Van Kleeck Volatile Solids Reduction

You cannot judge a digester by comparing volatile solids in and out directly, because the volatile matter that is destroyed leaves as methane and carbon dioxide while the inert ash stays behind — so the digested sludge is automatically richer in ash even if nothing else happened. Van Kleeck's equation uses that inert ash as an internal tracer, and needs no flow or mass measurement at all. Raw sludge at 70% volatile digesting down to 50% volatile is not a 29% reduction, it is (0.70 − 0.50)/(0.70 × 0.50) = 57.1%.

A healthy mesophilic anaerobic digester destroys 45–60% of the volatile solids it is fed, and US biosolids regulations lean on the number directly — 40 CFR Part 503 accepts 38% volatile solids reduction as one route to demonstrating vector attraction reduction, without which the biosolids cannot be land applied. The equation's weakness is the same as its strength: it assumes the ash is truly conserved. Grit carried in with the raw sludge, lime or ferric added for conditioning, or struvite precipitating inside the digester all add inorganic mass that never came from the feed, and every one of them inflates the apparent destruction. When Van Kleeck disagrees with a proper mass balance on a plant that adds chemicals, believe the mass balance.