Raw sludge fed to an anaerobic digester contains 72.0% volatile matter (In = 0.72). Digested sludge withdrawn contains 52.0% volatile matter (Out = 0.52). Using the Van Kleeck equation, what is the volatile solids reduction percentage?

Formula Used: VS Reduction (%) = [(In - Out) ÷ (In - (In × Out))] × 100

Step-by-Step Mathematical Derivation:

1. Calculate numerator: In - Out = 0.72 - 0.52 = 0.20.
2. Calculate denominator: In - (In × Out) = 0.72 - (0.72 × 0.52) = 0.72 - 0.3744 = 0.3456.
3. Calculate reduction: (0.20 ÷ 0.3456) × 100 = 57.87% (~57.9%).

⚠️ Common Exam Trap: Never just subtract the percentages (72% - 52% ≠ 20%). The Van Kleeck equation accounts for the fixed non-volatile ash remaining unchanged.