Question

How much energy will be available from a biogas plant with the following details: Burner efficiency 60%; methane proportion 0.8; the heat of combustion of methane \(28\text{ MJ/m}^3\); and volume of biogas produced per day is \(2.4\text{ m}^3\)

• A. \(16.8\text{ kWh/day}\)
• B. \(4.2\text{ kWh/day}\)
• C. \(12.4\text{ kWh/day}\)
• D. \(8.8\text{ kWh/day}\)

Hint:

Conversion key: Always divide MJ by $3.6$ to obtain kWh ($3.6\times 10^6\text{ J} = 1\text{ kWh}$).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Useful thermal energy extracted from biogas equals the total volume of methane generated multiplied by the lower heating value of methane and the combustion thermal efficiency of the burner.
Key Formula or Approach:
\[ E_{\text{useful}} = V_{\text{biogas}} \times f_{\text{methane}} \times \text{LHV}_{\text{methane}} \times \eta_{\text{burner}} \]
\[ 1\text{ kWh} = 3.6\text{ MJ} \]

Step 2: Detailed Explanation:
Given parameters:
- Volume of biogas produced per day: \(V = 2.4\text{ m}^3\text{/day}\)
- Methane proportion: \(f_m = 0.8\)
- Heat of combustion of methane: \(H_c = 28\text{ MJ/m}^3\)
- Burner efficiency: \(\eta = 60\% = 0.60\)

Step 1: Calculate daily volume of pure methane:
\[ V_{\text{methane}} = 2.4\text{ m}^3 \times 0.8 = 1.92\text{ m}^3 \]
Total heat energy released:
\[ E_{\text{total}} = 1.92\text{ m}^3 \times 28\text{ MJ/m}^3 = 53.76\text{ MJ/day} \]

Step 2: Useful heat output after burner efficiency:
\[ E_{\text{useful}} = 53.76\text{ MJ} \times 0.60 = 32.256\text{ MJ/day} \]

Step 3: Convert energy from MJ to kWh:
\[ E = \frac{32.256\text{ MJ}}{3.6\text{ MJ/kWh}} = 8.96\text{ kWh/day} \approx 8.8\text{ kWh/day} \]

Step 3: Final Answer:
Thus, the energy available from the plant is approximately \(8.8\text{ kWh/day}\), matching option (D).