Question:medium

An anaerobic digestion system is operated for methane gas generation from organic fraction of municipal solid waste (OFMSW). The moisture content and volatile solids (VS) content of OFMSW are 20% and 90%, respectively. The biodegradable volatile solids (BVS) in the VS is 70%, and the BVS conversion efficiency to methane gas is 85%.
If the methane gas generation in the system is 12 m3 per kg of BVS converted, the total volume of gas produced from one kilogram of OFMSW is ______ m3 (rounded off to two decimal places).

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Work through the mass chain step by step: total solids from moisture content, then VS from TS, then BVS from VS, then the converted BVS from the conversion efficiency, and finally multiply by the gas yield per kg BVS converted.
Updated On: Aug 14, 2026
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Correct Answer: 5.14

Solution and Explanation

Instead of carrying the mass through the chain one step at a time, we can combine all four percentage factors into a single overall conversion fraction first, and then apply it to the 1 kg of OFMSW in one multiplication. Each kilogram of OFMSW passes through four successive reductions before it becomes methane-generating BVS: it loses moisture, retaining a dry-solids fraction of $f_1 = 1 - 0.20 = 0.80$; of that, the volatile fraction is $f_2 = 0.90$; of the volatile solids, the biodegradable fraction is $f_3 = 0.70$; and of the biodegradable solids, the fraction actually converted is $f_4 = 0.85$. The combined fraction of the original 1 kg of OFMSW that ends up as converted BVS is

\[ f = f_1 \times f_2 \times f_3 \times f_4 = 0.80 \times 0.90 \times 0.70 \times 0.85 \]

Multiplying these out step by step, $0.80 \times 0.90 = 0.72$, then $0.72 \times 0.70 = 0.504$, then $0.504 \times 0.85 = 0.4284$. So exactly $0.4284$ kg out of every 1 kg of OFMSW ends up as BVS that is converted during digestion. Since each kilogram of converted BVS yields 12 m3 of methane gas, the total gas volume from 1 kg of OFMSW is

\[ V_{gas} = f \times 12 = 0.4284 \times 12 = 5.1408\ \text{m}^3 \]

Rounding to two decimal places,

\[\boxed{V_{gas} = 5.14\ \text{m}^3}\]
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