What a household charcoal filter can and cannot do

This paper sizes a household charcoal filter for a representative organic contaminant, phenol at 5.0 mg/L, from stated adsorption capacities and a contact-time model, and then applies the same arithmetic to two claims the filter cannot meet. For granular activated carbon at a stated capacity of 50 mg/g, usable volume before breakthrough at a utilisation factor of 0.50 is 5000.0 litres per kilogram; for plain wood charcoal at 10 mg/g it is 1000.0 litres per kilogram. A household using 20.0 litres per day needs, over 90 days (1800.0 litres), 0.36 kg of activated carbon or 1.8 kg of plain charcoal on capacity alone, or 0.72 kg and 3.6 kg with a factor of two for safety. Contact time sets flow: a 2.0 kg bed occupies 5.0 litres and, at a required empty-bed contact time of 10 minutes, may run at no more than 0.5 litres per minute. Salt removal fails by orders of magnitude: even at a generous capacity of 2.0 mg/g, 1 kg is exhausted by 4.0 litres at 500 mg/L salinity, and 90 days of salt removal would need 450.0 kg. Disinfection fails by mechanism: adsorption micropores are about 250 times narrower than a small bacterium, flow channels are far wider than bacteria, and a plain bed has no inactivation mechanism, so credited log removal is 0. Within its bound — taste, odour, free chlorine and many dissolved organics, for a stated volume at a slow flow — the filter is useful. It is not a desalinator and not a disinfecting device. **Design status: SIMULATED, NOT MEASURED.** The filter is a design study from stated inputs, not a tested device. Nothing here is described as built, tested or measured.