Question:
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).
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).
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: Jul 20, 2026
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Correct Answer: 5.14
Solution and Explanation
Step 1: Find the total solids (TS) in 1 kg of OFMSW.
The moisture content is 20%, so the dry solids fraction is \(1 - 0.20 = 0.80\). For 1 kg of OFMSW, \[ TS = 1 \times 0.80 = 0.80\ \text{kg} \]
Step 2: Find the volatile solids (VS) from the total solids.
The VS content is 90% of the total solids, so \[ VS = 0.80 \times 0.90 = 0.72\ \text{kg} \]
Step 3: Find the biodegradable volatile solids (BVS) from the VS.
The BVS fraction in the VS is 70%, so \[ BVS = 0.72 \times 0.70 = 0.504\ \text{kg} \]
Step 4: Find the BVS actually converted, using the conversion efficiency.
The BVS conversion efficiency is 85%, so \[ BVS_{converted} = 0.504 \times 0.85 = 0.4284\ \text{kg} \]
Step 5: Compute the total gas volume produced.
The gas yield is 12 m3 per kg of BVS converted, so \[ V_{gas} = 0.4284 \times 12 = 5.1408\ \text{m}^3 \]
Step 6: State the final answer.
Rounding to two decimal places, the total volume of gas produced from 1 kg of OFMSW is \(5.14\) m\(^3\).
The moisture content is 20%, so the dry solids fraction is \(1 - 0.20 = 0.80\). For 1 kg of OFMSW, \[ TS = 1 \times 0.80 = 0.80\ \text{kg} \]
Step 2: Find the volatile solids (VS) from the total solids.
The VS content is 90% of the total solids, so \[ VS = 0.80 \times 0.90 = 0.72\ \text{kg} \]
Step 3: Find the biodegradable volatile solids (BVS) from the VS.
The BVS fraction in the VS is 70%, so \[ BVS = 0.72 \times 0.70 = 0.504\ \text{kg} \]
Step 4: Find the BVS actually converted, using the conversion efficiency.
The BVS conversion efficiency is 85%, so \[ BVS_{converted} = 0.504 \times 0.85 = 0.4284\ \text{kg} \]
Step 5: Compute the total gas volume produced.
The gas yield is 12 m3 per kg of BVS converted, so \[ V_{gas} = 0.4284 \times 12 = 5.1408\ \text{m}^3 \]
Step 6: State the final answer.
Rounding to two decimal places, the total volume of gas produced from 1 kg of OFMSW is \(5.14\) m\(^3\).
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