Question 6.9: A gas engine-based trigeneration plant (refer to Figure 6.12......
A gas engine-based trigeneration plant (refer to Figure 6.12) delivers useful heat and power in two modes of operation:
• Power and heating mode (\tau_{1} = 10 hours per day):
P_\mathrm{el} = 65 kW of electricity and Q_\mathrm{heat} = 60 kJ/s of useful heat for heating
• Power and cooling mode (\tau_{2} = 14 hours per day):
P_\mathrm{el} = 65 kW of electricity and Q_\mathrm{cool} = 90 kJ/s of useful heat for absorption chillers
• Plant overall efficiency:
1. In power and heating mode \mathrm{EUF}_{1} = 0.85
2. In power and cooling mode \mathrm{EUF}_{2} = 0.73
• Fuel in the gas engine is natural gas with a heating value LHV of 49 MJ/kg
Calculate (i) the useful energy produced daily by the trigeneration plant, (ii) the trigeneration plant average EUF value, and (iii) the daily fuel energy and fuel requirements of the trigeneration plant.
1. Total daily useful energy production of the plant
E_{\mathrm{tot}}=\Sigma(P\ \mathrm{or}\ Q)\times\tau=60\mathrm{~kW}\times10\,\mathrm {h}+90\mathrm{~kW}\times14\,\mathrm{h}+65\ \mathrm{kW}\times24\,\mathrm{h}= 3420 kWh per day
2. Plant average EUF value
\mathrm{E U F}=\sum\mathrm{(E U F\times\tau)}/\Sigma\ \tau=(\mathrm{E U F}_{1}\ \tau_{1}+\operatorname{EUF}_{2}\ \tau_{2})/(\tau_{1}+\tau_{2})= (0.85 × 10 + 0.73 × 14)/24 = 0.78
3. Fuel energy requirements of the plant
Q_\mathrm{f}=E_{\mathrm{tot}}/\mathrm{EUF}=3420\,\mathrm{kWh}/0.78=4384.6\,\mathrm{kWh~per~day}4. Fuel requirements of the plant
m_\mathrm{f}=Q_\mathrm{f}/\mathrm{LHV}=4384.6\mathrm{~kWh}\times3600\,\mathrm{s}/\mathrm{h}/\,49,000\,\mathrm{kJ}/\mathrm{kg}=322\mathrm{~kg~per~day}