4,350; cost = $800; disposal = 25 x 3 = $75; net = $3,475/h, but C is infeasible because 22% ash exceeds the 20% contract limit. Under the current contract, B is the best feasible point at $3,645/h.
2. If the contract tightens to 17% ash with a price of $75/t, evaluate blending A and B versus operating at A only. Recommend.
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At A only, the product meets the 17% limit, so revenue = 55 x 75 = $4,125; reject disposal = 45 x 3 = $135; washing cost = $800; net = $3,190/h.
For a blend at exactly 17% ash, let the product mass fraction from A be y. Then 15y + 18(1 - y) = 17, giving y = 1/3. To obtain 100 t/h feed with one-third of product from A, solve the feed split: A product = P/3 and B product = 2P/3. Feed A = (P/3)/0.55 = 0.606P; feed B = (2P/3)/0.65 = 1.026P; total feed = 1.632P, so P = 61.3 t/h. Revenue = 61.3 x 75 = $4,598; reject = 38.7 t, disposal = $116; cost = $800; net = $3,682/h. Blending is better by about $492/h, but the product ash is exactly at the limit, so it needs on-line ash control and a small safety margin. Recommend blending with tight control; if variability is high, operate slightly below 17% ash.
3. What process control and contractual safeguards do you recommend?
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Install an on-line ash monitor on the product and a composite sampler for hourly check assays. Control the A:B blend ratio from the ash signal, and keep surge capacity so off-spec coal can be recirculated rather than shipped. Track raw-coal ash and yield daily; if raw ash rises, reduce the blend target below 17% or switch to a lower-ash operating point. Negotiate a clear penalty and rejection clause, and keep records of every cargo. The aim is to protect the contract margin, not just to maximise instantaneous revenue at the ash limit.