An anaerobic system treats OFMSW with moisture content 20%,volatile solids (VS) 90% of dry solids, and biodegradable VS (BVS) 70% of VS. BVS-to-methane conversion efficiency is 85%. The printed methane yield is 12 m³/kg BVS converted. Find gas from 1 kg OFMSW in m³,to two decimals.
Use a 1 kg wet-waste basis. Dry solids are $.8$ kg; VS are $.8(.9)=.72$ kg; BVS are $.72(.7)=.504$ kg. Converted BVS are $.504(.85)=.4284$ kg. Applying the supplied yield gives $V=.4284(12)=\mathbf{5.14}$ m³. The unusually large stated yield is used as printed rather than silently replacing it with a typical digestion yield.
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