Question 13.3: A trigeneration plant based on SOFC fuel cells stack (refer ......
A trigeneration plant based on SOFC fuel cells stack (refer to Figure 13.8b) is employed for simultaneous production of electric power and useful heat (hot water and heat for air conditioning unit) for an industrial complex under the following operating conditions:
• Power demand is P_{el} = 67 kW
• Power and useful heat consumption are simultaneous loads, that is, the load duration is: \tau_{el} = \tau_{h} = \tau_{AC} = 12 h/day
• Process heat demand for hot water production is Q_{h} = 31 kW
• Heat demand for air conditioning unit (absorption chillers) is Q_{AC} = 27 kW
• Fuel cell electrical efficiency is \eta_{el} = 0.45, efficiency of process heat production is \eta_{h} = 0.89 and efficiency of the absorption AC unit is \eta_{AC} = 0.77
• Fuel is a restated natural gas with an LHV of 49 MJ/kg
Calculate (i) the daily primary energy requirements, (ii) the overall efficiency of the trigeneration plant, and (iii) the plant daily fuel requirements.
1. Trigeneration plant daily primary energy (fuel) requirements
E_\mathrm{f,d}=\tau_ \mathrm{el} \times P_\mathrm{el}/\eta_\mathrm{el}=12\times 67/0.45=1787 \,\mathrm{kWh/day}2. Plant electric power generation per day
E_{\mathrm{el,}d}=\tau_{\mathrm{el}}\times P_{\mathrm{el}}=12\times67=804\ {\mathrm{kWh/day}}3. Daily heat requirements for process heat (hot water)
Q_{\mathrm{h,d}}=\tau_{\mathrm{h}}\,Q_{\mathrm{h}}/\eta_{\mathrm{h}}=12\times31/0.89=418\,\mathrm{kWh/day}4. Daily exhaust heat requirements for AC (absorption chillers)
Q_{\mathrm{AC,d}}=\tau_{\mathrm{AC}}~Q_{\mathrm{AC}}/\eta_{\mathrm{AC}}=12\times27/0.77=421{\mathrm{~kWh/day}}5. Overall efficiency of the trigeneration plant
\eta_{T G}=(E_{\mathrm{el,}{\mathrm{d}}}+Q_{\mathrm{h,d}}+Q_{\mathrm{AC,d}})/E_{\mathrm{f,d}}=(804+418+421)/1787=0.846. Fuel requirements of the trigeneration plant per day
m_\mathrm{f}=E_\mathrm{f,d}/\mathrm{LHV}=1787\mathrm{~kWh/day} \times3600\mathrm{~s/h/49,000}\,\mathrm{kJ/kg}=131.3\mathrm{~kg/day}