Question 6.3: A cogeneration plant comprising a gas turbine with electric ......
A cogeneration plant comprising a gas turbine with electric generator and waste heat boiler (WHB) (refer to Figure 6.6) produces electric power and useful heat for district heating operating under the following conditions:
• Compressor intake temperature T_{1} = 290 K
• Compressor pressure ratio \beta = 17
• Mass flow rate of air m = 100 kg/s. Mass flow rate of fuel in the turbine combustor may be ignored.
• Gas turbine inlet temperature T_{3} = 1600 K
• Isentropic efficiencies of turbine and compressor are \eta_{it} = 0.92 and \eta_{ic} = 0.89
• Stack gas temperature t_\mathrm{stack} = 130°C, T_\mathrm{stack} = 403 K
• Lower heating value of fuel (natural gas) LHV = 50 MJ/kg. Specific heat of the working fluid (air in compressor and gas in turbine) c_{p} is 1.05 kJ/(kg K).
Calculate: (i) the plant net power output, (ii) the rate of heat addition in combustor, (iii) the rate of useful heat output, (iv) the plant thermal and overall efficiencies, and (v) the plant heat-to-power ratio.
The specific heat of both air and gas c_\mathrm{p} is 1.05 kJ/(kg K). The heat loss of the WHB may be ignored.
1. Compressor discharge air temperatures for isentropic and actual (adiabatic) compression are, respectively,
T_{2s}\,=\,T_{1}{\bf b}^{(k-1)/k}\,=\,290\times17^{(1.4-1)/1.4}\,=\,651 .5\,K
T_{2}\,=\,T_{1}+(T_{2s}\,-\,T_{1})/\mathbf{h}_{\mathrm{ic}}\,=\,290\,+\,(65 1 .5\,-\,290)/0.89\,=\,696.2\,\mathrm{K}2. Work of compression per unit mass of air
w_{\mathrm{c}}\,=\,c_{\mathrm{p}}(T_{2}\,-\,T_{1})\,=\,1.05\times(696.2\,-\,2 90)\,=\,426.5\,\mathrm{kJ} /\mathrm{kg}3. Turbine exhaust gas temperature for isentropic and actual expansion, respectively,
T_{4s}\,=\,T_{3}/{\bf b}^{(k-1)/k}\,=\,1600/17^{(1.4-1)/1.4}\,=\,712.17\,\mathrm{K}{ T}_{4}\,=\,{ T}_{3}\,-\,({ T}_{3}-{ T}_{4s})\mathbf{h}_{i\bf{t}}\,=\,1600-(1600-712.17)\times0.92=783.19\,\mathrm{K}
4. Work of expansion in gas turbine per unit mass of gas
w_{t}\,=\,c_{\mathrm{p}}(T_{3}-T_{4})\,=\,1.05\times(1600-783.19)=\,857.65\,\mathrm{kJ}/\mathrm{kg}5. Plant net power output
P_{\mathrm{t}}\,=\,m\,\left(w_{\mathrm{t}}\,-\,w_{\mathrm{c}}\right)=100^{*}(857.65-426.5)=\,43115\,\mathrm{kW}6. Rate of heat addition in combustor
Q_{\mathrm{in}}\,=\,m\,\,c_{\mathrm{p}}(T_{3}-T_{2})=100^{*}1.05\times(1600-696.2)\,=\,94900\,\,{\mathrm{kJ}}/{\mathrm{s}}7. Plant thermal efficiency
\mathbf{h}_{\mathrm{{th}}}\,=\,P/Q_{\mathrm{{in}}}\,=\,43115\mathrm{{}}/94900\,=\,0.4548. Plant useful heat output rate
Q_{u}=m c_{\mathrm{p}}(T_{\mathrm{exh}}-T_{\mathrm{stack}})=100^{*}\ 1.05\times(783.2-403)=39920\,{\mathrm{kJ}}/{\mathrm{s}}9. Plant overall efficiency (or energy utilization factor)
\mathrm{E U F}=(P+Q_{u})/Q_{\mathrm{in}}=(43115+39920)/94900=0.87510. Plant heat-to-power ratio
\mathrm{HPR}=Q_{u}/P\,=\,39920/43115\,=\,0.926The gas turbine-based cogeneration plants can be utilized both as district energy supply plants and as industrial cogeneration plants. The former plant type produces power and heat for space heating, while the latter provides power and process hot water or steam.