A biomass gasifier consumes $15\text{ kg/h}$ of biomass having a higher calorific value of $16.5\text{ MJ/kg}$. It produces $36\text{ m}^3/\text{h}$ of producer gas having a calorific value of $5.0\text{ MJ/m}^3$. Calculate the cold gas efficiency of the gasifier in percentage.
Answer Key:
72.73
Step-by-Step Solution & Explanation
Energy input rate from biomass:
$E_{\text{in}} = 15\text{ kg/h} \times 16.5\text{ MJ/kg} = 247.5\text{ MJ/h}$
Energy output rate in clean producer gas:
$E_{\text{out}} = 36\text{ m}^3/\text{h} \times 5.0\text{ MJ/m}^3 = 180.0\text{ MJ/h}$
Cold gas efficiency:
$\eta_{\text{cg}} = \frac{E_{\text{out}}}{E_{\text{in}}} \times 100 = \frac{180.0}{247.5} \times 100 \approx 72.73\%$